[Paper Review] A maximum-caliber approach to predicting perturbed folding kinetics due to mutations

Vincent A. Voelz, Guangfeng Zhou+1 more|arXiv (Cornell University)|May 25, 2016

Protein Structure and Dynamics5 citations

TL;DR

This paper introduces a robust maximum-caliber method to predict perturbed protein folding kinetics from mutated equilibrium populations in Markov State Models (MSMs), leveraging prior transition rates and equilibrium data to infer new rates without requiring new simulation data. The method accurately predicts folding rate changes across diverse protein systems, including GB1, Fs peptide, and WW domain variants, demonstrating strong predictive power for non-native interaction effects.

ABSTRACT

We present a maximum-caliber method for inferring transition rates of a Markov State Model (MSM) with perturbed equilibrium populations, given estimates of state populations and rates for an unperturbed MSM. It is similar in spirit to previous approaches but given the inclusion of prior information it is more robust and simple to implement. We examine its performance in simple biased diffusion models of kinetics, and then apply the method to predicting changes in folding rates for several highly non-trivial protein folding systems for which non-native interactions play a significant role, including (1) tryptophan variants of GB1 hairpin, (2) salt-bridge mutations of Fs peptide helix, and (3) MSMs built from ultra-long folding trajectories of FiP35 and GTT variants of WW domain. In all cases, the method correctly predicts changes in folding rates, suggesting the wide applicability of maximum-caliber approaches to efficiently predict how mutations perturb protein conformational dynamics.

Motivation & Objective

• To develop a robust, simple method for predicting changes in protein folding kinetics due to mutations using only equilibrium population shifts and prior transition rates.
• To overcome limitations of existing maximum-caliber approaches that depend sensitively on poorly chosen dynamical constraints.
• To enable efficient prediction of kinetic perturbations in complex protein systems where non-native interactions significantly influence folding.
• To provide a framework applicable to protein design, disease mutation analysis, and force field correction by reweighting biased simulations.

Proposed method

• The method maximizes path entropy (caliber) subject to constraints on transition probability conservation and known equilibrium populations.
• It uses a Lagrangian multiplier approach to infer new transition rates $ p_{ij} $ from known unperturbed rates $ p_{ij}^* $ and perturbed equilibrium populations $ \pi_i $.
• The approach incorporates prior knowledge of the unperturbed MSM, including metastable state structure and local kinetic environments.
• It avoids reliance on arbitrary dynamical constraints by using the existing MSM as a prior, enhancing robustness.
• The method is applied to 2D biased diffusion models and real protein folding systems with non-native interactions.
• It is validated using ultra-long folding trajectories from FiP35 and GTT WW domain variants, with predictions compared to true folding timescales.

Experimental results

Research questions

• RQ1 Can a maximum-caliber approach accurately predict folding rate changes in proteins with non-native interactions due to mutations?
• RQ2 How well does the method perform when only equilibrium population changes are known, without new simulation data?
• RQ3 Does the method remain robust when applied to systems with complex kinetic traps or sampling limitations?
• RQ4 Can the method predict folding kinetics in systems with minimal transition counts or poor sampling?
• RQ5 How does the method compare to existing approaches like dTRAM in handling ensembles with no observed transitions?

Key findings

• The method accurately predicts folding relaxation timescales for FiP35 WW domain, with predictions closely matching true values from ultra-long trajectories.
• For the GTT variant, the method correctly predicts a slower folding relaxation timescale than FiP35, though with lower absolute accuracy, likely due to less trajectory data.
• The maximum-caliber predictions for GB1 hairpin tryptophan mutants correctly reflect changes in folding rates due to non-native interactions.
• Salt-bridge mutations in the Fs peptide helix are also well-predicted, indicating applicability to helical folding systems.
• The method fails to accurately predict the next-slowest relaxation timescale involving the trap state in GTT, likely due to insufficient sampling of that state.
• The approach outperforms previous maximum-caliber methods by avoiding reliance on sensitive dynamical constraints and instead using the prior MSM as a robust foundation.