Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions.
Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions.
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DOI：
10.1098/rspa.2015.0050
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发表时间：
2015-08-08
期刊：
影响因子：
--
通讯作者：
Jones NS
中科院分区：
文献类型：
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作者：
Johnston IG;Jones NS
随机动力学支配着细胞生物学中的许多重要过程，描述这些动力学的基本理论方法对于解决生物学和医学中的大量问题是可取的。数学工具存在治疗这些随机过程的几个重要例子，最显着的基因表达和随机分配在单细胞分裂或达到稳定状态后。相对较少的工作存在探索不同的和具体的方式，重复的细胞分裂可以导致不平衡的细胞群体的随机遗传。在这里，我们介绍了一个数学形式主义来描述细胞代理，随机创建，复制和/或降解，并继承根据一系列的随机动态在细胞分裂。我们得到封闭形式的生成函数描述系统在任何时间后，任何数量的细胞分裂二项式分区和分裂挑起一个确定性或随机，减法或加法的变化拷贝数，并表明这些解决方案完全同意随机模拟。我们将这种一般形式主义的几个例子的问题，涉及线粒体DNA在发展和生物体的生命周期的动态。
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes.