Molecular motors such as dynein are known to move by taking steps of different sizes, depending on the load. Here, we develop a simple, discrete, minimal ratchet model for a motor that can take steps of sizes δ∘ and 2δ∘ in order to provide a bare-bones description of dynein. We obtain the force–velocity curves and diffusivity for this motor for different concentrations of ATP. We also study the mechano-chemical energy transduction and thermodynamic efficiency of the motor. Further, by investigating the statistics of step sizes for the motor, we show that the average step size and fluctuation in step sizes have a non-monotonic force dependence. We develop closed-form analytical expressions for all our results, which despite the simplicity of the model give a reasonable match with the known experiments and simulations on dynein.

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Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is in equilibrium at stall. Conversely, we show that this additive property typically does not hold true when the system is not at equilibrium at stall. We thus present a novel and unified understanding of the existing models exhibiting such nonaddivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

We introduce exclusion models of two distinguishable species of hard rods with their distinct sites of entry and exit under open boundary conditions. In the first model both species of rods move in the same direction whereas in the other two models they move in the opposite direction. These models are motivated by the biological phenomenon known as Transcriptional Interference. Therefore, the rules for the kinetics of the models, particularly the rules for the outcome of the encounter of the rods, are also formulated to mimic those observed in Transcriptional Interference. By a combination of mean-field theory and computer simulation of these models we demonstrate how the flux of one species of rods is completely switched off by the other. Exploring the parameter space of the model we also establish the conditions under which switch-like regulation of two fluxes is possible; from the extensive analysis we discover more than one possible mechanism of this phenomenon.