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Biomolecular machines transduce between different forms of energy. These machines make directed progress and increase their speed by consuming free energy, typically in the form of nonequilibrium chemical concentrations. Machine dynamics…
Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one…
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and…
The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as…
A novel mechanism of reaction-induced active molecular motion, not involving any kind of self-propulsion, is proposed and analyzed. Because of the momentum exchange with the surrounding solvent, conformational transitions in…
The diffusion of a molecular motor in the presence of a constant external force is considered on the basis of a simple theoretical model. The motor is represented by a Brownian particle moving in a series of parabolic potentials placed…
Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models.…
We propose a simple theoretical model for a molecular chemical engine that catalyzes a chemical reaction and converts the free energy released by the reaction into mechanical work. Binding and unbinding processes of reactant and product…
Anomalously slow passive diffusion, $\langle \delta x^2(t)\rangle\simeq t^{\alpha}$, with $0<\alpha<1$, of larger tracers such as messenger RNA and endogenous submicron granules in the cytoplasm of living biological cells has been…
Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These…
A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor $\rm F_1$-ATPase. It turns…
A simple model of the two-state ratchet type is proposed for molecular chemical engines that convert chemical free energy into mechanical work and vice versa. The engine works by catalyzing a chemical reaction and turning a rotor.…
Chemical gradients provide the primordial energy for biological functions by driving the mechanical movement of microscopic engines. Their thermodynamic properties remain elusive, especially concerning the dynamic change in energy demand in…
Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between…
Dynamics of molecular motor dimers, consisting of rigidly bound particles that move along two parallel lattices and interact with underlying molecular tracks, is investigated theoretically by analyzing discrete-state stochastic…
Molecular machines are stochastic systems that catalyze the energetic processes keeping living cells alive and structured. Inspired by the examples of F1-ATP synthase and the bacterial flagellum, we present a minimal model of an externally…
Biological molecular machines are enzymes that simultaneously catalyze two processes, one donating free energy and second accepting it. Recent studies show that most native protein enzymes have a rich stochastic dynamics that often…
A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current…
Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the…
Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and…