Abstract
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.
Highlights
Estimating 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
The proposed procedure enjoys a clear advantage over other published estimation techniques: the estimated kinetic parameters satisfy the Wegscheider conditions imposed by the fundamental laws of thermodynamics
Since the true values of the kinetic parameters must lie on the thermodynamically feasible manifold in the parameter space, confining the Bayesian estimator to this manifold may lead to lower mean squared error due to a smaller variance
Summary
Estimating 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. Bayesian analysis allows us to effectively incorporate biophysical knowledge into the problem at hand and naturally draw statistical conclusions about the unknown kinetic parameters. This is done by employing a probability density function that encapsulates prior information about the rate constants of a biochemical reaction system and by deriving a posterior probability density function over the kinetic parameters after experimental data have been collected. The posterior allows us to quantify our confidence about estimation accuracy, compute probabilities over alternative calibrations, and design additional experiments to improve inference
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