One of the ultimate goals of computational biology and bioinformatics is to develop control strategies to find efficient medical treatments. One step towards this goal is to develop methods for changing the state condition of a cell into a new desirable state. Using a stochastic modeling framework generalized from Boolean Networks, this talk discusses a computationally efficient method that determines sequential combinations of network perturbations (control actions), that induce the transition of a cell towards a new predefined state. The method requires a set of possible control actions as input, every element of this set represents the silencing of a gene (node) or a disruption of the interaction between two molecules (edge). An optimal control policy defined as the best intervention at each state of the system, can be obtained using theory of Markov decision processes. However, these algorithms are computationally prohibitive for models of tens of nodes. The proposed method generates a sequence of actions that approximates the optimal control policy with high probability and with a computational efficiency that does not depend on the size of the state space of the system. The methods are validated by using published models where control targets have been identified.
It is known that there are gender differences in one-carbon metabolism (OCM) and these differences are accentuated in pregnancy. Women in the child-bearing years exhibit lower plasma homocysteine, higher betaine and choline, and lower S-andenosylmethionine. Various enzymes in OCM are up-regulated or down-regulated in women due to estrogen. Furthermore, insulin and glucose affect some enzymes of OCM and change during pregnancy. All of these results suggest that a mechanistic understanding of how enzymatic differences in women affect OCM is important for precision medicine.
The reaction diagram for the folate and methionine cycles in OCM is very complicated consisting of loops within loops. Furthermore, many substrates in the network influence, through allosteric binding, the activity level of enzymes at distant locations in the network. These are systems properties of the whole network and to understand them one needs a mathematical model of OCM, based on the real underlying biochemistry and biology, and machine computation.
A mathematical model of folate and methionine metabolism is used to study the enzymatic changes in women of child-bearing age and the resulting concentrations of metabolites. In each case the results are compared to clinical and experimental studies. The causal mechanisms by which the gene expression or enzyme activity changes in women that lead to the metabolite changes will be discussed.
The Rock-Paper-Scissors game, in which Rock blunts Scissors, Scissors cut Paper, and Paper wraps Rock, provides an appealing simple model of cyclic competition between different strategies or species in evolutionary game theory and biology. When spatial distribution and mobility of individuals is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations that has travelling wave solutions in one (spatial) dimension and spiral wave solutions in two (spatial) dimensions. In this talk, I will describe how we can understand what governs the wavespeed and wavelength of the travelling waves, by considering the dynamics near a robust heteroclinic cycle that arises when the PDEs are considered in a travelling frame. We find three new types of heteroclinic bifurcations, none of which have been seen in the literature before. I will finish by proposing some ideas on how to extend our work to understand what governs similar properties of the spiral wave solutions.
Vector-borne diseases affects approximately 1 billion people and accounts for 17% of all infectious diseases. With travel becoming more frequent across the global, it is important to understand the spatial dynamics of vector-borne diseases. Host movement plays a key part on how a disease can be distributed as it enables a pathogen to invade a new environment, and helps the persistence of a disease in locations that would otherwise be isolated. In this talk, we will explore how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics.
The problem of scoring protein models for some fit criteria, such as closeness to native structure or ability to bind, is one of the earliest problems recognized in the field of proteomics. Here, an approach capturing properties of the entire protein and utilizing this as input features for a machine learner will be presented. This approach allows us to better match the conditions of the Boltzmann approach that connects phase space states probability and energy. We test our approach on some recent results from CASP experiments. A partial review of this presentation is available from: Faraggi, Eshel, and Andrzej Kloczkowski. Proteins: Structure, Function, and Bioinformatics 82.5 (2014): 752-759.
Clustered ventilation defects are a hallmark of asthma, typically seen via imaging studies during asthma attacks. The mechanisms underlying the formation of these clusters is of great interest in understanding asthma. Because the clusters vary from event to event, many researchers believe they occur due to dynamic, rather than structural, causes. This talk will cover recent progress in understanding the mathematics behind clustered ventilation defect formation, interactions with structural factors, and the implications for understanding asthma and its treatment.
Homeostasis occurs when an output variable remains approximately constant as input parameters I vary over some intervals. We formulate homeostasis in the context of singularity theory by replacing ‘approximately constant over an interval’ with ‘zero derivative of the output with respect to the inputs at a point’. Unfolding theory then classifies all small perturbations of the input-output function. In particular, in one input systems the ‘chair’ singularity, which has been shown by Best, Nijhout, & Reed to be especially important in applications, is discussed in detail. In particular, the chair is the simplest singularity that can be obtained by evolution to homeostasis. We discuss several applications in biochemical and gene regulatory motifs. We also show that the hyperbolic umbilic can also organize evolution to homeostasis in two input systems. This work has been done jointly with Ian Stewart, Mike Reed, Janet Best, Fred Nijhout, and Fernando Antoneli.
In my talk I will present research on two projects. The first one involves measuring the effectivness of the therapeutic process based on polish and american data sets. The second one (in progress) is related to a new approach to the estimation of the mortality rates and forecast based on two extended Milevsky and Promislov models: firstly with colored excitations modeled by Gaussian linear filters, secondly with excitations modeled by a continuous non-Gaussian process. Markov Chains will be the common denominator of both projects.
The nuclear pore complex controls all transport between the nucleus and the cytoplasm. Most steps of this transport process are driven by thermal fluctuations, not by an active input of energy, and yet the nuclear pore complex achieves high throughput of cargo while efficiently filtering out macromolecules that should not be transported. In this talk, I will outline what is known and what is still a mystery about how the nuclear pore functions, and I will discuss preliminary attempts to model the mechanics of transport through the pore.
I will present recent results about a family of reaction–diffusion systems whose prototype is the Lotka–Volterra competitive system with diffusion and mutations. These systems are nonlinear and non-cooperative, which makes their study difficult; the idea is then to notice and to use the underlying KPP structure.
We present a Riemannian framework for comprehensive statistical shape analysis of 3D objects, represented by their boundaries (parameterized surfaces). By comprehensive framework, we mean tools for registration, comparison, averaging, and modeling of observed surfaces. Registration is analogous to removing all shape preserving transformations, which include translation, scale, rotation and re-parameterization. This framework is based on a special representation of surfaces termed square root normal fields and a closely related elastic metric. The main advantages of this method are: (1) the elastic metric provides a natural interpretation of shape deformations that are being quantified, (2) this metric is invariant to re-parameterizations of surfaces, and (3) under the square-root normal field transformation, the complicated elastic metric becomes the standard L2 metric, simplifying parts of the implementation. We present numerous examples of shape comparisons for various types of surfaces in different application areas. We also compute average shapes, covariances and perform principal component analysis to explore the variability in different shape classes. These quantities are used to define generative shape models and for random sampling. Specifically, we showcase the applicability of the proposed framework in shape analysis of anatomical structures in different medical applications including Attention Deficit Hyperactivity Disorder and endometriosis.
To survive and reproduce, an animal must adjust to changes in its internal state and the external environment. We refer to the ability of a motor system to maintain performance despite perturbations as “robustness”. Although it is well known that sensory feedback supports robust adaptive motor behaviors, specific mechanisms of robustness are not well understood either experimentally or theoretically. In this work, we explore how sensory feedback could alter a neuromechanical trajectory to enhance robustness for motor control. As a concrete example, we focus on a piecewise smooth neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk, Aplysia californica. To understand the mechanism of the robust sensory feedback control, we generalize variational and phase response analysis developed for stable limit cycle systems to the piecewise smooth neuromechanical system with hard boundary conditions. Based on our analysis, we investigate the mechanisms by which sensory feedback generates robust adaptive behavior, quantify the robustness of the Aplysia model to the applied perturbation, and compare them to the experimental observations.
As biotechnologies for data collection become more efficient and mathematical modeling becomes more ubiquitous in the life sciences, analyzing both high-dimensional data and high-dimensional model parameter spaces is of the utmost importance. We present a perspective inspired by differential geometry that allows for the exploration of complex datasets such as these. In the case of single-cell leukemia data we present a novel statistic for testing differential biomarker correlations between patients and within specific cell phenotypes. A key innovation here is that the statistic is agnostic to how the the single cells are clustered and can be used in broader situations. Finally, we consider a case where the data of interest are parameter sets for a nonlinear model of signal transduction and the classification of model dynamics is considered. We motivate how the aforementioned perspective can be used to avoid global bifurcation analysis and consider how parameter sets with distinct dynamics contrast.
Regular spatial patterns in the vegetation growth of dryland ecosystems provide a striking example of self-organization on a community scale. These patterns most often appear on very gentle slopes as bands of vegetation separated by bare soil with characteristic lengthscales of 10-100 meters and evolve on 100-1000 year time scales. I will discuss the role of water transport in determining both the shape of individual vegetation bands and the region of the landscape with patterned vegetation growth. A simple modeling framework that incorporates the influence of topography on water flow provides qualitative agreement with satellite imagery and other remote sensing data. I will also present modeling efforts in progress to capture plant feedbacks on surface/subsurface water transport in a more realistic way.
Abstract not submitted.
Carcinogenesis is a complex stochastic evolutionary process. Evolving tumors interact with and manipulate their surrounding microenvironment in a dynamic spatio-temporal manner. We develop mathematical models to gain some insight about the evolutionary dynamics of cancer. In this talk, I will discuss several computational models to investigate tumor evolutionary dynamics and finding novel therapeutic targets. In the first part of the talk, I will describe several stochastic models for stem cell dynamics to identify factors, which may influence the initiation and progression of tumors. In the second part of the talk, I will show that killing cancer cells might not be an optimal cancer treatment by developing a stochastic model for cell dynamics after conventional cancer treatments. Finally, I will introduce a bioinformatics technique to obtain personalized targeted therapies for cancer patients.
Statistical uncertainty quantification is a modern area of statistics concerned with modeling a wide variety of complex real-world processes that exhibit challenging features, such as high-dimensionality, non-linear response behavior, non-stationarity and ``big data’’. These problem features have lead to many innovations in flexible statistical models, methodology for statistical computation and efficient use of parallel computing for statistical inference and prediction. They can be broadly categorized into two subsets of problem types: (i) problems where a well-founded theoretical model is postulated but data collection is expensive or sparse; (ii) problems where a theoretical model is unavailable but data collection is cheap or dense. In this talk we will introduce some popular statistical methods used in this area, including Gaussian process models and Bayesian Additive Regression Trees (BART), and motivate the scientific application of these models with real-world examples.
Wild-type zebrafish feature black and yellow stripes across their body and fins, but mutations display a range of altered patterns, including spots and labyrinth curves. These diverse patterns form due to the self-organizing interactions of pigment cells, which sort out through movement, birth, competition, and transitions in shape. Cells regulate each others' behavior on the growing skin by communicating both locally and at long range through dendritic extensions. Working closely with the biological data, we develop an agent-based model of this pattern formation, coupling deterministic migration by ODEs with stochastic rules for updating population size on growing domains. Our model proposes how a combination of short- and long-range interactions between cells is able to robustly produce stripes, and it suggests cell behaviors that may be altered to produce patterns on mutations and close relatives of zebrafish. We also explore stripe formation on the tailfin, where bone rays and epithelial growth may help direct pigment cell placement. This work is joint with Bjorn Sandstede.
How could populations move "optimally" across heterogeneous spaces? Such “optimal” strategy is referred to as evolutionarily stable strategy (ESS) in evolution game theory. We will illustrate, via several mathematical models, how to find ESS in spatial models for evolution of movement.
The cellular cytoskeleton is made of polymers that ensure the dynamic transport, localization and anchoring of various proteins and vesicles. Microtubules are an example of such polymers that provide the basic organization of the cell and the positioning of various organelles. In the development of egg cells (oocytes) into embryos, messenger RNA (mRNA) dynamically switches between diffusion and active transport states along microtubule filaments in its journey to the periphery of the egg cell. The accumulation of mRNA creates a spatial axis of development for the organism and therefore must occur on a certain time and spatial scale. Using dynamical systems modeling and analysis, we show that models including the cytoskeleton structure better predict the spread of the particles, and can be used to investigate the contribution of an anchoring mechanism to the timescale of localization. Our numerical studies using model microtubule structures predict that anchoring of mRNA-molecular motor complexes may be most effective in keeping mRNA localized near the periphery and therefore in ensuring healthy development of oocytes into embryos.
This is joint work with Bjorn Sandstede and in collaboration with the Mowry Lab (Brown University).
The rural poor generally rely on their immediate natural environment for subsistence and suffer from high burdens of infectious diseases. We present a general framework for modeling the ecology of rural poverty, focusing on the exemplar drivers: infectious diseases, renewable resources, and land-use change. Interactions between these drivers and economics create reinforcing feedbacks resulting in three possible development regimes corresponding to globally stable wealthy/healthy development, globally stable unwealthy/unhealthy development, and bistability. We show that the proportion of parameters leading to poverty is larger than that resulting in healthy/wealthy development; bistability consistently emerges as a general property of generalized disease-economic systems and that the systems under consideration are most sensitive to human disease parameters. The framework highlights feedbacks, processes and parameters that are important to measure in future studies of development, to identify effective and sustainable pathways out of poverty.
Flocculation is the reversible combination and separation of suspended particles in a fluid. It is a phenomenon ubiquitous in a wide variety of fields such as meteorology, marine science, astronomy, polymer science, and biotechnology. Flocculation is an efficient liquid-solid separation technique and has a broad range of industrial applications including fermentation, biofuel production, mineral processing, and wastewater treatment. A common mathematical model for the microbial flocculation is a 1D nonlinear partial integro-differential equation, which has been used successfully in matching many flocculation experiments. In this talk, I will briefly talk about my Ph.D. dissertation, where I rigorously investigated the long-term behavior of the microbial flocculation equations.
When a locust detects an odor, the stimulus triggers a specific sequence of network dynamics of the neurons in its antennal lobe. The odor response begins with a series of synchronous oscillations, followed by a short quiescent period, with a transition to slow patterning of the neuronal firing rates, before the system finally returns to a background level of activity. We begin modeling this behavior using an integrate-and-fire neuronal network, composed of excitatory and inhibitory neurons, each of which has fast-excitatory, and fast- and slow-inhibitory conductance responses. We further derive a firing-rate model for each (excitatory and inhibitory) neuronal population, which allows for more detailed analysis of and insight into the plausible olfaction mechanisms seen in experiments, prior models, and our numerical model. We conclude that the transition of the network dynamics through fast oscillations, a pause in network activity, and the slow modulation of firing rates can be described by a system which has a limit cycle of the fast variables, slowly passes through a saddle-node-on-a-circle bifurcation eliminating the oscillations, and, eventually, slowly passes again by the bifurcation point, producing a new limit cycle with a slower period.
Visual transduction in rod and cone photoreceptor cells is one of the best experimentally quantified G-protein signaling cascades. Here photons of light are converted by a biochemical process into a system’s response by diffusion of the 2nd messengers cGMP and Ca2+. These messengers then cause the opening or closing of gated ion channels. The morphology of photoreceptor cells is finely structured with a repeating pattern of hundreds of membrane folds in the whole outersegment. These make for two disparate geometric scales. This feature renders it computationally expensive as is. This talk will present a spatiotemporal, homogenized and numerically implemented finite element model of cone phototransduction. The role of homogenization is to simplify the geometry while recasting the smaller scales into a novel partial differential equation’s law. The model is validated through its comparison with a standard finite element diffusion model set to the original geometry. The homogenized model’s performance in both time of simulation and memory use will be compared to the standard diffusion model’s. Some comparisons with well-stirred and longitudinal diffusion models will also be made to underscore the importance of using 3d resolved models. This numerical project is joint work with Giovanni Caruso. It builds on an investigation done for rods by an ongoing interdisciplinary team of researchers that, non-exhaustively, also includes E. DiBenedetto and V. Gurevich.
Homeostasis occurs in a biological or chemical system when some output variable remains approximately constant as input parameters vary over some range. The notion of homeostasis is often associated with regulating global physiological parameters like temperature in multicellular complex organisms, such as mammals. For unicellular organisms, homeostasis is related to how some internal cell state of interest (the copy number, or concentration, of an mRNA transcript or of a protein) responds to changes in the intra-cellular or extra-cellular environment. Recently, Golubitsky and Stewart ["Homeostasis, Singularities and Networks". J. Mathematical Biology, 74 (2017) 387-407] introduced the notion of "infinitesimal homeostasis" allowing the use of implicit differentiation to find regions of homeostasis in systems of differential equations. In this talk we explain how apply singularity theory to explicitly find regions of homeostasis to differential equation models associated to "motifs" (small sub-network patterns that appear with high frequency in large complex networks) in gene regulatory networks (GRN) of single-cell organisms.
Joint work with Martin Golubitsky and Ian Stewart.
The high dimensional structured data sharing model describes groups of observations by shared and per-group individual parameters, each with its own structure such as sparsity or group sparsity. In this talk we consider the general form of data sharing where data comes in a fixed but arbitrary number of groups G and the structure of both shared and individual parameters can be characterized by any function.
We propose a simple estimator for high dimensional data sharing model and provide conditions under which it consistently estimates both shared and private parameters. We also characterize sample complexity of the estimator and present high probability non-asymptotic bound on estimation error of all parameters. Interestingly the sample complexity of our estimator translates to conditions on both per-group sample size and the total number of samples. To the best of our knowledge, this is the first thorough statistical analysis of data sharing models despite its recent successful application. Finally, we discuss possible application of data sharing in uplift detection for cancer treatment.
Impairments of axonal transport lead to neurodegenerative diseases which are characterized by local axonal swellings containing accumulations of axonally transported cargoes (e.g. organelles). In many cases, these diseases are caused by mutations in proteins involved in intracellular transport. However, little is understood about the underlying mechanisms that lead to organelle accumulations. In this paper we investigated the underlying mechanism of axonal cargo accumulation induced by a global reduction of functional molecular motors in an axon. We hypothesized that a reduction in motor number leads to a reduction in the number of active motors on each cargo which in turn leads to less persistent movement, more frequent stops, and thus shorter runs; as cargoes stop more frequently, they block the passage of other cargoes, leading to a local “traffic jams”; collisions between moving and stopping cargoes can push stopping cargoes further away from microtubule tracks, preventing them from reattaching to microtubules and leading to the evolution of local cargo accumulations. We used a lattice-based stochastic model to test whether this mechanism can lead to the cargo accumulation patterns observed in experiments. Simulation results of the model verified our hypothesis.
The motivation for this work comes from an experiment in zebrafish conducted at the Medical College of Georgia. One goal was to at least partially determine how gene regulatory control structure allows the zebrafish to regenerate its tissue, in this case in the retina. Zebrafish exhibit regeneration abilities in a wide range of tissue, in contrast to the limited tissue-wide regeneration ability of higher-order animals, like humans. Reaction networks are an important class of models used to describe the interaction of systems’ species that are also potentially useful for understanding system-level properties. Exact inference in these models is notoriously difficult when the observed species’ trajectories are partially observed, leading to intractable likelihoods. An added complication is that often the full, or true, structure of the underlying network is unknown. Various strategies have been proposed in the literature to overcome these challenges, but most remain prohibitively expensive in terms of computational time for systems of interesting sizes. In this talk I will discuss methods we have developed for estimating reaction rate parameters and learning network structure, sometimes referred to as reverse engineering, from stochastic system trajectories measured at discrete time points. Finally, I will discuss some ongoing work that is loosely related to approximate Bayesian computation, and is based on the notion of synthetic likelihood, which we argue is valid via asymptotic sufficiency.
Algebraic relations among DNA site-pattern frequencies have proven useful for inferring phylogenetic relationships between species. Often, these algebraic relations can be expressed as rank conditions on certain matrices constructed from phylogenetic data. In this talk, we will discuss how certain rank conditions for phylogenetic sequence data can be interpreted as conditional independence statements that give evidence of the evolutionary tree that produced the sequences. We will also present some new results that generalize the classic phylogenetic rank conditions to coalescent models of evolution. We show that rank-based reconstruction methods based on these results are robust to violations of model assumptions and perform well even in the presence of gene flow.
Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of nearly 100 captive bred vaccinated devils into infected wild populations may help eliminate the disease and hence enable the population's recovery. Specifically, we demonstrate that with this release of captive bred vaccinated devils, the basic reproductive number is decreased to below one.
In this presentation I will present a theoretical framework to explain the emergence and persistence of racial health disparities as a function of historical poverty traps. I will attempt to link these poverty traps with the concept of complexity traps within neighborhoods in order to show mechanistically why racial health disparities may persist. The theoretical framework will be flexible enough to evaluate different theories for the emergence of residential racial segregation and include spatially explicit features that may be linked with observed data on discriminatory housing financing policies and illegal real estate practices, some of which persist to this day.
I will describe some ongoing work studying the network structure of far-right groups on Twitter.
Mental illnesses such as depression and bipolar disorder are highly prevalent and disabling. A mathematical/computational model for mood disorders (e.g., depression and bipolar), and one therapy method, are briefly overviewed. Then, key components of mood dynamics are analyzed: (i) “mood traps” (equilibria and stability), (ii) "mood-congruent attention" (stability and boundedness), and (iii) "mindfulness practice" as therapeutic attention re-balancing (stability, distraction rejection). Finally, an overview of how these can be used for the development of technology for treatment, and psychoeducation, via bio-signal-driven (e.g., via EEG) adaptive music and virtual reality (i.e. feedback control).