Exchanges between scaling factors are periodically attempted, with an acceptance probability based on a Metropolis criterion satisfying the detailed balance condition. In so doing, we observe a random diffusion of the scaling factors (or inverse "temperatures" s k β) while the HREM simulation proceeds. A replica is hence an MD trajectory spanning various Hamitonians with different scaling factors, providing a mechanism for transmitting conformations sampled in states with strongly scaled potential energy to the target (unscaled) state with s = 1 with the correct Boltzmann weight. The acceptance probability P acc (k, k ) for the k ↔ k exchange depends on the overlap of the corresponding potential energy distributions, 23 so that exchanges are normally attempted between contiguous replicas. In this case, we use the short-hand notation P acc (k) to denote the acceptance probability for the exchange k ↔ k + 1.