MBI Publications

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  • J. Chang and T. Chou
    Iterative graph cuts for image segmentation with a nonlinear statistical shape prior
    Journal of Mathematical Imaging and VisionVol. 49 No. 1 (2014) pp. 87-97

    Abstract

  • J. Chang, V. Savage and T. Chou
    A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation
    Journal of Statistical PhysicsVol. 157 No. 3 (2014) pp. 582–602

    Abstract

  • L. Comita, S. Queenborough, S. Murphy, J. Eck, K. Xu, M. Krishnadas, N. Beckman and Y. Zhu
    Testing predictions of the Janzen–Connell hypothesis: a meta-analysis of experimental evidence for distance- and density-dependent seed and seedling survival
    Journal of EcologyVol. 102 No. 4 (2014) pp. 845-856

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  • J. Kim, Z. Kilpatrick, M. Bennett and K. Josic
    Molecular mechanisms that regulate the coupled period of the mammalian circadian clock
    Biophysical JournalVol. 106 No. 9 (2014) pp. 2071–2081

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  • 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

  • R. Giedt, D. Pfeiffer, A. Matzavinos, C. Kao and B. Alevriadou
    Mitochondrial dynamics and motility inside living vascular endothelial cells: Role of bioenergetics
    Annals of Biomedical EngineeringVol. 40 No. 9 (2012) pp. 1903-1916

    Abstract

  • S. Liu, A. Matzavinos and S. Sethuraman
    Random walk distances in data clustering and applications
    Advances in Data Analysis and ClassificationVol. 7 No. 1 (2013) pp. 83-108

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  • A. Matzavinos, B. Shtylla, Z. Voller, S. Liu and M. Chaplain
    Stochastic modeling of chromosomal segregation: Errors can introduce correction
    Bulletin of Mathematical Biology (2014)

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  • L. Altenberg
    Evolvability and Robustness in Artificial Evolving Systems: Three Perturbations
    Genetic Programming and Evolvable Machines (2014) (In Press)

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  • B. Ermentrout and V. Billock
    Flicker-induced phosphenes
    Encyclopedia of Computational Neuroscience. Springer-Verlag (2014) (In Press)

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  • V. Billock and B. Tsou
    Bridging the divide between sensory integration and binding theory: Using a binding-like neural synchronization mechanism to model sensory enhancement during multisensory interactions.
    Journal of Cognitive NeuroscienceVol. 26 (2014) pp. 1587-1599 (In Press)

    Abstract

  • P. Bressloff and J. Newby
    Path integrals and large deviations in stochastic hybrid systems.
    Physical review. E, Statistical, nonlinear, and soft matter physicsVol. 89 No. 4 (2014) pp. 042701

    Abstract

    We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.
  • C. Diekman and M. Golubitsky
    Network symmetry and binocular rivalry experiments.
    Journal of mathematical neuroscienceVol. 4 (2014) pp. 12

    Abstract

    Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechanisms of Vision, pp. 399-417, 2009; The Constitution of Visual Consciousness: Lessons from Binocular Rivalry, pp. 281-304, 2013). In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call rivalry networks, can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend Wilson networks by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovács et al. (Proc. Natl. Acad. Sci. USA 93:15508-15511, 1996), Shevell and Hong (Vis. Neurosci. 23:561-566, 2006; Vis. Neurosci. 25:355-360, 2008), and Suzuki and Grabowecky (Neuron 36:143-157, 2002). We also analyze an experiment with four colored dots (a simplified version of a 24-dot experiment performed by Kovács), and a three-dot analog of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments.
  • M. Eisenberg, S. Robertson and J. Tien
    Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease.
    Journal of theoretical biologyVol. 324 (2013) pp. 84-102

    Abstract

    Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.
  • H. Kang, M. Crawford, M. Fabbri, G. Nuovo, M. Garofalo and A. Friedman
    A mathematical model for microRNA in lung cancer.
    PloS oneVol. 8 No. 1 (2013) pp. e53663

    Abstract

    Lung cancer is the leading cause of cancer-related deaths worldwide. Lack of early detection and limited options for targeted therapies are both contributing factors to the dismal statistics observed in lung cancer. Thus, advances in both of these areas are likely to lead to improved outcomes. MicroRNAs (miRs or miRNAs) represent a class of non-coding RNAs that have the capacity for gene regulation and may serve as both diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for several miRNAs have been identified in lung cancers. Specifically, let-7 and miR-9 are deregulated in both lung cancers and other solid malignancies. In this paper, we construct a mathematical model that integrates let-7 and miR-9 expression into a signaling pathway to generate an in silico model for the process of epithelial mesenchymal transition (EMT). Simulations of the model demonstrate that EGFR and Ras mutations in non-small cell lung cancers (NSCLC), which lead to the process of EMT, result in miR-9 upregulation and let-7 suppression, and this process is somewhat robust against random input into miR-9 and more strongly robust against random input into let-7. We elected to validate our model in vitro by testing the effects of EGFR inhibition on downstream MYC, miR-9 and let-7a expression. Interestingly, in an EGFR mutated lung cancer cell line, treatment with an EGFR inhibitor (Gefitinib) resulted in a concentration specific reduction in c-MYC and miR-9 expression while not changing let-7a expression. Our mathematical model explains the signaling link among EGFR, MYC, and miR-9, but not let-7. However, very little is presently known about factors that regulate let-7. It is quite possible that when such regulating factors become known and integrated into our model, they will further support our mathematical model.
  • C. Diekman, C. Wilson and P. Thomas
    Spontaneous autoresuscitation in a model of respiratory control.
    Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. ConferenceVol. 2012 (2012) pp. 6669-72

    Abstract

    We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)'s (1999) conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.
  • A. Lam and Y. Lou
    Evolution of conditional dispersal: evolutionarily stable strategies in spatial models.
    Journal of mathematical biologyVol. 68 No. 4 (2014) pp. 851-77

    Abstract

    We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.
  • W. Lo, M. Lee, M. Narayan, C. Chou and H. Park
    Polarization of diploid daughter cells directed by spatial cues and GTP hydrolysis of Cdc42 budding yeast.
    PloS oneVol. 8 No. 2 (2013) pp. e56665

    Abstract

    Cell polarization occurs along a single axis that is generally determined by a spatial cue. Cells of the budding yeast exhibit a characteristic pattern of budding, which depends on cell-type-specific cortical markers, reflecting a genetic programming for the site of cell polarization. The Cdc42 GTPase plays a key role in cell polarization in various cell types. Although previous studies in budding yeast suggested positive feedback loops whereby Cdc42 becomes polarized, these mechanisms do not include spatial cues, neglecting the normal patterns of budding. Here we combine live-cell imaging and mathematical modeling to understand how diploid daughter cells establish polarity preferentially at the pole distal to the previous division site. Live-cell imaging shows that daughter cells of diploids exhibit dynamic polarization of Cdc42-GTP, which localizes to the bud tip until the M phase, to the division site at cytokinesis, and then to the distal pole in the next G1 phase. The strong bias toward distal budding of daughter cells requires the distal-pole tag Bud8 and Rga1, a GTPase activating protein for Cdc42, which inhibits budding at the cytokinesis site. Unexpectedly, we also find that over 50% of daughter cells lacking Rga1 exhibit persistent Cdc42-GTP polarization at the bud tip and the distal pole, revealing an additional role of Rga1 in spatiotemporal regulation of Cdc42 and thus in the pattern of polarized growth. Mathematical modeling indeed reveals robust Cdc42-GTP clustering at the distal pole in diploid daughter cells despite random perturbation of the landmark cues. Moreover, modeling predicts different dynamics of Cdc42-GTP polarization when the landmark level and the initial level of Cdc42-GTP at the division site are perturbed by noise added in the model.
  • K. Liao, X. Bai and A. Friedman
    The role of CD200-CD200R in tumor immune evasion.
    Journal of theoretical biologyVol. 328 (2013) pp. 65-76

    Abstract

    CD200 is a cell membrane protein that interacts with CD200 receptor (CD200R) of myeloid lineage cells. During tumor initiation and progression, CD200-positive tumor cells can interact with M1 and M2 macrophages through CD200-CD200R-compex, and downregulate IL-10 and IL-12 productions secreted primarily by M2 and M1 macrophages, respectively. In the tumor microenvironment, IL-10 inhibits the activation of cytotoxic T lymphocytes (CTL), while IL-12 enhances CTL activation. In this paper, we used a system approach to determine the combined effect of CD200-CD200R interaction on tumor proliferation by developing a mathematical model. We demonstrate that blocking CD200 on tumor cells may have opposite effects on tumor proliferation depending on the "affinity" of the macrophages to form the CD200-CD200R-complex with tumor cells. Our results help understanding the complexities of tumor microenvironment.
  • C. Diekman, C. Fall, J. Lechleiter and D. Terman
    Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke.
    Biophysical journalVol. 104 No. 8 (2013) pp. 1752-63

    Abstract

    A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.
  • C. Diekman, M. Golubitsky and Y. Wang
    Derived patterns in binocular rivalry networks.
    Journal of mathematical neuroscienceVol. 3 No. 1 (2013) pp. 6

    Abstract

    Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Wilson proposed a class of neuronal network models that generalize rivalry to multiple competing patterns. The networks are assumed to have learned several patterns, and rivalry is identified with time periodic states that have periods of dominance of different patterns. Here, we show that these networks can also support patterns that were not learned, which we call derived. This is important because there is evidence for perception of derived patterns in the binocular rivalry experiments of Kovács, Papathomas, Yang, and Fehér. We construct modified Wilson networks for these experiments and use symmetry breaking to make predictions regarding states that a subject might perceive. Specifically, we modify the networks to include lateral coupling, which is inspired by the known structure of the primary visual cortex. The modified network models make expected the surprising outcomes observed in these experiments.
  • W. Lo, R. Arsenescu and A. Friedman
    Mathematical model of the roles of T cells in inflammatory bowel disease.
    Bulletin of mathematical biologyVol. 75 No. 9 (2013) pp. 1417-33

    Abstract

    Gut mucosal homeostasis depends on complex interactions among the microbiota, the intestinal epithelium, and the gut associated immune system. A breakdown in some of these interactions may precipitate inflammation. Inflammatory bowel diseases, Crohn's disease, and ulcerative colitis are chronic inflammatory disorders of the gastrointestinal tract. The initial stages of disease are marked by an abnormally high level of pro-inflammatory helper T cells, Th1. In later stages, Th2 helper cells may dominate while the Th1 response may dampen. The interaction among the T cells includes the regulatory T cells (Treg). The present paper develops a mathematical model by a system of differential equations with terms nonlocal in the space spanned by the concentrations of cytokines that represents the interaction among T cells through a cytokine signaling network. The model demonstrates how the abnormal levels of T cells observed in inflammatory bowel diseases can arise from abnormal regulation of Th1 and Th2 cells by Treg cells.
  • D. Koslicki and S. Foucart
    Quikr: a method for rapid reconstruction of bacterial communities via compressive sensing.
    Bioinformatics (Oxford, England)Vol. 29 No. 17 (2013) pp. 2096-102

    Abstract

    Many metagenomic studies compare hundreds to thousands of environmental and health-related samples by extracting and sequencing their 16S rRNA amplicons and measuring their similarity using beta-diversity metrics. However, one of the first steps--to classify the operational taxonomic units within the sample--can be a computationally time-consuming task because most methods rely on computing the taxonomic assignment of each individual read out of tens to hundreds of thousands of reads.
  • J. Chang, K. Brennan, D. He, H. Huang, P. Wilson and J. Wylie
    A mathematical model of the metabolic and perfusion effects on cortical spreading depression.
    PloS oneVol. 8 No. 8 (2013) pp. e70469

    Abstract

    Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism-aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium-ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD--vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization--found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease.
  • M. Eisenberg, G. Kujbida, A. Tuite, D. Fisman and J. Tien
    Examining rainfall and cholera dynamics in Haiti using statistical and dynamic modeling approaches.
    EpidemicsVol. 5 No. 4 (2013) pp. 197-207

    Abstract

    Haiti has been in the midst of a cholera epidemic since October 2010. Rainfall is thought to be associated with cholera here, but this relationship has only begun to be quantitatively examined. In this paper, we quantitatively examine the link between rainfall and cholera in Haiti for several different settings (including urban, rural, and displaced person camps) and spatial scales, using a combination of statistical and dynamic models. Statistical analysis of the lagged relationship between rainfall and cholera incidence was conducted using case crossover analysis and distributed lag nonlinear models. Dynamic models consisted of compartmental differential equation models including direct (fast) and indirect (delayed) disease transmission, where indirect transmission was forced by empirical rainfall data. Data sources include cholera case and hospitalization time series from the Haitian Ministry of Public Health, the United Nations Water, Sanitation and Health Cluster, International Organization for Migration, and Hôpital Albert Schweitzer. Rainfall data was obtained from rain gauges from the U.S. Geological Survey and Haiti Regeneration Initiative, and remote sensing rainfall data from the National Aeronautics and Space Administration Tropical Rainfall Measuring Mission. A strong relationship between rainfall and cholera was found for all spatial scales and locations examined. Increased rainfall was significantly correlated with increased cholera incidence 4-7 days later. Forcing the dynamic models with rainfall data resulted in good fits to the cholera case data, and rainfall-based predictions from the dynamic models closely matched observed cholera cases. These models provide a tool for planning and managing the epidemic as it continues.

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