Supplementary Material for: Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance

Opsonization and anaphylatoxin production are early events in the innate response to bacterial pathogens. Opsonization alone is frequently not lethal and production of anaphy-latoxins, especially C5a, allows for recruitment of cellular defenses. Complement biochemistry is extensively studied and computational models have been reported previously. However, a critical feature of complement-mediated attack is its spatial dependence: diffusion of mediators into and away from a bacterium is central to understanding C5a generation. Spatial dependence is especially important in biofilms, where diffusion limitation is crucial to bacterial counterdefense. Here we develop a model of opsonization and C5a production in the presence of a common blood-borne pathogen, <i>Staphylococcus epidermidis</i>. Our results indicate that when complement attacks a single cell, diffusion into the extracellular polymeric substance (EPS) is complete within 10 ms and that production of C5a peaks over the next 15 min. When longer diffusion lengths (as in an EPS-rich biofilm) are incorporated, diffusion limitation appears such that the intensity and duration of C5a production is increased. However, the amount of C5a produced under several likely clinical scenarios where single cells or sparse biofilms are present is below the k_D of the C5a receptor suggesting that complement activation by a single bacterium may be difficult to detect when diffusion is taken into account.

调理作用（opsonization）与过敏毒素（anaphylatoxin）生成是机体针对细菌病原体的固有免疫应答早期事件。仅依靠调理作用通常无法实现致死性杀伤，而过敏毒素——尤其是C5a——的生成可招募细胞防御机制。补体生化过程已得到广泛研究，此前亦有相关计算模型被报道。然而，补体介导的攻击存在一项关键特征：其空间依赖性（spatial dependence）——即介质向细菌周围扩散并远离细菌的过程，是解析C5a生成机制的核心环节。空间依赖性在生物被膜（biofilms）中尤为关键，此时扩散限制对细菌的对抗防御至关重要。
本研究针对常见血源性病原体表皮葡萄球菌（Staphylococcus epidermidis），构建了调理作用与C5a生成的计算模型。研究结果显示，当补体攻击单个细菌时，介质向细胞外聚合物（extracellular polymeric substance, EPS）的扩散可在10毫秒内完成，而C5a的生成量将在随后15分钟内达到峰值。当引入更长的扩散路径（如富含EPS的生物被膜场景）时，会出现扩散限制现象，使得C5a生成的强度与持续时间均有所提升。不过，在单个细菌或稀疏生物被膜等多种临床常见场景下，生成的C5a总量低于C5a受体（C5a receptor）的解离常数（K_D），这表明若考虑扩散效应，单个细菌引发的补体激活可能难以被检测到。