Dataset Information

Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.

ABSTRACT: Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform large-scale stochastic simulations. In this paper, we show that the infinite set of stationary moment equations describing the stochastic Brusselator and Schnakenberg oscillatory reactions networks can be truncated and solved using maximization of the entropy of the distributions. The results from our numerical experiments compare with the distributions obtained from well-established kinetic Monte Carlo methods and suggest that the accuracy of the prediction increases exponentially with the closure order chosen for the system. We conclude that maximum entropy models can be used as an efficient closure scheme alternative for moment equations to predict the non-equilibrium stationary distributions of stochastic chemical reactions with oscillatory dynamics. This prediction is accomplished without any prior knowledge of the system dynamics and without imposing any biased assumptions on the mathematical relations among species involved.

SUBMITTER: Constantino PH

PROVIDER: S-EPMC6424531 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature

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Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.

Constantino Pedro H PH Kaznessis Yiannis N YN

Chemical engineering science 20170522

Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform l ...[more]

PMID: 30899124

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Project description:BackgroundAfrican trypanosomiasis is a tsetse-borne parasitic infection that affects humans, wildlife, and domesticated animals. Tsetse flies are endemic to much of Sub-Saharan Africa and a spatial and temporal understanding of tsetse habitat can aid surveillance and support disease risk management. Problematically, current fine spatial resolution remote sensing data are delivered with a temporal lag and are relatively coarse temporal resolution (e.g., 16 days), which results in disease control models often targeting incorrect places. The goal of this study was to devise a heuristic for identifying tsetse habitat (at a fine spatial resolution) into the future and in the temporal gaps where remote sensing and proximal data fail to supply information.MethodsThis paper introduces a generalizable and scalable open-access version of the tsetse ecological distribution (TED) model used to predict tsetse distributions across space and time, and contributes a geospatial Bayesian Maximum Entropy (BME) prediction model trained by TED output data to forecast where, herein the Morsitans group of tsetse, persist in Kenya, a method that mitigates the temporal lag problem. This model facilitates identification of tsetse habitat and provides critical information to control tsetse, mitigate the impact of trypanosomiasis on vulnerable human and animal populations, and guide disease minimization in places with ephemeral tsetse. Moreover, this BME analysis is one of the first to utilize cluster and parallel computing along with a Monte Carlo analysis to optimize BME computations. This allows for the analysis of an exceptionally large dataset (over 2 billion data points) at a finer resolution and larger spatiotemporal scale than what had previously been possible.ResultsUnder the most conservative assessment for Kenya, the BME kriging analysis showed an overall prediction accuracy of 74.8% (limited to the maximum suitability extent). In predicting tsetse distribution outcomes for the entire country the BME kriging analysis was 97% accurate in its forecasts.ConclusionsThis work offers a solution to the persistent temporal data gap in accurate and spatially precise rainfall predictions and the delayed processing of remotely sensed data collectively in the - 45 days past to + 180 days future temporal window. As is shown here, the BME model is a reliable alternative for forecasting future tsetse distributions to allow preplanning for tsetse control. Furthermore, this model provides guidance on disease control that would otherwise not be available. These 'big data' BME methods are particularly useful for large domain studies. Considering that past BME studies required reduction of the spatiotemporal grid to facilitate analysis. Both the GEE-TED and the BME libraries have been made open source to enable reproducibility and offer continual updates into the future as new remotely sensed data become available.

Project description:When constructing discrete (binned) distributions from samples of a data set, applications exist where it is desirable to assure that all bins of the sample distribution have nonzero probability. For example, if the sample distribution is part of a predictive model for which we require returning a response for the entire codomain, or if we use Kullback-Leibler divergence to measure the (dis-)agreement of the sample distribution and the original distribution of the variable, which, in the described case, is inconveniently infinite. Several sample-based distribution estimators exist which assure nonzero bin probability, such as adding one counter to each zero-probability bin of the sample histogram, adding a small probability to the sample pdf, smoothing methods such as Kernel-density smoothing, or Bayesian approaches based on the Dirichlet and Multinomial distribution. Here, we suggest and test an approach based on the Clopper-Pearson method, which makes use of the binominal distribution. Based on the sample distribution, confidence intervals for bin-occupation probability are calculated. The mean of each confidence interval is a strictly positive estimator of the true bin-occupation probability and is convergent with increasing sample size. For small samples, it converges towards a uniform distribution, i.e., the method effectively applies a maximum entropy approach. We apply this nonzero method and four alternative sample-based distribution estimators to a range of typical distributions (uniform, Dirac, normal, multimodal, and irregular) and measure the effect with Kullback-Leibler divergence. While the performance of each method strongly depends on the distribution type it is applied to, on average, and especially for small sample sizes, the nonzero, the simple "add one counter", and the Bayesian Dirichlet-multinomial model show very similar behavior and perform best. We conclude that, when estimating distributions without an a priori idea of their shape, applying one of these methods is favorable.

Dataset Information

Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.

Publications

Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics.

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