Convergence of Molecular Dynamics Simulation of Protein Native States: Feasibility vs Self-Consistency Dilemma

All-atom molecular dynamics simulations need convergence tests to evaluate the quality of data. The notion of "true" convergence is elusive, and one can only hope to satisfy self-consistency checks (SCC). There are multiple SCC criteria, and their assessment of all-atom simulations of the native state for real globular proteins is sparse. Here, we present a systematic study of different SCC algorithms, both in terms of their ability to detect the lack of self-consistency and their computational demand, for the all-atom native state simulations of four globular proteins (CSP, CheA, CheW, and BPTI). Somewhat surprisingly, we notice some of the most stringent SCC criteria, e.g., the criteria demanding similarity of the cluster probability distribution between the first and the second halves of the trajectory or the comparison of fluctuations between different blocks using covariance overlap measure, can require tens of microseconds of simulation even for proteins with less than 100 amino acids. We notice such long simulation times can sometimes be associated with traps, but these traps cannot be detected by some of the common SCC methods. We suggest an additional, and simple, SCC algorithm to quickly detect such traps by monitoring the constancy of the cluster entropy (CCE). CCE is a necessary but not sufficient criteria, and additional SCC algorithms must be combined with it. Furthermore, as seen in the explicit solvent simulation of 1 ms long trajectory of BPTI,1 passing self-consistency checks at an earlier stage may be misleading due to conformational changes taking place later in the simulation, resulting in different, but segregated regions of SCC. Although there is a hierarchy of complex SCC algorithms, caution must be exercised in their application with the knowledge of their limitations and computational expense.