MBI Publications

MBI Publications for 2011 (54)

  • K. Zhao and T. Li
    Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model
    Network and Heterogeneous MediaVol. 6, 2011 No. 4 (2011) pp. 625-646

    Abstract

    This paper is concerned with an initial-boundary value problem



    on bounded domains for a one dimensional quasilinear hyperbolic model of



    blood flow with viscous damping. It is shown that L1 entropy weak solutions



    exist globally in time when the initial data are large, rough and contains



    vacuum states. Furthermore, based on entropy principle and the theory of



    divergence measure field, it is shown that any L1 entropy weak solution converges



    to a constant equilibrium state exponentially fast as time goes to infinity.



    The physiological relevance of the theoretical results obtained in this paper is



    demonstrated.
  • K. Zhao
    Large time behavior for Cahn-Hilliard-Boussinesq equations on bounded domains
    Electronic Journal of Differential EquationsVol. 2011 No. 46 (2011) pp. 1-21

    Abstract

    We study the asymptotic behavior of classical solutions to an


    initial-boundary value problem (IBVP) for a coupled


    Cahn-Hilliard-Boussinesq system on bounded domains with


    large initial data. A sufficient condition is established


    under which the solutions decay exponentially to constant


    states as time approaches infinity.
  • Y. Wang, P. Paszek, C. Horton, D. Kell, M. White, D. Broomhead and M. Muldoon
    Interactions among oscillatory pathways in NF- kB signalling
    BMC Systems BiologyVol. 5 No. 23 (2011)

    Abstract

    Sustained stimulation with tumour necrosis factor alpha (TNF-alpha) induces substantial oscillationsâ???observed at both the single cell and population levelsâ???in the nuclear factor kappa B (NF-kappa B) system. Although the mechanism has not yet been elucidated fully, a core system has been identified consisting of a negative feedback loop involving NF-kappa B (RelA:p50 hetero-dimer) and its inhibitor I-kappa B-alpha. Many authors have suggested that this core oscillator should couple to other oscillatory pathways.
  • R. Parshad and J. Gutierrez
    On the Global Attractor of the Trojan Y Chromosome Model
    Communications in Pure and Applied AnalysisVol. 10 No. 1 (2011) pp. 339-359

    Abstract

  • T. Yusuf, F. Benyah and F. Benyah
    Optimal strategy for controlling the spread of HIV/AIDS disease: A case study of South Africa
    Journal of Biological Dynamics (2011)

    Abstract

  • H. Jain and M. Meyer-Hermann
    The molecular basis of synergism between carboplatin and ABT-737 therapy targeting ovarian carcinomas
    Cancer Res.Vol. 71 (2011) pp. 705-715

    Abstract

  • S. Flaxman, Y. Lou and F. Meyer
    Evolutionary Ecology of Movement by Predators and Prey
    Theoretical EcologyVol. 4 (2011) pp. 255-267

    Abstract

  • A. Oster, B. Thomas, D. Terman and C. Fall
    The mitochondrial permeability transition pore confers excitability and CICR wave propagation
    J Theor BiolVol. 273 No. 1 (2011) pp. 216-31

    Abstract

  • A. Oster, B. Thomas, D. Terman and C. Fall
    The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model
    Journal of Theoretical BiologyVol. 273 No. 1 (2011) pp. 216-231

    Abstract

    Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.
  • A. Tuite, A. Tuite, J. Tien, M. Eisenberg, D. Earn, J. Ma, J. Ma and D. Fisman
    Cholera epidemic in Haiti, 2010 - using a transmission model to explain spatial spread of disease and identify optimal control interventions
    Annals of Internal MedicineVol. 154 No. 9 (2011) pp. 593-601

    Abstract

  • M. Eisenberg, J. Ash and D. Siegal-Gaskins
    In silico synchronization of cellular populations through expression data deconvolution
    Proceedings of the 48th ACM/EDAC/IEEE Design Automation Conference (2011) pp. 812-817

    Abstract

  • S. Kumar, S. Handelman, I. Voronkin, V. Mmapasa, D. Janies, S. Rogerson, S. Meshnick and J. Kwiek
    Different regions of HIV-1 subtype C env are associated with placental localization and in utero mother-to-child transmission
    J. virol. (2011)

    Abstract

  • A. Anderson, M. Chaplain and K. Rejniak
    Single Cell-Based-Models in Biology and Medicine
    Birkhauser-Verlag No. Series Mathematics and Biosciences in Interaction (2011)

    Abstract

  • D. Siegal-Gaskins, M. Mejia-Guerra, G. Smith and E. Grotewold
    Emergence of switch-like behavior in a large family of simple biochemical networks
    PLoS Comput BiolVol. 7 No. 5 (2011)

    Abstract

  • W. Just and G. Enciso
    Exponentially long orbits in Boolean networks with exclusively positive interactions
    Nonlinear Dynamics and Systems TheoryVol. 11 No. 3 (2011) pp. 275-284

    Abstract

  • T. Hallam and P. Federico
    The Panzootic White-nose Syndrome: An Environmentally Constrained Disease?
    Transboundary and Emerging Diseases (2011)

    Abstract

  • H. Jain, S. Clinton, A. Bhinder and A. Friedman
    Mathematical modeling of prostate cancer progression in response to androgen ablation therapy
    Proc Natl Acad Sci.Vol. 108 No. 49 (2011) pp. 19701-19706

    Abstract

  • M. Eisenberg, Y. Kim, R. Li, W. Ackerman, D. Kniss and A. Friedman
    Modeling the effects of myoferlin on tumor cell invasion
    Proc Natl Acad Sci USAVol. 108 No. 50 (2011) pp. 20078-20083

    Abstract

  • V. Guttal, F. Bartumeus, G. Hartvigsen and A. Nevai
    Retention time variability as a mechanism for animal mediated long distance dispersal
    PLoS OneVol. 6 (2011)

    Abstract

  • A. Oster and B. Gutkin
    A reduced model of DA neuronal dynamics that displays quiescence, tonic firing, and bursting
    J. Physiol. (2011)

    Abstract

  • C. Xue, E. Budrene and H. Othmer
    Radial and spiral streams in Proteus mirabilis colonies
    PLOS Computational BiologyVol. 7 No. 12 (2011)

    Abstract

  • S. Robertson and J. Cushing
    Spatial segregation in stage-structured populations with an application to Tribolium
    Journal of Biological DynamicsVol. 5 No. 5 (2011) pp. 398-409

    Abstract

  • D. DeAngelis, G. Wolkowicz , Y. Lou, Y. Jiang, M. Novak, R. Svanback, M. Araujo, Y. Jo and E. Cleary
    The Effect of Travel Loss on Evolutionarily Stable Distributions of Populations in Space
    The America NaturalistVol. 178 (2011)

    Abstract

  • B. Aguda, Y. Kim, H. Kim, A. Friedman and H. Fine
    Qualitative network modeling of the MYC-p53 control system of cell proliferation and differentiation
    Biophysical JournalVol. 101 No. 9 (2011) pp. 2082-2091

    Abstract

  • Y. Kim, S. Roh, S. Lawler and A. Friedman
    miR451 and AMPK mutual antagonism in glioma cells migration and proliferation
    PLoS OneVol. 6 No. 12 (2011)

    Abstract

  • Y. Kim and K. Boushaba
    An enzyme kinetics model of tumor dormancy, regulation of secondary metastases
    Discrete and Continuous Dynamical Systems-SVol. 4 No. 6 (2011) pp. 1465-1498

    Abstract

    In this paper we study 1 dimensional (1D) and 2D extended version of a two compartment model for tumor dormancy suggested by Boushaba et al. [3]. The model is based on the idea that the vascularization of a secondary tumor can be suppressed by inhibitor originating from a larger primary tumor. It has been observed emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites five to seven centimeters from the primary site within a period of one month after the excision of the primary site. 1D and 2D simulations show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumors while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumors, even after it is removed. The sensitivity analysis was carried out for the 1D model. It has been long observed that surgery should be followed by other treatment options such as chemotherapy. 2D simulation suggests a possible treatment options with different dosage schedule after a surgery in order to achieve better clinical outcome.
  • Y. Kim, M. Stolarska and H. Othmer
    The Role of the Microenvironment in Tumor Growth and Invasion
    Progress in Biophysics and Molecular BiologyVol. 106 (2011) pp. 353-379 (Submitted)

    Abstract

    Mathematical modeling and computational analysis are essential for understanding the dynamics of the complex gene networks that control normal development and homeostasis, and can help to under- stand how circumvention of that control leads to abnormal outcomes such as cancer. Our objectives here are to discuss the different mechanisms by which the local biochemical and mechanical microenvironment, which is comprised of various signaling molecules, cell types and the extracellular matrix (ECM), affects the progression of potentially-cancerous cells, and to present new results on two aspects of these effects. We first deal with the major processes involved in the progression from a normal cell to a cancerous cell at a level accessible to a general scientific readership, and we then outline a number of mathematical and computational issues that arise in cancer modeling. In Section 2 we present results from a model that deals with the effects of the mechanical properties of the environment on tumor growth, and in Section 3 we report results from a model of the signaling pathways and the tumor microenvironment (TME), and how their interactions affect the development of breast cancer. The results emphasize anew the complexities of the interactions within the TME and their effect on tumor growth, and show that tumor progression is not solely determined by the presence of a clone of mutated immortal cells, but rather that it can be â??community-controlledâ??.
  • A. Friedman and Y. Kim
    Tumor cells proliferation and migration under the influence of their microenvironment
    Mathematical Biosciences and EngineeringVol. 8 No. 2 (2011) pp. 373-385

    Abstract

    It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and de- scribe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.
  • J. Day, A. Friedman and L. Schlesinger
    Modeling the host response to inhalation anthrax
    J Theor BiolVol. 276 No. 1 (2011) pp. 199-208

    Abstract

    Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.
  • M. Eisenberg, J. Ash and D. Siegal-Gaskins
    In silico synchronization of cellular populations through expression data deconvolution
    Proceedings of the 48th ACM/IEEE Design Automation Conference (2011) pp. 812-817 (Submitted)

    Abstract

  • C. Xue, H. Hwang, K. Painter and R. Erban
    Traveling waves in bacterial chemotaxis
    Bul. Math. Biol (2011)

    Abstract

    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 consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically.
  • A. Friedman and C. Xue
    A mathematical model of chronic wounds
    Mathematical Biosciences and EngineeringVol. 8 No. 2 (2011) pp. 253-261

    Abstract

  • A. Yakubu, N. Li, J. Conrad and M. Zeeman
    Constant proportion harvest policies: Dynamic implications in the Pacific halibut and Atlantic cod fisheries
    Mathematical BiosciencesVol. 232 (2011) pp. 66-77

    Abstract

  • D. Li, T. Li and K. Zhao
    On a hyperbolic-parabolic system modeling repulsive chemotaxis
    Mathematical Models and Methods in Applied SciencesVol. 21 (2011) pp. 1631-1650

    Abstract

  • W. Price, S. Handelman, J. Everett, S. Tong, A. Bradic, J. Luff, V. Naumov, T. Acton, P. Manor, R. Xiao, G. Montelione and J. Hunt
    Large-scale experimental studies show unexpected amino acid effects on protein expression and solubility in vivo in E. coli
    Microbial Informatics and Experimentation (2011)

    Abstract

  • F. Gubellini, G. Verdon, N. Karpowich, J. Luff, G. Boel, N. Gauthier, S. Handelman, S. Ades and J. Hunt
    Physiological response to membrane protein overexpression in E. coli
    Mol Cell Proteomics (2011)

    Abstract

  • Y. Guo and J. Rubin
    Multi-site Stimulation of Subthalamic Nucleus Diminishes Thalamocortical Relay Error in a Biophysical Network Model
    Special Issue: Neurocomputational Models of Brain DisordersVol. 26 No. 6 (2011) pp. 602-616

    Abstract

  • J. Simpson, P. Hurtado, J. Medlock, G. Molei, T. Andreadis, A. Galvani and M. Diuk-Wasser
    Vector host-feeding preferences drive transmission of multi-host pathogens: West Nile virus as a model system
    Proc. R. Soc. B. (2011)

    Abstract

  • S. Robertson and J. Cushing
    A bifurcation analysis of stage-structured density dependent integrodifference equations
    Journal of Mathematical Analysis and ApplicationsVol. 388 (1) (2011) pp. 490-499

    Abstract

  • D. Lyles, J. Tien, D. McCobb and M. Zeeman
    Pituitary network connectivity as a mechanism for the LH surge
    Journal of NeuroendocrinologyVol. 22 No. 12 (2011) pp. 1267-1278

    Abstract

  • Y. Zhang and M. Golubitsky
    Periodically forced Hopf bifurcation
    SIAM J. Appl. Dynam. Sys.Vol. 10 (2011) pp. 1272-1306

    Abstract

  • I. Stewart and M. Golubitsky
    Synchrony-breaking bifurcation at a simple real eigenvalue for regular networks 1: 1-dimensional cells
    SIAM J. Appl. Dynam. Sys.Vol. 10 No. 4 (2011) pp. 1404-1442

    Abstract

  • Y. Lou and C. Wu
    Global dynamics of a trio-trophic model for two patches with travel losses
    SIAM J. Appl. Math.Vol. 71 (2011) pp. 1801-1820

    Abstract

  • J. Gutierrez, M. Hurdal, R. Parshad and J. Teem
    Analysis of the Trojan Y Chromosome Model for Eradication of Invasive Species in a Dendritic Riverine System
    Journal of Mathematical BiologyVol. 64 (1-2) (2011) pp. 319-340

    Abstract

  • D. Schmidt, J. Best and M. Blumberg
    Random graph and stochastic process contributions to network dynamics
    AIMS Proceedings 2011 (2011) (In Preparation)

    Abstract

  • R. Mpika Massoukou and K. Govinder
    The Two-Strain Model for TB and Dengue Fever: Constant and Non-constant populations
    Quaest Math (2011) (Submitted)

    Abstract

  • N. Li and A. Yakubu
    A Juvenile-Adult Discrete-time Production Model of Exploited Fishery System
    Natural Resource Modeling (2011) (In Press)

    Abstract

  • A. Friedman and A. Yakubu
    Fatal disease and demographic Allee effect: population persistence and extinction
    Journal of Biological Dynamics (2011) (In Press)

    Abstract

  • S. Robertson and I. Hamilton
    Ideal free habitat selection under the risk of infectious disease transmission
    (2011) (Submitted)

    Abstract

  • M. Eisenberg, S. Robertson and J. Tien
    Identifiability and estimation of multiple transmission pathways in waterborne disease
    (2011) (Under Revision)

    Abstract

  • H. Jain, S. Clinton, A. Bhinder and A. Friedman
    Impact of androgen ablation treatment on mutation acquisition in prostate cancer
    Proc Natl Acad Sci (2011) (In Press)

    Abstract

  • M. Eisenberg, Y. Kim, R. Li, W. Ackerman, D. Kniss and A. Friedman
    Mechanistic modeling of a novel cancer protein: myoferlin effects on tumor cell invasion
    Proc Natl Acad SciVol. 108 No. 50 (2011) pp. 20078-20083

    Abstract

  • R. Ben-Shachar, M. Eisenberg, S. Huang and J. Distefano
    Simulation of post thyroidectomy treatment alternatives for T3 or T4 replacement in pediatric thyroid cancer patients
    Thyroid (2011) (In Press)

    Abstract

  • J. Tien, H. Poinar, D. Fisman and D. Earn
    Herald waves of cholera in 19th century London
    Journal of the Royal Society InterfaceVol. 8 No. 58 (2011) pp. 756-760

    Abstract

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