MBI Publications

MBI Publications for 2009 (41)

  • M. Golubitsky and R. Lauterbach
    Bifurcations from synchrony in homogeneous networks: linear theory
    SIAM J. Appl.Vol. 8 No. 1 (2009) pp. 40-75

    Abstract

  • M. Aguiar, M. Aguiar, A. Dias, A. Dias, M. Golubitsky and M. Leite
    Bifurcations from regular quotient networks: A first insight
    Physica D.Vol. 238 No. 2 (2009) pp. 137-155

    Abstract

  • S. Flaxman and Y. Lou
    Tracking prey or tracking the prey’s resource? Mechanisms of movement and optimal habitat selection by predators
    J. Theo. Biol.Vol. 256 (2009) pp. 187-200

    Abstract

  • D. Schmidt and R. Durrett
    Reply to Michael Behe
    GeneticsVol. 181 (2009) pp. 821-822

    Abstract

  • M. Golubitsky, C. Postlethwaite, L. Shiau and Y. Zhang
    The feed-forward chain as a filter amplifier motif. In: Coherent Behavior in Neuronal Networks
    Springer (2009) pp. 95-120

    Abstract

  • L. Allen, Y. Lou and A. Nevai
    Spatial patterns in a discrete-time SIS patch model
    J. Math Biol.Vol. 58 (2009) pp. 339-375

    Abstract

  • B. Joshi, X. Wang, S. Banerjee, H. Tian, A. Matzavinos and M. Chaplain
    On immunotherapies and cancer vaccination protocols: A mathematical modelling approach
    Journal of Theoretical BiologyVol. 259 No. 4 (2009) pp. 820-827

    Abstract

  • G. Wright, M. Carlton and B. Smith
    A honeybee's ability to learn, recognize, and discriminate odors depends upon odor sampling time and concentration
    Behavioral NeuroscienceVol. 123 No. 1 (2009) pp. 123-133

    Abstract

  • M. Stolarska, Y. Kim and H. Othmer
    Multiscale models of cell and tissue dynamics
    Phil. Trans. Roy. Soc.Vol. 367 (2009) pp. 3525-3553

    Abstract

  • E. Green, S. Waters , K. Shakesheff and H. Byrne
    A mathematical model of liver cell aggregation in vitro
    Bulletin of Mathematical BiologyVol. 71 No. 4 (2009) pp. 906-930

    Abstract

    The behaviour of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that, provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work.
  • Y. Kim and K. Boushaba
    A PDE mathematical model for the regulation of tumor dormancy based on enzyme kinetics
    DCDS-S (2009) (Submitted)

    Abstract

  • Q. Chen, S. Kuppum and P. Srinivasan
    On the relation between the WRT invariant and the Hennings invariant
    Math. Proc. Camb. Phil. Soc.Vol. 146 (2009) pp. 151-163

    Abstract

  • E. Green, N. Ovenden and F. Smith
    Flow in a multi-branching channel with compliant walls
    Journal of Engineering MathematicsVol. 64 No. 4 (2009) pp. 353-365

    Abstract

    The problem of fluid flow in a compliant-walled channel which branches into two or more daughters is considered with the aim of understanding blood flow through arterio-venous malformations (AVMs) in the brain. The outer walls of the channel are assumed for definiteness to behave as spring-back plates, whilst the divider is taken as rigid. The fluid is assumed to be incompressible and inviscid. When the Strouhal number is small (as occurs in practice in the brain), there are two main axial length scales, one much longer than the vessel width and the other comparable with the vessel width. Also, in the case of small wall displacements, one can analyse the local flow-structure interaction problem using a complex variable method. The flow shows markedly different qualitative features downstream of the branching, depending on the wall stiffness. Keywords Branching channel ‚?Ę Compliant walls ‚?Ę Inviscid fluid flow ‚?Ę Matching A. Matzavinos, C.Y. Kao, J.E.F. Green, A. Sutradhar, M. Miller and A. Friedman, Modelling oxygen transport in surgical tissue transfer, Proceedings of the National Academy of Sciences, 106 (29) p12091-12096, 2009 http://www.pnas.org/content/106/29/12091.abstract Abstract Reconstructive microsurgery is a clinical technique used to transfer large amounts of a patient's tissue from one location used to another in order to restore physical deformities caused by trauma, tumors, or congenital abnormalities. The trend in this field is to transfer tissue using increasingly smaller blood vessels, which decreases problems associated with tissue harvest but increases the possibility that blood supply to the transferred tissue may not be adequate for healing. It would thus be helpful to surgeons to understand the relationship between the tissue volume and blood vessel diameter to ensure success in these operations. As a first step towards addressing this question, we present a simple mathematical model that might be used to predict successful tissue transfer based on blood vessel diameter, tissue volume, and oxygen delivery.
  • S. Sun, T. Zuo, P. Yan, T. Huang and S. Lin
    DNA methylation data analysis using mixed effect and generalized least square models
    Bioinformatics (2009) (Submitted)

    Abstract

  • L. Allen, Y. Lou and A. Nevai
    Spatial patterns in a discrete-time SIS patch model.
    J. Math. Biol.Vol. 58 (2009) pp. 339-375

    Abstract

  • H. Han, P. Grajdeanu, J. Sharpnack and D. Tello
    Mathematical modeling of cellular mechanisms in L-Dopa treated Parkinson's patients
    (2009) (In Preparation)

    Abstract

  • P. Grajdeanu, L. Moore and H. Layton
    Effect of spatial inhomogeneities on the tubuloglomerular feedback system
    (2009) (Submitted)

    Abstract

  • M. Rempe, J. Best and D. Terman
     A Neurobiological Model of the Human Sleep/Wake Cycle
    J Math BiolVol. 60 (2009) pp. 615-644

    Abstract

  • N. Meshkat, M. Eisenberg and J. Distefano
    Algorithm for finding globally identifiable parameter combinations and reparameterizations of nonlinear ODE models using Groebner Bases
    Math BiosciencesVol. 222 (2009) pp. 61-72

    Abstract

  • Y. Lou and S. Martinez
    Evolution of cross-diffusion and self-diffusion
    J. Biol. Dys.Vol. 3 (2009) pp. 410-429

    Abstract

  • M. Eisenberg and J. Distefano
    TSH Testing, Tablet Instability & Absorption Effects on L-T4 Bioequivalence Protocols
    ThyroidVol. 19 No. 2 (2009) pp. 103-110

    Abstract

  • D. Schmidt, R. Durrett and J. Schweinsberg
    A waiting time problem arising from the study of multi-stage carcinogenesis
    Annals of Applied Probability (2009) (Submitted)

    Abstract

  • D. Siegal-Gaskins, J. Ash and S. Crosson
    Model-based Deconvolution of Cell Cycle Time-series Data Reveals Gene Expression Details at High Resolution
    PLoS Computational BiologyVol. 5 No. 8 (2009)

    Abstract

  • G. Smith, E. Grotewold and D. Siegal-Gaskins
    The capacity for multistability in small gene regulatory networks.
    BMC Syst BiolVol. 3 No. 96 (2009) (Submitted)

    Abstract

  • C. Xue and H. Othmer
    Multiscale models of taxis-driven patterning in bacterial populations
    SIAM Journal of Applied MathematicsVol. 70 No. 1 (2009) pp. 133-167

    Abstract

    Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a ‚??run-and-tumble‚?? strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals.
  • H. Othmer, K. Painter, D. Umulis and C. Xue
    The intersection of theory and application in elucidating pattern formation in developmental biology
    Mathematical Modelling of Natural PhenomenaVol. 4 No. 4 (2009) pp. 3-82

    Abstract

  • C. Xue, H. Othmer and R. Erban
    From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems, Multiscale Phenomena in Biology
    Proceedings of the 2nd Okinawa Conference on Mathematics and Biology, AIPVol. 1167 (2009) pp. 3-14

    Abstract

  • Y. Kim, S. Lawler, M. Nowicki, E. Chiocca and A. Friedman
    A mathematical model of Brain tumor: pattern formation of glioma cells outside the tumor spheroid core
    J Theo BiolVol. 260 (2009) pp. 259-371

    Abstract

    Glioblastoma is the most common and the most aggressive type of brain cancer. The median survival time from the time of diagnosis is approximately one year. Invasion of glioma cells from the core tumor into the surrounding brain tissue is a major reason for treatment failure: these migrating cells are not eliminated in surgical resection and cause tumor recurrence. Variations are seen in number of invading cells, and in the extent and patterns of migration. Cells can migrate diffusely and can also be seen as clusters of cells distinct from the main tumor mass. This kind of clustering is also evident in vitro using 3D spheroid models of glioma invasion. This has been reported for U87 cells stably expressing the constitutively active EGFRVIII mutant receptor, often seen expressed in glioblastoma. In this case the cells migrate as clusters rather than as single cells migrating in a radial pattern seen in control wildtype U87 cells. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cell‚€“cell adhesion. The present paper develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on adhesion, haptotactic, and chemotactic parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as has been reported experimentally.
  • M. Stolarska, Y. Kim and H. Othmer
    Multiscale models of cell and tissue dynamics
    Phil. Trans. Toy. Soc.Vol. 367 (2009) pp. 3525-3553

    Abstract

    Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.
  • R. Bertram, P. Grajdeanu and S. Jafri
    Using phase relations to indtify potential mechanisms for metabolic oscillations in isolated beta-cell mitochondria
    IsletsVol. 1 No. 2 (2009) pp. 87-94

    Abstract

    There is a great deal of evidence for the existence of metabolic oscillations in pancreatic ő≤-cells. Mechanisms that have been proposed for these oscillations include glycolytic oscillations; oscillations due to the feedback of Ca2+ onto the mitochondrial inner membrane and on dehydrogenases; and oscillations intrinsic to the tricarboxylic (TCA) cycle or the downstream reactions of oxidative phosphorylation. MacDonald and co-workers (J. Biol. Chem., 278:51894-51900, 2003) showed examples of oscillations in TCA intermediates in isolated mitochondria from liver cells and pancreatic ő≤-cells. These oscillations were clearly not due to oscillations in glycolysis or Ca2+ feedback. In this article we consider several potential mechanisms for these TCA oscillations, using mathematical modeling to determine the phase relations that would result between the citrate and NAD+ concentrations in each case. We demonstrate that negative feedback at only one feedback point, isocitrate dehydrogenase, produces the correct phase relation if oscillations are intrinsic to the TCA cycle. Alternatively, the correct phase relation results if oscillations are due to oscillations in oxidative phosphorylation feeding back onto the TCA cycle. This analysis shows that the observed phase relation between citrate and NAD(P) places strict limits on the potential mechanism for the metabolic oscillations in isolated mitochondria that were observed by MacDonald and co-workers.
  • Y. Kim, S. Lim, S. Raman, O. Simonetti and A. Friedman
    Blood flow in a compliant vessel by the immersed boundary method
    Annals of Biomedical EngineeringVol. 37 No. 5 (2009) pp. 927-942

    Abstract

    In this paper we develop a computational approach to analyze hemodynamics in the aorta; this may serve as a useful tool in the development of noninvasive methods to detect early onset of diseases such as aneurysms and stenosis in major blood vessels. We introduce a mathematical model which describes the interaction of blood flow with the aortic wall; this model is based on the immersed boundary method. A two-dimensional vessel model is constructed, the velocity at the inlet is prescribed based on the information from the Magnetic Resonance Imaging data measured in the aorta of a healthy subject, and the velocity at the outlet is prescribed by driving the pressure level reproduced from the literature. The mathematical model is validated by comparing with well-known solutions of the viscous incompressible Navier√Ę‚?¨‚??Stokes equations, i.e., Womersley flow. The hysteresis behavior in the pressure√Ę‚?¨‚??diameter relation is observed when the viscoelastic material property of the arterial wall is taken into consideration. Five different shapes of aortic wall are considered for comparison of the flow patterns inside the aorta: one for the normal aorta, two for the dilated aorta, and two for the constrictive aorta.
  • J. Day, A. Friedman and L. Schlesinger
    Modeling the immune rheostat of macrophages in the lung in response to infection
    Proc. Natl Acad Sci USAVol. 106 No. 27 (2009) pp. 11246-11251

    Abstract

    In the lung, alternatively activated macrophages (AAM) form the first line of defense against microbial infection. Due to the highly regulated nature of AAM, the lung can be considered as an immunosuppressive organ for respiratory pathogens. However, as infection progresses in the lung, another population of macrophages, known as classically activated macrophages (CAM) enters; these cells are typically activated by IFN-. CAM are far more
    effective than AAM in clearing the microbial load, producing proinflammatory cytokines and antimicrobial defense mechanisms necessary to mount an adequate immune response. Here, we are concerned with determining the first time when the population of CAM becomes more dominant than the population of AAM. This proposed ‚€˜‚€˜switching time‚€™‚€™ is explored in the context of Mycobacterium tuberculosis (MTb) infection. We have developed a mathematical model that describes the interactions among cells, bacteria, and cytokines involved in the activation of both AAM and CAM. The model, based on a system of differential equations, represents a useful tool to analyze strategies for reducing the switching time, and to generate hypotheses for experimental testing.
  • J. Day, J. Rubin and C. Chow
    Competition between transients in the rate of approach to a fixed point
    SIAM J. Appl. Dyn. Syst.Vol. 8 No. 4 (2009) pp. 1523-1563

    Abstract

    The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
  • C. Xue, A. Friedman and C. Sen
    A mathematical model of ischemic cutaneous wounds
    PNASVol. 106 No. 39 (2009) pp. 16782-16787

    Abstract

    Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia, primarily caused by peripheral artery diseases, represents a major complicating factor in cutaneous wound healing. In this work, we sought to develop a mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model equations involve the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how ischemic conditions may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings.
  • C. Xue, H. Othmer and R. Erban
    From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems
    Multiscale Phenomena in Biology: Proceedings of the 2nd Okinawa Conference on Mathematics and Biology, AIPVol. 1167 (2009) pp. 3-14

    Abstract

  • H. Othmer, K. Painter, D. Umulis and C. Xue
    The intersection of theory and application in elucidating pattern formation in developmental biology
    Math. Model. Nat. Phenom.Vol. 4 No. 4 (2009) pp. 3-82

    Abstract

  • A. Matzavinos, C. Kao, E. Green, A. Sutradhar, M. Miller and A. Friedman
    Modelling oxygen transport in surgical tissue transfer
    PNASVol. 106 No. 29 (2009) pp. 12091-12096

    Abstract

  • D. Siegal-Gaskins, J. Ash and S. Crosson
    Model-based Deconvolution of Cell Cycle Time-series Data Reveals Gene Expression Details at High Resolution
    PLoS Comput BiolVol. 5 No. 8 (2009)

    Abstract

  • D. Siegal-Gaskins, E. Grotewold and G. Smith
    The capacity for multistability in small gene regulatory networks
    BMC Syst BiolVol. 3 No. 96 (2009)

    Abstract

  • R. Hambrock and Y. Lou
    Evolution of mixed dispersal strategy in spatially heterogeneous habitat
    Bull. Math. Biol.Vol. 71 (2009) pp. 1793-1817

    Abstract

  • S. Cantrell, C. Cosner and Y. Lou
    Evolution of dispersal in heterogeneous landscape, Spatial Ecology
    Chapman Hall/CRC Press (2009) pp. 213-229

    Abstract

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