Steven Hayward

Collective protein dynamics in relation to function

Several techniques for the analysis of the internal motions of proteins are available - separating large collective motions from small, presumably uninteresting motions. Such descriptions are helpful in the characterization of internal motions and provide insight into the energy landscape of proteins. The real challenge, however, is to relate large collective motions to functional properties, such as binding and regulation, or to folding. These issues have been recently addressed in several papers.

Improvements in the analysis of domain motions in proteins from conformational change: DynDom version 1.50

DynDom is a program that analyses conformational change in proteins for dynamic domains, hinge axes, and hinge-bending regions. Here, a number of improvements and additions are reported which have been implemented in the new version 1.50. The most significant improvement is in the determination of the hinge-bending residues. A new routine also compares quantities relating to the main-chain dihedrals of bending residues with the hinge-bending motion. This version of the program can now be run from the DynDom website at: http://www.sys.uea.ac.uk/dyndom.

Model-Free Methods of Analyzing Domain Motions in Proteins from Simulation: A Comparison of Normal Mode Analysis and Molecular Dynamics Simulation of Lysozyme

Model‐free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw‐axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha‐carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997.

COLLECTIVE VARIABLE DESCRIPTION OF NATIVE PROTEIN DYNAMICS

The importance of collective motions in proteins, such as hinge-bending motions or motions involving domains, has been recognized. Occurrence of such motions and their experimental and theoretical studies are reviewed. Normal-mode analysis and principal component analysis are powerful theoretical tools for studying such motions. The former is based on the assumption of harmonicity of the dynamics, while the latter is valid even when the dynamics is highly anharmonic. The results of the latter analysis indicate that most important conformational events are taking place in a conformational subspace spanned by a rather small number of principal modes, and this important subspace is also spanned by a small number of normal modes. The normal-mode refinement method of protein X-ray crystallography, which is developed based on the concept of the above important subspace, is discussed.

Energy landscape of a native protein: Jumping‐among‐minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping‐among‐minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra‐substate and inter‐substate motions. By examining intra‐substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean‐square atomic fluctuation. Inter‐substate motions are observed only in a small‐dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter‐substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low‐level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998.

DOMAIN MOTIONS IN BACTERIOPHAGE T4 LYSOZYME : A COMPARISON BETWEEN MOLECULAR DYNAMICS AND CRYSTALLOGRAPHIC DATA

A comparison of a series of extended molecular dynamics (MD) simulations of bacteriophage T4 lysozyme in solvent with X‐ray data is presented. Essential dynamics analyses were used to derive collective fluctuations from both the simulated trajectories and a distribution of crystallographic conformations. In both cases the main collective fluctuations describe domain motions. The protein consists of an N‐ and C‐terminal domain connected by a long helix. The analysis of the distribution of crystallographic conformations reveals that the N‐terminal helix rotates together with either of these two domains. The main domain fluctuation describes a closure mode of the two domains in which the N‐terminal helix rotates concertedly with the C‐terminal domain, while the domain fluctuation with second largest amplitude corresponds to a twisting mode of the two domains, with the N‐terminal helix rotating concertedly with the N‐terminal domain. For the closure mode, the difference in hinge‐bending angle between the most open and most closed X‐ray structure along this mode is 49 degrees. In the MD simulation that shows the largest fluctuation along this mode, a rotation of 45 degrees was observed. Although the twisting mode has much less freedom than the closure mode in the distribution of crystallographic conformations, experimental results suggest that it might be functionally important. Interestingly, the twisting mode is sampled more extensively in all MD simulations than it is in the distribution of X‐ray conformations. Proteins 31:116–127, 1998.

Structural principles governing domain motions in proteins

With the use of a recently developed method, twenty‐four proteins for which two or more X‐ray conformers are known have been analyzed to reveal structural principles that govern domain motions in proteins. In all 24 cases, the domain motion is a rotation about a physical axis created through local interactions both covalent and noncovalent. In many cases, two or more mechanical hinges separated in space create a stable hinge axis for precise control of the domain closure. The terminal regions of α‐helices and β‐sheets have been found to act as mechanical hinges in a significant number of cases. In some cases, the two terminal regions of neighboring strands of a single β‐sheet can create a hinge axis, as can the two termini of a single α‐helix. These two structures have been termed the “double‐hinged β‐sheet” and “double‐hinged α‐helix,” respectively. A flexible loop that attaches one domain to another and through which the effective hinge axis passes is another construct that is used to create a hinge. Noncovalent interactions between segments remote along the polypeptide chain can also form hinges. In addition α‐helices that preserve their hydrogen bonding structure when bent have been found to behave as mechanical hinges. It is suggested that these α‐helices act as a store of elastic energy that drives the closing of domains for rapid capture of the substrate. If the repertoire of possible interdomain structures is as limited as this study suggests, the dynamic behavior of proteins could soon be predicted using bioinformatics techniques. Proteins 1999;36:425–435.

The DynDom database of protein domain motions

UNLABELLED A relational database has been developed based on the results from the application of the DynDom program to a number of proteins for which multiple X-ray conformers are available. The database is populated via a web-based tool that allows visitors to the website to run the DynDom program server-side by selecting pairs of X-ray conformers by Protein Data Bank code and chain identifier. AVAILABILITY The website can be found at: http://www.sys.uea.ac.uk/dyndom.

Normal Modes and Essential Dynamics

Normal mode analysis and essential dynamics analysis are powerful methods used for the analysis of collective motions in biomolecules. Their application has led to an appreciation of the importance of protein dynamics in function and the relationship between structure and dynamical behavior. In this chapter, the methods and their implementation are introduced and recent developments such as elastic networks and advanced sampling techniques are described.

A method for the analysis of domain movements in large biomolecular complexes

A new method for the analysis of domain movements in large, multichain, biomolecular complexes is presented. The method is applicable to any molecule for which two atomic structures are available that represent a conformational change indicating a possible domain movement. The method is blind to atomic bonding and atom type and can, therefore, be applied to biomolecular complexes containing different constituent molecules such as protein, RNA, or DNA. At the heart of the method is the use of blocks located at grid points spanning the whole molecule. The rotation vector for the rotation of atoms from each block between the two conformations is calculated. Treating components of these vectors as coordinates means that each block is associated with a point in a “rotation space” and that blocks with atoms that rotate together, perhaps as part of the same rigid domain, will have colocated points. Thus a domain can be identified from the clustering of points from blocks that span it. Domain pairs are accepted for analysis of their relative movements in terms of screw axes based upon a set of reasonable criteria. Here, we report on the application of the method to biomolecules covering a considerable size range: hemoglobin, liver alcohol dehydrogenase, S‐Adenosylhomocysteine hydrolase, aspartate transcarbamylase, and the 70S ribosome. The results provide a depiction of the conformational change within each molecule that is easily understood, giving a perspective that is expected to lead to new insights. Of particular interest is the allosteric mechanism in some of these molecules. Results indicate that common boundaries between subunits and domains are good regions to focus on as movement in one subunit can be transmitted to another subunit through such interfaces. Proteins 2009.