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A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions.

ABSTRACT: Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP) capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ?Gr >-2 kJ/mol), a transition region (-2> ?Gr >-20 kJ/mol) and a constant elasticity region (?Gr <-20 kJ/mol). We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only the kinetic behaviour of these enzymes, but it also provided insights about the particular features underpinning the observed kinetics. Overall, this framework will enable systematic parameterization and sampling of enzymatic reactions.

SUBMITTER: Saa P

PROVIDER: S-EPMC4397067 | biostudies-literature | 2015 Apr

REPOSITORIES: biostudies-literature

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A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions.

Saa Pedro P Nielsen Lars K LK

PLoS computational biology 20150414 4

Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours ...[more]

PMID: 25874556

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Project description:BackgroundThe dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function.ResultsWe introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database.ConclusionsTCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.

Project description:Phosphate chemistry is involved in many key biological processes yet the underlying mechanism often remains unclear. For theoretical analysis to effectively complement experimental mechanistic analysis, it is essential to develop computational methods that can capture the complexity of the underlying potential energy surface and allow for sufficient sampling of the configurational space. To this end, we report the parameterization of an approximate density functional theory, Self-Consistent-Charge Density-Functional Tight-Binding (SCC-DFTB) method for systems containing phosphorus. Compared to high-level density functional theory and ab initio (MP2 and G3B3) results, the standard second-order parameterization is shown to give reliable structures for a diverse set of phosphate compounds but inaccurate energetics. With the on-site third-order terms included, referred to as SCC-DFTBPA, calculated proton affinities of phosphate compounds are substantially improved, although it remains difficult to obtain reliable proton affinity for both phosphates and compounds that do not contain phosphorus, indicating that further improvement in the formulation of SCC-DFTB is still a challenge to meet. To make SCC-DFTB applicable to phosphate reactions in the current (on-site-third-order-only) formulation, a "reaction-specific" parameterization, referred to as SCC-DFTBPR, is developed based on hydrolysis reactions of model phosphate species. Benchmark calculations in both the gas-phase and solution-phase indicate that SCC-DFTBPR gives reliable structural properties and semi-quantitative energetics for phosphate hydrolysis reactions. Since the number of reaction-specific parameters is small, it is likely that SCC-DFTBPR is applicable to a broad set of phosphate species. Indeed, for 56 reaction exothermicities and 47 energy barriers related to RNA catalysis model reactions collected from the QCRNA database, which involve molecules rather different from those used to parameterize SCC-DFTBPR, the corresponding root-mean-square difference between SCC-DFTBPR and high-level DFT results is only 5.3 kcal/mol. We hope that the parameterized SCC-DFTB models will complement NDDO based reaction-specific models (e.g., AM1-d/PhoT) and high-level ab initio QM/MM methods in better understanding the mechanism of phosphate chemistry in condensed phase, particularly biological systems.

Project description:BackgroundEstimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.ResultsWe introduce a Bayesian analysis approach for computing thermodynamically consistent estimates of the rate constants of a closed biochemical reaction system with known stoichiometry given experimental data. Our method employs an appropriately designed prior probability density function that effectively integrates fundamental biophysical and thermodynamic knowledge into the inference problem. Moreover, it takes into account experimental strategies for collecting informative observations of molecular concentrations through perturbations. The proposed method employs a maximization-expectation-maximization algorithm that provides thermodynamically feasible estimates of the rate constant values and computes appropriate measures of estimation accuracy. We demonstrate various aspects of the proposed method on synthetic data obtained by simulating a subset of a well-known model of the EGF/ERK signaling pathway, and examine its robustness under conditions that violate key assumptions. Software, coded in MATLAB®, which implements all Bayesian analysis techniques discussed in this paper, is available free of charge at http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html.ConclusionsOur approach provides an attractive statistical methodology for estimating thermodynamically feasible values for the rate constants of a biochemical reaction system from noisy time series observations of molecular concentrations obtained through perturbations. The proposed technique is theoretically sound and computationally feasible, but restricted to quantitative data obtained from closed biochemical reaction systems. This necessitates development of similar techniques for estimating the rate constants of open biochemical reaction systems, which are more realistic models of cellular function.

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A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions.

Publications

A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions.

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