Protein Conformational Transitions from All-Atom Adaptively Biased Path Optimization

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

TYROSINE KINASES: COMPLEX MOLECULAR SYSTEMS CHALLENGING COMPUTATIONAL METHODOLOGIES

Classical molecular dynamics (MD) simulations based on atomic models play an increasingly important role in a wide range of applications in physics, biology, and chemistry. Nonetheless, generating genuine knowledge about biological systems using MD simulations remains challenging. Protein tyrosine kinases are important cellular signaling enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Due to the large conformational changes and long timescales involved in their function, these kinases present particularly challenging problems to modern computational and theoretical frameworks aimed at elucidating the dynamics of complex biomolecular systems. Markov state models have achieved limited success in tackling the broader conformational ensemble and biased methods are often employed to examine specific long timescale events. Recent advances in machine learning continue to push the limitations of current methodologies and provide notable improvements when integrated with the existing frameworks. A broad perspective is drawn from a critical review of recent studies.

All-atom adaptively biased path optimization of Src kinase conformational inactivation: Switched electrostatic network in the concerted motion of αC helix and the activation loop

A method to optimize a conformational pathway through a space of well-chosen reduced variables is employed to advance our understanding of protein conformational equilibrium. The adaptively biased path optimization strategy utilizes unrestricted, enhanced sampling in the region of a path in the reduced-variable space to identify a broad path between two stable end-states. Application to the inactivation transition of the Src tyrosine kinase catalytic domain reveals new insight into this well studied conformational equilibrium. The mechanistic description gained from identifying the motions and structural features along the path includes details of the switched electrostatic network found to underpin the transition. The free energy barrier along the path results from rotation of a helix, αC, that is tightly correlated with motions in the activation loop (A-loop) as well as distal regions in the C-lobe. Path profiles of the reduced variables clearly demonstrate the strongly correlated motions. The exchange of electrostatic interactions among residues in the network is key to these interdependent motions. In addition, the increased resolution from an all-atom model in defining the path shows multiple components for the A-loop motion and that different parts of the A-loop contribute throughout the length of the path.

Perturb-Scan-Pull: A Novel Method Facilitating Conformational Transitions in Proteins

Conformational transitions in proteins facilitate precise physiological functions. Therefore, it is crucial to understand the mechanisms underlying these processes to modulate protein function. Yet, studying structural and dynamical properties of proteins is notoriously challenging due to the complexity of the underlying potential energy surfaces (PES). We have previously developed the perturbation-response scanning (PRS) method to identify key residues that participate in the communication network responsible for specific conformational transitions. PRS is based on a residue-by-residue scan of the protein to determine the subset of residues/forces which provide the closest conformational change leading to a target conformational state, inasmuch as linear response theory applies to these motions. Here, we develop a novel method to further evaluate if conformational transitions may be triggered on the PES. We aim to study functionally relevant conformational transitions in proteins by using results obtained from PRS and feeding them as inputs to steered molecular dynamics simulations. The success and the transferability of the method are evaluated on three protein systems having different complexities of motion on the PES: calmodulin, adenylate kinase, and bacterial ferric binding protein. We find that the method captures the target conformation, while providing key residues and the optimum paths with relatively low free energy profiles.