Individual molecular motors, or motor proteins, are enzymatic molecules that convert chemical energy, typically obtained from the hydrolysis of ATP (adenosine triphosphate), into mechanical work and motion. Processive motor proteins, such as kinesin, dynein, and certain myosins, step unidirectionally along linear tracks, specifically microtubules and actin filaments, and play a crucial role in cellular transport processes, organization, and function. In this review some theoretical aspects of motor-protein dynamics are presented in the light of current experimental methods that enable the measurement of the biochemical and biomechanical properties on a single-molecule basis. After a brief discussion of continuum ratchet concepts, we focus on discrete kinetic and stochastic models that yield predictions for the mean velocity, V(F, [ATP], …), and other observables as a function of an imposed load force F, the ATP concentration, and other variables. The combination of appropriate theory with single-molecule observations should help uncover the mechanisms underlying motor-protein function.

Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environments, strongly supporting fundamental cellular processes such as the transfer of genetic information, transport, organization and functioning. In the past two decades motor proteins have become a subject of intense research efforts, aimed at uncovering the fundamental principles and mechanisms of molecular motor dynamics. In this review, we critically discuss recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized to explain the non-equilibrium nature and mechanisms of molecular motors.

Significance: Biological processes are unique in showing a remarkable level of accuracy in discriminating between similar molecules. This characteristic is attributed to an error-correcting mechanism known as kinetic proofreading. It is widely believed that the enhancement of the accuracy in biological processes always slows them down. By analyzing the fundamental processes of DNA replication and protein translation, we established that these systems maximize speed rather than accuracy with additional energetic constraints. Our theoretical study further indicates that both speed and accuracy can be enhanced in certain parameter regimes. The resulting findings provide a microscopic picture of how complex biological processes can be accomplished so quickly with minimal errors.