Kinesin-1 is a processive molecular motor that converts the energy from adenosine triphosphate (ATP) hydrolysis and thermal fluctuations into motion along microtubules. This motion can be interpreted as a result of ATP-fueled nonlinear nonsmooth oscillations of coupled motor domains which interact with a microtubule to transport a cargo. This class of nano-scale motors transport cargoes for distances of several micrometers in cells. This transport can also be achieved in vitro, opening the possibility of developing robust and extremely versatile nano-scale actuators or sensors based on the machinery used by biological systems. These devices could be used in a range of nano-scale applications such as drug delivery and lab-on-a-chip. However, to design such systems, a quantitative, in-depth understanding of molecular motors is essential. Single-molecule techniques have allowed the experimental characterization of kinesin-1 in vitro at a range of loads and ATP concentrations. Existing models of kinesin movement are stochastic in nature and are not well suited to describing transient dynamics. However, kinesin-1 is expected to undergo transient dynamics when external perturbations (e.g. interaction with other kinesin molecules) cause the load to vary in time. It is thought that in the cell, several kinesin motors work cooperatively to transport a common load. Thus, a transient description is integral to capturing kinesin behavior. This paper presents a mechanistic model that describes, deterministically, the average motion of kinesin-1. The structure of the kinesin-1 molecule is approximated with a simplified geometry, explicitly describing the coupling between its two heads. The diffusion is modeled using a novel approach based on the mean first-passage time, where the potential in which the free head diffuses is time varying and updated at each instant during the motion. The mechanistic model is able to predict existing force-velocity data over a wide range of ATP concentrations (including the interval 1μM to 10 mM). More importantly, the model provides a transient description, allowing predictions of kinesin-1 pulling time-varying loads and coordinated transport involving several kinesin-1 molecules. The deterministic approach is validated by comparing results to experiments and Monte Carlo simulations of the stochastic dynamics. Furthermore, using this model, the synchronization of several kinesin-1 molecules transporting a common load is investigated. Novel methods to characterize synchronization, tailored to the particularities of these nonsmooth systems, are presented.

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