The shape of a cell, the sizes of subcellular compartments and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This talk describes how these spatial features can be included in mechanistic mathematical models of cell biology. The Virtual Cell (VCell) computational modeling and simulation software is designed for spatial modeling of cellular reaction-diffusion systems. VCell facilitates choices between physical formulations that implicitly or explicitly account for cell geometry and between deterministic vs, stochastic formulations for biochemical reactions. VCell allows modelers to separately define the model physiology, which includes the molecules, their reactions and membrane transport processes. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions and membrane flux processes of the reaction network. Initial conditions, diffusion coefficients, velocities and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically include a variety of ODE, PDE, and probabilistic solvers. A study of actin dynamics provides an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.
In this talk I describe work directed at understanding the origin of periodic hematological diseases, and how the mathematical modeling has led to better treatment strategies. I will also describe how our mathematical modeling may be useful in helping to avoid the hematological side effects of chemotherapy.
Phytoplankton motion in the ocean, at the scale of individual cells, involves the interaction of passive and actuated elastic structures with a surrounding fluid - a common theme in biological fluid dynamics. We present recent modeling results that shed light on the active swimming of dinoflagellates, as well as the passive motion of diatoms in shear flows. These diatoms may form chains or bear spines. In addition to examining how the flexibility and geometry of the diatoms affect their rotational dynamics, we will discuss how laboratory experiments and computational simulations are being calibrated in an effort to characterize the elastic properties of different species of chain-forming diatoms.
Our research focuses on the molecular mechanisms underlying ion channel and transporter targeting in cardiac and other excitable cells. In particular, we are interested in the role of membrane-associated ankyrin family of polypeptides in the targeting and function of ion channels and transporters. Our work establishes that loss-of-function mutation in ankyrin-B is the basis for a human cardiac arrhythmia syndrome associated with sinus node dysfunction, repolarization defects, and polymorphic tachyarrhythmia in response to stress and/or exercise ("ankyrin-B syndrome"). Additionally, our work revealed that reduction of ankyrin-B in mice results in reduced levels and abnormal localization of Na/Ca exchanger, Na/K ATPase, and InsP3 receptor at T-tubule/SR sites in cardiomyocytes and leads to altered Ca2+ signaling and extrasystoles that provide a rationale for the arrhythmia. A second line of work in the lab is focused on the role of ankyrin-G for targeting voltage-g ated Na channels in heart. These studies establish a physiological requirement for ankyrins in localization of a variety of ion channels in excitable membranes in the heart and demonstrate a new class of functional 'channelopathies' due to abnormal cellular localization of functionally-related ion channels and transporters.
Intracellular biological networks are highly complex and contain numerous regulatory loops. One of the challenges in cancer biology is to be able to understand and target sub-network that are aberrantly functioning in cancer cells. In this talk I will describe our integrated mathematical and experimental approach to understanding network function and identify targets for cancer therapy. The talk will focus on using network motif structures to reduce complexity and use of time course experimental proteomic data to train mathematical and computational models to identify targets.
In this talk I will be presenting two topics: (1) studying conducting and selectivity functions of ion channels and (2) exploring tumor growth under cancer-immune system interactions and therapeutic treatments. These complicated biological systems usually consists of composite materials and involve intensive interactions among components. The former is at molecular level: multiscale treatments (atomic and continuum) and multiphysics (classical and quantum) are applied to different components (water molecules, channel proteins, membranes, and mobile ions, etc) according to biological importances of objects and computational efficiency. The solute-solvent surface serves as a free boundary to couple the discrete and continuum scales. The cancer research is macroscopic: interactions pathways of a large amounts of cells and cytokines are outlined from experimental observations and modeled by a systems of governing equations; the tumor is described as a moving domain with free boundary and has obviously different phase-field from normal tissues.
Both of the two topics require advanced numerical techniques for solving partial differential equations and simulations are validated by experimental data. Analysis, such as existence and uniqueness of the solutions are performed to these free boundary problems.
Inspired by concepts from ergodic theory, we give new insight into coding sequence (CDS) density estimation for the human genome. Our approach is based on the introduction and study of topological pressure: a numerical quantity assigned to any finite sequence based on an appropriate notion of `weighted information content'. For human DNA sequences, each codon is assigned a suitable weight, and using a window size of approximately 60,000bp, we obtain a very strong positive correlation between CDS density and topological pressure. The weights are selected by an optimization procedure, and can be interpreted as quantitative data on the relative importance of different codons for the density estimation of coding sequences. This gives new insight into codon usage bias which is an important subject where long standing questions remain open. Inspired again by ergodic theory, we use the weightings on the codons to define a probability measure on finite sequences. We demonstrate that this measure is effective in distinguishing between coding and non-coding human DNA sequences of lengths approximately 5,000bp. We emphasize that topological pressure is a flexible tool and we expect it to be useful for the investigation of many other features of DNA sequences such as interspecies comparison of codon usage bias. We give a first result in this direction, investigating CDS density in the mouse genome and comparing our results with those for the human genome.
Task switching has been used as an experimental index of limitations on human cognitive flexibility. When switching from one task to another, participants exhibit increased reaction time, even when given ample time to prepare for the switch. Classical explanations of this "residual switch cost" typically presuppose that participants are fully motivated to perform the experimental task. This leads to interpretations of the residual switch cost in terms of structural cognitive factors. More recently, alternative explanations have proposed a role for motivational factors, arguing that preparation for task switches requires effort that participants are typically unwilling to expend, leading to only partial preparation (and residual switch costs) on average. In order to formalize the competing motivational and structural hypotheses of the residual switch cost into two alternative models, we employ a formal rational analysis of task switching experiments. This analysis shows that it is difficult to adjudicate between motivation and structural interpretations given existing data. We then conduct two new experiments to more conclusively test these ideas. Both experiments provide evidence for motivation-insensitive preparatory processes. Overall, this work casts doubt on the motivational interpretations of the residual switch cost, and provides a rigorous and principled framework for specifying and testing future hypotheses about motivational effects in the task switching paradigm.
Lung cancer is the leading cause of cancer-related deaths worldwide. Lack of early detection and the 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, both 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.
In total variation denoising, one attempts to enhance an image by solving a constrained minimization problem with a total variation objective. The method has proven very effective at smoothing functions with discontinuities. More recently, it was also shown that such a model is capable of preserving regularity of the data. In this talk, I will present a convergent Rayleigh-Ritz method for approximating the smooth solutions of the L^2 total variation denoising model. The proof exploits the properties of functions of bounded variation, the approximation power of spline functions, and the non-expansiveness of the TV-denoising operator.
Systems biology aims to explain how a biological system functions by investigating the interactions of its individual components from a systems perspective. Modeling is a vital tool as it helps to elucidate the underlying mechanisms of the system. Many discrete model types can be translated into the framework of polynomial dynamical systems (PDS), that is, time- and state-discrete dynamical systems over a finite field where the transition function for each variable is given as a polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods. In this talk, we show how a mathematical model helped us to inhibit tumor growth in melanoma cells.
We consider a two-species reaction-diffusion-advection competition model in which the species have the same population dynamics but different dispersal strategies. Regarding the advection coefficients as movement strategies of species, we investigate their course of evolution in the game-theoretical setting. 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 at least three evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of directed movement of organisms depends upon the spatial heterogeneity of the environment in a subtle way.
Parasites are ubiquitous in nature, and the various biotic and abiotic processes that shape host population dynamics can also affect the host-parasite interaction. In this talk I'll discuss the dynamic consequences of such processes in three examples. First, I'll briefly discuss a project motivated by Mycoplasma gallisepticum infections in the House Finch, in which we consider virulence evolution under two trade-offs: the classic virulence-transmission tradeoff as well as a host movement tradeoff. Second, I'll briefly discuss the three-species dynamics of Daphnia (aquatic invertebrates), their parasites, and their algal food source, and I'll explain how analyzing the dynamics such a system has helped us clarify how certain biological phenomena drive some of the more interesting dynamics that can arise in this and other three-species models. Third, I'll spend the second half of the talk discussing more recent work modelling fish movement and population dynamics in response to changes in their physical environment (water temperature and dissolved oxygen [DO] levels), focusing on the population consequences of seasonal hypoxia in Lake Erie. I'll present results from a spatially explicit model that incorporates fish bioenergetics and nearly two decades of temperature and DO data from Lake Erie which we are using to explore how seasonal hypoxia impacts these populations, and I'll briefly discuss ongoing work using an extension of this fish movement model to assess how seasonal hypoxia will affect infectious disease transmission among fish.