Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases

JOURNAL OF THEORETICAL BIOLOGY

卷:372

Article

Chou, Tom^1,2  Wang, Yu³ 

[1] Univ Calif Los Angeles, Dept Biomath, Los Angeles, CA 90095 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] Xi An Jiao Tong Univ, Inst Informat & Syst Sci, Xian 710049, Peoples R China

关键词: Stochastic evolution;    Bellman-Harris branching process;   

DOI  :  10.1016/j.jtbi.2015.02.021

来源: Elsevier

【 摘 要 】

Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or fitness landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a wild-type state to a given terminally differentiated, resistant, or cancerous state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be nonlinear (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times. Published by Elsevier Ltd.

【 授权许可】

Free