[Paper Review] Quantifying the uncertainty of molecular dynamics simulations : Good-Turing statistics revisited

Vasiliki Tsampazi, Nicholas M. Glykos|arXiv (Cornell University)|Jan 2, 2026

Protein Structure and Dynamics0 citations

TL;DR

This paper revisits Good-Turing statistics for estimating the probability of observing completely new biomolecular structures in molecular dynamics trajectories and introduces a memory-efficient variant scalable to extremely long simulations.

ABSTRACT

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 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 with 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.

Motivation & Objective

• Demonstrate that Good-Turing statistics can quantify the emergence of new biomolecular structures in MD trajectories.
• Address scalability limitations by reducing memory requirements from the previous two-dimensional RMSD matrix approach.
• Provide a variant of the algorithm with linear memory scaling suitable for extremely long simulations.
• Show that the new method yields results essentially identical to the older implementation.
• Make the accompanying software publicly available for researchers to apply to long MD trajectories.

Proposed method

• Develop a new variant of the Good-Turing algorithm with linear memory scaling.
• Validate that the new method produces essentially identical results to the previous implementation.
• Apply the method to MD trajectories containing up to 22 million structures.
• Provide a software implementation released to standard repositories.

Experimental results

Research questions

• RQ1 Can Good-Turing statistics be applied to long molecular dynamics trajectories without prohibitive memory usage?
• RQ2 Does the linear-memory variant preserve the accuracy of the original Good-Turing approach?
• RQ3 What are the practical limits in trajectory size where the method remains reliable?
• RQ4 Is there accessible software to implement the revised algorithm?

Key findings

• The linear-memory variant yields results essentially identical to the older implementation.
• The method was demonstrated on trajectories containing up to 22 million structures.
• The approach remains stable and dependable for estimating the probability of observing new biomolecular structures in MD data.
• A computer program implementing the new algorithm is available from standard repositories.