A spatial measure-valued model for chemical reaction networks in heterogeneous systems

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1904
Lea Popovic, Amandine Veber
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引用次数: 3

Abstract

We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the process, with appropriate rescaling depending on the abundance of different molecular types. In particular, when the mass of some species in the scaling limit is discrete while the mass of the others is continuous, we obtain a new type of spatial random evolution process. This process can be shown, in some situations, to correspond to a measure-valued piecewise deterministic Markov process in which the discrete mass of the process evolves stochastically, and the continuous mass evolves in a deterministic way between consecutive jump times of the discrete part.
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非均相系统中化学反应网络的空间测度值模型
我们提出了一种新的测量值过程,该过程模拟了空间异构系统中化学反应网络的行为。它模拟了不同分子种类之间的反应动力学和分子在空间中的连续运动。在一个空间位置上的反应速率与当地存在的不同物种的质量成正比,也与特定位置的化学速率成正比,这也可能是当地或全球物种质量的函数。我们获得了该过程的渐近极限,并根据不同分子类型的丰度进行了适当的重新缩放。特别是当尺度极限内某些物种的质量是离散的,而其他物种的质量是连续的时,我们得到了一种新型的空间随机演化过程。在某些情况下,这一过程可以被证明对应于一个测量值分段确定性马尔可夫过程,在这个过程中,过程的离散质量是随机演变的,而连续质量在离散部分的连续跳跃时间之间以确定性的方式演变。
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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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