Motor protein accumulation on antiparallel microtubule overlaps

Biopolymers serve as one-dimensional tracks on which motor proteins move to perform their biological roles. Motor protein phenomena have inspired theoretical models of one-dimensional transport, crowding, and jamming. Experiments studying the motion of Xklp1 motors on reconstituted antiparallel microtubule overlaps demonstrated that motors recruited to the overlap walk toward the plus end of individual microtubules and frequently switch between filaments. We study a model of this system that couples the totally asymmetric simple exclusion process (TASEP) for motor motion with switches between antiparallel filaments and binding kinetics. We determine steady-state motor density profiles for fixed-length overlaps using exact and approximate solutions of the continuum differential equations and compare to kinetic Monte Carlo simulations. Overlap motor density profiles and motor trajectories resemble experimental measurements. The phase diagram of the model is similar to the single-filament case for low switching rate, while for high switching rate we find a new low density-high density-low density-high density phase. The overlap center region, far from the overlap ends, has a constant motor density as one would naively expect. However, rather than following a simple binding equilibrium, the center motor density depends on total overlap length, motor speed, and motor switching rate. The size of the crowded boundary layer near the overlap ends is also dependent on the overlap length and switching rate in addition to the motor speed and bulk concentration. The antiparallel microtubule overlap geometry may offer a previously unrecognized mechanism for biological regulation of protein concentration and consequent activity.

💡 Research Summary

In this paper the authors develop a quantitative theoretical framework to explain the accumulation of kinesin‑4 motor Xklp1 on antiparallel microtubule (MT) overlaps, a system that was experimentally characterized by Bieling, Telley, and Surrey (BTS). The experimental system consists of two MTs aligned in opposite polarity, cross‑linked by the protein PRC1, which concentrates Xklp1 within the overlap region. Motors bind to and unbind from the MT lattice, walk unidirectionally toward the plus end of each MT, and switch stochastically between the two filaments at a relatively high rate.

To capture these processes the authors construct a lattice model that combines three key ingredients: (i) a totally asymmetric simple exclusion process (TASEP) describing forward stepping with hard‑core exclusion, (ii) Langmuir kinetics for binding (rate k_on·c, where c is bulk motor concentration) and unbinding (rate k_off), and (iii) inter‑lane switching with rate s. The overlap is discretized into N sites; each site can be occupied on either the right‑oriented filament (R) or the left‑oriented filament (L). Boundary conditions are set by the influx α at the minus ends (motors entering the overlap from single‑MT regions) and the outflux β at the plus ends (motors leaving the overlap).

Summing the master equations over all sites yields a global binding constraint that relates the total number of bound motors to the Langmuir equilibrium density ρ_0 = k_on·c/(k_on·c + k_off) and to the boundary fluxes α and β. This constraint is the analogue of the zero‑current condition known from single‑lane TASEP with open boundaries, but now incorporates the additional contribution of binding/unbinding.

Taking the continuum limit and applying a mean‑field factorization leads to two coupled nonlinear differential equations for the steady‑state densities ρ_R(x) and ρ_L(x):

0 = (2ρ_R−1)∂_xρ_R + K_on(1−ρ_R) − K_offρ_R − Sρ_R + Sρ_L
0 = (1−2ρ_L)∂_xρ_L + K_on(1−ρ_L) − K_offρ_L + Sρ_R − Sρ_L

where K_on = k_on·c·L/v, K_off = k_off·L/v, and S = s·L/v are dimensionless parameters, and x∈