Applications of the molecular dynamics flexible fitting method

In recent years, cryo-electron microscopy (cryo-EM) has established itself as a key method in structural biology, permitting the structural characterization of large biomolecular complexes in various functional states. The data obtained through single-particle cryo-EM has recently seen a leap in resolution thanks to landmark advances in experimental and computational techniques, resulting in sub-nanometer resolution structures being obtained routinely. The remaining gap between these data and revealing the mechanisms of molecular function can be closed through hybrid modeling tools that incorporate known atomic structures into the cryo-EM data. One such tool, molecular dynamics flexible fitting (MDFF), uses molecular dynamics simulations to combine structures from X-ray crystallography with cryo-EM density maps to derive atomic models of large biomolecular complexes. The structures furnished by MDFF can be used subsequently in computational investigations aimed at revealing the dynamics of the complexes under study. In the present work, recent applications of MDFF are presented, including the interpretation of cryo-EM data of the ribosome at different stages of translation and the structure of a membrane-curvature-inducing photosynthetic complex.     

Using enhanced sampling and structural restraints to refine atomic structures into low-resolution electron microscopy maps

For a variety of problems in structural biology, low-resolution maps generated by electron microscopy imaging are often interpreted with the help of various flexible-fitting computational algorithms. In this work, we systematically analyze the quality of final models of various proteins obtained via molecular dynamics flexible fitting (MDFF) by varying the map-resolution, strength of structural restraints, and the steering forces. We find that MDFF can be extended to understand conformational changes in lower-resolution maps if larger structural restraints and lower steering forces are used to prevent overfitting. We further show that the capabilities of MDFF can be extended by combining it with an enhanced conformational sampling method, temperature-accelerated molecular dynamics (TAMD). Specifically, either TAMD can be used to generate better starting configurations for MDFF fitting or TAMD-assisted MDFF (TAMDFF) can be performed to accelerate conformational search in atomistic simulations.     

Symmetry-restrained flexible fitting for symmetric EM maps

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.     

Simulations of the p97 complex suggest novel conformational states of hydrolysis intermediates

The vitally important AAA (ATPases associated with various cellular activities) protein p97 is involved in cellular functions ranging from replication to degradation of misfolded proteins and has recently been proposed as a novel chemotherapeutic target. p97 is a large molecular machine that has been shown to hexamerize in vitro, with each monomer consisting of an N domain responsible for binding to effector proteins and two AAA repeats (D1 and D2). However, structural studies are inconclusive or in disagreement with one another on several important features such as the locations of the N domains, the relative orientations of the D1 and D2 rings, and the dimensions of the central pore. Here, we present atomic-scale simulations of the p97 hexamer in the prehydrolysis, transition, and post-hydrolysis states. To improve the agreement between low- and high-resolution experimental studies, we first use a biased simulation technique, molecular dynamics flexible fitting (MDFF), to improve the correlation between the structures described in these experiments. We follow this with extended, classical molecular dynamics simulations, which not only show that structures generated in the MDFF phase are stable, but reveal insights into the dynamics important to each state. Simulation results suggest a hybrid model for hydrolysis, in which the N and D2 domains are dynamic while the D1 domains are relatively static, salt bridges stabilize the position of the N domains in the pre-hydrolysis state, and the rings formed by D1 and D2 rotate relative to one another.     

Cryo-electron microscopy modeling by the molecular dynamics flexible fitting method

The increasing power and popularity of cryo-electron microscopy (cryo-EM) in structural biology brought about the development of so-called hybrid methods, which permit the interpretation of cryo-EM density maps beyond their nominal resolution in terms of atomic models. The Cryo-EM Modeling Challenge 2010 is the first community effort to bring together developers of hybrid methods as well as cryo-EM experimentalists. Participating in the challenge, the molecular dynamics flexible fitting (MDFF) method was applied to a number of cryo-EM density maps. The results are described here with special emphasis on the use of symmetry-based restraints to improve the quality of atomic models derived from density maps of symmetric complexes; on a comparison of the stereochemical quality of atomic models resulting from different hybrid methods; and on application of MDFF to electron crystallography data.     

NMMD: Efficient Cryo-EM Flexible Fitting Based on Simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.     

Flexible fitting of high-resolution x-ray structures into cryoelectron microscopy maps using biased molecular dynamics simulations

A methodology for flexible fitting of all-atom high-resolution structures into low-resolution cryoelectron microscopy (cryo-EM) maps is presented. Flexibility of the modeled structure is simulated by classical molecular dynamics and an additional effective potential is introduced to enhance the fitting process. The additional potential is proportional to the correlation coefficient between the experimental cryo-EM map and a synthetic map generated for an all-atom structure being fitted to the map. The additional forces are calculated as a gradient of the correlation coefficient. During the molecular dynamics simulations under the additional forces, the molecule undergoes a conformational transition that maximizes the correlation coefficient, which results in a high-accuracy fit of all-atom structure into a cryo-EM map. Using five test proteins that exhibit structural rearrangement during their biological activity, we demonstrate performance of our method. We also test our method on the experimental cryo-EM of elongation factor G and show that the model obtained is comparable to previous studies. In addition, we show that overfitting can be avoided by assessing the quality of the fitted model in terms of correlation coefficient and secondary structure preservation.     

HingeProt: automated prediction of hinges in protein structures

Proteins are highly flexible molecules. Prediction of molecular flexibility aids in the comprehension and prediction of protein function and in providing details of functional mechanisms. The ability to predict the locations, directions, and extent of molecular movements can assist in fitting atomic resolution structures to low-resolution EM density maps and in predicting the complex structures of interacting molecules (docking). There are several types of molecular movements. In this work, we focus on the prediction of hinge movements. Given a single protein structure, the method automatically divides it into the rigid parts and the hinge regions connecting them. The method employs the Elastic Network Model, which is very efficient and was validated against a large data set of proteins. The output can be used in applications such as flexible protein-protein and protein-ligand docking, flexible docking of protein structures into cryo-EM maps, and refinement of low-resolution EM structures. The web server of HingeProt provides convenient visualization of the results and is available with two mirror sites at http://www.prc.boun.edu.tr/appserv/prc/HingeProt3 and http://bioinfo3d.cs.tau.ac.il/HingeProt/.     

An Intrinsically Disordered Region of the Adenovirus Capsid Is Implicated in Neutralization by Human Alpha Defensin 5

Human α-defensins are proteins of the innate immune system that suppress viral and bacterial infections by multiple mechanisms including membrane disruption. For viruses that lack envelopes, such as human adenovirus (HAdV), other, less well defined, mechanisms must be involved. A previous structural study on the interaction of an α-defensin, human α-defensin 5 (HD5), with HAdV led to a proposed mechanism in which HD5 stabilizes the vertex region of the capsid and blocks uncoating steps required for infectivity. Studies with virus chimeras comprised of capsid proteins from sensitive and resistant serotypes supported this model. To further characterize the critical binding site, we determined subnanometer resolution cryo-electron microscopy (cryoEM) structures of HD5 complexed with both neutralization-sensitive and -resistant HAdV chimeras. Models were built for the vertex regions of these chimeras with monomeric and dimeric forms of HD5 in various initial orientations. CryoEM guided molecular dynamics flexible fitting (MDFF) was used to restrain the majority of the vertex model in well-defined cryoEM density. The RGD-containing penton base loops of both the sensitive and resistant virus chimeras are predicted to be intrinsically disordered, and little cryoEM density is observed for them. In simulations these loops from the sensitive virus chimera, interact with HD5, bridge the penton base and fiber proteins, and provides significant stabilization with a three-fold increase in the intermolecular nonbonded interactions of the vertex complex. In the case of the resistant virus chimera, simulations revealed fewer bridging interactions and reduced stabilization by HD5. This study implicates a key dynamic region in mediating a stabilizing interaction between a viral capsid and a protein of the innate immune system with potent anti-viral activity.     

Refinement of a cryo-EM structure of hERG: Bridging structure and function

The human-ether-a-go-go-related gene (hERG) encodes the voltage-gated potassium channel (KCNH2 or Kv11.1, commonly known as hERG). This channel plays a pivotal role in the stability of phase 3 repolarization of the cardiac action potential. Although a high-resolution cryo-EM structure is available for its depolarized (open) state, the structure surprisingly did not feature many functionally important interactions established by previous biochemical and electrophysiology experiments. Using molecular dynamics flexible fitting (MDFF), we refined the structure and recovered the missing functionally relevant salt bridges in hERG in its depolarized state. We also performed electrophysiology experiments to confirm the functional relevance of a novel salt bridge predicted by our refinement protocol. Our work shows how refinement of a high-resolution cryo-EM structure helps to bridge the existing gap between the structure and function in the voltage-sensing domain (VSD) of hERG.     

Functional conformations of the L11-ribosomal RNA complex revealed by correlative analysis of cryo-EM and molecular dynamics simulations

The interaction between the GTPase-associated center (GAC) and the aminoacyl-tRNA.EF-Tu.GTP ternary complex is of crucial importance in the dynamic process of decoding and tRNA accommodation. The GAC includes protein L11 and helices 43-44 of 23S rRNA (referred to as L11-rRNA complex). In this study, a method of fitting based on a systematic comparison between cryo-electron microscopy (cryo-EM) density maps and structures obtained by molecular dynamics simulations has been developed. This method has led to the finding of atomic models of the GAC that fit the EM maps with much improved cross-correlation coefficients compared with the fitting of the X-ray structure. Two types of conformations of the L11-rRNA complex, produced by the simulations, match the cryo-EM maps representing the states either bound or unbound to the aa-tRNA.EF-Tu.GTP ternary complex. In the bound state, the N-terminal domain of L11 is extended from its position in the crystal structure, and the base of nucleotide A1067 in the 23S ribosomal RNA is flipped out. This position of the base allows the RNA to reach the elbow region of the aminoacyl-tRNA when the latter is bound in the A/T site. In the unbound state, the N-terminal domain of L11 is rotated only slightly, and A1067 of the RNA is flipped back into the less-solvent-exposed position, as in the crystal structure. By matching our experimental cryo-EM maps with much improved cross-correlation coefficients compared to the crystal structure, these two conformations prove to be strong candidates of the two functional states.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

Rigid-body fitting to atomic force microscopy images for inferring probe shape and biomolecular structure

Atomic force microscopy (AFM) can visualize functional biomolecules near the physiological condition, but the observed data are limited to the surface height of specimens. Since the AFM images highly depend on the probe tip shape, for successful inference of molecular structures from the measurement, the knowledge of the probe shape is required, but is often missing. Here, we developed a method of the rigid-body fitting to AFM images, which simultaneously finds the shape of the probe tip and the placement of the molecular structure via an exhaustive search. First, we examined four similarity scores via twin-experiments for four test proteins, finding that the cosine similarity score generally worked best, whereas the pixel-RMSD and the correlation coefficient were also useful. We then applied the method to two experimental high-speed-AFM images inferring the probe shape and the molecular placement. The results suggest that the appropriate similarity score can differ between target systems. For an actin filament image, the cosine similarity apparently worked best. For an image of the flagellar protein FlhA_C, we found the correlation coefficient gave better results. This difference may partly be attributed to the flexibility in the target molecule, ignored in the rigid-body fitting. The inferred tip shape and placement results can be further refined by other methods, such as the flexible fitting molecular dynamics simulations. The developed software is publicly available.     

Relative flexibility of DNA and RNA: a molecular dynamics study

State of the art molecular dynamics simulations are used to study the structure, dynamics, molecular interaction properties and flexibility of DNA and RNA duplexes in aqueous solution. Special attention is paid to the deformability of both types of structures, revisiting concepts on the relative flexibility of DNA and RNA duplexes. Our simulations strongly suggest that the concepts of flexibility, rigidity and deformability are much more complex than usually believed, and that it is not always true that DNA is more flexible than RNA.     

The investigation of the effects of counterions in protein dynamics simulations.

Molecular simulations able to exactly represent solvated charged proteins are helpful in understanding protein dynamics, structure and function. In the present study we have used two different starting structures of papain (a typical, stable, globular protein of intermediate net charge) and different modeling procedures to evaluate some effects of counterions in simulations. A number of configurations have been generated and relaxed for each system by various combinations of constrained simulated annealing and molecular dynamics procedures, using the AMBER force field. The analysis of trajectories shows that the simulations of solvated proteins are moderately sensitive to the presence of counterions. However, this sensitivity is highly dependent on the starting model and different procedures of equilibration used. The neutralized systems tend to evince smaller root mean square deviations regardless of the system investigated and the simulation procedure used. The results of parameterized fitting of the simulated structures to the crystallographic data, giving quantitative measure of the total charge influence on the stability of various elements of the secondary structure, revealed a clear scatter of different reactions of various systems' secondary structures to counterions addition: some systems apparently were stabilized when neutralized, while the others were not. Thus, one cannot unequivocally state, despite consideration of specific simulation conditions, whether protein secondary structures are more stable when they have neutralized charges. This suggests that caution should be taken when claiming the stabilizing effect of counterions in simulations other than those involving small, unstable polypeptides or highly charged proteins.     

Implicit solvent models for flexible protein-protein docking by molecular dynamics simulation

The suitability of three implicit solvent models for flexible protein-protein docking by procedures using molecular dynamics simulation is investigated. The three models are (i) the generalized Born (GB) model implemented in the program AMBER6.0; (ii) a distance-dependent dielectric (DDD) model; and (iii) a surface area-dependent model that we have parameterized and call the NPSA model. This is a distance-dependent dielectric model modified by neutralizing the ionizable side-chains and adding a surface area-dependent solvation term. These solvent models were first tested in molecular dynamics simulations at 300 K of the native structures of barnase, barstar, segment B1 of protein G, and three WW domains. These protein structures display a range of secondary structure contents and stabilities. Then, to investigate the performance of the implicit solvent models in protein docking, molecular dynamics simulations of barnase/barstar complexation, as well as PIN1 WW domain/peptide complexation, were conducted, starting from separated unbound structures. The simulations show that the NPSA model has significant advantages over the DDD and GB models in maintaining the native structures of the proteins and providing more accurate docked complexes.     

All-atom structural investigation of kinesin-microtubule complex constrained by high-quality cryo-electron-microscopy maps

In this study, we have performed a comprehensive structural investigation of three major biochemical states of a kinesin complexed with microtubule under the constraint of high-quality cryo-electron-microscopy (EM) maps. In addition to the ADP and ATP state which were captured by X-ray crystallography, we have also modeled the nucleotide-free or APO state for which no crystal structure is available. We have combined flexible fitting of EM maps with regular molecular dynamics simulations, hydrogen-bond analysis, and free energy calculation. Our APO-state models feature a subdomain rotation involving loop L2 and α6 helix of kinesin, and local structural changes in active site similar to a related motor protein, myosin. We have identified a list of hydrogen bonds involving key residues in the active site and the binding interface between kinesin and microtubule. Some of these hydrogen bonds may play an important role in coupling microtubule binding to ATPase activities in kinesin. We have validated our models by calculating the binding free energy between kinesin and microtubule, which quantitatively accounts for the observation of strong binding in the APO and ATP state and weak binding in the ADP state. This study will offer promising targets for future mutational and functional studies to investigate the mechanism of kinesin motors.     

Refinement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers

We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the alpha/gamma concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the alpha/gamma = (g+,t) backbone that were seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm94-99). The force field has been derived by fitting to high-level quantum mechanical data and verified by comparison with very high-level quantum mechanical calculations and by a very extensive comparison between simulations and experimental data. The set of validation simulations includes two of the longest trajectories published to date for the DNA duplex (200 ns each) and the largest variety of NA structures studied to date (15 different NA families and 97 individual structures). The total simulation time used to validate the force field includes near 1 mus of state-of-the-art molecular dynamics simulations in aqueous solution.