Multi-scale biophysical modeling of fungal colony growth

Fungal colony growth is shaped by the fundamental physical operating principles of hyphal elongation, branching, and anastomosis, which collectively organize into macroscopic foraging networks. While sophisticated 3D models utilizing adaptive mesh refinement (AMR) on high-performance computing architectures can explicitly capture these discrete cellular mechanics, their immense computational cost prevents their integration into predictive ecosystem simulators. Here, building upon the Biological Modeling and interface eXchange (BMX) framework, we combine high-fidelity discrete hyphal mechanics with an analytically tractable, stochastic traveling-wave surrogate (sBARE) to provide multiscale simulations of fungal colonies at a fraction of the computational cost. By leveraging demographic fluctuations at the advancing front, our framework uniquely resolves macroscopic parameter degeneracies, separating the directed forward drift of leading tips from their effective diffusion to capture the macroscopic signature of negative autotropism in 3D networks. Simulations reproduce experimentally observed traveling wave profiles and confirm that interior network density under replete conditions emerges as an invariant self-regulated by fusion. Furthermore, global sensitivity analysis reveals that expansion speed and network density are governed by largely disjoint microscopic parameters. We demonstrate that because the physics of hyphal growth permit networks that are both exceptionally fast and dense, the empirical trade-off between sparse 'explorer' and dense 'exploiter' strategies observed in nature is not a strict mechanical constraint, pointing instead to metabolic limits on local growth rules. Our mathematically tractable approach bridges exascale-level cellular mechanics with macroscopic wave dynamics, enabling the integration of trait-driven advective fluxes and carrying capacities into the spatial transport and reaction network schemes of large-scale biogeochemical models.