Theoretical Investigation of Distributions of Run Lengths for Biological Molecular Motors

Motor proteins, also known as biological molecular motors, are active enzymatic molecules that support a variety of fundamental biological processes, including cellular transport, cell division, and cell motility. They usually function by transforming chemical energy into mechanical motion, which propels them along linear structures such as protein filaments and nucleic acids. Recent single-molecule experiments measured with high-precision distributions of various dynamic properties of molecular motors. However, it is difficult to utilize these observations to obtain a better description of molecular mechanisms in motor proteins because of the lack of corresponding theoretical methods. To fill this gap, we developed a new theoretical framework to describe the distributions of dynamic properties of biological molecular motors. It is based on the method of first-passage processes. To illustrate our approach, the distributions of run lengths of motor proteins are analyzed. It is found that these distributions depend on the finite length of linear tracks along which the motors move, on the initial position of the motor proteins along the filaments, and on the intermediate chemical transitions during the enzymatic cycle. The physical mechanisms of the observed phenomena are discussed.