Model-free inference of memory in conformational dynamics of a multi-domain protein

TL;DR

This paper introduces a model-free method to detect and quantify memory effects in the conformational dynamics of proteins from single-molecule experiments, revealing significant non-Markovian behavior in Hsp90.

Contribution

It develops a model-free approach to infer and measure memory in protein dynamics, avoiding assumptions of Markovian behavior common in traditional analyses.

Findings

Memory effects in Hsp90 extend up to 50 seconds.

Markov assumption is violated in observed protein dynamics.

Memory influences protein motions even at slow timescales.

Abstract

Single-molecule experiments provide insight into the motion (conformational dynamics) of individual protein molecules. Usually, a well-defined but coarse-grained intramolecular coordinate is measured and subsequently analysed with the help of Hidden Markov Models (HMMs) to deduce the kinetics of protein conformational changes. Such approaches rely on the assumption that the microscopic dynamics of the protein evolve according to a Markov-jump process on some network. However, the manifestation and extent of memory in the dynamics of the observable strongly depends on the chosen underlying Markov model, which is generally not known and therefore can lead to misinterpretations. Here, we combine extensive single-molecule plasmon ruler experiments on the heat shock protein Hsp90, computer simulations, and theory to infer and quantify memory in a model-free fashion. Our analysis is based on the bare definition of non-Markovian behaviour and does not require any underlying model. In the case of Hsp90 probed by a plasmon ruler, the Markov assumption is found to be clearly and conclusively violated on timescales up to roughly 50 s, which corresponds roughly to $\sim$50% of the inferred correlation time of the signal. The extent of memory is striking and reaches biologically relevant timescales. This implies that memory effects penetrate even the slowest observed motions. We provide clear and reproducible guidelines on how to test for the presence and duration of memory in experimental single-molecule data.