Motor Protein Accumulation on Antiparallel Microtubule Overlaps

Abstract

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 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 (to our knowledge) 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 naïvely 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.

Geometry of antiparallel microtubule bundles regulates relative sliding and stalling by PRC1 and Kif4A

“…At the nanometer length-scale, numerous tubulin isotypes and post-11 translational modifications on tubulin act as a code to tune the activity of microtubule 12 associated proteins (MAPs) [7][8][9][10]. In addition, it is becoming apparent that at the 13 micron length-scale, the geometrical properties of microtubule bundles, such as 14 orientation, filament length and overlap length, also modulate the output of motor and 15 non-motor proteins [11][12][13]. Currently, we have a limited understanding of the 16 mechanisms by which the micron-sized features of a microtubule network are 'read' and 17 'translated' by associated proteins.…”

Theory of microtubule length regulation in antiparallel overlaps

“…Here we develop a theory of overlap length regulation induced by motor proteins that shorten MTs at their plus-ends, inspired by Bieling and Surrey's experiments [23]. In our model, motors bind to and unbind from sites on the overlap, step toward the MT plus-end (if not sterically blocked by another motor), and switch between filaments [34,35] A steady state is reached when the average number of motors entering the overlap equals the number leaving. The steady-state overlap length therefore depends on motor density at MT plus-ends, which can be described by balancing the inward and outward fluxes at the ends [10,11] or by a total binding constraint [34,35].…”

“…In our model, motors bind to and unbind from sites on the overlap, step toward the MT plus-end (if not sterically blocked by another motor), and switch between filaments [34,35] A steady state is reached when the average number of motors entering the overlap equals the number leaving. The steady-state overlap length therefore depends on motor density at MT plus-ends, which can be described by balancing the inward and outward fluxes at the ends [10,11] or by a total binding constraint [34,35]. Since the motor exit rate depends on microtubule shrinking, higher bulk motor concentration leads to shorter overlap length.…”

“…Each site i on each MT can be occupied by a motor (τ i = 1) or empty (τ i = 0). Motors in the overlap step and are sterically excluded in a totally asymmetric exclusion process (TASEP), bind and unbind according to Langmuir kinetics (LK), and switch MTs [23,34,35]. For simplicity, we normalize rates by the motor speed, so the stepping rate is 1.…”

“…where i labels the site on the filament, R, L label the orientation of the MT, k on c is the normalized motor binding rate, k off the unbinding rate, and s the switching rate. Parameter values were estimated from previous measurements [23] or comparison of our simulations to the data [34] (table S1 [44]).…”