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The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

ABSTRACT: We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

SUBMITTER: Matsoukas T

PROVIDER: S-EPMC7597352 | biostudies-literature | 2020 Oct

REPOSITORIES: biostudies-literature

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The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

Matsoukas Themis T

Entropy (Basel, Switzerland) 20201020 10

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynami ...[more]

PMID: 33286949

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Project description:Kinetic models of metabolism can be constructed to predict cellular regulation and devise metabolic engineering strategies, and various promising computational workflows have been developed in recent years for this. Due to the uncertainty in the kinetic parameter values required to build kinetic models, these workflows rely on ensemble modeling (EM) principles for sampling and building populations of models describing observed physiologies. Sensitivity coefficients from metabolic control analysis (MCA) of kinetic models can provide important insight about cellular control around a given physiological steady state. However, despite considering populations of kinetic models and their model outputs, current approaches do not provide adequate tools for statistical inference. To derive conclusions from model outputs, such as MCA sensitivity coefficients, it is necessary to rank/compare populations of variables with each other. Currently existing workflows consider confidence intervals (CIs) that are derived independently for each comparable variable. Hence, it is important to derive simultaneous CIs for the variables that we wish to rank/compare. Herein, we used an existing large-scale kinetic model of Escherichia Coli metabolism to present how univariate CIs can lead to incorrect conclusions, and we present a new workflow that applies three different multivariate statistical approaches. We use the Bonferroni and the exact normal methods to build symmetric CIs using the normality assumptions. We then suggest how bootstrapping can compute asymmetric CIs whilst relaxing this normality assumption. We conclude that the Bonferroni and the exact normal methods can provide simple and efficient ways for constructing reliable CIs, with the exact normal method favored over the Bonferroni when the compared variables present dependencies. Bootstrapping, despite its significantly higher computational cost, is recommended when comparing non-normal distributions of variables. Additionally, we show how the Bonferroni method can readily be used to estimate required sample numbers to attain a certain CI size.

Dataset Information

The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

Publications

The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

Similar Datasets

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