Quantifying the Uncertainty of Molecular Dynamics Simulations: Good-Turing Statistics Revisited

We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus-far unobserved) biomolecular structures and showed that the method is stable, dependable, and its predictions verifiable. The major problem with that initial algorithm was the requirement for calculating and storing in memory the two-dimensional RMSD matrix of the currently available trajectory. This quadratic memory requirement precluded the application of the method to very long simulations. Here we describe a new variant of the Good-Turing algorithm whose memory requirements scale linearly with the number of structures in the trajectory, making it suitable even for extremely long simulations. We show that the new method gives essentially identical results to the older implementation and present results obtained from trajectories containing up to 22 million structures. A computer program implementing the new algorithm is available from standard repositories.