Wan Frederic Y M, Enciso Germán A
Department of Mathematics, University of California, Irvine, CA 92697.
Stud Appl Math. 2017 Jul;139(1):129-178. doi: 10.1111/sapm.12175. Epub 2017 May 30.
is a bacterium that causes eye infection and blindness in humans. It has an unusual life cycle involving two developmental forms. Within a cytoplasmic inclusion, the reticulate body (RB) repeatedly divides by binary fission and asynchronously differentiates into the infectious elementary body (EB). Upon the death of the mammalian cell that host many such inclusions, only the EB form of the bacteria survive and proceed to infect other cells. Given the bacteria's fast spreading infection, conventional wisdom would have the few initial EB turn into RB, divide and proliferate first, and then eventually start converting in order to maximize the terminal EB population upon host cell lysis. Several biological processes are seen as possible mechanisms for implementing such a conversion strategy. However, the optimality of an instinctual strategy with a period of proliferate without conversion prior to the onset of differentiation has never been substantiated theoretically or justified mathematically. This paper formulates three relatively simple models that capture the essential features of the Chlamydia life cycle. When the initial infection is caused by the endocytosis of a small EB population well below the carrying capacity of the host cell, the Maximum Principle requires for these models an optimal conversion strategy that confirms and rigorously justifies the prevailing view of no conversion at the early stage of the host cell infection. However, the conventional supposition is found to be inappropriate for an initial EB (-to-RB) population near or above the carrying capacity. Previously suggested and new biological mechanisms are examined for their role in implementing the different optimal conversion strategies associated with models investigated herein.
是一种可导致人类眼部感染和失明的细菌。它具有不同寻常的生命周期，涉及两种发育形式。在细胞质内含物中，网状体（RB）通过二分裂反复分裂，并异步分化为具有感染性的原体（EB）。当宿主许多此类内含物的哺乳动物细胞死亡时，只有细菌的EB形式存活下来并继续感染其他细胞。鉴于这种细菌感染传播迅速，按照传统观点，最初少量的EB会先转变为RB，进行分裂和增殖，然后最终开始转变，以便在宿主细胞裂解时使最终的EB数量最大化。有几个生物学过程被视为实现这种转变策略的可能机制。然而，在分化开始之前存在一段不转变而增殖的本能策略的最优性，从未在理论上得到证实，也未在数学上得到论证。本文构建了三个相对简单的模型，这些模型捕捉了衣原体生命周期的基本特征。当初始感染是由远低于宿主细胞承载能力的少量EB群体通过内吞作用引起时，对于这些模型，最大值原理要求一种最优转变策略，该策略证实并严格论证了在宿主细胞感染早期不发生转变的普遍观点。然而，人们发现传统假设对于接近或高于承载能力的初始EB（从EB到RB）群体并不适用。本文研究了先前提出的以及新的生物学机制在实施与本文所研究模型相关的不同最优转变策略中所起的作用。
