An Integrative Approach for Modeling and Simulation of Heterocyst Pattern Formation in Cyanobacteria Filaments

Heterocyst differentiation in cyanobacteria filaments is one of the simplest examples of cellular differentiation and pattern formation in multicellular organisms. Despite of the many experimental studies addressing the evolution and sustainment of heterocyst patterns and the knowledge of the genetic circuit underlying the behavior of single cyanobacterium under nitrogen deprivation, there is still a theoretical gap connecting these two macroscopic and microscopic processes. As an attempt to shed light on this issue, here we explore heterocyst differentiation under the paradigm of systems biology. This framework allows us to formulate the essential dynamical ingredients of the genetic circuit of a single cyanobacterium into a set of differential equations describing the time evolution of the concentrations of the relevant molecular products. As a result, we are able to study the behavior of a single cyanobacterium under different external conditions, emulating nitrogen deprivation, and simulate the dynamics of cyanobacteria filaments by coupling their respective genetic circuits via molecular diffusion. These two ingredients allow us to understand the principles by which heterocyst patterns can be generated and sustained. In particular, our results point out that, by including both diffusion and noisy external conditions in the computational model, it is possible to reproduce the main features of the formation and sustainment of heterocyst patterns in cyanobacteria filaments as observed experimentally. Finally, we discuss the validity and possible improvements of the model.

蓝细菌（cyanobacteria）丝状体中的异形胞（heterocyst）分化，是多细胞生物细胞分化与模式形成的最简范例之一。尽管已有诸多实验研究探讨异形胞模式的演化与维持机制，且学界已明晰氮剥夺（nitrogen deprivation）条件下单株蓝细菌行为背后的遗传回路（genetic circuit），但连接宏观与微观两类过程的理论空白仍未填补。
为阐明这一问题，本文基于系统生物学（systems biology）范式开展异形胞分化相关研究。该框架可将单株蓝细菌遗传回路的核心动力学要素，转化为一组描述相关分子产物浓度随时间演化的微分方程。借此，我们可在不同外部条件下（模拟氮剥夺环境）研究单株蓝细菌的行为，并通过分子扩散（molecular diffusion）耦合各蓝细菌的遗传回路，以此模拟蓝细菌丝状体的动力学过程。
通过这两项核心要素，我们得以解析异形胞模式形成与维持的内在原理。尤为关键的是，本研究结果表明：若在计算模型中纳入扩散效应与含噪声的外部环境条件，即可复现实验中观测到的蓝细菌丝状体异形胞模式形成与维持的核心特征。最后，本文对该模型的有效性及潜在优化方向展开讨论。