Engineering microbial consortia is an important new frontier for synthetic biology given its efficiency in performing complex tasks and endurance to environmental uncertainty. Most synthetic circuits regulate population level behaviors via cell-to-cell communications, which are affected by spatially heterogeneous environments. Therefore, it is important to understand the limits on controlling system dynamics that are determined by interconnections among cell agents and provide a control strategy for engineering consortia. Here, we build a network model for a fractional population control circuit in two-strain consortia, and characterize the cell-to-cell communication network by topological properties, such as symmetry, locality and connectivity. Using linear network control theory, we relate the network topology to system output tracking performance. We analytically and numerically demonstrate that the minimum network control energy for accurate tracking depends on locality difference between two cell populations and how strongly the controller node contributes to communication strength. To realize robust consortia, we can manipulate the communication network topology and construct strongly connected consortia by altering chemicals in environments. Our results ground the expected cell population dynamics in its spatially organized communication network, and inspire directions in cooperative control in microbial consortia.
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