MedWorm.com provides a medical RSS filtering service. Over 6000 RSS medical sources are combined and output via different filters. This feed contains the latest items from the 'Bulletin of Mathematical Biology' source. Thu, 09 Feb 2012 22:12:26 +0100 http://www.medworm.com/index.php?rid=5657622&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22297621%26dopt%3DAbstract Authors: Wikan A Abstract Discrete stage-structured density-dependent and discrete age-structured density-dependent population models are considered. Regarding the former, we prove that the model at hand is permanent (i.e., that the population will neither go extinct nor exhibit explosive oscillations) and given density dependent fecundity terms we also show that species with delayed semelparous life histories tend to be more stable than species which possess precocious semelparous life histories. Moreover, our findings together with results obtained from other stage-structured models seem to illustrate a fairly general ecological principle, namely that iteroparous species are more stable than semelparous species. Our analysis of various age-structured models does not necessarily s... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5657622 Thu, 02 Feb 2012 05:00:00 +0100 5657622 http://www.medworm.com/index.php?rid=5657621&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22297622%26dopt%3DAbstract Authors: Cummings LJ, Perez-Castillejos R, Mack ET Abstract This paper analyzes the biochemical equilibria between bivalent receptors, homo-bifunctional ligands, monovalent inhibitors, and their complexes. Such reaction schemes arise in the immune response, where immunoglobulins (bivalent receptors) bind to pathogens or allergens. The equilibria may be described by an infinite system of algebraic equations, which accounts for complexes of arbitrary size n (n being the number of receptors present in the complex). The system can be reduced to just 3 algebraic equations for the concentrations of free (unbound) receptor, free ligand and free inhibitor. Concentrations of all other complexes can be written explicitly in terms of these variables. We analyze how concentrations of key (exp... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5657621 Thu, 02 Feb 2012 05:00:00 +0100 5657621 http://www.medworm.com/index.php?rid=5597531&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22246694%26dopt%3DAbstract Authors: Murphy KE, Hall CL, Maini PK, McCue SW, McElwain DL Abstract Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: The cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5597531 Fri, 13 Jan 2012 05:00:00 +0100 5597531 http://www.medworm.com/index.php?rid=5597532&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22234418%26dopt%3DAbstract Authors: Kawasaki K, Asano K, Shigesada N Abstract To address the effect of taxis of invasive animals on their spreading speed in heterogeneous environments, we deal with an advection-diffusion-reaction equation (ADR) in a periodic patchy environment. Two-types of advection that spatially vary depending on environmental heterogeneity are taken into consideration: a stepwise taxis function and a saw-like taxis function. We first analyze the ADR with the stepwise taxis advection, and derive an invasion criterion. When the invasion criterion holds, an initially localized population evolves to a traveling periodic wave (TPW). The asymptotic speed of the TPW is found to be equal to the minimal speed of the TPW analytically derived. Thus, we examine how the minimal speed is influenced by... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5597532 Wed, 11 Jan 2012 05:00:00 +0100 5597532 http://www.medworm.com/index.php?rid=5597533&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22231521%26dopt%3DAbstract Authors: Tian JP, Jin Z, Xie T Abstract In the Drosophila germline stem cell ovary niche, two stem cells compete with each other for niche occupancy to maintain stem cell quality by ensuring that differentiated stem cells are rapidly pushed out the niche and replenished by normal ones (Jin et al. in Cell Stem Cell 2:39-49, 2008). To gain a deeper understanding of this biological phenomenon, we have derived a mathematical model for explaining the physical interactions between two stem cells. The model is a system of two nonlinear first order and one second order differential equations coupled with E-cadherins expression levels. The model can explain the dynamics of the competition process of two germline stem cells and may help to reveal missing information obtained from experimenta... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5597533 Tue, 10 Jan 2012 05:00:00 +0100 5597533 http://www.medworm.com/index.php?rid=5577605&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22218880%26dopt%3DAbstract We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5577605 Thu, 05 Jan 2012 05:00:00 +0100 5577605 http://www.medworm.com/index.php?rid=5546657&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22190043%26dopt%3DAbstract Authors: Mendoza-Juez B, Martínez-González A, Calvo GF, Pérez-García VM Abstract We propose a mathematical model of tumor cell nutrient uptake governed by the presence of two key biomolecular fuels: glucose and lactate. The model allows us to describe, in a remarkably simple way, different in vitro scenarios previously reported in experiments of tumor cell metabolism using distinct energy sources. The predictions of our model show good agreement with all the examined tumor cell lines (cervix, colon, and glioma) and provide a first step toward the development of more comprehensive frameworks accounting for in vivo cancer dynamics under complex spatial heterogeneities. PMID: 22190043 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5546657 Thu, 22 Dec 2011 05:00:00 +0100 5546657 http://www.medworm.com/index.php?rid=5531232&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22160520%26dopt%3DAbstract Authors: Cheer A, Cheung S, Hung TC, Piedrahita RH, Sanderson SL Abstract We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow traveling across the filter surface rather than traveling perpendicularly to the filter. Here we identify physical parameters and hydrodynamic processes that determine food particle movement and retention inside the fish oral cavity. We demonstrate how five variables affect flow patterns and particle trajectories: (1) flow speed inside the fish oral cavity, (2) incident angle of the flow approachi... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5531232 Tue, 13 Dec 2011 05:00:00 +0100 5531232 http://www.medworm.com/index.php?rid=5492568&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22147102%26dopt%3DAbstract Authors: Lee S, Golinski M, Chowell G Abstract In the context of pandemic influenza, the prompt and effective implementation of control measures is of great concern for public health officials around the world. In particular, the role of vaccination should be considered as part of any pandemic preparedness plan. The timely production and efficient distribution of pandemic influenza vaccines are important factors to consider in mitigating the morbidity and mortality impact of an influenza pandemic, particularly for those individuals at highest risk of developing severe disease. In this paper, we use a mathematical model that incorporates age-structured transmission dynamics of influenza to evaluate optimal vaccination strategies in the epidemiological context of the Spring 2009 A (H... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5492568 Wed, 07 Dec 2011 05:00:00 +0100 5492568 http://www.medworm.com/index.php?rid=5492567&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22147103%26dopt%3DAbstract Authors: Bennett MR, Farnell L, Gibson WG Abstract Neuregulin (Nrg) through its receptor ErbB4 modulates the activity of the N-Methyl-D-Aspartate (NMDA) receptor (NMDAR) at synapses. As modification of this pathway has been implicated in schizophrenia, it is of great interest to define it in precise quantitative terms. Kinetic models of the epidermal growth factor (EGF)/ErbB receptor signalling pathway describing activation, desensitization, and tyrosine phosphorylation of EGFR/ErbB followed by binding and activation of Src family kinases that is subsequently followed by phosphorylation of target proteins are available. We have adapted these to give a kinetic description of NMDAR modulation by Nrg that recapitulates the observed kinetics of autophosphorylation of the ErbB dimer as ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5492567 Wed, 07 Dec 2011 05:00:00 +0100 5492567 http://www.medworm.com/index.php?rid=5492566&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22147104%26dopt%3DAbstract Authors: Chen Z, Ghosal S Abstract In a previous paper (Ghosal and Chen in Bull. Math. Biol. 72:2047, 2010), it was shown that the evolution of the solute concentration in capillary electrophoresis is described by a nonlinear wave equation that reduced to Burger's equation if the nonlinearity was weak. It was assumed that only strong electrolytes (fully dissociated) were present. In the present paper, it is shown that the same governing equation also describes the situation where the electrolytic buffer consists of a single weak acid (or base). A simple approximate formula is derived for the dimensionless peak variance which is shown to agree well with published experimental data. PMID: 22147104 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5492566 Wed, 07 Dec 2011 05:00:00 +0100 5492566 http://www.medworm.com/index.php?rid=5492569&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22139748%26dopt%3DAbstract Authors: Layne L, Dimitrova E, Macauley M Abstract We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input perturbations as the canalyzing depth increases, but exhibit rap... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5492569 Sat, 03 Dec 2011 05:00:00 +0100 5492569 http://www.medworm.com/index.php?rid=5473953&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22135094%26dopt%3DAbstract Authors: Robertson SL, Cushing JM, Costantino RF Abstract In many stage-structured species, different life stages often occupy separate spatial niches in a heterogeneous environment. Life stages of the giant flour beetle Tribolium brevicornis (Leconte), in particular adults and pupae, occupy different locations in a homogeneous habitat. This unique spatial pattern does not occur in the well-studied stored grain pests T. castaneum (Herbst) and T. confusum (Duval). We propose density dependent dispersal as a causal mechanism for this spatial pattern. We model and explore the spatial dynamics of T. brevicornis with a set of four density dependent integrodifference and difference equations. The spatial model exhibits multiple attractors: a spatially uniform attractor and a patchy attra... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5473953 Fri, 02 Dec 2011 05:00:00 +0100 5473953 http://www.medworm.com/index.php?rid=5473954&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22131185%26dopt%3DAbstract Authors: Mašić A, Eberl HJ Abstract We consider a mathematical model for a bacterial population in a continuously stirred tank reactor (CSTR) with wall attachment. This is a modification of the Freter model, in which we model the sessile bacteria as a microbial biofilm. Our analysis indicates that the results of the algebraically simpler original Freter model largely carry over. In a computational simulation study, we find that the vast majority of bacteria in the reactor will eventually be sessile. However, we also find that suspended biomass is relatively more efficient in removing substrate from the reactor than biofilm bacteria. PMID: 22131185 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5473954 Thu, 01 Dec 2011 05:00:00 +0100 5473954 http://www.medworm.com/index.php?rid=5473955&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22108739%26dopt%3DAbstract Authors: Binder BJ, Landman KA, Newgreen DF, Simkin JE, Takahashi Y, Zhang D Abstract Hindbrain (vagal) neural crest cells become relatively uniformly distributed along the embryonic intestine during the rostral to caudal colonization wave which forms the enteric nervous system (ENS). When vagal neural crest cells are labeled before migration in avian embryos by in ovo electroporation, the distribution of labeled neural crest cells in the ENS varies vastly. In some cases, the labeled neural crest cells appear evenly distributed and interspersed with unlabeled neural crest cells along the entire intestine. However, in most specimens, labeled cells occur in relatively discrete patches of varying position, area, and cell number. To determine reasons for these differences, we use a dis... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5473955 Thu, 24 Nov 2011 05:00:00 +0100 5473955 http://www.medworm.com/index.php?rid=5473957&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22108737%26dopt%3DAbstract We present three models of the agr operon belonging to strains competing for dominance, each comprising one of the three possible phosphorylation cascades governing the two component system (TCS) of the agr system. Bifurcation analyses clarify the aspects of QS most crucial in determining the efficacy of using a non-pathogenic strain for therapeutic purposes if the target TCS cascade is known and illustrate the qualitative and quantitative differences which occur as a result of mechanistic differences between the models. We highlight those results that, in concert with appropriate experimental data, would be most useful in ascertaining whether or not a classical TCS is in operation in a particular strain if this information is unknown. PMID: 22108737 [PubMed - as supplied by publisher]... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5473957 Wed, 23 Nov 2011 05:00:00 +0100 5473957 http://www.medworm.com/index.php?rid=5473956&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22108738%26dopt%3DAbstract Authors: Jabbari S, King JR, Williams P Abstract Staphylococcus aureus uses quorum sensing (QS) to enhance its pathogenicity. An intriguing aspect of this is that different strains are capable of inactivating the QS systems of opposing strains. In Part 1 of this study, we presented a model of this phenomenon in a well-mixed environment; here, we incorporate spatial structure. Two competitive strains occupying adjacent habitats with freely diffusing QS signal molecules (QSSMs) are considered. We investigate the effect of the QSSM diffusion coefficient and the relative size of the two populations on the ability of one population to dominate the other. Regarding population size, a larger population is generally at an advantage (initial conditions permitting), while the implications of... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5473956 Wed, 23 Nov 2011 05:00:00 +0100 5473956 http://www.medworm.com/index.php?rid=5417893&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22083513%26dopt%3DAbstract Authors: Simms K, Bean N, Koerber A Abstract In this paper, we present a model of cell cycle progression and apply it to cells of the MCF-7 breast cancer cell line. We consider cells existing in the three typical cell cycle phases determined using flow cytometry: the G1, S, and G2/M phases. We further break each phase up into model phases in order to capture certain features such as cells remaining in phases for a minimum amount of time. The model is also able to capture the environmentally responsive part of the G1 phase, allowing for quantification of the number of environmentally responsive cells at each point in time. The model parameters are carefully chosen using data from various sources in the biological literature. The model is then validated against a variety of experimen... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5417893 Tue, 15 Nov 2011 05:00:00 +0100 5417893 http://www.medworm.com/index.php?rid=5417894&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22072186%26dopt%3DAbstract Authors: Klika V, Baker RE, Headon D, Gaffney EA Abstract Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction struct... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5417894 Thu, 10 Nov 2011 05:00:00 +0100 5417894 http://www.medworm.com/index.php?rid=5417895&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22057950%26dopt%3DAbstract Authors: Peña-Miller R, Lähnemann D, Schulenburg H, Ackermann M, Beardmore R Abstract Using optimal control theory as the basic theoretical tool, we investigate the efficacy of different antibiotic treatment protocols in the most exacting of circumstances, described as follows. Viewing a continuous culture device as a proxy for a much more complex host organism, we first inoculate the device with a single bacterial species and deem this the 'commensal' bacterium of our host. We then force the commensal to compete for a single carbon source with a rapidly evolving and fitter 'pathogenic bacterium', the latter so-named because we wish to use a bacteriostatic antibiotic to drive the pathogen toward low population densities. Constructing a mathematical model to mimic the biology, we ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5417895 Sat, 05 Nov 2011 04:00:00 +0100 5417895 http://www.medworm.com/index.php?rid=5343741&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D22015479%26dopt%3DAbstract Authors: Merkey BV, Chopp DL Abstract A multidimensional biofilm model is developed to simulate biofilm growth on the anode of a Microbial Fuel Cell (MFC). The biofilm is treated as a conductive material, and electrons produced during microbial growth are assumed to be transferred to the anode through a conductive biofilm matrix. Growth of Geobacter sulfurreducens is simulated using the Nernst-Monod kinetic model that was previously developed and later validated in experiments. By implementing a conduction-based biofilm model in two dimensions, we are able to explore the impact of anode density and arrangement on current production in a MFC. PMID: 22015479 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343741 Thu, 20 Oct 2011 04:00:00 +0100 5343741 http://www.medworm.com/index.php?rid=5343743&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21997361%26dopt%3DAbstract Authors: Kealy BJ, Wollkind DJ Abstract The development of spontaneous stationary vegetative patterns in an arid flat environment is investigated by means of a weakly nonlinear diffusive instability analysis applied to the appropriate model system for this phenomenon. In particular, that process can be modeled by a partial differential interaction-diffusion equation system for the plant biomass density and the surface water content defined on an unbounded flat spatial domain. The main results of this analysis can be represented by closed-form plots in the rate of precipitation versus the specific rate of plant density loss parameter space. From these plots, regions corresponding to bare ground and vegetative patterns consisting of parallel stripes, labyrinth-like mazes, hexagonal a... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343743 Fri, 14 Oct 2011 04:00:00 +0100 5343743 http://www.medworm.com/index.php?rid=5343742&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21997362%26dopt%3DAbstract Authors: Hughes J, Hancock WO, Fricks J Abstract We develop a stochastic model for variable-length stepping of kinesins engineered with extended neck linkers. This requires that we consider the separation in microtubule binding sites between the heads of the motor at the beginning of a step. We show that this separation is stationary and can be included in the calculation of standard experimental quantities. We also develop a corresponding matrix computational framework for conducting computer experiments. Our matrix approach is more efficient computationally than large-scale Monte Carlo simulation. This efficiency greatly eases sensitivity analysis, an important feature when there is considerable uncertainty in the physical parameters of the system. We demonstrate the application ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343742 Fri, 14 Oct 2011 04:00:00 +0100 5343742 http://www.medworm.com/index.php?rid=5343744&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21993950%26dopt%3DAbstract We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343744 Thu, 13 Oct 2011 04:00:00 +0100 5343744 http://www.medworm.com/index.php?rid=5343748&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21989564%26dopt%3DAbstract Authors: Floyd W, Kay L, Shapiro M Abstract In this paper, we introduce a new class of epidemics on networks which we call SI(S/I). SI(S/I) networks differ from SIS networks in allowing an infected individual to become reinfected without first passing to the susceptible state. We use a covering-graph construction to compare SIR, SIS, and SI(S/I) networks. Like the SIR networks that cover them, SI(S/I) networks exhibit infection probabilities that are monotone with respect to both transmission probabilities and the initial set of infectives. The same covering-graph construction allows us to characterize the recurrent states in an SIS or SI(S/I) network with reinfection. PMID: 21989564 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343748 Wed, 12 Oct 2011 04:00:00 +0100 5343748 http://www.medworm.com/index.php?rid=5343747&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21989565%26dopt%3DAbstract Authors: Pérez Millán M, Dickenstein A, Shiu A, Conradi C Abstract Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have tor... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343747 Wed, 12 Oct 2011 04:00:00 +0100 5343747 http://www.medworm.com/index.php?rid=5343746&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21989566%26dopt%3DAbstract Authors: Bazil JN, Buzzard GT, Rundell AE Abstract Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343746 Wed, 12 Oct 2011 04:00:00 +0100 5343746 http://www.medworm.com/index.php?rid=5343745&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21989567%26dopt%3DAbstract Authors: Glimm T, Zhang J, Shen YQ, Newman SA Abstract We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction-diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-o... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5343745 Wed, 12 Oct 2011 04:00:00 +0100 5343745 http://www.medworm.com/index.php?rid=5295322&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21979463%26dopt%3DAbstract Authors: Smith JH, Starkweather KA, García JJ Abstract A nonlinear, coupled biphasic-mass transport model that includes transvascular fluid exchange is proposed for flow-controlled infusions in brain tissue. The model accounts for geometric and material nonlinearities, a hydraulic conductivity dependent on deformation, and transvascular fluid exchange according to Starling's law. The governing equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite-element algorithm. Results of the model indicate that, using normal physiological values of vascular permeability, transvascular fluid exchange has negligible effects on tissue deformation, fluid pressure, and transport of the infused agent. As vascular permeability may be i... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5295322 Fri, 07 Oct 2011 04:00:00 +0100 5295322 http://www.medworm.com/index.php?rid=5295324&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21975643%26dopt%3DAbstract Authors: Sumner JG, Holland BR, Jarvis PD Abstract It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the "splitting" operator that generates the branching process on phylogenetic trees. For simplicity,... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5295324 Thu, 06 Oct 2011 04:00:00 +0100 5295324 http://www.medworm.com/index.php?rid=5295323&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21975644%26dopt%3DAbstract Authors: Scianna M Abstract Cytosolic calcium machinery is one of the principal signaling mechanisms by which endothelial cells (ECs) respond to external stimuli during several biological processes, including vascular progression in both physiological and pathological conditions. Low concentrations of angiogenic factors (such as VEGF) activate in fact complex pathways involving, among others, second messengers arachidonic acid (AA) and nitric oxide (NO), which in turn control the activity of plasma membrane calcium channels. The subsequent increase in the intracellular level of the ion regulates fundamental biophysical properties of ECs (such as elasticity, intrinsic motility, and chemical strength), enhancing their migratory capacity. Previously, a number of continuous models have... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5295323 Thu, 06 Oct 2011 04:00:00 +0100 5295323 http://www.medworm.com/index.php?rid=5295326&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21972030%26dopt%3DAbstract Authors: Hu WY, Zhong WR, Wang FH, Li L, Shao YZ Abstract Based on the logistic growth law for a tumour derived from enzymatic dynamics, we address from a physical point of view the phenomena of synergism, additivity and antagonism in an avascular anti-tumour system regulated externally by dual coupling periodic interventions, and propose a theoretical model to simulate the combinational administration of chemotherapy and immunotherapy. The in silico results of our modelling approach reveal that the tumour population density of an anti-tumour system, which is subject to the combinational attack of chemotherapeutical as well as immune intervention, depends on four parameters as below: the therapy intensities D, the coupling intensity I, the coupling coherence R and the phase-shifts... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5295326 Wed, 05 Oct 2011 04:00:00 +0100 5295326 http://www.medworm.com/index.php?rid=5295325&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21972031%26dopt%3DAbstract Authors: Garnier J, Roques L, Hamel F Abstract We analyze the role of the spatial distribution of the initial condition in reaction-diffusion models of biological invasion. Our study shows that, in the presence of an Allee effect, the precise shape of the initial (or founding) population is of critical importance for successful invasion. Results are provided for one-dimensional and two-dimensional models. In the one-dimensional case, we consider initial conditions supported by two disjoint intervals of length L/2 and separated by a distance α. Analytical as well as numerical results indicate that the critical size L (∗)(α) of the population, where the invasion is successful if and only if L>L (∗)(α), is a continuous function of α and tends to increas... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5295325 Wed, 05 Oct 2011 04:00:00 +0100 5295325 http://www.medworm.com/index.php?rid=5217522&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21901527%26dopt%3DAbstract Authors: Fudenberg D, Imhof LA Abstract Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genoty... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5217522 Wed, 07 Sep 2011 04:00:00 +0100 5217522 http://www.medworm.com/index.php?rid=5217526&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21882077%26dopt%3DAbstract Authors: Maggio CD, Jennings SR, Robichaux JL, Stapor PC, Hyman JM Abstract We extend and analyze the Wang and Politi modified Hai-Murphy model of smooth muscle cell contractions to capture uterine muscle cell response to variations in intracellular calcium concentrations. This model is used to estimate values of unknown parameters in uterine smooth muscle cell cross-bridging. Uterine motility is responsible for carrying out important processes throughout all phases of the nonpregnant female reproductive cycle, including sperm transport, menstruation, and embryo implantation. The modified Hai-Murphy partial differential equation model accounts for the displacement of myosin cross-bridge heads relative to their binding sites. This model was originally developed for the study of airw... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5217526 Thu, 01 Sep 2011 04:00:00 +0100 5217526 http://www.medworm.com/index.php?rid=5174429&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21870200%26dopt%3DAbstract Authors: Sun Q, Tang M, Yu J Abstract Gene transcription is a central cellular process and is stochastic in nature. The stochasticity has been studied in real cells and in theory, but often for the transcription activated by a single signaling pathway at steady-state. As transcription of many genes is involved with multiple pathways, we investigate how the transcription efficiency and noise is modulated by cross-talking pathways. We model gene transcription as a renewal process for which the gene can be turned on by different pathways. We determine the transcription efficiency by solving a system of differential equations, and obtain the mathematical formula of the noise strength by the Laplace transform and standard techniques in renewal theory. Our numerical examples demonstrate ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5174429 Thu, 25 Aug 2011 23:00:00 +0100 5174429 http://www.medworm.com/index.php?rid=5174428&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21870201%26dopt%3DAbstract Authors: Kelly WP, Stumpf MP Abstract Protein interaction networks comprise thousands of individual binary links between distinct proteins. Whilst these data have attracted considerable attention and been the focus of many different studies, the networks, their structure, function, and how they change over time are still not fully known. More importantly, there is still considerable uncertainty regarding their size, and the quality of the available data continues to be questioned. Here, we employ statistical models of the experimental sampling process, in particular capture-recapture methods, in order to assess the false discovery rate and size of protein interaction networks. We uses these methods to gauge the ability of different experimental systems to find the true binary inter... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5174428 Thu, 25 Aug 2011 23:00:00 +0100 5174428 http://www.medworm.com/index.php?rid=5140865&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21826564%26dopt%3DAbstract Authors: Curto C, Degeratu A, Itskov V Abstract Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network's connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H (1)(X;ℤ)=0, where X is the clique complex associated to the network's constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5140865 Mon, 08 Aug 2011 23:00:00 +0100 5140865 http://www.medworm.com/index.php?rid=5140866&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21822766%26dopt%3DAbstract Authors: Browne CJ, Pilyugin SS Abstract Floquet theory and perturbation techniques are used to analyze a classical within-host virus model with periodic drug treatment. Both single and multidrug treatment strategies are investigated. Specifically, the effects of both RT-inhibitors and P-inhibitors on the stability of the infection-free steady state are studied. It is found that when both classes of drugs have periodic drug efficacy functions, then shifting the phase of these functions can critically affect the stability of the infection-free steady state. A numerical study is conducted to illustrate the theoretical results and provide additional insights. PMID: 21822766 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5140866 Fri, 05 Aug 2011 23:00:00 +0100 5140866 http://www.medworm.com/index.php?rid=5140867&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21818674%26dopt%3DAbstract Authors: Gurney WS, Bacon PJ, Speirs DC, McGinnity P, Verspoor E Abstract Atlantic salmon exhibit a partially heritable polymorphism in which the morphs are distinguished by the duration and location of the sea-phase of their life-cycle. These morphs co-occur, albeit in characteristically different proportions, in most Scottish rivers and in both the spring and autumn spawner runs; early running fish being generally associated with upland spawning locations while late running fish are associated with lowland spawning. Thus, differences in riverine and marine environment appear to be linked to differences in the relative abundance of the morphs, rather than to the specific morph which is optimally adapted. In this paper, we report a model-based synthetic study aimed at understanding... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5140867 Thu, 04 Aug 2011 23:00:00 +0100 5140867 http://www.medworm.com/index.php?rid=5095793&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21814880%26dopt%3DAbstract Authors: Eladdadi A, Isaacson D In this paper, we present a mathematical model predicting the fraction of proliferating cells in G1, S, and G2/M phases of the cell cycle as a function of EGFR and HER2. We show that it is possible to find parameters for the mathematical model so that its predictions agree with the experimental observations that HER2 over-expression results in: (1) a shorter G1-phase and early S-phase entry; (2) and that with a 1-to-1 ration between EGFR and HER2, the growth advantage in HER2 over-expressing cells is indeed associated with the increase of the HER2 expression level. PMID: 21814880 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5095793 Thu, 04 Aug 2011 23:00:00 +0100 5095793 http://www.medworm.com/index.php?rid=5095794&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21800229%26dopt%3DAbstract We present a progression of three distinct three-zone, continuum models for swarm behavior based on social interactions with neighbors in order to explain simple coherent structures in popular biological models of aggregations. In continuum models, individuals are replaced with density and velocity functions. Individual behavior is modeled with convolutions acting within three interaction zones corresponding to repulsion, orientation, and attraction, respectively. We begin with a variable-speed first-order model in which the velocity depends directly on the interactions. Next, we present a variable-speed second-order model. Finally, we present a constant-speed second-order model that is coordinated with popular individual-based models. For all three models, linear stability analysis shows ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5095794 Thu, 28 Jul 2011 23:00:00 +0100 5095794 http://www.medworm.com/index.php?rid=5049803&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21769516%26dopt%3DAbstract Authors: Zhang L, Lin Z, Pedersen M The physiological-structured population models assume that a fixed fraction of energy intake is utilized for individual growth and maintenance while the remaining for adult fertility. The assumption results in two concerns: energy loss for juveniles and a reproduction dilemma for adults. The dilemma results from the possibility that adults have to breed even if metabolic costs fail to be covered. We consider a size-structured population model, where standard metabolism is given top priority for utilizing energy intake and the surplus energy, if there is any, is distributed to individual growth and reproduction. Moreover, the portion of surplus energy for reproduction is size-dependent and increases monotonically with size. Using the newly developed p... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=5049803 Fri, 15 Jul 2011 23:00:00 +0100 5049803 http://www.medworm.com/index.php?rid=4855612&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21557035%26dopt%3DAbstract Authors: Gejji R, Lou Y, Munther D, Peyton J We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For non... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4855612 Mon, 09 May 2011 23:00:00 +0100 4855612 http://www.medworm.com/index.php?rid=4802701&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21544676%26dopt%3DAbstract Authors: Hiebeler DE, Michaud IJ, Ackerman HH, Reed Iosevich S, Robinson A An SIR epidemiological community-structured model is constructed to investigate the effects of clustered distributions of unvaccinated individuals and the distribution of the primary case relative to vaccination levels. The communities here represent groups such as neighborhoods within a city or cities within a region. The model contains two levels of mixing, where individuals make more intra-group than inter-group contacts. Stochastic simulations and analytical results are utilized to explore the model. An extension of the effective reproduction ratio that incorporates more spatial information by predicting the average number of tertiary infections caused by a single infected individual is introduced to charact... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802701 Wed, 04 May 2011 23:00:00 +0100 4802701 http://www.medworm.com/index.php?rid=4802703&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21533664%26dopt%3DAbstract Authors: Hand PE, Griffith BE We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802703 Fri, 29 Apr 2011 23:00:00 +0100 4802703 http://www.medworm.com/index.php?rid=4802702&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21533774%26dopt%3DAbstract Authors: Hu G, Wang Z, Qiu WY Current synthetic biology has witnessed a revolution that natural DNA molecule steps onto a broad scientific area by assembling a large variety of three-dimensional structures with the connectivity of polyhedra. A mathematical model of these biomolecules is crucial to clarify the biological self-assembly principle, and unravel a first-step understanding of biological regulation and controlling mechanisms. In this paper, mechanisms of two different enzymatic actions on DNA polyhedra are elucidated through theoretical models of polyhedral links: (1) topoisomerase that untangles DNA polyhedral links produces separated single-stranded DNA circles through the crossing change operation; (2) recombinase generates a class of polyhedral circular paths or polyhed... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802702 Thu, 28 Apr 2011 23:00:00 +0100 4802702 http://www.medworm.com/index.php?rid=4802704&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21523510%26dopt%3DAbstract Authors: Feliu E, Knudsen M, Andersen LN, Wiuf C Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes.We demonstrate that many steady-state concentrations are related through rational functio... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802704 Tue, 26 Apr 2011 23:00:00 +0100 4802704 http://www.medworm.com/index.php?rid=4802705&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21512833%26dopt%3DAbstract Authors: Drobnjak I, Fowler AC In certain blood diseases, oscillations are found in blood cell counts. Particularly, such oscillations are sometimes found in chronic myelogenous leukaemia, and then occur in all the derived blood cell types: red blood cells, white blood cells, and platelets. It has been suggested that such oscillations arise because of an instability in the pluri-potential stem cell population, associated with its regulatory control system. In this paper, we consider how such oscillations can arise in a model of competition between normal (S) and genetically altered abnormal (A) stem cells, as the latter population grows at the expense of the former. We use an analytic model of long period oscillations to describe regions of oscillatory behaviour in the S-A phase plane,... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802705 Thu, 21 Apr 2011 23:00:00 +0100 4802705 http://www.medworm.com/index.php?rid=4802706&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21509627%26dopt%3DAbstract Authors: Li MY, Lim AG Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease, and adult T-cell leukemia (ATL). Chronically infected individuals often harbor high proviral loads despite maintaining a persistently activated immune response. Based on a new hypothesis for the persistence of HTLV-I infection, a three-dimensional compartmental model is constructed that describes the dynamic interactions among latently infected target cells, target-cell activation, and immune responses to HTLV-I, with an emphasis on understanding the role of Tax expression in the persistence of HTLV-I. PMID: 21509627 [PubMed - as supplied by publisher] (Source: Bul... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802706 Wed, 20 Apr 2011 23:00:00 +0100 4802706 http://www.medworm.com/index.php?rid=4802707&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21505932%26dopt%3DAbstract Authors: Moore SM, Manore CA, Bokil VA, Borer ET, Hosseini PR Many generalist pathogens are influenced by the spatial distributions and relative abundances of susceptible host species. The spatial structure of host populations can influence patterns of infection incidence (or disease outbreaks), and the effects of a generalist pathogen on host community dynamics in a spatially heterogeneous community may differ from predictions derived via simple models. In this paper, we model the transmission of a generalist pathogen within a patch framework that incorporates the movement of vectors between discrete host patches to investigate the effects of local host community composition and vector movement rates on disease dynamics.We use barley and cereal yellow dwarf viruses (B/CYDV), a suite o... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802707 Tue, 19 Apr 2011 23:00:00 +0100 4802707 http://www.medworm.com/index.php?rid=4802708&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21503834%26dopt%3DAbstract Authors: Gopalkrishnan M We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is "on" in the presence of certain catalysts and "off" in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman et al., and normal networks of Gnacadja. We define autocat... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802708 Mon, 18 Apr 2011 23:00:00 +0100 4802708 http://www.medworm.com/index.php?rid=4802710&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21476110%26dopt%3DAbstract Authors: Eftimie R, Dushoff J, Bridle BW, Bramson JL, Earn DJ Recent advances in virology, gene therapy, and molecular and cell biology have provided insight into the mechanisms through which viruses can boost the anti-tumor immune response, or can infect and directly kill tumor cells. A recent experimental report (Bridle et al. in Molec. Ther. 18(8):1430-1439, 2010) showed that a sequential treatment approach that involves two viruses that carry the same tumor antigen leads to an improved anti-tumor response compared to the effect of each virus alone. In this article, we derive a mathematical model to investigate the anti-tumor effect of two viruses, and their interactions with the immune cells. We discuss the conditions necessary for permanent tumor elimination and, in this context,... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802710 Thu, 07 Apr 2011 23:00:00 +0100 4802710 http://www.medworm.com/index.php?rid=4802709&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21476111%26dopt%3DAbstract Authors: Hove-Musekwa SD, Nyabadza F, Mambili-Mamboundou H In sub-Saharan Africa, the model of care for people who are living with HIV/AIDS has changed from hospital care to home-based care. In this paper, a mathematical model describing the dynamics of HIV transmission, hospitalization, and home-based care is constructed and analysed. The model reproduction number R ( e ) is determined and discussed. The equilibria are determined and analysed in terms of R ( e ). It is shown that if R ( e )<1, the disease free equilibrium is both locally and globally asymptotically stable. The model has a unique endemic equilibrium and is locally asymptotically stable whenever R ( e )>1. Five cases arise in the discussion of R ( e ) pertaining to intervention strategies. Numerical simulations a... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802709 Thu, 07 Apr 2011 23:00:00 +0100 4802709 http://www.medworm.com/index.php?rid=4802711&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21468779%26dopt%3DAbstract Authors: Sanches RP, Ferreira CP, Kraenkel RA This paper presents a mathematical model for cholera epidemics which comprises seasonality, loss of host immunity, and control mechanisms acting to reduce cholera transmission. A collection of data related to cholera disease allows us to show that outbreaks in endemic areas are subject to a resonant behavior, since the intrinsic oscillation period of the disease (∼1 year) is synchronized with the annual contact rate variation. Moreover, we argue that the short period of the host immunity may be associated to secondary peaks of incidence observed in some regions (a bimodal pattern). Finally, we explore some possible mechanisms of cholera control, and analyze their efficiency. We conclude that, besides mass vaccination-which may be imprac... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802711 Tue, 05 Apr 2011 23:00:00 +0100 4802711 http://www.medworm.com/index.php?rid=4802712&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21445700%26dopt%3DAbstract Authors: Thibodeaux JJ, Schlittenhardt TP We develop a numerical method for estimating optimal parameters in a mathematical model of the within-host dynamics of malaria infection. The model consists of a quasilinear system of partial differential equations. Convergence theory for the computed parameters is provided. Following this analysis, we present several numerical simulations that suggest that periodic treatments that are in synchronization with the periodic bursting rate of infected erythrocytes are the most productive strategies. PMID: 21445700 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4802712 Mon, 28 Mar 2011 23:00:00 +0100 4802712 http://www.medworm.com/index.php?rid=4637831&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21431450%26dopt%3DAbstract Authors: Kang Y, Lanchier N In order to understand the role of space in ecological communities where each species produces a certain type of resource and has varying abilities to exploit the resources produced by its own species and by the other species, we carry out a comparative study of an interacting particle system and its mean-field approximation. For a wide range of parameter values, we show both analytically and numerically that the spatial model results in predictions that significantly differ from its nonspatial counterpart, indicating that the use of the mean-field approach to describe the evolution of communities in which individuals only interact locally is invalid. In two-species communities, the disagreements between the models appear either when both species compete by ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637831 Wed, 23 Mar 2011 00:00:00 +0100 4637831 http://www.medworm.com/index.php?rid=4637832&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21424232%26dopt%3DAbstract We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling. PMID: 21424232 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637832 Fri, 18 Mar 2011 00:00:00 +0100 4637832 http://www.medworm.com/index.php?rid=4637835&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21409511%26dopt%3DAbstract Authors: Wells CR, Tchuenche JM, Meyers LA, Galvani AP, Bauch CT Ring vaccination can be a highly effective control strategy for an emerging disease or in the final phase of disease eradication, as witnessed in the eradication of smallpox. However, the impact of behavioural dynamics on the effectiveness of ring vaccination has not been explored in mathematical models. Here, we analyze a series of stochastic models of voluntary ring vaccination. Contacts of an index case base vaccinating decisions on their own individual payoffs to vaccinate or not vaccinate, and they can also imitate the behaviour of other contacts of the index case. We find that including imitation changes the probability of containment through ring vaccination considerably. Imitation can cause a strong majority of co... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637835 Wed, 16 Mar 2011 00:00:00 +0100 4637835 http://www.medworm.com/index.php?rid=4637834&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21409512%26dopt%3DAbstract Authors: Sotero RC, Iturria-Medina Y A theoretical framework is presented for converting Blood Oxygenation Level Dependent (BOLD) images to brain temperature maps, based on the idea that disproportional local changes in cerebral blood flow (CBF) as compared with cerebral metabolic rate of oxygen consumption (CMRO (2)) during functional brain activity, lead to both brain temperature changes and the BOLD effect. Using an oxygen limitation model and a BOLD signal model, we obtain a transcendental equation relating CBF and CMRO (2) changes with the corresponding BOLD signal, which is solved in terms of the Lambert W function. Inserting this result in the dynamic bioheat equation describing the rate of temperature changes in the brain, we obtain a nonautonomous ordinary differential equatio... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637834 Wed, 16 Mar 2011 00:00:00 +0100 4637834 http://www.medworm.com/index.php?rid=4637833&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21409513%26dopt%3DAbstract Authors: Malaspinas AS, Eriksson N, Huggins P To infer a phylogenetic tree from a set of DNA sequences, typically a multiple alignment is first used to obtain homologous bases. The inferred phylogeny can be very sensitive to how the alignment was created. We develop tools for analyzing the robustness of phylogeny to perturbations in alignment parameters in the NW algorithm. Our main tool is parametric alignment, with novel improvements that are of general interest in parametric inference. Using parametric alignment and a Gaussian distribution on alignment parameters, we derive probabilities of optimal alignment summaries and inferred phylogenies. We apply our method to analyze intronic sequences from Drosophila flies. We show that phylogeny estimates can be sensitive to the choice of a... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637833 Wed, 16 Mar 2011 00:00:00 +0100 4637833 http://www.medworm.com/index.php?rid=4637836&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21404132%26dopt%3DAbstract Authors: Yao W, Huang H, Miura RM Cortical spreading depression (CSD) waves can occur in the cortices of various brain structures and are associated with the spread of depression of the electroencephalogram signal. In this paper, we present a continuum neuronal model for the instigation and spreading of CSD. Our model assumes that the brain-cell microenvironment can be treated as a porous medium consisting of extra- and intracellular compartments. The main mechanisms in our model for the transport of ions into and out of neurons are cross-membrane ionic currents and (active) pumps, coupled with diffusion in the extracellular space. To demonstrate the applicability of our model, we have carried out extensive numerical simulations under different initial conditions and inclusion of vario... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637836 Tue, 15 Mar 2011 00:00:00 +0100 4637836 http://www.medworm.com/index.php?rid=4637837&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21400021%26dopt%3DAbstract Authors: Laubenbacher R PMID: 21400021 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4637837 Sat, 12 Mar 2011 00:00:00 +0100 4637837 http://www.medworm.com/index.php?rid=4578091&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21390561%26dopt%3DAbstract Authors: Pearson YE, Castronovo E, Lindsley TA, Drew DA A stochastic model is proposed for the position of the tip of an axon. Parameters in the model are determined from laboratory data. The first step is the reduction of inherent error in the laboratory data, followed by estimating parameters and fitting a mathematical model to this data. Several axonogenesis aspects have been investigated, particularly how positive axon elongation and growth cone kinematics are coupled processes but require very different theoretical descriptions. Preliminary results have been obtained through a series of experiments aimed at isolating the response of axons to controlled gradient exposures to guidance cues and the effects of ethanol and similar substances. We show results based on the following task... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578091 Thu, 10 Mar 2011 00:00:00 +0100 4578091 http://www.medworm.com/index.php?rid=4578092&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21387191%26dopt%3DAbstract We present a minimal model of the onset of synchronization in the individual smooth muscle cell that is manifested as a transition from calcium waves to whole-cell calcium oscillations. We discuss how different types of ion currents may influence both amplitude and frequency in the regime of whole-cell oscillations. The model may also explain the occurrence of mixed-mode oscillations and chaotic oscillations frequently observed in the experimental system. PMID: 21387191 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578092 Wed, 09 Mar 2011 00:00:00 +0100 4578092 http://www.medworm.com/index.php?rid=4578095&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21373974%26dopt%3DAbstract Authors: Lang M, Marquez-Lago TT, Stelling J, Waldherr S Synthetic biology has recently provided functional single-cell oscillators. With a few exceptions, however, synchronization across a population has not been achieved yet. In particular, designing a cell coupling mechanism to achieve autonomous synchronization is not straightforward since there are usually several different design alternatives. Here, we propose a method to mathematically predict autonomous synchronization properties, and to identify the network structure with the best performance, thus increasing the feasibility for a successful implementation in vivo.Our method relies on the reduction of ODE-based models for synthetic oscillators to a phase description, and the subsequent analysis of the phase model either in th... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578095 Fri, 04 Mar 2011 00:00:00 +0100 4578095 http://www.medworm.com/index.php?rid=4578094&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21373975%26dopt%3DAbstract Authors: Haws DC, Hodge TL, Yoshida R Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. The BME method is related to the Neighbor Joining (NJ) Algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ Algorithm returns a BME tree for small numbers of taxa. In this paper we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578094 Fri, 04 Mar 2011 00:00:00 +0100 4578094 http://www.medworm.com/index.php?rid=4578093&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21373976%26dopt%3DAbstract Authors: Bewick S, Wu J, Lenaghan SC, Yang R, Zhang M, Hamel W In this paper, we show how a game theoretic analysis can provide a model to explain the interdependence of host produced APOBEC3G levels and virus encoded Vif levels. We then use the relationship between these two opposing proteins in order to predict the success of two different HIV-1 viral variants, R5 and X4. From our analysis, we show that when APOBEC3G strongly favors mutation from an R5 strain to an X4 strain, it can be optimal for HIV-1 to suppress transmission of the X4 variant, despite the loss of X4 fitness potential. This is particularly true when the X4 strain significantly interferes with the host adaptive immune response, when Vif production is limited, or when host APOBEC3G targets the X4 strain more severely... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578093 Fri, 04 Mar 2011 00:00:00 +0100 4578093 http://www.medworm.com/index.php?rid=4578096&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21359613%26dopt%3DAbstract Authors: Willson SJ Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The meaning of a species tree is made more complicated by the recent discovery of the importance of hybridizations and lateral gene transfers. Hence, it is desirable to describe uniform well-defined procedures that yield a tree given a network N.A useful tool toward this end is a connected surjective digraph (CSD) map φ:N→N' where N' is generally a much simpler network than N. A set W of vertices in N is "restricted" if there is at most one vertex u∉W from which there is an arc into W, thus yielding a bottleneck in N. A CSD map φ:N→... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4578096 Sat, 26 Feb 2011 00:00:00 +0100 4578096 http://www.medworm.com/index.php?rid=4524878&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347814%26dopt%3DAbstract Authors: Chaffee J, Kuske R The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nea... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524878 Thu, 24 Feb 2011 00:00:00 +0100 4524878 http://www.medworm.com/index.php?rid=4524877&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347815%26dopt%3DAbstract We present results for the proto-typical Schnakenberg and Gierer-Meinhardt systems: exploring the dynamics of these systems suggests a reconsideration of the basic Turing mechanism for pattern formation on morphogen-regulated growing domains as well as highlighting when feedback delays on domain growth are important for pattern formation. PMID: 21347815 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524877 Thu, 24 Feb 2011 00:00:00 +0100 4524877 http://www.medworm.com/index.php?rid=4524876&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347816%26dopt%3DAbstract Authors: Lou Y, Zhao XQ Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host-vector interaction and the predator-prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theori... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524876 Thu, 24 Feb 2011 00:00:00 +0100 4524876 http://www.medworm.com/index.php?rid=4524881&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347811%26dopt%3DAbstract Authors: Lemaire T, Capiez-Lernout E, Kaiser J, Naili S, Rohan E, Sansalone V This paper presents a theoretical investigation of the multiphysical phenomena that govern cortical bone behaviour. Taking into account the piezoelectricity of the collagen-apatite matrix and the electrokinetics governing the interstitial fluid movement, we adopt a multiscale approach to derive a coupled poroelastic model of cortical tissue. Following how the phenomena propagate from the microscale to the tissue scale, we are able to determine the nature of macroscopically observed electric phenomena in bone. PMID: 21347811 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524881 Wed, 23 Feb 2011 00:00:00 +0100 4524881 http://www.medworm.com/index.php?rid=4524880&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347812%26dopt%3DAbstract Authors: Parvinen K We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various p... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524880 Wed, 23 Feb 2011 00:00:00 +0100 4524880 http://www.medworm.com/index.php?rid=4524879&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21347813%26dopt%3DAbstract Authors: Childs LM, Paskow M, Morris SM, Hesse M, Strogatz S Macrophages are fundamental cells of the innate immune system. Their activation is essential for such distinct immune functions as inflammation (pathogen-killing) and tissue repair (wound healing). An open question has been the functional stability of an individual macrophage cell: whether it can change its functional profile between different immune responses such as between the repair pathway and the inflammatory pathway. We studied this question theoretically by constructing a rate equation model for the key substrate, enzymes and products of the pathways; we then tested the model experimentally. Both our model and experiments show that individual macrophages can switch from the repair pathway to the inflammation pathway b... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524879 Wed, 23 Feb 2011 00:00:00 +0100 4524879 http://www.medworm.com/index.php?rid=4524882&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21327881%26dopt%3DAbstract Authors: Krishnan A, Epureanu BI Renewal-reward processes are used to provide a framework for the mathematical description of single-molecule bead-motor assays for processive motor proteins. The formulation provides a more powerful, general approach to the fluctuation analysis of bead-motor assays begun by Svoboda et al. (Proc. Natl. Acad. Sci. USA 91(25):11782, 1994). Fluctuation analysis allows one to gain insight into the mechanochemical cycle of motor proteins purely by measuring the statistics of the displacement of the cargo (e.g., bead) the protein transports. The statistical parameters of interest are shown to be the steady-state slopes (in time) of the cumulants of the bead (the cumulant rates). The first two cumulant rates are the steady-state velocity and slope of the varia... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4524882 Thu, 17 Feb 2011 00:00:00 +0100 4524882 http://www.medworm.com/index.php?rid=4469542&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21308418%26dopt%3DAbstract Authors: Wright JJ PMID: 21308418 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4469542 Thu, 10 Feb 2011 00:00:00 +0100 4469542 http://www.medworm.com/index.php?rid=4469544&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21301981%26dopt%3DAbstract Authors: Gopalakrishnan M, Govindan BS The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. Several mechanisms are at work toward the formation of the spindle, one of which is the 'capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters t... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4469544 Tue, 08 Feb 2011 00:00:00 +0100 4469544 http://www.medworm.com/index.php?rid=4469543&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21301982%26dopt%3DAbstract Authors: Beim Graben P, Wright J PMID: 21301982 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4469543 Tue, 08 Feb 2011 00:00:00 +0100 4469543 http://www.medworm.com/index.php?rid=4469545&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21286832%26dopt%3DAbstract Authors: Aubert M, Chaplain MA, McDougall SR, Devlin A, Mitchell CA Angiogenesis, the process of new vessel growth from pre-existing vasculature, is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis is also a key regulator of pathogenesis in many clinically important disease processes, for instance, solid tumour progression and ocular diseases. Over the past 10-20 years, tumour-induced angiogenesis has received a lot of attention in the mathematical modelling community and there have also been some attempts to model angiogenesis during wound healing. However, there has been little modelling work of vascular growth during normal development. In this paper, we describe an in silico representation of the developing retinal vasculature in the mouse... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4469545 Tue, 01 Feb 2011 00:00:00 +0100 4469545 http://www.medworm.com/index.php?rid=4469546&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21271294%26dopt%3DAbstract Authors: Jang T, Kwon HD, Lee J The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4469546 Thu, 27 Jan 2011 00:00:00 +0100 4469546 http://www.medworm.com/index.php?rid=4400003&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21258969%26dopt%3DAbstract Authors: Mincheva M Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contains at least one cycle, i.e., a sequence of nodes and directed edges which starts and ends at the same species node. Cycles can be positive or negative, and it has been shown that oscillations can arise as a result of either a positive cycle or a negative cycle. In earlier work it was shown that oscillations associated with a positive cycle can arise from subnetworks with an odd number of positive cycles. In this article we... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4400003 Sat, 22 Jan 2011 00:00:00 +0100 4400003 http://www.medworm.com/index.php?rid=4400004&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21240563%26dopt%3DAbstract Authors: Klapper I, Szomolay B Much of the earth's microbial biomass resides in sessile, spatially structured communities such as biofilms and microbial mats, systems consisting of large numbers of single-celled organisms living within self-secreted matrices made of polymers and other molecules. As a result of their spatial structure, these communities differ in important ways from well-mixed (and well-studied) microbial systems such as those present in chemostats. Here we consider a widely used class of 1D biofilm models in the context of a description of their basic ecology. It will be shown via an exclusion principle resulting from competition for space that these models lead to restrictions on ecological structure. Mathematically, this result follows from a classification of steady... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4400004 Sat, 15 Jan 2011 00:00:00 +0100 4400004 http://www.medworm.com/index.php?rid=4400005&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21225357%26dopt%3DAbstract Authors: Schnepf A, Jones D, Roose T Arbuscular mycorrhizas, associations between plant roots and soil fungi, are ubiquitous among land plants. Arbuscular mycorrhizas can be beneficial for plants by overcoming limitations in nutrient supply. Hyphae, which are long and thin fungal filaments extending from the root surface into the soil, increase the volume of soil accessible for plant nutrient uptake. However, no models so far specifically consider individual hyphae. We developed a mathematical model for nutrient uptake by individual fungal hyphae in order to assess suitable temporal and spatial scales for a new experimental design where fungal uptake parameters are measured on the single hyphal scale. The model was developed based on the conservation of nutrients in an artificial cylin... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4400005 Wed, 12 Jan 2011 00:00:00 +0100 4400005 http://www.medworm.com/index.php?rid=4400007&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21221829%26dopt%3DAbstract Authors: Jones DA, Smith HL The Levin-Stewart model of bacteriophage predation of bacteria in a chemostat is modified for a flow reactor in which bacteria are motile, phage diffuse, and advection brings fresh nutrient and removes medium, cells and phage. A fixed latent period for phage results in a system of delayed reaction-diffusion equations with non-local nonlinearities. Basic reproductive numbers are obtained for bacteria and for phage which predict survival of each in the bio-reactor. These are expressed in terms of physical and biological parameters. Persistence and extinction results are obtained for both bacteria and phage. Numerical simulations are in general agreement with those for the chemostat model. PMID: 21221829 [PubMed - as supplied by publisher] (Source: Bulletin... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4400007 Sat, 08 Jan 2011 00:00:00 +0100 4400007 http://www.medworm.com/index.php?rid=4400006&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21221830%26dopt%3DAbstract Authors: Schumaker MF, Kramer DM We have programmed a Monte Carlo simulation of the Q-cycle model of electron transport in cytochrome b(6)f complex, an enzyme in the photosynthetic pathway that converts sunlight into biologically useful forms of chemical energy. Results were compared with published experiments of Kramer and Crofts (Biochim. Biophys. Acta 1183:72-84, 1993). Rates for the simulation were optimized by constructing large numbers of parameter sets using Latin hypercube sampling and selecting those that gave the minimum mean square deviation from experiment. Multiple copies of the simulation program were run in parallel on a Beowulf cluster. We found that Latin hypercube sampling works well as a method for approximately optimizing very noisy objective functions of 15 or 22 v... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4400006 Sat, 08 Jan 2011 00:00:00 +0100 4400006 http://www.medworm.com/index.php?rid=4331398&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21210241%26dopt%3DAbstract Authors: Andreasen V We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number [Formula: see text]: There is a unique positive solution giving the size of the epidemic if and only if [Formula: see text] exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number [Formula: see text]. For other mixing patterns... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331398 Thu, 06 Jan 2011 00:00:00 +0100 4331398 http://www.medworm.com/index.php?rid=4331397&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21210242%26dopt%3DAbstract Authors: Miȩkisz J, Poleszczuk J, Bodnar M, Foryś U In many biochemical reactions occurring in living cells, number of various molecules might be low which results in significant stochastic fluctuations. In addition, most reactions are not instantaneous, there exist natural time delays in the evolution of cell states. It is a challenge to develop a systematic and rigorous treatment of stochastic dynamics with time delays and to investigate combined effects of stochasticity and delays in concrete models.We propose a new methodology to deal with time delays in biological systems and apply it to simple models of gene expression with delayed degradation. We show that time delay of protein degradation does not cause oscillations as it was recently argued. It follows from our rigorous ana... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331397 Thu, 06 Jan 2011 00:00:00 +0100 4331397 http://www.medworm.com/index.php?rid=4331396&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21210243%26dopt%3DAbstract Authors: Michaels JL, Naudot V, Liebovitch LS The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these two genes reveals that constant levels of self-excitation and cross-inhibition allow the most self-exciting or cross-inhibiting gene to dominate the system. However, since biological systems rarely exist in an unchanging equilibrium, we modeled this gene circuit using discrete time-dependent changes in the parameters in lieu of steady state parameters. These time-dependent parameters lead to new phe... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331396 Thu, 06 Jan 2011 00:00:00 +0100 4331396 http://www.medworm.com/index.php?rid=4331395&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21210244%26dopt%3DAbstract Authors: Dickenstein A, Pérez Millán M We clarify the relation between the algebraic conditions that must be satisfied by the reaction constants in general (mass-action) kinetics systems for the existence of detailed or complex balancing equilibria. These systems have a wide range of applications in chemistry and biology. Their main properties have been set by Horn, Jackson and Feinberg. We expect to extend our point of view to the study of qualitative features of the dynamical behavior of chemical interactions in molecular systems biology. PMID: 21210244 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331395 Thu, 06 Jan 2011 00:00:00 +0100 4331395 http://www.medworm.com/index.php?rid=4331400&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21207175%26dopt%3DAbstract Authors: Weber A, Sturm T, Abdel-Rahman EO We investigate algorithmic methods to tackle the following problem: Given a system of parametric ordinary differential equations built by a biological model, does there exist ranges of values for the model parameters and variables which are both meaningful from a biological point of view and where oscillating trajectories, can be found? We show that in the common case of polynomial vector fields known criteria excluding the existence of non-constant limit cycles lead to quantifier elimination problems over the reals.We apply these criteria to various models that have been previously investigated in the context of algebraic biology. PMID: 21207175 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331400 Wed, 05 Jan 2011 00:00:00 +0100 4331400 http://www.medworm.com/index.php?rid=4331399&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21207176%26dopt%3DAbstract Authors: Hower V, Heitsch CE Motivated by recent work in parametric sequence alignment, we study the parameter space for scoring RNA folds and construct an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common branching. We use this polytope and its normal fan to study the effect of varying three parameters in the free energy model that are not determined experimentally. Our results indicate that variation of these specific parameters does not have a dramatic effect on the structures predicted by the free energy model. We additionally map a collection of known RNA secondary structures to the RNA polytope. PMID: 21207176 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331399 Wed, 05 Jan 2011 00:00:00 +0100 4331399 http://www.medworm.com/index.php?rid=4331401&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21194012%26dopt%3DAbstract Authors: Garlick MJ, Powell JA, Hooten MB, McFarlane LR A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impa... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331401 Sat, 01 Jan 2011 00:00:00 +0100 4331401 http://www.medworm.com/index.php?rid=4331403&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21191662%26dopt%3DAbstract Authors: Cartwright RA The ability of humans to communicate via language is a complex, adapted phenotype, which undoubtedly has a recently evolved genetic component. However, the evolutionary dynamics of language-associated alleles are poorly understood. To improve our knowledge of such systems, a population-genetics model for language-associated genes is developed. (The model is general and applicable to social interactions other than communication.) When an allele arises that potentially improves the ability of individuals to communicate, it will experience positive frequency-dependent selection because its fitness will depend on how many other individuals communicate the same way. Consequently, new and rare alleles are selected against, posing a problem for the evolutionary origin o... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331403 Thu, 30 Dec 2010 00:00:00 +0100 4331403 http://www.medworm.com/index.php?rid=4331402&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21191663%26dopt%3DAbstract Authors: Sen SM, Bagci EZ, Camurdan MC Bistability in apoptosis, or programmed cell death, is crucial for the healthy functioning of multicellular organisms. The aim in this study is to show the presence of bistability in a mitochondria-dependent apoptosis model under nitric oxide effects using chemical reaction network theory. The model equations are a set of coupled ordinary differential equations arising from the assumed mass action kinetics. Whether these equations have a capacity for bistability (cell survival and apoptosis) is determined using a modular approach in which the model is decomposed into modules. Each module contains only a subset of the whole model and is analyzed separately. It is seen that bistability in a module is preserved throughout the whole model after adding... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331402 Thu, 30 Dec 2010 00:00:00 +0100 4331402 http://www.medworm.com/index.php?rid=4331407&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21181502%26dopt%3DAbstract Authors: Hilbe C Classical replicator dynamics assumes that individuals play their games and adopt new strategies on a global level: Each player interacts with a representative sample of the population and if a strategy yields a payoff above the average, then it is expected to spread. In this article, we connect evolutionary models for infinite and finite populations: While the population itself is infinite, interactions and reproduction occurs in random groups of size N. Surprisingly, the resulting dynamics simplifies to the traditional replicator system with a slightly modified payoff matrix. The qualitative results, however, mirror the findings for finite populations, in which strategies are selected according to a probabilistic Moran process. In particular, we derive a one-third la... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331407 Thu, 23 Dec 2010 00:00:00 +0100 4331407 http://www.medworm.com/index.php?rid=4331406&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21181503%26dopt%3DAbstract Authors: Sainudiin R, Thornton K, Harlow J, Booth J, Stillman M, Yoshida R, Griffiths R, McVean G, Donnelly P Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods, we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infinitely-many-sites mutatio... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331406 Thu, 23 Dec 2010 00:00:00 +0100 4331406 http://www.medworm.com/index.php?rid=4331405&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21181504%26dopt%3DAbstract Authors: Blöchl F, Wittmann DM, Theis FJ Signaling networks are abundant in higher organisms. They play pivotal roles, e.g., during embryonic development or within the immune system. In this contribution, we study the combined effect of the various kinetic parameters on the dynamics of signal transduction. To this end, we consider hierarchical complex systems as prototypes of signaling networks. For given topology, the output of these networks is determined by an interplay of the single parameters. For different kinetics, we describe this by algebraic expressions, the so-called effective parameters.When modeling switch-like interactions by Heaviside step functions, we obtain these effective parameters recursively from the interaction graph. They can be visualized as directed trees, wh... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331405 Thu, 23 Dec 2010 00:00:00 +0100 4331405 http://www.medworm.com/index.php?rid=4331404&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21181505%26dopt%3DAbstract Authors: McCaig C, Begon M, Norman R, Shankland C Superspreaders are an important phenomenon in the spread of infectious disease, accounting for a higher than average number of new infections in the population. We use mathematical models to compare the impact of supershedders and supercontacters on population dynamics. The stochastic, individual based models are investigated by conversion to deterministic, population level Mean Field Equations, using process algebra. The mean emergent population dynamics of the models are shown to be equivalent with and without superspreaders; however, simulations confirm expectations of differences in variability, having implications for individual epidemics. PMID: 21181505 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biol... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331404 Thu, 23 Dec 2010 00:00:00 +0100 4331404 http://www.medworm.com/index.php?rid=4331409&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21174230%26dopt%3DAbstract Authors: Bennett MR, Farnell L, Gibson WG Synaptic spines grow as a consequence of the formation of F-actin filaments at the spine head. The dynamics of F-actin in the spine head upon excitation of N-methy-D-aspartate (NMDA) receptors has recently been investigated experimentally, but there is no quantitative account of how these dynamic changes occur upon activation of these receptors; this we now supply. Dynamics of F-actin at the apex of lamellipodia have been investigated in detail, giving rise to the treadmilling theory of F-actin dynamics, involving catalysis by profilin, for which quantitative models are now available. Here, we adapt such a model to describe the dynamics of F-actin in the synaptic-spine head and show that it gives quantitative descriptions of this treadmilling p... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331409 Tue, 21 Dec 2010 00:00:00 +0100 4331409 http://www.medworm.com/index.php?rid=4331408&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21174231%26dopt%3DAbstract Authors: Bóna M, Sitharam M, Vince A This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the capsid is modeled by a polyhedron whose facets represent the monomers. The assembly process is modeled by a rooted tree, the leaves representing the facets of the polyhedron, the root representing the assembled polyhedron, and the internal vertices representing intermediate stages of assembly (subsets of facets). Besides its virological motivation, the enumeration of orbits of trees under the action of a finite group is of independent mathematical interest... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331408 Tue, 21 Dec 2010 00:00:00 +0100 4331408 http://www.medworm.com/index.php?rid=4331410&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21170598%26dopt%3DAbstract Authors: Siebert H A discrete model of a biological regulatory network can be represented by a discrete function that contains all available information on interactions between network components and the rules governing the evolution of the network in a finite state space. Since the state space size grows exponentially with the number of network components, analysis of large networks is a complex problem. In this paper, we introduce the notion of symbolic steady state that allows us to identify subnetworks that govern the dynamics of the original network in some region of state space. We state rules to explicitly construct attractors of the system from subnetwork attractors. Using the results, we formulate sufficient conditions for the existence of multiple attractors resp. a cyclic at... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4331410 Sat, 18 Dec 2010 00:00:00 +0100 4331410 http://www.medworm.com/index.php?rid=4216916&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21108012%26dopt%3DAbstract Authors: Salinas DG, Reyes JG, De La Fuente M Biological membranes contain many domains enriched in phospholipid lipids and there is not yet clear explanation about how these domains can control the activity of phospholipid metabolizing enzymes. Here we used the surface dilution kinetic theory to derive general equations describing how complex substrate distributions affect the activity of enzymes following either the phospholipid binding kinetic model (which assumes that the enzyme molecules directly bind the phospholipid substrate molecules), or the surface-binding kinetic model (which assumes that the enzyme molecules bind to the membrane before binding the phospholipid substrate). Our results strongly suggest that, if the enzyme follows the phospholipid binding kinetic model, any s... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4216916 Thu, 25 Nov 2010 00:00:00 +0100 4216916 http://www.medworm.com/index.php?rid=4216915&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21108013%26dopt%3DAbstract Authors: Sánchez-Garduño F, Breña-Medina VF This paper deals with the spatio-temporal dynamics of a pollinator-plant-herbivore mathematical model. The full model consists of three nonlinear reaction-diffusion-advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases. The first one is a model for a mutualistic interaction (pollinator-plant), later on a sort of predator-prey (plant-herbivore) interaction model is studied. In both cases, the interaction term is described by a Holling response of type II. Finally, by considering that the plant population is the unique feeding source for the herbivores, a mathematical model for the three interacting populations is considered. By incorpora... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4216915 Thu, 25 Nov 2010 00:00:00 +0100 4216915 http://www.medworm.com/index.php?rid=4216917&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21103945%26dopt%3DAbstract Authors: Goor RM, Forman Neall L, Hoffman D, Sherry ST Multiplex DNA profiles are used extensively for biomedical and forensic purposes. However, while DNA profile data generation is automated, human analysis of those data is not, and the need for speed combined with accuracy demands a computer-automated approach to sample interpretation and quality assessment. In this paper, we describe an integrated mathematical approach to modeling the data and extracting the relevant information, while rejecting noise and sample artifacts. We conclude with examples showing the effectiveness of our algorithms. PMID: 21103945 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4216917 Sat, 20 Nov 2010 00:00:00 +0100 4216917 http://www.medworm.com/index.php?rid=4200788&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21088995%26dopt%3DAbstract Authors: Gorban AN, Pokidysheva LI, Smirnova EV, Tyukina TA The "Law of the Minimum" states that growth is controlled by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth (Justus von Liebig, 1840, Salisbury, Plant physiology, 4th edn., Wadsworth, Belmont, 1992) and quantitatively supported by many experiments. Some generalizations based on more complicated "dose-response" curves were proposed. Violations of this law in natural and experimental ecosystems were also reported. We study models of adaptation in ensembles of similar organisms under load of environmental factors and prove that violation of Liebig's law follows from adaptation effects. If the fitness of an organism in a fixed environment satisfies the Law of the Minimum then a... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4200788 Fri, 19 Nov 2010 00:00:00 +0100 4200788 http://www.medworm.com/index.php?rid=4184689&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21082274%26dopt%3DAbstract Authors: Delgado-Eckert E, Ojosnegros S, Beerenwinkel N RNA viruses exist in large intra-host populations which display great genotypic and phenotypic diversity. We analyze a model of viral competition between two viruses infecting a constantly replenished cell pool. We assume a trade-off between the ability of the virus to colonize new cells (cell killing rate or virulence) and its local competitiveness (replicative success within coinfected cells). We characterize the conditions that allow for viral spread by means of the basic reproductive number and show that a local coexistence equilibrium exists, which is asymptotically stable. At this equilibrium, the less virulent competitor has a reproductive advantage over the more virulent colonizer reflected by a larger equilibrium populati... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4184689 Wed, 17 Nov 2010 00:00:00 +0100 4184689 http://www.medworm.com/index.php?rid=4152391&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21061077%26dopt%3DAbstract Authors: Srinivasu PD, Prasad BS Necessity to understand the role of additional food as a tool in biological control programs is being increasingly felt, particularly due to its eco-friendly nature. A thorough mathematical analysis in this direction revealed the vital role of quality and quantity of the additional food in the controllability of the predator-prey systems. In this article controllability of the additional food-provided predator-prey system is studied from perspectives of pest eradication and biological conservation. Time optimal paths have been constructed to drive the state of the system to a desired terminal state by choosing quantity of the additional food as control variable. The theory developed in this article has been illustrated by solving problems related to pes... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4152391 Tue, 09 Nov 2010 00:00:00 +0100 4152391 http://www.medworm.com/index.php?rid=4152390&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21061078%26dopt%3DAbstract Authors: Ben-Ari I, Boushaba K, Matzavinos A, Roitershtein A In this paper, we formulate and analyze a Markov process modeling the motion of DNA nanomechanical walking devices. We consider a molecular biped restricted to a well-defined one-dimensional track and study its asymptotic behavior. Our analysis allows for the biped legs to be of different molecular composition, and thus to contribute differently to the dynamics. Our main result is a functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model. A law of large numbers, a recurrence/transience characterization and large deviations estimates are also obtained. Our approach is applicable to a variety of other biological motors such as myos... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4152390 Tue, 09 Nov 2010 00:00:00 +0100 4152390 http://www.medworm.com/index.php?rid=4152389&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D21061079%26dopt%3DAbstract Authors: Davis JM, Pozrikidis C A numerical method is implemented for computing unsteady blood flow through a branching capillary network. The evolution of the discharge hematocrit along each capillary segment is computed by integrating in time a one-dimensional convection equation using a finite-difference method. The convection velocity is determined by the local and instantaneous effective capillary blood viscosity, while the tube to discharge hematocrit ratio is deduced from available correlations. Boundary conditions for the discharge hematocrit at divergent bifurcations arise from the partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q≥1. When q=1, the cells are partitioned in proportion to the flow rate; as q tends to infinity, the cells are... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4152389 Tue, 09 Nov 2010 00:00:00 +0100 4152389 http://www.medworm.com/index.php?rid=4107731&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20976565%26dopt%3DAbstract Authors: Sapsis T, Peng J, Haller G We study the dynamics of plankton in the wake of a jellyfish. Using an analytical approach, we derive a reduced-order equation that governs the prey motion which is modeled as neutrally-buoyant inertial particle. This modified equation takes into account both the effects of prey inertia and self-propulsion and enables us to calculate both the attracting and repelling Lagrangian coherent structures for the prey motion. For the case of zero self-propulsion, it is simplified to the equation of motion for infinitesimal fluid particles. Additionally, we determine the critical size of prey over which instabilities on its motion occur resulting in different dynamics from those predicted by the reduced-order equation even for the case of zero self-propulsion... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4107731 Mon, 25 Oct 2010 23:00:00 +0100 4107731 http://www.medworm.com/index.php?rid=4107730&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20976566%26dopt%3DAbstract In this study, we show through a simple mathematical model that time delays in the CTL response process to HTLV-I infection can lead to the coexistence of multiple stable periodic solutions, which differ in amplitude and period, with their own basins of attraction. Our results imply that the dynamic interactions between the CTL immune response and HTLV-I infection are very complex, and that multi-stability in CTL response dynamics can exist in the form of coexisting stable oscillations instead of stable equilibria. Biologically, our findings imply that different routes or initial dosages of the viral infection may lead to quantitatively and qualitatively different outcomes. PMID: 20976566 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4107730 Mon, 25 Oct 2010 23:00:00 +0100 4107730 http://www.medworm.com/index.php?rid=4107734&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20972714%26dopt%3DAbstract Authors: Rodrigues LA, Mistro DC, Petrovskii S Understanding of population dynamics in a fragmented habitat is an issue of considerable importance. A natural modelling framework for these systems is spatially discrete. In this paper, we consider a predator-prey system that is discrete both in space and time, and is described by a Coupled Map Lattice (CML). The prey growth is assumed to be affected by a weak Allee effect and the predator dynamics includes intra-specific competition. We first reveal the bifurcation structure of the corresponding non-spatial system. We then obtain the conditions of diffusive instability on the lattice. In order to reveal the properties of the emerging patterns, we perform extensive numerical simulations. We pay a special attention to the system properties... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4107734 Fri, 22 Oct 2010 23:00:00 +0100 4107734 http://www.medworm.com/index.php?rid=4107733&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20972715%26dopt%3DAbstract Authors: Liu R, Del Rio CM, Wu J Mistletoes are common aerial stem-parasites and their seeds are dispersed by fruit-eating birds. In the mutually beneficial relationships between mistletoes and bird species that disperse mistletoes' seeds, the preference of birds for infected trees influences the spread of mistletoes and the spatiotemporal pattern formation of mistletoes. We formulate a deterministic model to describe the dynamics of mistletoes in an isolated patch containing an arbitrary number of trees. We establish concrete criterions, expressed in terms of the model parameters, for mistletoes establishing in this area. We conduct numerical simulations based on a field study to reinforce and expand our results. PMID: 20972715 [PubMed - as supplied by publisher] (Source: Bulletin... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4107733 Fri, 22 Oct 2010 23:00:00 +0100 4107733 http://www.medworm.com/index.php?rid=4107732&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20972716%26dopt%3DAbstract Authors: Huynh GT, Adler FR Epstein-Barr virus (EBV) infects and can persist in a majority of people worldwide. Within an infected host, EBV targets two major cell types, B cells and epithelial cells, and viruses emerging from one cell type preferentially infect the other. We use mathematical models to understand why EBV infects epithelial cells when B cells serve as a stable refuge for the virus and how switching between infecting each cell type affects virus persistence and shedding. We propose a mathematical model to describe the regulation of EBV infection within a host. This model is used to study the effects of parameter values on optimal viral strategies for transmission, persistence, and intrahost competition. Most often, the optimal strategy to maximize transmission is for vir... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4107732 Fri, 22 Oct 2010 23:00:00 +0100 4107732 http://www.medworm.com/index.php?rid=4088173&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20953911%26dopt%3DAbstract Authors: Saccomani MP Realistic HIV models tend to be rather complex and many recent models proposed in the literature could not yet be analyzed by traditional identifiability testing techniques. In this paper, we check a priori global identifiability of some of these nonlinear HIV models taken from the recent literature, by using a differential algebra algorithm based on previous work of the author. The algorithm is implemented in a software tool, called DAISY (Differential Algebra for Identifiability of SYstems), which has been recently released (DAISY is freely available on the web site http://www.dei.unipd.it/~pia/ ). The software can be used to automatically check global identifiability of (linear and) nonlinear models described by polynomial or rational differential equations, th... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4088173 Sat, 16 Oct 2010 23:00:00 +0100 4088173 http://www.medworm.com/index.php?rid=4088175&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20953725%26dopt%3DAbstract Authors: Huang H, Wylie JJ, Miura RM We consider the diffusion of molecules in a one-dimensional medium consisting of a large number of cells separated from the extra-cellular space by permeable membranes. The extra-cellular space is completely connected and allows unrestricted diffusion of the molecules. Furthermore, the molecules can diffuse within a given cell, i.e., the intra-cellular space; however, direct diffusion from one cell to another cell cannot occur. There is a movement of molecules across the permeable membranes between the intra- and extra-cellular spaces. Molecules from one cell can cross the permeable membrane into the extra-cellular space, then diffuse through the extra-cellular space, and eventually enter the intra-cellular space of a second cell. Here, we develop a... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4088175 Fri, 15 Oct 2010 23:00:00 +0100 4088175 http://www.medworm.com/index.php?rid=4088174&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20953726%26dopt%3DAbstract Authors: Xue C, Hwang HJ, Painter KJ, Erban R Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into conside... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4088174 Fri, 15 Oct 2010 23:00:00 +0100 4088174 http://www.medworm.com/index.php?rid=4061749&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20936368%26dopt%3DAbstract Authors: Dallon JC, Dalton B, Malani C Recent experimental work involving Dictyostelium discoideum seems to contradict several theoretical models. Experiments suggest that localization of the release of the chemoattractant cyclic adenosine monophosphate to the uropod of the cell is important for stream formation during aggregation. Yet several mathematical models are able to reproduce streaming as the cells aggregate without taking into account localization of the chemoattractant. A careful analysis of the experiments and the theory suggests the two major features of the system which are important to stream formation are random cell motion and chemotaxis to regions of higher cell density. Random cell motion acts to reduce streaming, whereas chemotaxis to regions of higher cell density... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4061749 Fri, 08 Oct 2010 23:00:00 +0100 4061749 http://www.medworm.com/index.php?rid=4061750&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20931293%26dopt%3DAbstract Authors: Mossel E, Roch S, Sly A The accurate reconstruction of phylogenies from short molecular sequences is an important problem in computational biology. Recent work has highlighted deep connections between sequence-length requirements for high-probability phylogeny reconstruction and the related problem of the estimation of ancestral sequences. In Daskalakis et al. (in Probab. Theory Relat. Fields 2010), building on the work of Mossel (Trans. Am. Math. Soc. 356(6):2379-2404, 2004), a tight sequence-length requirement was obtained for the simple CFN model of substitution, that is, the case of a two-state symmetric rate matrix Q. In particular the required sequence length for high-probability reconstruction was shown to undergo a sharp transition (from O(log n) to poly(n), where n ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4061750 Thu, 07 Oct 2010 23:00:00 +0100 4061750 http://www.medworm.com/index.php?rid=4041492&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20924797%26dopt%3DAbstract This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations. PMID: 20924797 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4041492 Wed, 06 Oct 2010 23:00:00 +0100 4041492 http://www.medworm.com/index.php?rid=4041493&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20886303%26dopt%3DAbstract Authors: Kim PS, Lee PP, Levy D Immunodominance refers to the phenomenon in which simultaneous T cell responses against multiple target epitopes organize themselves into distinct and reproducible hierarchies. In many cases, eliminating the response to the most dominant epitope allows responses to subdominant epitopes to expand more fully. The mechanism that drives immunodominance is still not well understood, although various hypotheses have been proposed. One of the more prevalent views is that immunodominance is driven by passive T cell competition for space on antigen presenting cells (APCs) or for access to specific MHC:epitope complexes on the surface of APCs. However, several experimental studies suggest that passive competition alone may not fully explain the robustness of immu... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4041493 Thu, 30 Sep 2010 23:00:00 +0100 4041493 http://www.medworm.com/index.php?rid=4026241&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20878493%26dopt%3DAbstract Authors: Hinkelmann F, Murrugarra D, Jarrah AS, Laubenbacher R Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4026241 Tue, 28 Sep 2010 23:00:00 +0100 4026241 http://www.medworm.com/index.php?rid=4026242&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20878250%26dopt%3DAbstract Authors: Coskun H, Coskun H Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, is of paramount importance. The mathematical model developed in this paper determines some physical features and material properties of the cells locally through analysis of live cell image sequences and uses this information to make further inferences about the molecular structures, dynamics, and processes within the cells, such as the actin network, microdomains, chemotaxis, adhesion, and retrograde flow. The generality of the principals used i... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=4026242 Mon, 27 Sep 2010 23:00:00 +0100 4026242 http://www.medworm.com/index.php?rid=3999406&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20844974%26dopt%3DAbstract Authors: Tsukada M, Fukushima Y This paper presents a possible context-sensitive mechanism in a neural network and at single neuron levels based on the experiments of hippocampal CA1 and their theoretical models. First, the spatiotemporal learning rule (STLR, non-Hebbian) and the Hebbian rule (HEBB) are experimentally shown to coexist in dendrite-soma interactions in single hippocampal pyramidal cells of CA1. Second, the functional differences between STLR and HEBB are theoretically shown in pattern separation and pattern completion. Third, the interaction between STLR and HEBB in neural levels is proposed to play an important role in forming a selective context determined by value information, which is related to expected reward and behavioral estimation. PMID: 20844974 [PubMed - ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3999406 Wed, 15 Sep 2010 23:00:00 +0100 3999406 http://www.medworm.com/index.php?rid=3962363&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20830610%26dopt%3DAbstract Authors: González-Olivares E, Rojas-Palma A This work aims to examine the global behavior of a Gause type predator-prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also been shown that it is the ω-limit of a wide set of trajectories of the system, due to the existence of a separatrix curve determined by the stable manifold of the equilibrium point (m,0), which is associated to the Allee effect on prey. When a weak Allee effect on the prey is assumed, an important result is obtained, involving the existence of two limit cycles surrounding a unique positive equilibrium point: the innermost ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3962363 Thu, 09 Sep 2010 23:00:00 +0100 3962363 http://www.medworm.com/index.php?rid=3955258&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20827511%26dopt%3DAbstract Authors: Gotzen B, Liebscher V, Walcher S Generalising a site-based stochastic model due to Royama, Solé et al. and Sumpter et al., we investigate competition in a single species with discrete, non-overlapping generations. We show that the deterministic limit of the dynamics depends on a few easily interpretable parameters only. Further, we discuss qualitative properties and limit sets of the corresponding difference equations, and we relate these to modes of competition. Moreover, a detailed analysis of stochastic effects in some relevant scenarios indicates that the behaviour of the stochastic model is very sensitive to further details of the model. PMID: 20827511 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955258 Wed, 08 Sep 2010 23:00:00 +0100 3955258 http://www.medworm.com/index.php?rid=3955257&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20827512%26dopt%3DAbstract Authors: Chai J, Housworth EA We give an explicit construction to solve a conjecture of Mike Steel and David Penny that any phylogeny involving N taxa can be recovered unambiguously using on the order of log N binary characters and the method of maximum parsimony. Biologically, this means that homoplasy need not be a deterrent to parsimony methods. Some patterns of homoplasy are phylogenetically informative and can exponentially reduce the amount of data needed to resolve a phylogeny. PMID: 20827512 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology) Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955257 Wed, 08 Sep 2010 23:00:00 +0100 3955257 http://www.medworm.com/index.php?rid=3955265&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821061%26dopt%3DAbstract Authors: Jirsa VK, Stefanescu RA Large scale brain networks are understood nowadays to underlie the emergence of cognitive functions, though the detailed mechanisms are hitherto unknown. The challenges in the study of large scale brain networks are amongst others their high dimensionality requiring significant computational efforts, the complex connectivity across brain areas and the associated transmission delays, as well as the stochastic nature of neuronal processes. To decrease the computational effort, neurons are clustered into neural masses, which then are approximated by reduced descriptions of population dynamics. Here, we implement a neural population mode approach (Assisi et al. in Phys. Rev. Lett. 94(1):018106, 2005; Stefanescu and Jirsa in PLoS Comput. Biol. 4(11):e1000219... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955265 Fri, 03 Sep 2010 23:00:00 +0100 3955265 http://www.medworm.com/index.php?rid=3955264&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821062%26dopt%3DAbstract Authors: Afraimovich V, Young T, Muezzinoglu MK, Rabinovich MI Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural systems. Understanding the time-varying relationship of emotion and cognition is a challenging goal with important implications for neuroscience. We formulate here the dynamical model of emotion-cognition interaction that is based on the following principles: (1) the temporal evolution of cognitive and emotion modes are captured by the incoming stimuli and competition withi... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955264 Fri, 03 Sep 2010 23:00:00 +0100 3955264 http://www.medworm.com/index.php?rid=3955263&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821063%26dopt%3DAbstract Authors: Steyn-Ross ML, Steyn-Ross DA, Sleigh JW, Wilson MT When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations ( approximately 0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated b... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955263 Fri, 03 Sep 2010 23:00:00 +0100 3955263 http://www.medworm.com/index.php?rid=3955262&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821064%26dopt%3DAbstract Authors: Kay JW, Phillips WA Signal processing in the cerebral cortex is thought to involve a common multi-purpose algorithm embodied in a canonical cortical micro-circuit that is replicated many times over both within and across cortical regions. Operation of this algorithm produces widely distributed but coherent and relevant patterns of activity. The theory of Coherent Infomax provides a formal specification of the objectives of such an algorithm. It also formally derives specifications for both the short-term processing dynamics and for the learning rules whereby the connection strengths between units in the network can be adapted to the environment in which the system finds itself. A central assumption of the theory is that the local processors can combine reliable signal coding w... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955262 Fri, 03 Sep 2010 23:00:00 +0100 3955262 http://www.medworm.com/index.php?rid=3955261&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821065%26dopt%3DAbstract Authors: Galka A, Wong KF, Ozaki T, Muhle H, Stephani U, Siniatchkin M Decomposition of multivariate time series data into independent source components forms an important part of preprocessing and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a methodology from statistical time series analysis, can be employed for the same purpose. State space modelling, a generalization of classical ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data, while this information remains inaccessible to FA and most ICA algorithms. As a result, much more detailed... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955261 Fri, 03 Sep 2010 23:00:00 +0100 3955261 http://www.medworm.com/index.php?rid=3955260&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821066%26dopt%3DAbstract Authors: Wright JJ Ongoing changes in attention and cognition depend upon cortical/subcortical interactions, which select sequences of different spatial patterns of activation in the cortex.It is proposed that each pattern of cortical activation permits evolution of electrocortical wave activity toward statistically stationary states, analogous to thermodynamic equilibrium. In each steady-state, neurons fire with an intrinsic Poisson spike probability and also with a bursting pattern related to network oscillations. Excitatory cell dendrites act as a regenerative reservoir in which pulse generation is balanced against dissipations.Equilibria exhibit contrasting limits. One limit, at high cortical activation, generates widespread zero-lag synchrony among excitatory cells, with partial s... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955260 Fri, 03 Sep 2010 23:00:00 +0100 3955260 http://www.medworm.com/index.php?rid=3955259&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20821067%26dopt%3DAbstract Authors: Mizraji E, Lin J The ability of the human brain to carry out logical reasoning can be interpreted, in general, as a by-product of adaptive capacities of complex neural networks. Thus, we seek to base abstract logical operations in the general properties of neural networks designed as learning modules. We show that logical operations executable by McCulloch-Pitts binary networks can also be programmed in analog neural networks built with associative memory modules that process inputs as logical gates. These modules can interact among themselves to generate dynamical systems that extend the repertoire of logical operations. We demonstrate how the operations of the exclusive-OR or the implication appear as outputs of these interacting modules. In particular, we provide a model of... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955259 Fri, 03 Sep 2010 23:00:00 +0100 3955259 http://www.medworm.com/index.php?rid=3955266&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20811781%26dopt%3DAbstract We present here deterministic and stochastic models for the transmission of rotavirus in a pediatric hospital ward and draw on published data to compare the efficacy of several possible control measures in reducing the number of infections during a 90-day outbreak, including cohorting, changes in healthcare worker-patient ratio, improving compliance with preventive hygiene measures, and vaccination. Although recently approved vaccines have potential to curtail most nosocomial rotavirus transmission in the future, even short-term improvement in preventive hygiene compliance following contact with symptomatic patients may significantly limit transmission as well, and remains an important control measure, especially where resources are limited. PMID: 20811781 [PubMed - as supplied by publ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3955266 Tue, 31 Aug 2010 23:00:00 +0100 3955266 http://www.medworm.com/index.php?rid=3912168&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20798994%26dopt%3DAbstract Authors: Bloomfield JM, Painter KJ, Sherratt JA In this paper, we present a two-population continuous integro-differential model of cell differentiation, using a non-local term to describe the influence of the local environment on differentiation. We investigate three different versions of the model, with differentiation being cell autonomous, regulated via a community effect, or weakly dependent on the local cellular environment. We consider the spatial patterns that such different modes of differentiation produce, and investigate the formation of both stripes and spots by the model. We show that pattern formation only occurs when differentiation is regulated by a strong community effect. In this case, permanent spatial patterns only occur under a precise relationship between the para... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3912168 Thu, 26 Aug 2010 23:00:00 +0100 3912168 http://www.medworm.com/index.php?rid=3912170&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20737226%26dopt%3DAbstract Authors: Didier G We give a formal study of the relationships between the transition cost parameters and the generalized maximum parsimonious reconstructions of unknown (ancestral) binary character states [Formula: see text] over a phylogenetic tree. As a main result, we show there are two thresholds [Formula: see text] and [Formula: see text], generally confounded, associated to each node n of the phylogenetic tree and such that there exists a maximum parsimonious reconstruction associating state [Formula: see text] to n (resp. state [Formula: see text] to n) if the ratio "[Formula: see text]-cost"/"[Formula: see text]-cost" is smaller than [Formula: see text] (resp. greater than [Formula: see text]). We propose a dynamic programming algorithm computing these thresholds in a quadratic... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3912170 Tue, 24 Aug 2010 23:00:00 +0100 3912170 http://www.medworm.com/index.php?rid=3912169&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20737227%26dopt%3DAbstract Authors: Altenberg L A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (Evolutionary Biology, vol. 14, pp. 61-204, 1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models.A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface-a generalization of the hyperplane found by Zhivotovsky et al. (Proc. Natl. Acad. Sci. USA 91, 1079-1083, 1994) for a multilocus recombination modifier. Increases in mutation rates at some ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3912169 Tue, 24 Aug 2010 23:00:00 +0100 3912169 http://www.medworm.com/index.php?rid=3890811&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20725794%26dopt%3DAbstract Authors: Schley D, Ward J, Zhang Z Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3890811 Thu, 19 Aug 2010 23:00:00 +0100 3890811 http://www.medworm.com/index.php?rid=3890810&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20725795%26dopt%3DAbstract We present a versatile continuous stochastic model-the correlated velocity helical movement (CVHM) model-that characterizes helical swimming with intrinsic randomness and autocorrelation. The model separates an organism's instantaneous velocity into a slowly varying advective component and a perpendicularly oriented rotation, with velocities, magnitude of stochasticity, and autocorrelation scales defined for both components. All but one of the parameters of the 3D model can be estimated directly from a two-dimensional projection of helical movement with no numerical fitting, making it computationally very efficient. As a case study, we estimate swimming parameters from videotaped trajectories of a toxic unicellular alga, Heterosigma akashiwo (Raphidophyceae). The algae were reared from fiv... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3890810 Thu, 19 Aug 2010 23:00:00 +0100 3890810 http://www.medworm.com/index.php?rid=3890809&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20725796%26dopt%3DAbstract Authors: José MV, Morgado ER, Govezensky T Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and thi... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3890809 Thu, 19 Aug 2010 23:00:00 +0100 3890809 http://www.medworm.com/index.php?rid=3890808&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20725797%26dopt%3DAbstract Authors: Liu M, Wang K, Wu Q Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived. PMID: 20725797... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3890808 Thu, 19 Aug 2010 23:00:00 +0100 3890808 http://www.medworm.com/index.php?rid=3890807&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20725798%26dopt%3DAbstract We present a tuberculosis dynamics model taking into account the fact that some people in the population are smoking in order to assess the effects of smoking on tuberculosis transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Qualitative analysis of the model including positivity and persistence of solutions are presented. The model is numerically analyzed to assess the effects of smoking on the transmission dynamics of tuberculosis. Numerical simulations of the model show that smoking enhances tuberculosis transmission, progression to active disease and in a population of smokers, tuberculosis cannot be controlled even when treatment success is assumed to be as high as 88%. Further, analysis of the ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3890807 Thu, 19 Aug 2010 23:00:00 +0100 3890807 http://www.medworm.com/index.php?rid=3804372&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20658199%26dopt%3DAbstract Authors: Eskola HT, Geritz SA, Gyllenberg M We study the evolution of an individual's reproductive strategy in a mechanistic modeling framework. We assume that the total number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed during the season, given the types of inter-individual interactions and mortality processes included in the model. The evolution of the timing of reproduction in this modeling framework has already been studied earlier in the case of equilibrium resident dynamics, but we generalize the situation to also fluctuating population dynamics. We find that, as in the equilibrium case, the presence or absence of inter-juvenile aggression affects the functional form of the evolutionarily stable reproducti... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3804372 Fri, 23 Jul 2010 23:00:00 +0100 3804372 http://www.medworm.com/index.php?rid=3804371&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20658200%26dopt%3DAbstract Authors: Teka W, Tsaneva-Atanasova K, Bertram R, Tabak J Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudo-plateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one ty... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3804371 Fri, 23 Jul 2010 23:00:00 +0100 3804371 http://www.medworm.com/index.php?rid=3777405&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20640525%26dopt%3DAbstract We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The s... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3777405 Fri, 16 Jul 2010 23:00:00 +0100 3777405 http://www.medworm.com/index.php?rid=3777404&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20640526%26dopt%3DAbstract Authors: Drew DA, Koch GA, Hitchcock S, Kowalski J, Talati R, Valakh V DNA replication in Escherichia coli is initiated by DnaA binding to oriC, the replication origin. During the process of assembly of the replication factory, the DnaA is released back into the cytoplasm, where it is competent to reinitiate replication. Premature reinitiation is prevented by binding SeqA to newly formed GATC sites near the replication origin. Resolution of the resulting SeqA cluster is one aspect of timing for reinitiation. A Markov model accounting for the competition between SeqA binding and methylation for one or several GATC sites relates the timing to reaction rates, and consequently to the concentrations of SeqA and methylase. A model is proposed for segregation, the motion of the two daughter D... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3777404 Fri, 16 Jul 2010 23:00:00 +0100 3777404 http://www.medworm.com/index.php?rid=3777403&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20640527%26dopt%3DAbstract Authors: Cueto MA, Matsen FA It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue ... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3777403 Fri, 16 Jul 2010 23:00:00 +0100 3777403 http://www.medworm.com/index.php?rid=3673812&cid=s_37645_79_f&fid=37645&url=http%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fentrez%2Fquery.fcgi%3Ftmpl%3DNoSidebarfile%26db%3DPubMed%26cmd%3DRetrieve%26list_uids%3D20556530%26dopt%3DAbstract Authors: Aydemir E, Breward CJ, Witelski TP In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liqu... Bulletin of Mathematical Biology journals http://www.medworm.com/rss/comments.php?id=3673812 Wed, 16 Jun 2010 23:00:00 +0100 3673812