Decoding pattern formation rules by integrating mechanistic modeling and deep learning

Predictive programming of self-organized pattern formation using living cells is challenging in major part due to the difficulty in navigating through the high-dimensional design space effectively. The emergence and characteristics of patterns are highly sensitive to both system and environmental parameters. Often, the optimal conditions able to generate patterns represent a small fraction of the possible design space. Furthermore, the experimental generation and quantification of patterns is typically labor intensive and low throughput, making it impractical to optimize pattern formation solely based on trials and errors. To this end, simulations using a well-formulated mechanistic model can facilitate the identification of optimal experimental conditions for pattern formation. However, even a moderately complex system can make these simulations computationally prohibitive when applied to a large parameter space. In this study, we demonstrate how integrating mechanistic modeling with machine learning can significantly accelerate the exploration of design space for patterning circuits and aid in deriving human-interpretable design rules. We apply this strategy to program self-organized ring patterns in Pseudomonas aeruginosa using a synthetic gene circuit. Our approach involved training a neural network with simulated data to predict pattern formation 10 million times faster than the mechanistic model. This neural network was then used to predict pattern formation across a vast array of parameter combinations, far exceeding the size of the training dataset and what was computationally feasible using the mechanistic model alone. By doing so, we identified many parameter combinations able to generate desirable patterns, which still represent an extremely small fraction of explored parametric space. We next used the mechanistic model to validate top candidates and identify coarse-grained rules for patterning. We experimentally demonstrated the generation and control of patterning guided by the learned rules. Our work highlights the effectiveness in integrating mechanistic modeling and machine learning for rational engineering of complex dynamics in living cells.