Modeling Subcellular Protein Recruitment Dynamics for Synthetic Biology

Compartmentalized protein recruitment is a fundamental feature of signal transduction. Accordingly, the cell cortex is a primary site of signaling supported by the recruitment of protein regulators to the plasma membrane. Recent emergence of optogenetic strategies designed to control localized protein recruitment has offered valuable toolsets for investigating spatiotemporal dynamics of associated signaling mechanisms. However, determining proper recruitment parameters is important for optimizing synthetic control. In this chapter, we describe a stepwise process for building linear differential equation models that characterize the kinetics and spatial distribution of optogenetic protein recruitment to the plasma membrane. Specifically, we outline how to construct (1) ordinary differential equations that capture the kinetics, efficiency, and magnitude of recruitment and (2) partial differential equations that model spatial recruitment dynamics and diffusion. Additionally, we explore how these models can be used to evaluate the overall system performance and determine how component parameters can be tuned to optimize synthetic recruitment.