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Voit, Eberhard O.

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Constructing stochastic models from deterministic process equations by propensity adjustment

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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The role of systems modeling in drug discovery and predictive health

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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Integrative Analysis of Transgenic Alfalfa (Medicago sativa L.) Suggests New Metabolic Control Mechanisms for Monolignol Biosynthesis

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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The internal state of medium spiny neurons varies in response to different input signals

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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Statistical Inference Methods for Sparse Biological Time Series Data

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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