Table of markov transition probabilities.

During fertilization, mammalian sperm undergo a winnowing selection process that reduces the candidate pool of potential fertilizers from ~106-1011 cells to 101-102 cells (depending on the species). Classical sperm competition theory addresses the positive or ‘stabilizing’ selection acting on sperm phenotypes within populations of organisms but does not strictly address the developmental consequences of sperm traits among individual organisms that are under purifying selection during fertilization. It is the latter that is of utmost concern for improving assisted reproductive technologies (ART) because low-fitness sperm may be inadvertently used for fertilization during interventions that rely heavily on artificial sperm selection, such as intracytoplasmic sperm injection (ICSI). Importantly, some form of sperm selection is used in nearly all forms of ART (e.g., differential centrifugation, swim-up, or hyaluronan binding assays, etc.). To date, there is no unifying quantitative framework (i.e., theory of sperm selection) that synthesizes causal mechanisms of selection with observed natural variation in individual sperm traits. In this report, we reframe the physiological function of sperm as a collective diffusive search process and develop multi-scale computational models to explore the causal dynamics that constrain sperm fitness during fertilization. Several experimentally useful concepts are developed, including a probabilistic measure of sperm fitness as well as an information theoretic measure of the magnitude of sperm selection, each of which are assessed under systematic increases in microenvironmental selective pressure acting on sperm motility patterns.

在受精过程中，哺乳动物精子会经历一轮筛选淘汰过程，将潜在受精者的候选池从约10^6至10^11个细胞缩减至10^1至10^2个细胞（具体数值因物种而异）。经典精子竞争理论探讨的是作用于生物种群内精子表型的正向选择或"稳定化选择"，但并未严格阐明受精过程中经历纯化选择的个体生物的精子性状所带来的发育后果。而后者正是辅助生殖技术（assisted reproductive technologies, ART）改良过程中最受关注的问题：因为在高度依赖人工精子筛选的辅助生殖干预手段（如卵胞浆内单精子注射（intracytoplasmic sperm injection, ICSI））中，低适配度的精子可能被意外用于受精。值得注意的是，几乎所有类型的辅助生殖技术都会采用某种形式的精子筛选手段（例如差速离心、上游法、透明质酸结合实验等）。迄今为止，尚未存在一个统一的量化框架（即精子选择理论），能够将选择的因果机制与个体精子性状的自然观测变异相结合。本研究将精子的生理功能重新定义为一种集体扩散搜索过程，并构建多尺度计算模型，以探究受精过程中制约精子适配度的因果动力学机制。本研究提出了多个具备实验应用价值的概念，包括精子适配度的概率性度量指标，以及衡量精子选择强度的信息论度量指标；上述指标均通过系统性递增作用于精子运动模式的微环境选择压力进行评估。