Bradde Serena, Vucelja Marija, Teşileanu Tiberiu, Balasubramanian Vijay
Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York, United States of America.
David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America.
PLoS Comput Biol. 2017 Apr 17;13(4):e1005486. doi: 10.1371/journal.pcbi.1005486. eCollection 2017 Apr.
The CRISPR (clustered regularly interspaced short palindromic repeats) mechanism allows bacteria to adaptively defend against phages by acquiring short genomic sequences (spacers) that target specific sequences in the viral genome. We propose a population dynamical model where immunity can be both acquired and lost. The model predicts regimes where bacterial and phage populations can co-exist, others where the populations exhibit damped oscillations, and still others where one population is driven to extinction. Our model considers two key parameters: (1) ease of acquisition and (2) spacer effectiveness in conferring immunity. Analytical calculations and numerical simulations show that if spacers differ mainly in ease of acquisition, or if the probability of acquiring them is sufficiently high, bacteria develop a diverse population of spacers. On the other hand, if spacers differ mainly in their effectiveness, their final distribution will be highly peaked, akin to a "winner-take-all" scenario, leading to a specialized spacer distribution. Bacteria can interpolate between these limiting behaviors by actively tuning their overall acquisition probability.
CRISPR（成簇规律间隔短回文重复序列）机制使细菌能够通过获取靶向病毒基因组中特定序列的短基因组序列（间隔序列）来适应性地抵御噬菌体。我们提出了一个种群动力学模型，其中免疫既能获得也会丧失。该模型预测了细菌和噬菌体种群可以共存的状态，还有种群呈现阻尼振荡的状态，以及另一些种群中一个种群被驱向灭绝的状态。我们的模型考虑两个关键参数：（1）获取的难易程度和（2）间隔序列赋予免疫的有效性。分析计算和数值模拟表明，如果间隔序列主要在获取难易程度上存在差异，或者获取它们的概率足够高，细菌会形成多样化的间隔序列群体。另一方面，如果间隔序列主要在其有效性上存在差异，它们的最终分布将高度集中，类似于“赢家通吃”的情形，导致形成专门化的间隔序列分布。细菌可以通过主动调整其总体获取概率在这些极限行为之间进行插值。
