Abstract
Individual-based modeling (IbM) has emerged as a powerful approach for studying microbial populations, offering a bottom-up framework to simulate cellular behaviors and their interactions. Unlike continuum-based models, IbM explicitly captures the heterogeneity and emergent dynamics of microbial communities, making it invaluable for studying spatially structured phenomena such as nutrient competition, biofilm formation, and colony interactions. However, IbM faces significant computational challenges, particularly in resolving spatial overlaps during simulations of large microbial populations. Traditional approaches, such as pairwise comparisons or kd-trees, are computationally expensive and scale poorly with population size. The Discretized Overlap Resolution Algorithm (DORA) introduces a novel grid-based solution to overcome these limitations. By encoding spatial information into an occupancy matrix, DORA achieves a time complexity of O(N), enabling efficient resolution of overlaps while maintaining spatial fidelity. To validate its capabilities, we applied DORA to a case study of microbial colony merging. Two scenarios were tested: (1) colonies inoculated 40 µm apart merged at the center due to nutrient depletion, and (2) colonies inoculated 120 µm apart remained separate, with a no-growth zone forming between them. In both cases, DORA replicated observed phenomena with high accuracy and demonstrated linear scalability, significantly reducing simulation time compared to traditional methods. DORA's computational efficiency and scalability position it as a robust tool for large-scale IbM simulations, advancing our ability to study complex microbial systems in diverse ecological and industrial contexts.