Abedon Stephen T, Katsaounis Tena I
Department of Microbiology, The Ohio State University, 299 Bromfield, Columbus, OH, 43210, USA.
Department of Mathematics, The Ohio State University, Columbus, OH, USA.
Methods Mol Biol. 2018;1681:3-30. doi: 10.1007/978-1-4939-7343-9_1.
Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.
基本的数学描述在噬菌体生态学、应用噬菌体生态学（如在噬菌体治疗过程中）中很有用，并且对于追踪在实验室操作噬菌体时所观察到的预期噬菌体 - 细菌相互作用也很有帮助。噬菌体最基本的数学描述指标是其滴度，即它们在储存液、实验容器或其他环境中的浓度。各种现象都可能改变噬菌体滴度，实际上，噬菌体滴度会因测量方式的不同而有所变化。滴度变化如何发生的一个重要方面源于噬菌体与细菌的相互作用。这些变化的程度往往会随着环境中细菌密度的变化而变化，特别是那些对特定噬菌体类型敏感或至少可被其吸附的细菌的密度。使用简单的数学模型可以描述特别是导致噬菌体吸附事件的噬菌体 - 细菌相互作用。进一步细化，可以将噬菌体和细菌密度的变化视为时间以及这些相互作用的函数。此外，噬菌体及其对细菌的影响可以被视为受空间限制的过程。在本章中，我们将考虑这些概念中较为简单的部分，特别提供详细的文字解释以便于获得数学见解。主要目标是促进在实验室中更明智地使用和操控噬菌体及噬菌体群体，以及在实验室之外更有效地应用噬菌体，例如在噬菌体治疗期间。更一般地说，我们还会考虑噬菌体定量的众多问题和方法，以及噬菌体个体、生态和应用特性的定量。
