Model for bidirectional movement of cytoplasmic dynein

Cytoplasmic dynein exhibits a directional processive movement on microtubule filaments and is known to move in steps of varying length based on the number of ATP molecules bound to it and the load that it carries. It is experimentally observed that dynein takes occasional backward steps and the frequency of such backward steps increases as the load approaches the stall force. Using a stochastic process model, we investigate the bidirectional movement of single head of a dynein motor. The probability for backward step is implemented based on Crook’s fluctuation theorem of non-equilibrium statistical mechanics. We find that the movement of dynein motor is characterized with negative velocity implying backward motion beyond stall force. We observe that the motor moves backward for super stall forces by hydrolyzing the ATP exactly the same way as it does while moving forward for sub stall forces.

💡 Research Summary

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The paper presents a stochastic‐process model for the bidirectional stepping of a single head of cytoplasmic dynein, incorporating backward steps through Crooks’ fluctuation theorem. The authors first review experimental observations that dynein, although a minus‑end directed motor, occasionally takes backward steps and that the frequency of these steps rises as the external load approaches the stall force. Existing theoretical work has modeled dynein’s load‑dependent step size, ATP binding/unbinding, and hydrolysis kinetics, but none have explicitly linked backward stepping to a non‑equilibrium thermodynamic principle.

In the model, the microtubule is represented as a one‑dimensional lattice with spacing a = 8 nm. The dynein head possesses one primary ATP‑binding site and up to three secondary sites. The occupancy of the secondary sites determines the possible step length: when n secondary sites are occupied (n = 0…3) the step size is 4a/(n + 1), giving steps of 8, 16, 24 or 32 nm. Three variants are defined—2a, 3a and 4a models—corresponding to one, two or three secondary sites being considered, leading to 4, 8 or 16 distinct chemical states.

Kinetic parameters are taken from earlier studies. Primary and secondary binding rates (k_on) and unbinding rates (k_off) are fixed, while the binding rates of secondary sites are made load‑dependent via an exponential factor exp(F d₀/k_BT) (d₀ = 6 nm). Hydrolysis rates at the primary site depend on both load and secondary‑site occupancy:
k_cat,i = A(i) k_cat,0 exp