Processive molecular motors, such as kinesins, myosins and helicases, take multiple discrete steps on linear polar tracks such as microtubules, filamentous actin, and DNA/RNA substrates. Insights into the mechanisms and functions of this important class of biological motors have been obtained through observations from single-molecule experiments and structural studies. Such information includes the distribution of n, the number of steps motors take before dissociating, and v, the motor velocity, in the presence and absence of an external resistive force from single molecule experiments; and different structures of different states of motors at different conditions. Based on those available data, this thesis focuses on using both analytical and computational theoretical tools to investigate the workings of processive motors. Two examples of processive motors considered here are kinesins that walk on microtubules while transporting vesicles, and helicases which translocate on DNA/RNA substrate while unwinding the helix substrate. New physical principles and predictions related to their motility emerge from the proposed theories.

The most significant results reported in this thesis are:

Exact and approximate equations for velocity distribution, P(v), and runlength distribution, P(n), have been derived. Application of the theory to kinesins shows that P(v) is non-Gaussian and bimodal at high resistive forces. This unexpected behavior is a consequence of the discrete spacing between the alpha/beta tubulins, the building blocks of microtubule. In the case of helicases, we demonstrate that P(v) of typical helicases T7 and T4 shows signatures of heterogeneity, inferred from large variations in the velocity from molecule to molecule. The theory is used to propose experiments in order to distinguish between different physical basis for heterogeneity.

We generated a one-microsecond atomic simulation trajectory capturing the docking process of the neck-linker, a crucial element deemed to be important in the motility of Kinesin-1. The conformational change in the neck linker is important in the force generation in this type of motor. The simulations revealed new conformations of the neck-linker that have not been noted in previous structural studies of Kinesin-1, but which are demonstrated to be relevant to another superfamily member, Kinesin-5. By comparing the simulation results with currently available data, we suggest that the two superfamilies might actually share more similarities in the neck-linker docking process than previously thought.