Universality of stable multi-cluster periodic solutions in a population model of the cell cycle with negative feedback.

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Kiattisak Prathom, Todd R Young
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引用次数: 0

Abstract

We study a population model where cells in one part of the cell cycle may affect the progress of cells in another part. If the influence, or feedback, from one part to another is negative, simulations of the model almost always result in multiple temporal clusters formed by groups of cells. We study regions in parameter space where periodic 'k-cyclic' solutions are stable. The regions of stability coincide with sub-triangles on which certain events occur in a fixed order. For boundary sub-triangles with order 'rs1', we prove that the k-cyclic periodic solution is asymptotically stable if the index of the sub-triangle is relatively prime with respect to the number of clusters k and neutrally stable otherwise. For negative linear feedback, we prove that the interior of the parameter set is covered by stable sub-triangles, i.e. a stable k-cyclic solution always exists for some k. We observe numerically that the result also holds for many forms of nonlinear feedback, but may break down in extreme cases.

负反馈细胞周期种群模型中稳定多簇周期解的通用性。
我们研究了一个群体模型,其中细胞周期的一部分细胞可能影响另一部分细胞的进展。如果从一个部分到另一个部分的影响或反馈是负的,则模型的模拟几乎总是导致由细胞群形成的多个时间簇。我们研究了参数空间中周期“k-循环”解稳定的区域。稳定区域与子三角形重合,在这些子三角形上某些事件以固定的顺序发生。对于阶为'rs1'的边界子三角形,证明了如果子三角形的指数相对于簇k的数目是相对素数,则k循环周期解是渐近稳定的,否则证明了k循环周期解是中性稳定的。对于负线性反馈,我们证明了参数集的内部被稳定的子三角形覆盖,即对于某个k,一个稳定的k循环解总是存在。我们在数值上观察到,该结果也适用于许多形式的非线性反馈,但在极端情况下可能会失效。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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