Response to Vilfan: Constructing structure-based free energy surfaces is the key to understand myosin V unidirectionality

Analyzing the unidirectionality of myosin motors can be futile without the ability to understand, generate, and use the relevant free energy landscapes. An example is the failure of ref. 1 to understand the landscape in ref. 2, which resulted in unjustified arguments. The directionality in ref. 2 should be estimated by comparing the forward (II–III) barrier in figure 5A of ref. 2 to the backward (IV′–V′) barrier in figure 5B. Of course, the II–III and other barriers in figure 5A correspond to milliseconds processes, when one uses the correct frequency factor of ~10¹² (forgotten in ref. 1), with a reasonable friction coefficient. More careful analysis can be obtained by running Langevin dynamics (LD) with the landscapes in figure 5 of ref. 2. Similarly, almost all of the presumptions of ref. 1 are problematic and we consider the following:

• i)The 11 kcal/mol free energy change ($\mathrm{\Delta }{G}_{\text{elec}}^{\mathrm{\theta }}$) is calculated from the protein structure and is crucial for unidirectionality (2). Unfortunately, the author of ref. 1 used $\mathrm{\Delta }{G}_{\text{elec}}^{\mathrm{\theta }}$ in estimating the rate constant, overlooking the fact that this does not represent any relevant activation barrier and also forgetting the frequency factor.
• ii)The repriming step (−$\mathrm{\Delta }{G}_{\text{elec}}^{\mathrm{\theta }}$ + actin release) not only biases the trailing leg (pink) to release actin, but the powerstroke ($\mathrm{\Delta }{G}_{\text{elec}}^{\mathrm{\theta }}$) also penalizes reverse stepping of the blue leg until subsequent actin binding and/or P_i (phosphate) release in the pink leg. More importantly, our approach couples different steps (actin binding/release, ATP binding, and ADP and P_i release) to the conformational step and arrives at a structure-based functional surface, which is missing in any prior analyses.
• iii)The author of ref. 1 failed to understand that the powerstroke (lever up to down conformation change) does not have to be downhill for the overall process of the ADP.P_i to ADP transition to be downhill (that includes actin binding and P_i release in the pink leg + $\mathrm{\Delta }{G}_{\text{elec}}^{\mathrm{\theta }}$ in the blue leg).
• iv)Suggesting corrections to figure 4 of ref. 2 requires the understanding that we considered all of the relevant experimental values carefully. One should realize that building the surface is a step-by-step task, starting with table S2, building figure S3, and adding concentration effects in figure 3 (all from ref. 2). It would be constructive if the author of ref. 1 could look at table S2 of ref. 2 and then try to move to the next steps. In fact, table S2 of ref. 2 uses largely similar numbers to those of ref. 1 but then adds the correct concentration dependence.
• v)Despite the knowledge of the chemical steps and the load-dependent behavior, knowledge of the structure-based conformational free energy changes was missing before the study in ref. 2, making it hard to construct nonphenomenological functional landscapes. In particular, none of the presumptions in ref. 1 and the references cited therein have led to a free energy landscape and consequently to any structure-based unidirectional model. Thus, it is not productive to argue with the proposal of ref. 1, even after we overlook its major misconceptions.

The fact that it is almost impossible to logically discuss the outcome of different functional proposals without considering a well-defined landscape also remains an issue for other complex problems (see figure S6 in ref. 3).