Generalized exclusion processes in biological transport: interference, crowding, and search dynamics

Exclusion processes provide a minimal framework for understanding nonequilibrium transport in biological systems, where molecular machines operate under crowded and interacting conditions. In this mini-review, we discuss recent extensions of the totally asymmetric simple exclusion process that incorporate key features of intracellular transport, including multi-species interactions, competing processes on shared tracks, stochastic search, and multi-lane dynamics. Particular emphasis is placed on three interconnected themes: interference between distinct agents, crowding-induced modification of transport and search dynamics, and adaptive redistribution of particles across parallel pathways. These generalized models reveal that simple exclusion-based interactions can give rise to rich collective phenomena such as switch-like regulation of flux, effective rectification of diffusion, and nontrivial spatial organization. In addition, they highlight how crowding can both hinder and enhance transport, leading to optimal regimes of efficiency. Together, these results provide a unified perspective on how local stochastic rules generate emergent behavior in driven biological systems. The insights reviewed here point toward the importance of incorporating interactions, fluctuations, and adaptability in developing realistic models of intracellular transport.