Maximizing Kinetic Information Gain of Markov State Models for Optimal Design of Spectroscopy Experiments.

Spectroscopic techniques such as Trp-Tyr quenching, luminescence resonance energy transfer, and triplet-triplet energy transfer are widely used for understanding the dynamic behavior of proteins. These experiments measure the relaxation of a particular labeled set of residue pairs, and the choice of residue pairs requires careful thought. As a result, experimentalists must pick residue pairs from a large pool of possibilities. In the current work, we show that molecular simulation datasets of protein dynamics can be used to systematically select an optimal set of residue positions to place probes for conducting spectroscopic experiments. The method described in this work, called Optimal Probes, can be used to rank trial sets of residue pairs in terms of their ability to capture the conformational dynamics of the protein. Optimal probes ensures two conditions: residue pairs capture the slow dynamics of the protein and their dynamics is not correlated for maximum information gain to score each trial set. Eventually, the highest scored set can be used for biophysical experiments to study the kinetics of the protein. The scoring methodology is based on kinetic network models of protein dynamics and a variational principle for molecular kinetics to optimize the hyperparameters used for the model. We also discuss that the scoring strategy used by Optimal Probes is the best possible way to ensure the ideal choice of residue pairs for experiments. We predict the best experimental probe positions for proteins λ-repressor, ß2-adrenergic receptor, and villin headpiece domain. These proteins have been well-studied and allow for a rigorous comparison of Optimal Probes predictions with already available experiments. Additionally, we also illustrate that our method can be used to predict the best choice for experiments by including any previous experiment choices available from other studies on the same protein. We consistently find that the best choice cannot be based on intuition or structural information such as distance difference between few known stable structures of the protein. Therefore, we show that incorporating protein dynamics could be used to maximize the information gain from experiments.

Predicting Optimal DEER Label Positions to Study Protein Conformational Heterogeneity.

Double electron-electron resonance (DEER) spectroscopy is a powerful experimental technique for understanding the conformational heterogeneity of proteins. It involves attaching nitroxide spin labels to two residues in the protein to obtain a distance distribution between them. However, the choice of residue pairs to label in the protein requires careful thought, as experimentalists must pick label positions from a large set of all possible residue-pair combinations in the protein. In this article, we address the problem of the choice of DEER spin-label positions in a protein. For this purpose, we utilize all-atom molecular dynamics simulations of protein dynamics, to rank the sets of labeled residue pairs in terms of their ability to capture the conformational dynamics of the protein. Our design methodology is based on the following two criteria: (1) An ideal set of DEER spin-label positions should capture the slowest conformational-change processes observed in the protein dynamics, and (2) any two sets of residue pairs should describe orthogonal conformational-change processes to maximize the overall information gain and reduce the number of labeled residue pairs. We utilize Markov state models of protein dynamics to identify slow dynamical processes and a genetic-algorithm-based approach to predict the optimal choices of residue pairs with limited computational time requirements. We predict the optimal residue pairs for DEER spectroscopy in ß2 adrenergic receptor, the C-terminal domain of calmodulin, and peptide transporter PepTSo. We find that our choices were ranked higher than those used to perform DEER experiments on the proteins investigated in this study. Hence, the predicted choices of DEER residue pairs determined by our method provide maximum insight into the conformational heterogeneity of the protein while using the minimum number of labeled residues.