Filtering molecular dynamics trajectories to reveal low-frequency collective motions: phospholipase A2

A novel method for analysing molecular dynamics trajectories has been developed, which filters out high frequencies using digital signal processing techniques and facilitates focusing on the low-frequency collective motions of proteins. These motions involve low energy slow motions, which lead to important biological phenomena such as domain closure and allosteric effects in enzymes. The filtering method treats each of the atomic trajectories obtained from the molecular dynamics simulation as a "signal". The trajectories of each of the atoms in the system (or any subset of interest) are Fourier transformed to the frequency domain, a filtering function is applied and then an inverse transformation back to the time domain yields the filtered trajectory. The filtering method has been used to study the dynamics of the enzyme phospholipase A2. In the filtered trajectory, all the high frequency bond and valence angle vibrations were eliminated, leaving only low-frequency motion, mainly fluctuations in torsions and conformational transitions. Analysis of this trajectory revealed interesting motions of the protein, including concerted movements of helices, and changes in shape of the active site cavity. Unlike normal mode analysis, which has been used to study the motion of proteins, this method does not require converged minimizations or diagonalization of a matrix of second derivatives. In addition, anharmonicity, multiple minima and conformational transitions are treated explicitly. Thus, the filtering method avoids most of the approximations implicit in other investigations of the dynamic behaviour of large systems.     

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.     

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.     

Temperature-dependent molecular dynamics and restrained X-ray refinement simulations of a Z-DNA hexamer

Molecular dynamics simulations of the Z-DNA hexamer 5BrdC-dG-5BrdC-dG-5BrdC-dG were performed at several temperatures between 100 K and 300 K. Above 250 K, a strong sequence-dependent flexibility in the nucleic acid is observed, with the guanine sugar and the phosphate of GpC sequences much more mobile than the cytosine sugar and phosphate of CpG sequences. At 300 K, the hexamer is in dynamic equilibrium between several Z forms, including the crystallographically determined ZI and ZII forms. The local base-pair geometry, however, is not very variable, except for the roll of the base-pairs. The hexamer molecular dynamics trajectories have been used to test the restrained parameter crystallographic refinement model for nucleic acids. X-ray diffraction intensities corresponding to observed diffraction data were computed. The average structures obtained from the simulations were then refined against the calculated intensities, using a restrained least-squares program developed for nucleic acids in order to analyse the effects of the refinement model on the derived quantities. In general, the temperature dependence of the atomic fluctuations determined directly from the refined Debye-Waller factors is in reasonably good agreement with the results obtained by calculating the atomic fluctuations directly from the Z-DNA molecular dynamics trajectories. The agreement is best for refinement of temperature factors without restraints. At the highest temperature studied (300 K), the effect of the refinement on the most mobile atoms (phosphates) is to significantly reduce the mean-square atomic fluctuations estimated from the refined Debye-Waller factors below the actual values (less than (delta r)2 greater than congruent to 0.5 A2). Analysis of the temperature-dependence of the mean-square atomic fluctuations provides information concerning the conformational potential within which the atoms move. The calculated temperature-dependence and anharmonicity of the Z-DNA helix are compared with the results observed for proteins. The average structures from the simulations were refined against the experimental X-ray intensities. It is found that low-temperature molecular dynamics simulations provide a useful tool for optimizing the refinement of X-ray structures.     

The essential dynamics of thermolysin: Confirmation of the hinge-bending motion and comparison of simulations in vacuum and water

Comparisons of the crystal structures of thermolysin and the thermolysin-like protease produced by B. cereus have recently led to the hypothesis that neutral proteases undergo a hinge-bending motion. We have investigated this hypothesis by analyzing molecular dynamics simulations of thermolysin in vacuum and water, using the essential dynamics method. This method is able to extract large concerted atomic motions of biological importance from a molecular dynamics trajectory. The analysis of the thermolysin trajectories indeed revealed a large rigid body hinge-bending motion of the Nterminal and C-terminal domains, similar to the motion hypothesized from the crystal structure comparisons. In addition, it appeared that the essential dynamics properties derived from the vacuum simulation were similar to those derived from the solvent simulation. © 1995 Wiley-Liss, Inc.     

Nucleic acid solvation: from outside to insight

Nucleic acids are polyanionic molecules that were historically considered to be solely surrounded by a shell of water molecules and a neutralizing cloud of monovalent and divalent cations. In this respect, recent experimental and theoretical reports demonstrate that water molecules within complex nucleic acid structures can display very long residency times, and assist drug binding and catalytic reactions. Finally, anions can also bind to these polyanionic systems. Many of these recent insights are provided by state-of-the-art molecular dynamics simulations of nucleic acid systems, which will be described together with relevant methodological issues.     

Computer simulations of the flexibility of a series of synthetic cyclic peptide analogues

The flexibility of a series of cyclic peptides derived from the epitope of a snake toxin is investigated using computer simulation techniques. Molecular dynamics (MD) simulations and vibrational analyses are performed on chemically constrained peptides modeled on the parent protein loop. In the 50 ps MD simulations, large variations in the atomic fluctuations are seen between the peptides, and can be related to the nature of the chemical constraints present in the molecules. Normal mode analyses are performed on energy-minimized configurations derived from the dynamics trajectories. The atomic fluctuations calculated from the normal modes are about 30% of those of the molecular dynamics for the more flexible peptides and 70% for the more constrained molecules. The calculated differences in flexibility between the molecules are much less significant in the harmonic approximation. © 1993 John Wiley & Sons, Inc.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

DROIDS 3.0—Detecting Genetic and Drug Class Variant Impact on Conserved Protein Binding Dynamics

The application of statistical methods to comparatively framed questions about the molecular dynamics (MD) of proteins can potentially enable investigations of biomolecular function beyond the current sequence and structural methods in bioinformatics. However, the chaotic behavior in single MD trajectories requires statistical inference that is derived from large ensembles of simulations representing the comparative functional states of a protein under investigation. Meaningful interpretation of such complex forms of big data poses serious challenges to users of MD. Here, we announce Detecting Relative Outlier Impacts from Molecular Dynamic Simulation (DROIDS) 3.0, a method and software package for comparative protein dynamics that includes maxDemon 1.0, a multimethod machine learning application that trains on large ensemble comparisons of concerted protein motions in opposing functional states generated by DROIDS and deploys learned classifications of these states onto newly generated MD simulations. Local canonical correlations in learning patterns generated from independent, yet identically prepared, MD validation runs are used to identify regions of functionally conserved protein dynamics. The subsequent impacts of genetic and/or drug class variants on conserved dynamics can also be analyzed by deploying the classifiers on variant MD simulations and quantifying how often these altered protein systems display opposing functional states. Here, we present several case studies of complex changes in functional protein dynamics caused by temperature, genetic mutation, and binding interactions with nucleic acids and small molecules. We demonstrate that our machine learning algorithm can properly identify regions of functionally conserved dynamics in ubiquitin and TATA-binding protein (TBP). We quantify the impact of genetic variation in TBP and drug class variation targeting the ATP-binding region of Hsp90 on conserved dynamics. We identify regions of conserved dynamics in Hsp90 that connect the ATP binding pocket to other functional regions. We also demonstrate that dynamic impacts of various Hsp90 inhibitors rank accordingly with how closely they mimic natural ATP binding.     

Generalized correlation for biomolecular dynamics

Correlated motions in biomolecules are often essential for their function, e.g., allosteric signal transduction or mechanical/thermodynamic energy transport. Because correlated motions in biomolecules remain difficult to access experimentally, molecular dynamics (MD) simulations are particular useful for their analysis. The established method to quantify correlations from MD simulations via calculation of the covariance matrix, however, is restricted to linear correlations and therefore misses part of the correlations in the atomic fluctuations. Herein, we propose a general statistical mechanics approach to detect and quantify any correlated motion from MD trajectories. This generalized correlation measure is contrasted with correlations obtained from covariance matrices for the B1 domain of protein G and T4 lysozyme. The new method successfully quantifies correlations and provides a valuable global overview over the functionally relevant collective motions of lysozyme. In particular, correlated motions of helix 1 together with the two main lobes of lysozyme are detected, which are not seen by the conventional covariance matrix. Overall, the established method misses more than 50% of the correlation. This failure is attributed to both, an interfering and unnecessary dependence on mutual orientations of the atomic fluctuations and, to a lesser extent, attributed to nonlinear correlations. Our generalized correlation measure overcomes these problems and, moreover, allows for an improved understanding of the conformational dynamics by separating linear and nonlinear contributions of the correlation.     

An introduction to biomolecular simulations and docking

The biomolecules in and around a living cell – proteins, nucleic acids, lipids and carbohydrates – continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given biomolecule also samples (and is sampled by) a rapidly fluctuating local environment comprising other biopolymers, small molecules, water, ions, etc. that diffuse to within a few nanometres, leading to inter-molecular contacts that stitch together large supramolecular assemblies. Indeed, all biological systems can be viewed as dynamic networks of molecular interactions. As a complement to experimentation, molecular simulation offers a uniquely powerful approach to analyse biomolecular structure, mechanism and dynamics; this is possible because the molecular contacts that define a complicated biomolecular system are governed by the same physical principles (forces and energetics) that characterise individual small molecules, and these simpler systems are relatively well-understood. With modern algorithms and computing capabilities, simulations are now an indispensable tool for examining biomolecular assemblies in atomic detail, from the conformational motion in an individual protein to the diffusional dynamics and inter-molecular collisions in the early stages of formation of cellular-scale assemblies such as the ribosome. This text introduces the physicochemical foundations of molecular simulations and docking, largely from the perspective of biomolecular interactions.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Double-strand DNA end-binding and sliding of the toroidal CRISPR-associated protein Csn2

The adaptive immunity of bacteria against foreign nucleic acids, mediated by CRISPR (clustered regularly interspaced short palindromic repeats), relies on the specific incorporation of short pieces of the invading foreign DNA into a special genomic locus, termed CRISPR array. The stored sequences (spacers) are subsequently used in the form of small RNAs (crRNAs) to interfere with the target nucleic acid. We explored the DNA-binding mechanism of the immunization protein Csn2 from the human pathogen Streptococcus agalactiae using different biochemical techniques, atomic force microscopic imaging and molecular dynamics simulations. The results demonstrate that the ring-shaped Csn2 tetramer binds DNA ends through its central hole and slides inward, likely by a screw motion along the helical path of the enclosed DNA. The presented data indicate an accessory function of Csn2 during integration of exogenous DNA by end-joining.     

DNA conformation and dynamics

Nucleotide conformation and dynamics are important for the study of radiation damage to DNA at the atomic level. It is necessary to study not only normal oligonucleotide structure but also those containing modified bases which result from interaction with OH-radicals. There are now over 8000 atomic coordinate entries in the Brookhaven Protein Data Bank, of which over 900 relate to experimentally determined structures of nucleic acids and nucleic acid/protein complexes. We review some of these data which have led to the elucidation of novel DNA conformations, insight into DNA sequence specificity and knowledge of protein/DNA interactions. Further understanding of the conformation, stability and dynamics of nucleic acids has come from molecular modelling. We have used such techniques to study chemical modifications to bases such as alkylation of thymine and guanine and the effects of curvature in longer sequences. Recent improvements in this area include the inclusions of explicit counter-ions and solvent molecules, the use of Particle Mesh Ewald methods to incorporate the long-range electrostatic interactions and the use of longer time scale simulations. We have employed these methods to analyse the effects of incorporation of 8-oxodeoxyguanosine into duplex DNA. This lesion is a common result of radiation damage and is known to have important effects in mutagenesis, cancer and ageing. Received: 7 October 1998 / Accepted in revised form: 18 January 1999     

Effect of atom- and group-based truncations on biomolecules simulated with reaction-field electrostatics

The performance of the reaction-field method of electrostatics is tested in molecular dynamics simulations of protein human interleukin-4 and a short DNA fragment in explicit solvent. Two truncation schemes are considered: one based on the position of atomic charges in water molecules and the other on the position of groups of charges. The group-based truncation leads to the melting of the DNA double helix. In contrast, the atom-based truncation maintains the helical structure intact. Similarly for the protein, the group-based truncation leads to an unfolding at pH 2 while the atom-based truncation produces stable trajectories at low and normal pH, in agreement with experiment. Artificial repulsion between charged residues associated with the group-based truncation is identified as the microscopic reason behind unfolding of the protein. Implications of different truncation schemes in reaction-field simulations of biomolecules are discussed.     

Visualization of energetics and conformations from molecular computer simulations

The quantity of data generated from molecular dynamics simulations and energy minimizations of macromolecules is overwhelming. It is an arduous task to extract the relevant and interesting information from the numerous coordinate sets produced. To help solve this problem, the authors have developed a method to aid the visualization of the relevant information from the simulations. This approach combines animation of the results on a high performance graphics device, such as the PS300, with colour-coded atoms based on changes in energy or conformation. The method will be illustrated using as examples: the molecular mechanics minimization of a nonapeptide, the molecular dynamics simulation of the protein myoglobin, including the analysis of the motion of helices during a 300ps trajectory, and changes in sugar puckering that occur during the molecular dynamics simulation of a DNA oligomer. The method is also applicable for analysing energy components and conformational properties of a fixed conformation.     

Extraction of the energetics of selected types of motion from molecular dynamics trajectories by filtering

A novel method for analyzing molecular dynamics trajectories has been developed which enables the study of selected motions and the corresponding energetics. In particular, it is possible to filter out the high-frequency motions and focus on the structural and energetic features of low-frequency collective motions. The trajectories of the properties of interest are Fourier transformed to the frequency domain, a filtering function is applied, and then an inverse transformation back to the time domain yields the filtered trajectory. The method is demonstrated for harmonic fluctuations and conformational transitions of acetamide and N-acetylalanine N-methylamide, as models for peptides and proteins.     

Molecular dynamics simulations of G-DNA and perspectives on the simulation of nucleic acid structures

The article reviews the application of biomolecular simulation methods to understand the structure, dynamics and interactions of nucleic acids with a focus on explicit solvent molecular dynamics simulations of guanine quadruplex (G-DNA and G-RNA) molecules. While primarily dealing with these exciting and highly relevant four-stranded systems, where recent and past simulations have provided several interesting results and novel insight into G-DNA structure, the review provides some general perspectives on the applicability of the simulation techniques to nucleic acids.     

Molecular dynamics study of conformational changes in human serum albumin by binding of fatty acids

Human serum albumin (HSA) binds with fatty acids under normal physiologic conditions. To date, there is little published information on the tertiary structure of HSA-fatty acid complex in aqueous solution. In the present study, we used molecular dynamics (MD) simulations to elucidate possible structural changes of HSA brought about by the binding of fatty acids. Both unliganded HSA and HSA-fatty acid complex models for MD calculations were constructed based on the X-ray crystal structures. Five myristates (MYRs) were bound in the HSA-fatty acid complex model. In the present MD study, the motion of domains I and III caused by the binding of MYR molecules increased the radius of gyration of HSA. Root-mean-square fluctuations from the MD simulations revealed that the atomic fluctuations of the specific amino acids at drug-binding site I that can regulate the drug-binding affinity were increased by the binding of MYR molecules. Primary internal motions, characterized by the first three principal components, were observed mainly at domains I and III in the principal component analysis for trajectory data. The directional motion projected on the first principal component of unliganded HSA was conserved in HSA-MYR complex as the third principal directional motion with higher frequency. However, the third principal directional motion in unliganded HSA turned into the first principal directional motion with lower frequency in the HSA-MYR complex. Thus, the present MD study provides insights into the possible conformational changes of HSA caused by the binding of fatty acids.