Physics-Informed Neural Network Framework for Time-Dependent Modelling of Bacterial Quorum Sensing and Population Dynamics

In silico studies of microbiological systems are essential for predicting and controlling the impact of external factors on bacterial communities. Quorum sensing represents one of the key mechanisms of bacterial communication, particularly in pathogenic bacteria, realized as a cell-density-dependent regulatory process governed by diffusible signaling molecules. The present study proposes a Physics-Informed Neural Network (PINN)-based computational framework for a spatially independent model of bacterial quorum sensing and population dynamics. The approach solves both the forward and inverse problems for a spatially independent model formalized by a system of nonlinear ordinary differential equations. The forward problem is solved numerically by reconstructing the dynamics of three key characteristics: signaling molecule concentration, degrading enzyme concentration, and bacterial biomass density. The obtained PINN solutions are compared with numerical solutions computed using the Radau IIA implicit Runge–Kutta method. The inverse problem capability is evaluated by recovering system parameters that are difficult to measure directly in experimental settings. The framework is implemented using the DeepXDE library with a PyTorch backend, employing hard constraints for initial conditions, singularity-avoiding loss reformulations, and a multi-stage Adam–L-BFGS optimization strategy. Validation is performed on a Monod chemostat benchmark and the Pseudomonas putida IsoF quorum sensing regulatory network. The proposed PINN-based framework extends the applied mathematical toolkit for in silico studies of microbial systems, enabling accurate reconstruction of emergent population dynamics and robust inference of regulatory parameters that are inaccessible to direct experimental measurement.