Among the multiple steps constituting the kinesin mechanochemical cycle, one of the most interesting events is observed when kinesins move an 8-nm step from one microtubule (MT)-binding site to another. The stepping motion that occurs within a relatively short time scale (Ϸ100 s) is, however, beyond the resolution of current experiments. Therefore, a basic understanding to the real-time dynamics within the 8-nm step is still lacking. For instance, the rate of power stroke (or conformational change) that leads to the undocked-to-docked transition of neck-linker is not known, and the existence of a substep during the 8-nm step still remains a controversial issue in the kinesin community. By using explicit structures of the kinesin dimer and the MT consisting of 13 protofilaments, we study the stepping dynamics with varying rates of power stroke (k p ATPase activity and organelle transport along microtubules (MTs) (1, 2), kinesins have received broad attention as a prototype of molecular motors for the past two decades. Recent singlemolecule (SM) experiments have shown that, with each stepping motion being strongly coupled to the ATP, the kinesin moves toward the (ϩ) ends of MTs by taking discrete 8-nm steps (3-7) in a hand-over-hand fashion (4,7,8). Although the ultimate understanding of kinesin's motility is still far from completion, the SM experiments (3-9), together with the series of kinetic ensemble measurements (10-13) and theoretical studies (14-19), begin providing glimpses to the physical principle of how kinesin walks.Along the kinesin mechanochemical cycle (supporting information (SI) Fig. 7), one of the main observations of the SM experiments is the stepping dynamics that enables the kinesin to move forward. The actual time spent for the stepping motion itself (Շ100 s), compared with the ATP binding and hydrolysis (տ10 ms), is too short, however, to detect the details of the dynamics with the spatial and temporal resolution of current instruments. Thus, it is still difficult to answer many basic questions (20) related to the stepping dynamics. Some of those questions are: (i) During the 8-nm step, how does the swiveling motion of the tethered head occur? Does any detectable substep exist that reflects a transient intermediate (5,21,22)? (ii) What fraction of the time and length scales is contributed from the power stroke and the diffusional search? (iii) Does the kinesin walk parallel to the single protofilament (PF) or walk astride by using two parallel PFs (23, 24)? To shed light on these questions, we propose to take advantage of the native topology of kinesins and MTs. For instance, our earlier study clarified the regulation mechanism between the two heads (6, 25) by using the native topology-based, two-head bound model of kinesin on the MT (19). Following the same line of thought, we show that even the dynamical pathways of kinesins reflect ''the topological constraints emanating from the molecular architecture.'' In the present work, we have adapted our previous two-head bound model (19) to stud...