MBI Publications

MBI Publications for 2013 (26)

  • L. Hu and D. Chen
    High-order fractional partial differential equation transform for molecular surface construction.
    Molecular based mathematical biologyVol. 1 (2013)

    Abstract

    Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.
  • H. Kang, M. Crawford, M. Fabbri, G. Nuovo, M. Garofalo, P. Nana-Sinkam and A. Friedman
    A mathematical model for microRNA in lung cancer
    PLoS OneVol. 8 No. 1 (2013)

    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.
  • S. Adams, C. Zhang, H. Zambrano and T. Conlisk
    Antibody-antigen binding in a flow-through microfluidic device
    51st AIAA Aerospace Sciences Conference (2013)

    Abstract

  • E. Martin, A. Friedman and W. Lo
    Mathematical Model of Colitis-associated Colon Cancer
    Journal of Theoretical BiologyVol. 317 (2013) pp. 2. 20-29

    Abstract

    As a result of chronic inflammation of their colon, patients with ulcerative colitis or Crohn's disease are at risk of developing colon cancer. In this paper, we consider the progression of colitis-associated colon cancer. Unlike normal colon mucosa, the inflammed colon mucosa undergoes genetic mutations, affecting, in particular, tumor suppressors TP53 and adenomatous polyposis coli (APC) gene. We develop a mathematical model that involves these genes, under chronic inflammation, as well as NF-�ºB, �²-catenin, MUC1 and MUC2. The model demonstrates that increased level of cells with TP53 mutations results in abnormal growth and proliferation of the epithelium; further increase in the epithelium proliferation results from additional APC mutations. The model may serve as a conceptual framework for further data-based study of the early stage of colon cancer.
  • H. Park, C. Chou and W. Lo
    Polarization of Diploid Daughter Cells Directed by Spatial Cues and GTP Hydrolysis of Cdc42 in Budding Yeast.
    PLoS ONEVol. 8 No. 2 (2013)

    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.
  • C. Diekman, C. Fall, J. Lechleiter and D. Terman
    Modeling the neuroprotective role of enhancing astrocyte mitochondrial metabolism during stroke
    Biophysical Journal (2013) (In Press)

    Abstract

    A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and ER Ca2+ handling, IP3 production and GTP-binding protein coupled receptor (GPCR) signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GPCR (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed in order 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 Ca2+ release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting v
  • A. Lam and Y. Lou
    Evolution of Conditional Dispersal: Evolutionarily Stable Strategies in Spatial Models
    Journal of Mathematical Biology (2013)

    Abstract

    We consider a two-species competition model in which the species have the same population dynamics but dierent dispersal strategies. Both species disperse by a combination of random diusion and advection along environmental gradients, with the same random dispersal rates but dierent advection coecients. Regarding these advection coecients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we and 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 at least three 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.
  • R. Azencott , A. Beri, A. Jain and I. Timofeyev
    Sub-sampling and Parametric Estimation for Multiscale Dynamics
    Communications in Mathematical Sciences (2013) (To Appear)

    Abstract

    We study the problem of adequate data sub-sampling for consistent parametric estimation of unobservable stochastic differential equations (SDEs), when the data are generated by multiscale dynamic systems approximating these SDEs in some suitable sense. The challenge is that the approximation accuracy is scale dependent, and degrades at very small temporal scales. Therefore, maximum likelihood parametric estimation yields inconsistent results when the sub-sampling time-step is too small. We use data from three multiscale dynamic systems, the Additive triad, the Truncated Burgers-Hopf models, and the model with the Fast-Oscillating Potential to illustrate this sub-sampling problem. In addition, we also discuss an important practical question of constructing the bias-corrected estimators for a fixed but unknown value of the multiscale parameter.
  • 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

    Abstract

  • H. Kang and T. Kurtz
    Separation of time-scales and model reduction for stochastic reaction networks
    Annals of Applied ProbabilityVol. 23 No. 1 (2013) pp. 529-583

    Abstract

    A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate choices of the exponents that can be applied to large complex networks. When the scaling implies subnetworks have different time-scales, the subnetworks can be approximated separately, providing insight into the behavior of the full network through the analysis of these lower-dimensional approximations.
  • R. Azencott , A. Beri, Y. Gadhyan, N. Joseph, C. Lehalle and M. Rowley
    Realtime market microstructure analysis: online Transaction Cost Analysis
    Quantitative Finance (2013) (Submitted)

    Abstract

    Motivated by the practical challenge in monitoring the performance of a large number of algorithmic trading orders, this paper provides a methodology that leads to automatic discovery of the causes that lie behind a poor trading performance. It also gives theoretical foundations to a generic framework for real-time trading analysis. Academic literature provides different ways to formalize these algorithms and show how optimal they can be from a mean-variance, a stochastic control, an impulse control or a statistical learning viewpoint. This paper is agnostic about the way the algorithm has been built and provides a theoretical formalism to identify in real-time the market conditions that influenced its efficiency or inefficiency. For a given set of characteristics describing the market context, selected by a practitioner, we first show how a set of additional derived explanatory factors, called anomaly detectors, can be created for each market order. We then will present an online methodology to quantify how this extended set of factors, at any given time, predicts which of the orders are under performing while calculating the predictive power of this explanatory factor set. Armed with this information, which we call influence analysis, we intend to empower the order monitoring user to take appropriate action on any affected orders by re-calibrating the trading algorithms working the order through new parameters, pausing their execution or taking over more direct trading control. Also we intend that use of this method in the post trade analysis of algorithms can be taken advantage of to automatically adjust their trading action.
  • K. Liao, X. Bai and A. Friedman
    The role of CD200-CD200R in tumor immune evasion
    J. Theor. Biol. (2013) (Accepted)

    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.
  • D. Koslicki
    Quikr: a Method for Rapid Reconstruction of Bacterial Communities via Compressive Sensing
    Oxford Journal of Bioinformatics (2013) (Under Review)

    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 withing the sample - can be a computationally time-consuming task since most methods rely on computing the taxonomic assignment of each individual read out of tens to hundreds of thousands of reads.

    We introduce Quikr: a QUadratic, K-mer based, Iterative, Reconstruction method which computes a vector of taxonomic assignments and their proportions in the sample using an optimization technique motivated from the mathematical theory of compressive sensing. On both simulated and actual biological data, we demonstrate that Quikr is typically more accurate as well as typically orders of magnitude faster than the most commonly utilized taxonomic assignment technique (the Ribosomal Database Project�s Naive Bayesian Classifier). Furthermore, the technique is shown to be unaffected by the presence of chimeras thereby allowing for the circumvention of the time-intensive step of chimera filtering.The Quikr computational package (using MATLABor Octave) for the Linux and Mac platforms is available at http://sourceforge.net/projects/quikr/.
  • V. Krivan and R. Cressman
    Competition in di-and tri-trophic food web modules
    Journal of Theoretical BiologyVol. 343 (2013) pp. 127-137

    Abstract

    Competition in di-and tri-trophic food web modules with many competing species is studied.The food web modules considered are apparent competition between n species sharing a single predator and a diamond-like food web with a single resource,a single top predator and many competing middle species.The predators have either fixed preferences for their prey,or they switch between available prey in away that maximizes their fitness. Dependence of these food web dynamics on environmental carrying capacity and food web connectance is studied.The results predict that optimal flexible for aging strongly weakens apparent competition and promotes species coexistence. Food web robustness (defined here as the proportion of surviving species) does not decrease with increased connectance in these food-webs. Moreover, it is shown that flexible prey switching leads to the same population equilibria as in corresponding food webs with highly specialized predators. The results show that flexible for aging behavior by predators can have very strong impact on species richness, as well as the response of communities to changes in resource enrichment and food web connectance when compared to the same food-web topology with inflexible top predators. Several results on global stability using Lyapunov functions areprovided.
  • 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.
  • 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.
  • R. Cressman and V. Krivan
    Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds
    J. Math. Biol.Vol. 67 (2013) pp. 329–358

    Abstract

    The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.
  • 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.
  • 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.
  • 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.
  • W. Hao and A. Sommese
    Completeness of solutions of Bethe's equations.
    Physical review. E, Statistical, nonlinear, and soft matter physicsVol. 88 No. 5 (2013) pp. 052113

    Abstract

    We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equation. We briefly comment on implications for thermodynamical computations based on the string hypothesis.
  • 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 HĂ´pital 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.
  • 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.
  • 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, 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.
  • 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.

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