Intracellular transport relies on the collective behavior of molecular motors, such as Kinesin-II, which must navigate crowded microtubule environments efficiently. While standard exclusion models like the Totally Asymmetric Simple Exclusion Process (TASEP) predict significant velocity reduction at high densities, Kinesin-II exhibits resilience to crowding, suggesting a mechanism of cooperative transport that remains poorly understood in both physical and mathematical theory.

This thesis addresses this gap by combining a rigorous mathematical derivation of hydrodynamic limits with a biologically motivated particle model. Mathematically, we derive the hydrodynamic limit for an active particle system where the active direction of the particles is governed by mean-field Curie-Weiss rates with parameter β for both local and global interactions. We prove that the microscopic stochastic dynamics converge to a macroscopic reaction-diffusion-advection PDE. Through linearization and Fourier-Laplace analysis, we
derive analytical expressions for the velocity and diffusion coefficients, showing significant dependence on β.

Physically, we extend this framework to include exclusion and different interaction ranges σ. Our simulations reveal that exclusion introduces spatial correlation that breaks mean-field assumptions, leading to deviations from the predictions for the global transport coefficients.
We show that for strong coupling β > 1, local interactions lead to the formation of clusters and altered relaxation times. Finally, we validate our model against experimental velocity-density data for Kinesin-II. We show that our mean-field exclusion model provides a statistically more accurate description compared to the standard TASEP-LK model.
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