Organizational Unit:
Wallace H. Coulter Department of Biomedical Engineering

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Now showing 1 - 10 of 28
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    Constructing stochastic models from deterministic process equations by propensity adjustment
    (Georgia Institute of Technology, 2011-11) Wu, Jialiang ; Vidakovic, Brani ; Voit, Eberhard O.
    BACKGROUND: Gillespie's stochastic simulation algorithm (SSA) for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME) in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. RESULTS: We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. CONCLUSIONS: The construction of a stochastic model for a biochemical network requires the utilization of information associated with an equation-based model. The conversion strategy proposed here guides a model design process that ensures a valid transition between deterministic and stochastic models.
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    Integrative Analysis of Transgenic Alfalfa (Medicago sativa L.) Suggests New Metabolic Control Mechanisms for Monolignol Biosynthesis
    (Georgia Institute of Technology, 2011-05) Lee, Yun ; Chen, Fang ; Gallego-Giraldo, Lina ; Dixon, Richard A. ; Voit, Eberhard O.
    The entanglement of lignin polymers with cellulose and hemicellulose in plant cell walls is a major biological barrier to the economically viable production of biofuels from woody biomass. Recent efforts of reducing this recalcitrance with transgenic techniques have been showing promise for ameliorating or even obviating the need for costly pretreatments that are otherwise required to remove lignin from cellulose and hemicelluloses. At the same time, genetic manipulations of lignin biosynthetic enzymes have sometimes yielded unforeseen consequences on lignin composition, thus raising the question of whether the current understanding of the pathway is indeed correct. To address this question systemically, we developed and applied a novel modeling approach that, instead of analyzing the pathway within a single target context, permits a comprehensive, simultaneous investigation of different datasets in wild type and transgenic plants. Specifically, the proposed approach combines static flux-based analysis with a Monte Carlo simulation in which very many randomly chosen sets of parameter values are evaluated against kinetic models of lignin biosynthesis in different stem internodes of wild type and lignin-modified alfalfa plants. In addition to four new postulates that address the reversibility of some key reactions, the modeling effort led to two novel postulates regarding the control of the lignin biosynthetic pathway. The first posits functionally independent pathways toward the synthesis of different lignin monomers, while the second postulate proposes a novel feedforward regulatory mechanism. Subsequent laboratory experiments have identified the signaling molecule salicylic acid as a potential mediator of the postulated control mechanism. Overall, the results demonstrate that mathematical modeling can be a valuable complement to conventional transgenic approaches and that it can provide biological insights that are otherwise difficult to obtain.
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    Statistical Inference Methods for Sparse Biological Time Series Data
    (Georgia Institute of Technology, 2011-04) Ndukum, Juliet ; Fonseca, Luís L. ; Santos, Helena ; Voit, Eberhard O. ; Datta, Susmita
    Background: Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. Results: The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been–or had not been–preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values <0.0001). Conclusion: We have developed a nonlinear mixed effects model that is appropriate for the analysis of sparse metabolic and physiological time profiles. The model permits sound statistical inference procedures, based on ANOVA likelihood ratio tests, for testing the significance of differences between short time course data under different biological perturbations.
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    The role of systems modeling in drug discovery and predictive health
    (Georgia Institute of Technology, 2010-05-04) Voit, Eberhard O.
    Systems biology is the result of a confluence of recent advances in molecular biology, engineering, and the computational sciences. It can loosely be categorized into experimental and computational systems biology. Experimental high-throughput methods, assisted by robotics, image analysis, and bioinformatics, have been used in the drug industry for quite a while, and current screening tests for drug efficacy and toxicity regularly involve genomic, proteomic, and molecular modeling approaches. By contrast, the role of computational methods of biological systems analysis is still emerging. This presentation focuses on computational systems modeling and its increasingly important role at several junctures of the drug development pipeline. Examples to be discussed include mathematical models for receptor dynamics, pharmacokinetics, and metabolic and signaling pathway analysis. In the context of the latter, Biochemical Systems Theory is proposed as a highly advantageous default framework for model design, diagnostics, manipulation, and system optimization. The development of dynamic models for complex disease processes permits the straightforward inclusion of methods for custom-tailoring models, which is a key step toward personalized medicine and predictive health.
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    The internal state of medium spiny neurons varies in response to different input signals
    (Georgia Institute of Technology, 2010-03) Qi, Zhen ; Miller, Gary W. ; Voit, Eberhard O.
    Background Parkinson's disease, schizophrenia, Huntington's chorea and drug addiction are manifestations of malfunctioning neurons within the striatum region at the base of the human forebrain. A key component of these neurons is the protein DARPP-32, which receives and processes various types of dopamine and glutamate inputs and translates them into specific biochemical, cellular, physiological, and behavioral responses. DARPP-32's unique capacity of faithfully converting distinct neurotransmitter signals into appropriate responses is achieved through a complex phosphorylation-dephosphorylation system that evades intuition and predictability. Results To gain deeper insights into the functioning of the DARPP-32 signal transduction system, we developed a dynamic model that is robust and consistent with available clinical, pharmacological, and biological observations. Upon validation, the model was first used to explore how different input signal scenarios are processed by DARPP-32 and translated into distinct static and dynamic responses. Secondly, a comprehensive perturbation analysis identified the specific role of each component on the system's signal transduction ability. Conclusions Our study investigated the effects of various patterns of neurotransmission on signal integration and interpretation by DARPP-32 and showed that the DARPP-32 system has the capability of discerning surprisingly many neurotransmission scenarios. We also screened out potential mechanisms underlying this capability of the DARPP-32 system. This type of insight deepens our understanding of neuronal signal transduction in normal medium spiny neurons, sheds light on neurological disorders associated with the striatum, and might aid the search for intervention targets in neurological diseases and drug addiction.
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    Estimating parameters for generalized mass action models with connectivity information
    (Georgia Institute of Technology, 2009-05) Ko, Chih-Lung ; Voit, Eberhard O. ; Wang, Feng-Sheng
    Background: Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems. Results: In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters. Conclusion: The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.
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    Identification of neutral sets of biochemical systems models from time series data
    (Georgia Institute of Technology, 2009-05) Vilela, Marco ; Vinga, Susana ; Grivet, Marco A. ; Maia, Mattoso ; Voit, Eberhard O. ; Almeida, Jonas S.
    Background The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines. Results In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity. Conclusion The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments
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    Collective decision making in bacterial viruses
    (Georgia Institute of Technology, 2008-09) Weitz, Joshua S. ; Mileyko, Yuriy ; Joh, Richard I. ; Voit, Eberhard O.
    For many bacterial viruses, the choice of whether to kill host cells or enter a latent state depends on the multiplicity of coinfection. Here, we present a mathematical theory of how bacterial viruses can make collective decisions concerning the fate of infected cells. We base our theory on mechanistic models of gene regulatory dynamics. Unlike most previous work, we treat the copy number of viral genes as variable. Increasing the viral copy number increases the rate of transcription of viral mRNAs. When viral regulation of cell fate includes nonlinear feedback loops, very small changes in transcriptional rates can lead to dramatic changes in steady-state gene expression. Hence, we prove that deterministic decisions can be reached, e.g., lysis or latency, depending on the cellular multiplicity of infection within a broad class of gene regulatory models of viral decision-making. Comparisons of a parameterized version of the model with molecular studies of the decision structure in the temperate bacteriophage l are consistent with our conclusions. Because the model is general, it suggests that bacterial viruses can respond adaptively to changes in population dynamics, and that features of collective decision-making in viruses are evolvable life history traits.
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    Computational systems analysis of dopamine metabolism
    (Georgia Institute of Technology, 2008-06) Qi, Zhen ; Miller, Gary W. ; Voit, Eberhard O.
    A prominent feature of Parkinson’s disease (PD) is the loss of dopamine in the striatum, and many therapeutic interventions for the disease are aimed at restoring dopamine signaling. Dopamine signaling includes the synthesis, storage, release, and recycling of dopamine in the presynaptic terminal and activation of pre- and post-synaptic receptors and various downstream signaling cascades. As an aid that might facilitate our understanding of dopamine dynamics in the pathogenesis and treatment in PD, we have begun to merge currently available information and expert knowledge regarding presynaptic dopamine homeostasis into a computational model, following the guidelines of biochemical systems theory. After subjecting our model to mathematical diagnosis and analysis, we made direct comparisons between model predictions and experimental observations and found that the model exhibited a high degree of predictive capacity with respect to genetic and pharmacological changes in gene expression or function. Our results suggest potential approaches to restoring the dopamine imbalance and the associated generation of oxidative stress. While the proposed model of dopamine metabolism is preliminary, future extensions and refinements may eventually serve as an in silico platform for prescreening potential therapeutics, identifying immediate side effects, screening for biomarkers, and assessing the impact of risk factors of the disease.
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    Parameter optimization in S-system models
    (Georgia Institute of Technology, 2008-04) Vilela, Marco ; Chou, I-Chun ; Vinga, Susana ; Vasconcelos, Ana Tereza R. ; Voit, Eberhard O. ; Almeida, Jonas S.
    Background: The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential Ssystem equations, which results in a set of algebraic equations. Results: A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases. Conclusion: A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well.