Normal mode analysis of protein dynamics in a non-Eckart frame

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.

Principal component analysis of molecular dynamics: on the use of Cartesian vs. internal coordinates

Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail.

Classification and annotation of the relationship between protein structural change and ligand binding

The causal relationship between protein structural change and ligand binding was classified and annotated for 839 nonredundant pairs of crystal structures in the Protein Data Bank-one with and the other without a bound low-molecular-weight ligand molecule. Protein structural changes were first classified into either domain or local motions depending on the size of the moving protein segments. Whether the protein motion was coupled with ligand binding was then evaluated based on the location of the ligand binding site and by application of the linear response theory of protein structural change. Protein motions coupled with ligand binding were further classified into either closure or opening motions. This classification revealed the following: (i) domain motions coupled with ligand binding are dominated by closure motions, which can be described by the linear response theory; (ii) local motions frequently accompany order-disorder or α-helix-coil conformational transitions; and (iii) transferase activity (Enzyme Commission number 2) is the predominant function among coupled domain closure motions. This could be explained by the closure motion acting to insulate the reaction site of these enzymes from environmental water.