Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae

• We model transport of early endosomes by kinesin and dynein on microtubules (MT).
• Quasi-steady state reduction to a Fokker–Plank equation is solvable in closed form.
• We relate bulk diffusion-advection rates to motor speeds and state transition rates.
• MT polarity and motor competition bias cargo density (towards cell ends or centre).
• Motor mutations (kin-ts, dyn-ts) are linked to changes in motor/cargo distributions.

We consider bidirectional transport of cargo by molecular motors dynein and kinesin that walk along microtubules, and/or diffuse in the cell. The motors compete to transport cargo in opposite directions with respect to microtubule polarity (towards the plus or minus end of the microtubule). In recent work, Gou et al. (2014) used a hierarchical set of models, each consisting of continuum transport equations to track the evolution of motors and their cargo (early endosomes) in the specific case of the fungus Ustilago maydis. We complement their work using a framework of quasi-steady state analysis developed by Newby and Bressloff (2010) and Bressloff and Newby (2013) to reduce the models to an approximating steady state Fokker–Plank equation. This analysis allows us to find analytic approximations to the steady state solutions in many cases where the full models are not easily solved. Consequently, we can make predictions about parameter dependence of the resulting spatial distributions. We also characterize the overall rates of bulk transport and diffusion, and how these are related to state transition parameters, motor speeds, microtubule polarity distribution, and specific assumptions made.