To validate and further assess the relative efficiency of BLUES compared to MD, we built a statistical model of convergence of populations in these two cases. Specifically, we wanted to use transition matrices between the four states (in both cases) to propagate the populations over a long time in order to analyze convergence properties. We obtained the MSM transition matrix for the MD case. For the NCMC case we constructed a transition matrix from our BLUES simulation (as described in Section 2.8). We then built a model of convergence using these two matrices as a starting point. In each case, we started a hypothetical simulation from binding mode A1 and used the transition matrix to propagate the populations, at each timestep choosing a new state to transition based on the probabilities in the transition matrix. In the MD case the transition matrix was constructed using a lagtime of 6 ns so our simulation timesteps corresponded to 6 ns, whereas in the BLUES case the transition matrix was constructed for a 40 ps MD/NCMC iteration so timesteps were 40 ps. We then repeated 1000 such simulations for each case and examined the mean population as a function of time and the standard deviation over trials. These are shown in Figure .