Chlamydia trachomatis 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.

中文翻译：

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沙眼衣原体的最佳增殖与分化

沙眼衣原体是一种导致人类眼部感染和失明的细菌。它有一个不寻常的生命周期，涉及两种发育形式。在细胞质包涵体中，网状体 (RB) 通过二元裂变反复分裂并异步分化为传染性基本体 (EB)。在宿主许多此类内含物的哺乳动物细胞死亡后，只有 EB 形式的细菌存活并继续感染其他细胞。考虑到细菌的快速传播感染，传统观点会将少数初始 EB 转变为 RB，首先分裂和增殖，然后最终开始转化，以便在宿主细胞裂解时最大化终端 EB 种群。几种生物过程被视为实施这种转化策略的可能机制。然而，在分化开始之前有一段增殖期而没有转化的本能策略的最优性从未在理论上得到证实或在数学上得到证实。本文制定了三个相对简单的模型，它们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小 EB 群体的内吞作用引起时，最大原则要求这些模型采用最佳转化策略，以确认并严格证明早期不转化的流行观点宿主细胞感染。然而，发现传统假设不适用于接近或高于承载能力的初始 EB（-to-RB）种群。