# Using Time Dependent Rate Analysis to Evaluate the Quality of Machine Learned Reaction Coordinates for Biasing and Computing Kinetics

## TL;DR

This paper introduces a metric called γ to evaluate the quality of machine-learned reaction coordinates for predicting molecular kinetics.

## Contribution

The study shows that γ from the EATR method can guide the selection of effective reaction coordinates for kinetic predictions.

## Key findings

- γ increases closer to 1 as reaction coordinates improve, indicating better performance.
- Mean accelerated times decrease consistently with improved γ values.
- γ and τ̅accel show an inverse correlation, validating γ as a practical evaluation criterion.

## Abstract

Having an accurate reaction coordinate (RC) is essential
for reliable
kinetic characterization of molecular processes, but there are few
quantitative metrics to evaluate RC quality. In this study, we consider
the dimensionless γ metric from the Exponential Average Time-dependent
Rate (EATR) method, which represents the fraction of a biasing potential
along the RC that contributes to increasing the rate constant. We
demonstrate that γ can be used to test whether the utility of
a RC for predicting kinetics with a Metadynamics bias improves as
the coordinate is iteratively updated to include new data. We evaluate
RCs approximated via the iterative State Predictive Information Bottleneck
(SPIB) approach, which was previously shown to be accurate across
six protein–ligand dissociation systems. For these same systems,
we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters,
the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation.
These results demonstrate that γ serves as a practical criterion
for RC evaluation and offers guidance for selecting SPIB–derived
coordinates yielding quantitative kinetic predictions.