Traffic of single-headed motor proteins KIF1A: effects of lane changing

KIF1A kinesins are single-headed motor proteins which move on cylindrical nano-tubes called microtubules (MT). A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. Does lane-changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}]. By carrying out analytical calculations and computer simulations of this extended model, we predict that the flux per lane can increase or decrease with the increasing rate of lane changing, depending on the concentrations of motors and the rate of hydrolysis of ATP, the ``fuel’’ molecules. Our predictions can be tested, in principle, by carrying out {\it in-vitro} experiments with fluorescently labelled KIF1A molecules.

💡 Research Summary

This paper investigates how lane‑changing influences the collective transport of the single‑headed kinesin KIF1A along microtubules (MTs), which consist of 13 parallel protofilaments that act as discrete lanes. Building on a previously published one‑lane model (Phys. Rev. E 75, 041905, 2007) that combined the totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics, the authors extend the framework to a 13‑lane system and explicitly incorporate inter‑lane transitions. The model includes four fundamental processes: forward stepping driven by ATP hydrolysis (rate p, hydrolysis rate ω_h), backward stepping (rate q), stochastic attachment/detachment from the solution (rates ω_a and ω_d), and lane‑changing (forward and backward rates ω_c^+ and ω_c^–). By applying a mean‑field approximation, the steady‑state density ρ_i and flux J_i on each lane are derived from coupled balance equations that account for all these processes.

Analytical results reveal that lane‑changing does not have a monotonic effect on the per‑lane flux. At low motor densities (the low‑density, LD, regime) lane‑changing alleviates local jams, allowing motors to bypass congested lanes and thereby increasing J_i. In contrast, at high densities (the high‑density, HD, regime) lane‑changing spreads the congestion to neighboring lanes, reducing the overall throughput per lane. The transition between these behaviors is governed by the ATP hydrolysis rate: a high ω_h (fast hydrolysis) increases the forward stepping rate p, so motors tend to move forward before they have a chance to switch lanes, diminishing the impact of ω_c. Conversely, a low ω_h makes lane‑changing more influential, producing a pronounced non‑linear dependence of flux on ω_c.

Monte‑Carlo simulations using random‑sequential updates confirm the analytical predictions. The simulations reproduce the expected phase diagram (LD, maximal‑current MC, and HD regions) and show that increasing ω_c shifts the boundaries: the MC region expands, indicating that moderate lane‑changing can enlarge the parameter space where the system operates at maximal efficiency. Moreover, the simulations demonstrate that the flux per lane can either rise or fall with ω_c, depending on the combination of motor concentration (set by ω_a and ω_d) and ATP hydrolysis rate.

The authors propose that these theoretical findings are experimentally testable. By labeling KIF1A with fluorescent tags and observing its motion on in‑vitro MT bundles under controlled ATP concentrations, one could vary motor density (through protein concentration) and modulate lane‑changing propensity (for example, by engineering asymmetric binding sites or applying external forces). Measuring the resulting flux per protofilament would directly verify the predicted non‑monotonic relationship.

In conclusion, the study provides a comprehensive, quantitative description of how inter‑lane dynamics modulate motor traffic on multi‑lane cytoskeletal tracks. It demonstrates that lane‑changing can be a double‑edged sword—enhancing transport under sparse conditions while impairing it when the system is crowded—and that the balance is finely tuned by the biochemical energy supply (ATP hydrolysis). The extended multi‑lane TASEP‑Langmuir framework introduced here offers a versatile platform for exploring more complex intracellular transport scenarios, such as heterogeneous filament arrays, motor‑motor interactions, and external mechanical loads.