自走杆排列的波尔兹曼型模型分解。

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-08 DOI:10.1016/j.mbs.2024.109266
Patrick Murphy , Misha Perepelitsa , Ilya Timofeyev , Matan Lieber-Kotz , Brandon Islas , Oleg A. Igoshin
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引用次数: 0

摘要

对生物体集体运动的研究采用了一系列分析方法,从描述个体相互作用的规则或方程出发,建立集体动力学的连续动力学模型。然而,这些动力学模型的推导通常依赖于玻尔兹曼的 "分子混沌 "假设,即假设个体之间的相关性是短暂的。虽然这一假设通常是推导可控模型的最简单方法,但由于生物系统中存在高度的合作和自组织,这一假设在实践中往往并不成立。在这项工作中,我们通过考虑自走棒排列的一般玻尔兹曼型动力学模型来说明这一点。我们通过比较连续方程的数值解与基于代理的模型(该模型实现了微观配准的基本规则),检验了动力学模型的准确性。即使是在最简单的情况下,我们的比较也表明,动力学模型无法复制离散动力学,原因是杆簇的形成违反了统计独立性。此外,我们还表明,引入噪声来限制簇的形成有助于改善分析模型与代理模拟之间的一致性,但并不能完全恢复一致性。这些结果凸显了开发和推广用于生物和活性物质系统建模的改进型矩封闭方法的必要性。
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Breakdown of Boltzmann-type models for the alignment of self-propelled rods

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann’s “molecular chaos” hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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