Stall force of polymerizing microtubules and filament bundles

We investigate stall force and polymerization kinetics of rigid protofilaments in a microtubule or interacting filaments in bundles under an external load force in the framework of a discrete growth model. We introduce the concecpt of polymerization cycles to describe the stochastic growth kinetics, which allows us to derive an exact expression for the stall force. We find that the stall force is independent of ensemble geometry and load distribution. Furthermore, the stall force is proportional to the number of filaments and increases linearly with the strength of lateral filament interactions. These results are corroborated by simulations, which also show a strong influence of ensemble geometry on growth kinetics below the stall force.

💡 Research Summary

This paper presents a rigorous theoretical and computational study of the stall force and polymerization kinetics of rigid protofilaments (PFs) in microtubules (MTs) or interacting filaments in bundles when they grow against an external load. The authors formulate a discrete stochastic growth model in which each filament consists of monomers of size d (tubulin dimers for MTs or actin monomers for bundles). Attachment and detachment occur with rates k_on and k_off that satisfy the detailed‑balance condition k_on/k_off = exp(E_p/k_BT), where E_p is the free‑energy gain per added monomer. In addition to the longitudinal polymerization energy, neighboring PFs experience an attractive lateral interaction energy ε_l per unit of contact length. When a monomer is added, the leading PF advances by Δx and creates an extra lateral contact length Δℓ; removal reverses these changes.

To keep the model thermodynamically consistent under load, the authors introduce load‑distribution (θ_F) and lateral‑energy‑distribution (θ_l) factors that allocate the mechanical work F·Δx and the lateral energy ε_l·Δℓ between the forward (attachment) and reverse (detachment) rates. The resulting modified rates are

k*_on = k_on exp