反应网络中多平稳性和绝对浓度鲁棒性的普遍性

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Badal Joshi, Nidhi Kaihnsa, Tung D. Nguyen, Anne Shiu
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引用次数: 2

摘要

SIAM应用数学杂志,83卷,第6期,2260-2283页,2023年12月。摘要。对于系统生物学中产生的反应网络,具有两个或多个稳定状态的能力,即多平稳性,是生化开关的重要特性。另一个最近受到广泛关注的性质是绝对浓度鲁棒性(ACR),这意味着某些物种的浓度在所有正稳态下都是相同的。在这项工作中,我们调查了每个属性的普遍性,同时密切关注这些属性何时一起出现。具体来说,我们考虑了一个随机块框架来生成随机网络,并证明了边缘概率阈值,在该阈值下,多平稳性在高概率下出现,并且ACR变得罕见。我们还表明,两种性质同时出现的小窗口只出现在有许多物种的网络中。综上所述,我们的结果证实,在随机可逆网络中,ACR和多平稳性一起,甚至单独的ACR,都是非典型的。我们的证明依赖于两个先前的结果,一个与缺乏性为零的网络的普遍性有关,另一个将多平稳性从小型网络“提升”到大型网络。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prevalence of Multistationarity and Absolute Concentration Robustness in Reaction Networks
SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2260-2283, December 2023.
Abstract. For reaction networks arising in systems biology, the capacity for two or more steady states, that is, multistationarity, is an important property that underlies biochemical switches. Another property receiving much attention recently is absolute concentration robustness (ACR), which means that some species concentration is the same at all positive steady states. In this work, we investigate the prevalence of each property while paying close attention to when the properties occur together. Specifically, we consider a stochastic block framework for generating random networks and prove edge-probability thresholds at which, with high probability, multistationarity appears and ACR becomes rare. We also show that the small window in which both properties occur only appears in networks with many species. Taken together, our results confirm that, in random reversible networks, ACR and multistationarity together, or even ACR on its own, is highly atypical. Our proofs rely on two prior results, one pertaining to the prevalence of networks with deficiency zero and the other “lifting” multistationarity from small networks to larger ones.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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