Browsing by Author "Maletic-Savatic, Mirjana"
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Item Bayesian graphical models for biological network inference(2013-11-20) Peterson, Christine; Vannucci, Marina; Ensor, Katherine B.; Kavraki, Lydia E.; Maletic-Savatic, Mirjana; Stingo, Francesco C.In this work, we propose approaches for the inference of graphical models in the Bayesian framework. Graphical models, which use a network structure to represent conditional dependencies among random variables, provide a valuable tool for visualizing and understanding the relationships among many variables. However, since these networks are complex systems, they can be difficult to infer given a limited number of observations. Our research is focused on development of methods which allow incorporation of prior information on particular edges or on the model structure to improve the reliability of inference given small to moderate sample sizes. First, we propose an approach to graphical model inference using the Bayesian graphical lasso. Our method incorporates informative priors on the shrinkage parameters specific to each edge. We demonstrate through simulations that this method allows improved learning of the network structure when relevant prior information is available, and illustrate the approach on inference of the cellular metabolic network under neuroinflammation. This application highlights the strength of our method since the number of samples available is fairly small, but we are able to draw on rich reference information from publicly available databases describing known metabolic interactions to construct informative priors. Next, we propose a modeling approach for settings where we would like to estimate networks for a collection of possibly related sample groups, where the sample size for each subgroup may be limited. We use a Markov random field prior to link the graphs within each group, and a selection prior to infer which groups have shared network structure. This allows us to encourage common edges across sample groups, when supported by the data. We provide simulation studies to illustrate the properties of our method and compare its performance to competing approaches. We conclude by demonstrating use of the proposed method to infer protein networks for various subtypes of acute myeloid leukemia and to infer signaling networks under different experimental perturbations.Item Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors(International Press, 2013) Peterson, Christine; Vannucci, Marina; Karakas, Cemal; Choi, William; Ma, Lihua; Maletic-Savatic, MirjanaMetabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation.Item Multitype Bellman-Harris branching model provides biological predictors of early stages of adult hippocampal neurogenesis(BioMed Central, 2017) Li, Biao; Sierra, Amanda; Deudero, Juan J; Semerci, Fatih; Laitman, Andrew; Kimmel, Marek; Maletic-Savatic, MirjanaAbstract Background Adult hippocampal neurogenesis, the process of formation of new neurons, occurs throughout life in the hippocampus. New neurons have been associated with learning and memory as well as mood control, and impaired neurogenesis has been linked to depression, schizophrenia, autism and cognitive decline during aging. Thus, understanding the biological properties of adult neurogenesis has important implications for human health. Computational models of neurogenesis have attempted to derive biologically relevant knowledge, hard to achieve using experimentation. However, the majority of the computational studies have predominantly focused on the late stages of neurogenesis, when newborn neurons integrate into hippocampal circuitry. Little is known about the early stages that regulate proliferation, differentiation, and survival of neural stem cells and their immediate progeny. Results Here, based on the branching process theory and biological evidence, we developed a computational model that represents the early stage hippocampal neurogenic cascade and allows prediction of the overall efficiency of neurogenesis in both normal and diseased conditions. Using this stochastic model with a simulation program, we derived the equilibrium distribution of cell population and simulated the progression of the neurogenic cascade. Using BrdU pulse-and-chase experiment to label proliferating cells and their progeny in vivo, we quantified labeled newborn cells and fit the model on the experimental data. Our simulation results reveal unknown but meaningful biological parameters, among which the most critical ones are apoptotic rates at different stages of the neurogenic cascade: apoptotic rates reach maximum at the stage of neuroblasts; the probability of neuroprogenitor cell renewal is low; the neuroblast stage has the highest temporal variance within the cell types of the neurogenic cascade, while the apoptotic stage is short. Conclusion At a practical level, the stochastic model and simulation framework we developed will enable us to predict overall efficiency of hippocampal neurogenesis in both normal and diseased conditions. It can also generate predictions of the behavior of the neurogenic system under perturbations such as increase or decrease of apoptosis due to disease or treatment.Item Regularized partial least squares with an application to NMR spectroscopy(John Wiley & Sons, Inc., 2013) Allen, Genevera I.; Peterson, Christine; Vannucci, Marina; Maletic-Savatic, MirjanaHigh-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexibility, general penalties, easy interpretation of results, and fast computation in high-dimensional settings. We also outline extensions of our methods leading to novel methods for non-negative PLS and generalized PLS, an adoption of PLS for structured data. We demonstrate the utility of our methods through simulations and a case study on proton Nuclear Magnetic Resonance (NMR) spectroscopy data.Item Spatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description(Wiley, 2014) Shetty, Anil N.; Chiang, Sharon; Maletic-Savatic, Mirjana; Kasprian, Gregor; Vannucci, Marina; Lee, WesleyIn this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.Item Stochastic Modeling and Simulation of Biological Phenomena with Applications in Population Genetics and in Cell Populations(2013-07-09) Li, Biao; Deem, Michael W.; Kimmel, Marek; Cox, Dennis D.; Igoshin, Oleg A.; Maletic-Savatic, Mirjana; Peng, BoStochastic modeling and simulation play important roles in population genetics, statistical genetics, cell biology, molecular biology and evolutionary theory. This thesis explores four aspects of stochastic modeling and simulation of biological phenomena with applications. Research carried out is focused on two major themes. The first one (Chapters 2 and 3) concerns application of stochastic modeling in genetics, specifically to identify biases in analysis of genetics data. Two problems that are considered are ascertainment bias in estimation of microsatellite diversity in interspecies comparisons, and sample-selection bias in comparing different methods of rare variant analysis. The second theme (Chapters 4 and 5) concerns application of Poisson and branching process models to understand various aspects of cell proliferation, using S-phase labeling. Two model systems are: transient dynamics of proliferation of neurogenic progenitors in mouse brain with emphasis on differentiation and apoptosis, and balanced growth under different assumptions concerning DNA-replication pattern. In the first part, we investigate factors that are influencing the ascertainment bias of microsatellite allele sizes and explore the impact on estimates of mutation rates. Microsatellite loci play an important role as markers for identification, disease gene mapping and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which however are subject to ascertainment bias. This bias arises for example when a locus is selected based on its large allele size in one species (cognate species 1), in which it is first discovered. It is reflected in average allele length in any non-cognate species 2 being smaller than that in species 1. We derive an analytical model based on coalescence theory to calculate the average allele length difference between species 1 and 2 under effects of both ascertainment bias and intrinsic genetic influences, such as demography, genetic drift, mutation, etc. Analytical results are confirmed by forward-time simulations using simuPOP. Re-analyzing literature data, we demonstrate that despite bias, the microsatellite mutation rate estimate in Human exceeds that in Chimpanzee, and also that population bottlenecks and expansions in the recent human history have little impact on the conclusion. The second part of the thesis introduces a simulation framework, SimRare, to generate sequence-based data for rare variant association studies and evaluating association test methods. Currently, it is difficult to compare rare variant association methods present in the literature because different methods are used to generate data. In any given study, variant and/or disease model is often generated using a test set that makes a particular method to appear superior to other methods. The SimRare program is developed to provide an easy way to generate validation data sets for both variant and phenotype data using realistic models, and to evaluate association methods in an unbiased manner, including novel methods. Using SimRare we validate existing association methods using data generated under various scenarios of demographic history and disease etiology. We demonstrate that the power of each method depends on the underlying model and differences in power between methods are usually modest. The third part is devoted to the study of early stages of adult hippocampal neurogenesis, a process of formation of newborn neurons, which occurs throughout life in the hippocampus responsible for learning and memory. The majority of hippocampal neurogenesis studies have predominantly focused on late stages, while little is known about its early stages that regulate the proliferation and differentiation of neural stem cells and progenitor cells to form neurons. Based on the branching process theory we develop a stochastic model with simulation program to analyze cell labeling data obtained from BrdU pulse-and-chase labeling experiments. By fitting data our simulation results reveal unknown but meaningful biological parameters, such as apoptotic rate and duration time at each stage, etc., to allow us to predict overall efficiency of hippocampal neurogenesis in both normal and diseased conditions. The fourth part focuses on the modeling of DNA replication and bivariate cell labeling experiments. Understanding kinetics of DNA replication gives an insight into mechanisms revealing specifics of normal and cancer cells proliferation. We propose a multiscale modeling of stochastic events related to the measured labeling intensities of both DNA content and replication progression over various exposure times in proliferating cells. We demonstrate that the experimental asymmetry in DNA replication scatterplots is the hallmark of an increasing replication initiation rate in the S-phase of the cell cycle. In summary, the research results justify the hypothesis that application of stochastic modeling, simulation and statistical analysis leads to results which would be impossible to obtain otherwise.