Theory of antiparallel microtubule overlap stabilization by motors and diffusible crosslinkers

Abstract

Antiparallel microtubule bundles are essential structural elements of many cytoskeletal structures, for instance, the mitotic spindle. Sliding of microtubules relative to each other can lead to an overall elongation of the bundle. However, such sliding must be accompanied by microtubule growth, to maintain the overlap, which is a landmark of anaphase. Diffusive crosslinkers of the Ase1/PRC1/MAP65 family are able to form stable overlaps in combination with kinesin‐14 motors. This process is thought to arise through a balance of forces between motors and crosslinkers, the latter effectively producing an entropic pressure. We provide a continuous theory to explain the formation of stable overlaps, in which steric effects caused by the finite number of binding sites available on the microtubule lattice play a leading role. We confirmed the validity of this approach using discrete stochastic simulations performed with the Open Source simulation engine Cytosim. From the densities of motors and crosslinkers, their diffusion rates, and the velocities of motors, the theory predicts the sliding speed of microtubules and explains the force production and breaking effect of crosslinkers and motors containing diffusible microtubule‐binding domains. Finally, we discuss a mechanism by which sliding and microtubule growth can be coordinated without the need for fine‐tuning the parameters of the system, in line with the known robustness of mitosis.

Cross-linker design determines microtubule network organization by opposing motors

“…When the motor is not bound, the force is null and the diffusible subunit undergoes unbiased diffusion. However, when the motor is bound, the force would bias the plus and minus end-directed hopping rates in a thermodynamically consistent manner, as described previously (49,50). Unlike KIF11 motor units, the HSET motor unit only binds transiently to a microtubule, taking on average two steps before unbinding.…”

Active Bending of Disordered Microtubule Bundles by Kinesin Motors

“…We also observed that a small kinesin cluster population exists that shows a reversal in the direction of motion, for instance, due to the detachment from a filament and the reattachement to another microtubule with opposite polarity in the bundle. By elucidating the microtubule bundle dynamics, our study contributes to the understanding of active bundles that accomplish many vital functions in the cell, for instance, the formation of mitotic spindles . Furthermore, the understanding of isolated active bundles is a prerequisite for studying synthetic active networks with a dynamics frequently driven by extensile microtubule bundles. ,, …”

“…By elucidating the microtubule bundle dynamics, our study contributes to the understanding of active bundles that accomplish many vital functions in the cell, for instance, the formation of mitotic spindles. 38 Furthermore, the understanding of isolated active bundles is a prerequisite for studying synthetic active networks with a dynamics frequently driven by extensile microtubule bundles. 8,14,15 ■ ASSOCIATED CONTENT * sı Supporting Information…”

Micron-scale geometrical features of microtubules as regulators of microtubule organization

“…In vitro studies have shown that Ase1p resists motor forces by producing a braking force that increases as motor-mediated sliding progresses ( Figure 3(ii) ; Janson et al, 2007 ; Braun et al, 2011 ). Mechanistically, this has been explained by drawing an analogy to confined gas molecules which exert entropic forces to minimize density by maximizing containment volume ( Braun et al, 2011 ; Lera-Ramirez and Nédélec, 2019 ; Braun et al, 2016 ). In the absence of an external force, Ase1p molecules undergo one-dimensional diffusion within a microtubule overlap zone and can exert forces to minimize their density and maximize the overlap length.…”