On the Road Again: How the $N$-Lane TASEP and Local Reservoirs Drive Jamming in Axonal Transport
Intracellular transport by molecular motors along microtubules is essential for cellular function, particularly in neuronal axons where track disruption drives neurodegenerative disease. We develop an \(N\)-track totally asymmetric simple exclusion process (TASEP) model where motors reversibly detach into local off-track states. Using mean-field, continuum, and fast-switching approximations, we derive an effective nonlinear transport equation for total motor density. This reduced model retains the classical TASEP phase structure but reveals that increasing \(N\) shifts the boundaries between low-density, high-density, and maximal-current regimes. Crucially, under source-driven boundary conditions reflecting constant cargo production, the entrance density undergoes a saddle-node bifurcation when the production rate exceeds the network's transport capacity, \(N/4\). This triggers persistent cargo accumulation that propagates throughout the domain. Our results establish a physical mechanism by which gradual microtubule degradation drives a transition from efficient transport to jammed pathological states.