A new cooperation mechanism of kinesin motors when extracting membrane tube

Membrane tubes are important elements for living cells to organize many functions. Experiments have found that membrane tube can be extracted from giant lipid vesicles by a group of kinesin. How these motors cooperate in extracting the fluid-like membrane tube is still unclear. In this paper, we propose a new cooperation mechanism called two-track-dumbbell model, in which kinesin is regarded as a dumbbell with an end (tail domain) tightly bound onto the fluid-like membrane and the other end (head domain) stepping on or unbinding from the microtubule. Taking account of the elasticity of kinesin molecule and the exclude volume effect of both the head domain and the tail domain of kinesin, which are not considered in previous models, we simulate the growth process of the membrane tube pulled by kinesin motors. Our results indicate that motors along a single microtubule protofilament can generate enough force to extract membrane tubes from vesicles, and the average number of motors pulling the tube is about 8~9. These results are quite different from previous studies (Ref. \cite{camp.08}), and further experimental tests are necessary to elucidate the cooperation mechanism.

💡 Research Summary

This paper addresses the long‑standing question of how a group of kinesin motors can collectively extract a fluid‑like membrane tube from a giant lipid vesicle, a process that requires forces (~27 pN) far exceeding the stall force of a single kinesin (~6–7 pN). Existing theoretical frameworks either treat the cargo as a rigid or simple elastic object, or assume that only the leading motor can apply force, both of which fail to explain the experimentally observed tube extraction. Campàs et al. (2017) proposed that three microtubule protofilaments act simultaneously, but this hypothesis lacks direct experimental support.

The authors introduce a novel “two‑track‑dumbbell” model that explicitly incorporates two physical ingredients previously neglected: (i) the elasticity of the kinesin stalk, modeled as a linear spring with constant k_spring, and (ii) the excluded‑volume interaction between the head and tail domains of neighboring motors. In this picture, each kinesin is a dumbbell whose tail domain is tightly bound to the membrane tube and can slide laterally, while the head domain binds to a microtubule site, steps forward, or detaches. When a motor bears load, its stalk stretches, transmitting force to the leading motor; simultaneously, the steric repulsion between adjacent tail domains pushes neighboring motors forward, allowing non‑leading motors to contribute indirectly to the pulling force.

To explore the consequences of this model, the authors perform stochastic simulations using the Gillespie algorithm. The membrane tube is discretized into a one‑dimensional lattice with spacing d = 8 nm (the microtubule periodicity). Each lattice site can host multiple “free” motors (those attached to the membrane but not bound to the microtubule) and at most one bound motor. Transition rates include: (a) force‑dependent unbinding k_u(f) = k_u0 exp(f/f_d) with f_d ≈ 3 pN, (b) force‑velocity relation V(f) derived from the Fisher‑Kolomeisky two‑state model, (c) diffusion of free motors along the tube with rate D/d², and (d) stochastic binding to vacant microtubule sites with rate k_b. Excluded‑volume constraints are enforced by setting prohibited transition rates to zero (e.g., two motors cannot occupy the same microtubule site or overlap tail domains beyond a minimal spacing).

Key simulation parameters are taken from published experiments (e.g., k_u0, D, κ, membrane bending modulus) while the binding rate k_b = 4.7 s⁻¹ is fitted to reproduce observed tube formation frequencies. The authors first determine the “threshold retreat force” F_m for a given surface motor density ρ₀: they incrementally increase a constant opposing force until, in 200 independent runs, at least one tube fails to grow. This procedure yields a functional relationship F_m(ρ₀).

Results show that F_m rises monotonically with ρ₀, from ~14 pN at ρ₀ = 1 µm⁻² to ~36 pN at ρ₀ = 1000 µm⁻². The experimentally measured extraction force (~27.5 ± 2.5 pN) corresponds to a threshold density of roughly 100 µm⁻², in excellent agreement with the reported range of 100–200 µm⁻² required for tube formation. Importantly, the simulations reveal that the average number of “pulling” motors at the tube tip is 8–9, even though all motors are confined to a single microtubule protofilament. This demonstrates that cooperative force generation does not require multiple protofilaments; instead, the combination of stalk elasticity and tail‑domain steric repulsion enables many motors to share the load.

A sensitivity analysis on the binding rate k_b shows that F_m increases sharply for k_b < 4 s⁻¹ and saturates near 36 pN for larger values. When k_b exceeds ~2 s⁻¹, the threshold force already surpasses the experimentally required 27.5 pN, indicating that modest changes in motor‑membrane binding kinetics can dramatically affect tube extraction efficiency.

The authors contrast their findings with the Campàs model, emphasizing that their two‑track‑dumbbell framework predicts sufficient pulling force from a single protofilament, thereby challenging the necessity of three‑protofilament cooperation. They argue that the excluded‑volume interaction—absent in earlier models—is the key to enabling non‑leading motors to contribute force without directly stepping on the microtubule.

In the discussion, the paper proposes experimental tests: (i) altering the effective size of the tail domain (e.g., by attaching bulky tags) to modulate steric repulsion, (ii) engineering kinesin variants with different stalk stiffness to probe the role of elasticity, and (iii) measuring the binding rate k_b directly using single‑molecule fluorescence assays. Such experiments would validate whether the predicted cooperative mechanism operates in vivo.

Overall, the study provides a physically grounded, quantitatively validated model for kinesin‑driven membrane tube extraction. By integrating motor elasticity and steric interactions, it reconciles theoretical predictions with experimental observations and opens new avenues for investigating motor cooperation in cellular morphogenesis and for designing synthetic nanotransport systems.