Effects of Disease Causing Mutations on the Essential Motions in Proteins

Abstract

This study embodies a detailed comparative analysis of the essential motions of the Wild type and the eight different disease mutant forms of the Human CYPlbl. The mutations considered in this study have been implicated in Primary Congenital Glaucoma, an in-born, genetic disorder associated with eye-abnormality. The principal component analysis for Wild type and the Mutants was carried out using the stabilized molecular dynamics trajectories, which ranged from 35 to 45 nanoseconds. Investigations revealed the nature of the collective motions that characterize functionally relevant ‘essential motions’. The essential motions in Wild type are characterized by the collective motions of the Substrate Access Channel including the β-rich domain and the loops in the region of p450-reductase interaction. Comparative analysis of the essential motions of the Wild type and Mutants, especially those involving the functionally important regions indicated distinct differences in their magnitudes as well as the residue-wise distribution. The Mutants in general are associated with higher root mean square fluctuations, and involve some of the relatively intact core regions of the protein, in large collective motions. This study sheds light on the possible effects of disease causing mutations on the large functionally important collective motions in proteins.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.     

Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.     

Frustration‐guided motion planning reveals conformational transitions in proteins

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics‐inspired motion planning procedure called dCC‐RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non‐native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC‐RRT to examine how collective, small‐scale motions of four side‐chains in the active site of cyclophilin A propagate through the protein. dCC‐RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non‐canonical capsid binding site 25 Å away, rationalizing NMR and multi‐temperature crystallography experiments. In all, dCC‐RRT can reveal detailed, all‐atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/ .     

THz time scale structural rearrangements and binding modes in lysozyme-ligand interactions

Predicting the conformational changes in proteins that are relevant for substrate binding is an ongoing challenge in the aim of elucidating the functional states of proteins. The motions that are induced by protein-ligand interactions are governed by the protein global modes. Our measurements indicate that the detected changes in the global backbone motion of the enzyme upon binding reflect a shift from the large-scale collective dominant mode in the unbound state towards a functional twisting deformation that assists in closing the binding cleft. Correlated motion in lysozyme has been implicated in enzyme function in previous studies, but detailed characterization of the internal fluctuations that enable the protein to explore the ensemble of conformations that ultimately foster large-scale conformational change is yet unknown. For this reason, we use THz spectroscopy to investigate the picosecond time scale binding modes and collective structural rearrangements that take place in hen egg white lysozyme (HEWL) when bound by the inhibitor (NAG) ₃. These protein thermal motions correspond to fluctuations that have a role in both selecting and sampling from the available protein intrinsic conformations that communicate function. Hence, investigation of these fast, collective modes may provide knowledge about the mechanism leading to the preferred binding process in HEWL-(NAG) ₃. Specifically, in this work we find that the picosecond time scale hydrogen-bonding rearrangements taking place in the protein hydration shell with binding modify the packing density within the hydrophobic core on a local level. These localized, intramolecular contact variations within the protein core appear to facilitate the large cooperative movements within the interfacial region separating the α- and β- domain that mediate binding. The THz time-scale fluctuations identified in the protein-ligand system may also reveal a molecular mechanism for substrate recognition.     

A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.     

Coarse-grained normal mode analysis in structural biology

The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained normal mode analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained normal mode analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.     

Exploring the Contribution of Collective Motions to the Dynamics of Forced-Unfolding in Tubulin

Decomposition of the intrinsic dynamics of proteins into collective motions among distant regions of the protein structure provides a physically appealing approach that couples the dynamics of the system with its functional role. The cellular functions of microtubules (an essential component of the cytoskeleton in all eukaryotic cells) depend on their dynamic instability, which is altered by various factors among which applied forces are central. To shed light on the coupling between forces and the dynamic instability of microtubules, we focus on the investigation of the response of the microtubule subunits (tubulin) to applied forces. We address this point by adapting an approach designed to survey correlations for the equilibrium dynamics of proteins to the case of correlations for proteins forced-dynamics. The resulting collective motions in tubulin have a number of functional implications, such as the identification of long-range couplings with a role in blocking the dynamic instability of microtubules. A fundamental implication of our study for the life of a cell is that, to increase the likelihood of unraveling of large cytoskeletal filaments under physiological forces, molecular motors must use a combination of pulling and torsion rather than just pulling.     

Concerted motions in copper plastocyanin and azurin: an essential dynamics study

Essential dynamics analysis of molecular dynamics simulation trajectories (1.1 ns) of two copper containing electron transfer proteins, plastocyanin and azurin, has been performed. The protein essential modes have been analysed in order to identify large concerted motions which could be relevant for the electron transfer function exerted by these proteins. The analysis, conducted for temporal windows of different lengths along the protein trajectories, shows a rapid convergence and indicates that for both the proteins the predominant internal motions occur in a subspace of only a few degrees of freedom. Moreover, it is found that for both the proteins the likely binding sites (i.e. the hydrophobic and negative patches) with the reaction partners move in a concerted fashion with a few structural regions far from the active site. Such results are discussed in connection with the possible involvement of large concerted motions in the recognition and binding interaction with physiological electron transfer partners.     

A Direct Coupling between Global and Internal Motions in a Single Domain Protein? MD Investigation of Extreme Scenarios

Proteins are not rigid molecules, but exhibit internal motions on timescales ranging from femto- to milliseconds and beyond. In solution, proteins also experience global translational and rotational motions, sometimes on timescales comparable to those of the internal fluctuations. The possibility that internal and global motions may be directly coupled has intriguing implications, given that enzymes and cell signaling proteins typically associate with binding partners and cellular scaffolds. Such processes alter their global motion and may affect protein function. Here, we present molecular dynamics simulations of extreme case scenarios to examine whether a possible relationship exists. In our model protein, a ubiquitin-like RhoGTPase binding domain of plexin-B1, we removed either internal or global motions. Comparisons with unrestrained simulations show that internal and global motions are not appreciably coupled in this single-domain protein. This lack of coupling is consistent with the observation that the dynamics of water around the protein, which is thought to permit, if not stimulate, internal dynamics, is also largely independent of global motion. We discuss implications of these results for the structure and function of proteins.     

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Anisotropic network model: systematic evaluation and a new web interface

MOTIVATION: The Anisotropic Network Model (ANM) is a simple yet powerful model for normal mode analysis of proteins. Despite its broad use for exploring biomolecular collective motions, ANM has not been systematically evaluated to date. A lack of a convenient interface has been an additional obstacle for easy usage. RESULTS: ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability. Residue fluctuations in globular proteins are shown to be more accurately predicted than those in nonglobular proteins, and core residues are more accurately described than solvent-exposed ones. Significant improvement in agreement with experiments is observed with increase in the resolution of the examined structure. A new server for ANM calculations is presented, which offers flexible options for controlling model parameters and output formats, interactive animation of collective modes and advanced graphical features. AVAILABILITY: ANM server (http://www.ccbb.pitt.edu/anm)     

Collective motions in glucosamine-6-phosphate synthase: influence of ligand binding and role in ammonia channelling and opening of the fructose-6-phosphate binding site

The large protein motions of the bacterial enzyme glucosamine-6-phosphate synthase have been addressed using full atom normal modes analysis for the empty, the glucose-6-phosphate and the glucose-6-phosphate + glutamate bound proteins. The approach that was used involving energy minimizations along the normal modes coordinates identified functional motions of the protein, some of which were characterized earlier by X-ray diffraction studies. This method made it possible for the first time to highlight significant energy differences according to whether none, only one or both of the active sites of the protein were occupied. Our data favoured a specific motion of the glutamine binding domain following the fixation of fructose-6-phosphate and suggested a rigidified structure with both sites occupied. Here, we show that most of the collective large amplitude motions of glucosamine-6-phosphate synthase that are modulated by ligand binding are crucial for the enzyme catalytic cycle, as they strongly modify the geometry of both the ammonia channel and the C-tail, demonstrating their role in ammonia transfer and ligand binding.     

Subtle functional collective motions in pancreatic-like ribonucleases: from ribonuclease A to angiogenin

The analysis of the dynamic behavior of enzymes is fundamental to structural biology. A direct relationship between protein flexibility and biological function has been shown for bovine pancreatic ribonuclease (RNase A) (Rasmussen et al., Nature 1992;357:423-424). More recently, crystallographic studies have shown that functional motions in RNase A involve the enzyme beta-sheet regions that move concertedly on substrate binding and release (Vitagliano et al., Proteins 2002;46:97-104). These motions have been shown to correspond to intrinsic dynamic properties of the native enzyme by molecular dynamics (MD) simulations. To unveil the occurrence of these collective motions in other members of pancreatic-like superfamily, we carried out MD simulations on human angiogenin (Ang). Essential dynamics (ED) analyses performed on the trajectories reveal that Ang exhibits collective motions similar to RNase A, despite the limited sequence identity (33%) of the two proteins. Furthermore, we show that these collective motions are also present in ensembles of experimentally determined structures of both Ang and RNase A. Finally, these subtle concerted beta-sheet motions were also observed for other two members of the pancreatic-like superfamily by comparing the ligand-bound and ligand-free structures of these enzymes. Taken together, these findings suggest that pancreatic-like ribonucleases share an evolutionary conserved dynamic behavior consisting of subtle beta-sheet motions, which are essential for substrate binding and release.     

Diagonalization in a mixed basis: A method to compute low-frequency normal modes for large macromolecules

Low-frequency collective motions in proteins are generally very important for their biological functions. To study such motions, harmonic dynamics proved most useful since it is a straightforward method; it consists of the diagonalization of the Hessian matrix of the potential energy, yielding the vibrational spectrum and the directions of internal motions. Unfortunately, the diagonalization of this matrix requires a large computer memory, which is a limiting factor when the protein contains several thousand atoms. To circumvent this limitation we have developed three methods that enable us to diagonalize large matrices using much less computer memory than the usual harmonic dynamics. The first method is approximate; it consists of diagonalizing small blocks of the Hessian matrix, followed by the coupling of the low-frequency modes obtained for each block. It yields the low-frequency vibrational spectrum with a maximum error of 20%. The second method consists, after diagonalizing small blocks, of coupling the high- and low-frequency modes using an iterative procedure. It yields the exact low-frequency normal modes, but requires a long computational time with convergence problems. The third method, DIMB (Diagonalization in a Mixed Basis), which has the best performance, consists of coupling the approximate low-frequency modes with the mass-weighted cartesian coordinates, also using an iterative procedure. It reduces significantly the required computer memory and converges rapidly. The eigenvalues and eigenvectors obtained by this method are without significant error in the chosen frequency range. Moreover, it is a general method applicable to any problem of diagonalization of a large matrix. We report the application of these methods to a deca-alanine helix, trypsin inhibitor, a neurotoxin, and lysozyme. © 1993 John Wiley & Sons, Inc.     

Terahertz spectroscopy of bacteriorhodopsin and rhodopsin: similarities and differences

We studied the low-frequency terahertz spectroscopy of two photoactive protein systems, rhodopsin and bacteriorhodopsin, as a means to characterize collective low-frequency motions in helical transmembrane proteins. From this work, we found that the nature of the vibrational motions activated by terahertz radiation is surprisingly similar between these two structurally similar proteins. Specifically, at the lowest frequencies probed, the cytoplasmic loop regions of the proteins are highly active; and at the higher terahertz frequencies studied, the extracellular loop regions of the protein systems become vibrationally activated. In the case of bacteriorhodopsin, the calculated terahertz spectra are compared with the experimental terahertz signature. This work illustrates the importance of terahertz spectroscopy to identify vibrational degrees of freedom which correlate to known conformational changes in these proteins.     

Protein conformational transitions explored by mixed elastic network models

We develop a mixed elastic network model (MENM) to study large-scale conformational transitions of proteins between two (or more) known structures. Elastic network potentials for the beginning and end states of a transition are combined, in effect, by adding their respective partition functions. The resulting effective MENM energy function smoothly interpolates between the original surfaces, and retains the beginning and end structures as local minima. Saddle points, transition paths, potentials of mean force, and partition functions can be found efficiently by largely analytic methods. To characterize the protein motions during a conformational transition, we follow "transition paths" on the MENM surface that connect the beginning and end structures and are invariant to parameterizations of the model and the mathematical form of the mixing scheme. As illustrations of the general formalism, we study large-scale conformation changes of the motor proteins KIF1A kinesin and myosin II. We generate possible transition paths for these two proteins that reveal details of their conformational motions. The MENM formalism is computationally efficient and generally applicable even for large protein systems that undergo highly collective structural changes.