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.
The syncytial organization of the blastoderm stage of Drosophila development affords unique advantages for the study of transcriptional control. With respect to the control of transcription, it is possible to use the entire embryo as a spatially resolved microarray in which the response of reporters to quantitatively assayed transcription factors can be monitored at cellular resolution. This affords the opportunity to construct quantitative and predictive models of transcriptional control that are not limited to single enhancers. I will discuss progress in constructing such models, including applications to evolution and synthetic biology.
Recent advances in noninvasive neuroimaging have set the stage for the systematic exploration of human brain circuits in health and disease. One such effort is the Human Connectome Project (HCP), which will characterize brain circuitry and its variability in healthy adults. A consortium of investigators at Washington University, University of Minnesota, University of Oxford, and 7 other institutions is engaged in a 5-year project to characterize the human connectome in 1,200 individuals (twins and their non-twin siblings). Information about structural and functional connectivity will be acquired using diffusion MRI and resting-state fMRI, respectively. Additional modalities will include task-evoked fMRI and MEG/EEG, plus extensive behavioral testing and genotyping. Advanced visualization and analysis methods will enable characterization of brain circuits in individuals and group averages at high spatial resolution and at the level of functionally distinct brain parcels (cortical areas and subcortical nuclei). Comparisons across subjects will reveal aspects of brain circuitry which are related to particular behavioral capacities and which are heritable or related to specific genetic variants. Data from the HCP will be made freely available to the neuroscience community. A user-friendly informatics platform will enable investigators around the world to carry out many types of data mining on these freely accessible, information-rich datasets. The emergence of massive amounts of high quality and consistently acquired neuroimaging and behavioral data from the HCP and other large-scale projects raises exciting opportunities and challenges on the computational and informatics fronts. Just as bioinformatics emerged as an exciting new discipline once vast amounts of genomic and proteomic data became available, it is likely that neuroinformatics will rapidly evolve as new methods and approaches are developed to capitalize on the ongoing explosion of human neuroimaging data.
Abstract. Cortical spreading depression (CSD) is a slowly propagating wave of ionic and metabolic disturbances in cortical brain tissue. In addition to massive cellular depolarization, CSD involves significant changes in tissue perfusion and metabolism. CSD has been linked to migraine with aura, which affects about 20% of the people who suffer from migraine. The triggers for this disease are mainly undiagnosed. To devise rational treatments of migraine with aura, we need to learn much more about the brain and about CSD. CSD was discovered almost 70 years ago by A.A.P. Leao, a Brazilian physiologist during his PhD research on epilepsy at the Harvard Medical School. CSD is characterized by nonlinear chemical waves that propagate at very slow speeds, on the order of mm/min, in the cortex of different brain structures in various experimental animals, and occurs in humans. CSD waves generate massive changes in extracellular ion concentrations. In this talk, I will review some of the characteristics of CSD wave propagation and describe some of the mechanisms that are believed to be important for CSD. We develop a new mathematical model for CSD where the sodium-potassium ATPase, responsible for cellular polarization and recovery from CSD, operates at a rate that is dependent on local oxygen concentration. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree. Our model replicates the qualitative and quantitative behavior of CSD found in experimental studies and elucidates the effect of oxygen deprivation on CSD recovery. Our key findings are that during CSD, the metabolic activity of the cortex exceeds the physiological limits placed on oxygen delivery and changes in perfusion alter the intensity and duration of the event. The combination of experimentation and modeling should accelerate our understanding of how these mechanisms conspire to form CSD.
Heart muscle starts to contract when Ca2+ released from the sarcoplasmic reticulum (SR) binds to contractile proteins. The Ca2+ is released from the SR (a Ca2+ storage organelle) through calcium-selective ion channels called ryanodine receptors (RyRs). RyRs are activated (opened) by changes in cytosolic Ca2+ concentrations. Therefore, when some RyRs open to release Ca2+, neighboring RyRs are activated to release even more Ca2+ in a process called calcium-induced calcium release (CICR). Experiments suggest that this positive-feedback process does, however, terminate long before the SR is depleted of Ca2+, but how is not currently understood.
Several aspects of this Ca2+ movement will be discussed from the point of view of physics and mathematics. These include how RyRs select and efficiently conduct Ca2+ for sustained release, how probability theory can help us understand CICR, and how the physics of phase transitions might explain CICR initiation and, more importantly, its termination before the SR is deleted of Ca2+.
One of the long-standing questions in plant community ecology concerns the maintenance of savannas and other communities which exclude plant species which would typically out-compete the species present in the system. Savannas are communities that exist in many locations around the world, consisting of a mixture of grass-dominated ground cover and an over-story of trees with a distinct canopy layer. Savannas are open to invasion by species such as hardwood trees which out-compete the species present. I will present a collection of models that elaborate one of the proposed mechanisms to maintain savanna communities: disturbance arising from processes such as fire and hurricanes. A focus in these models is the nature of the feedbacks and the potential for climate change to impact the disturbance regime and modify the global pattern of savanna systems. As a cautionary tale, I will end with a discussion of limits to prediction in complex ecological systems, and discuss the potential computational irreducibility of invasion and global change projections.
Predicting the native structure of a protein from its amino acid sequence is a long standing problem. A significant bottleneck of computational prediction is the lack of efficient sampling algorithms to explore the configuration space of a protein. In this talk we will introduce a sequential Monte Carlo method to address this challenge: fragment regrowth via energy-guided sequential sampling (FRESS). The FRESS algorithm combines statistical learning (namely, learning from the protein data bank) with sequential sampling to guide the computation, resulting in a fast and effective exploration of the configurations. We will illustrate the FRESS algorithm through examples.
The dramatic diversity of form and function found between closely related species is likely driven by changes to non-coding DNA that modify the complex patterns of gene expression observed throughout development. To pinpoint regions of the human genome that evolved rapidly since divergence from the chimp-human ancestor, we developed a statistical phylogenetic method for detecting lineage-specific changes in the rate or pattern of nucleotide substitutions. We analyzed vertebrate whole-genome multiple sequence alignments and found 721 Human Accelerated Regions (HARs). The vast majority of HARs are located in unannotated non-coding regions of the human genome. However, they are enriched nearby transcription factors and developmental genes, and many have epigenetic marks and transcription factor binding sites suggestive of enhancer function. To test this hypothesis we trained a multi-kernel support vector machine using experimentally validated developmental enhancers and diverse feature data (e.g., k-mers, transcription factor (TF) binding sites, cell type specific histone modifications, chromatin state). We predicted that ~2% of the human genome and over 200 HARs function as enhancers in different embryonic tissues. To explore whether human mutations in HARs alter their function, we developed a novel measure of regulatory sequence divergence based on cumulative loss and gain of predicted TF binding sites and showed that it identifies enhancers whose mutations affect activity in vivo. We used regulatory divergence in combination with expression patterns and functions of nearby genes to predict which candidate HAR enhancers are most likely to affect human-specific developmental gene regulation. We tested 15 of these predictions with transient transgenic mouse enhancer assays that compare activity of ancestral and derived HAR sequences. We found many novel developmental enhancers, several of which have human-specific activity.
Previous work has suggested deep connections between statistical mechanics and certain aspects of both information theory and statistical inference, based primarily on the shared concept of entropy. In this talk I go beyond familiar information theoretic treatments of entropy to develop purely information-based interpretations of both the 1st and 2nd laws of thermodynamics. This allows us to ask and answer a question that has gone begging until now: What is the analogue of temperature (T) on the information/inferential side? I argue that the physical quantity T has a familiar, but surprising, interpretation as statistical evidence. Moreover, this formulation provides a template for measuring evidence on an absolute (Kelvin) scale for the first time. This has far reaching implications for bioinformatics, since the measurement and interpretation of statistical evidence is a critical element of how we make scientific use of bioinformatic results. In a more speculative vein, this work also raises the question of whether our physical theories require us to posit the existence of matter. If fundamental physical laws can be interpreted in purely informational terms, perhaps it is mathematically cogent to say that the universe is in fact made of information.