The first step in estimating a reversible MSM is projecting the MD trajectories onto the proposed basis states, χ. Transitions between each basis state at time t and time t + τ are tabulated in a count matrix, C 0t (the subscript 0 and t refer to the fact that the counted transitions are between t and t + τ ). The population of each state is given by the diagonal matrix, C 00 calculated as the row-sum of the count matrix [C 00 ] i,i = j [C 0t ] i,j . A nonreversible transition matrix is then given by T irrev = C 0t C -1 00 . It is non-reversible because of the finite amount of simulation data will not be in perfect equilibrium. A transition matrix and stationary vector which obey detailed balance, T rev and π rev , can be estimated from C 0t using maximum likelihood estimation with constraints. The constraints ensure that detailed balance is obeyed by T and its dynamics are reversible. However, once T rev and π rev have been estimated, they are now inconsistent with C 0t and C 00 , as obtained from the MD trajectory.