Dynamical network of residue-residue contacts reveals coupled allosteric effects in recognition, catalysis, and mutation.

Detailed understanding of how conformational dynamics orchestrates function in allosteric regulation of recognition and catalysis remains ambiguous. Here, we simulate CypA using multiple-microsecond-long atomistic molecular dynamics in explicit solvent and carry out NMR experiments. We analyze a large amount of time-dependent multidimensional data with a coarse-grained approach and map key dynamical features within individual macrostates by defining dynamics in terms of residue-residue contacts. The effects of substrate binding are observed to be largely sensed at a location over 15 Å from the active site, implying its importance in allostery. Using NMR experiments, we confirm that a dynamic cluster of residues in this distal region is directly coupled to the active site. Furthermore, the dynamical network of interresidue contacts is found to be coupled and temporally dispersed, ranging over 4 to 5 orders of magnitude. Finally, using network centrality measures we demonstrate the changes in the communication network, connectivity, and influence of CypA residues upon substrate binding, mutation, and during catalysis. We identify key residues that potentially act as a bottleneck in the communication flow through the distinct regions in CypA and, therefore, as targets for future mutational studies. Mapping these dynamical features and the coupling of dynamics to function has crucial ramifications in understanding allosteric regulation in enzymes and proteins, in general.

Enhanced molecular dynamics sampling of drug target conformations.

Computational docking and virtual screening are two main important methods employed in structure-based drug design. Unlike the traditional approach that allows docking of a flexible ligand against a handful of receptor structures, receptor flexibility has now been appreciated and increasingly incorporated in computer-aided docking. Using a diverse set of receptor conformations increases the chances of finding potential drugs and inhibitors. Molecular dynamics (MD) is greatly useful to generate various receptor conformations. However, the diversity of the structures of the receptor, which is usually much larger than the ligand, depends on the sampling efficiency of MD. Enhanced sampling methods based on accelerated molecular dynamics (aMD) can alleviate the sampling limitation of conventional MD and aid in representation of the phase space to a much greater extent. RaMD-db, a variant of aMD that applies boost potential to the rotatable dihedrals and non-bonded diffusive degrees of freedom has been proven to reproduce the equilibrium properties more accurately and efficiently than aMD. Here, we discuss recent advances in the aMD methodology and review the applicability of RaMD-db as an enhanced sampling method. RaMD-db is shown to be able to generate a broad distribution of structures of a drug target, Cyclophilin A. These structures that have never been observed previously in very long conventional MD can be further used for structure-based computer-aided drug discovery, and docking, and thus, in the identification and design of potential novel inhibitors.

Towards fast, rigorous and efficient conformational sampling of biomolecules: Advances in accelerated molecular dynamics.

BACKGROUND: Accelerated molecular dynamics (aMD) has been proven to be a powerful biasing method for enhanced sampling of biomolecular conformations on general-purpose computational platforms. Biologically important long timescale events that are beyond the reach of standard molecular dynamics can be accessed without losing the detailed atomistic description of the system in aMD. Over other biasing methods, aMD offers the advantages of tuning the level of acceleration to access the desired timescale without any advance knowledge of the reaction coordinate. SCOPE OF REVIEW: Recent advances in the implementation of aMD and its applications to small peptides and biological macromolecules are reviewed here along with a brief account of all the aMD variants introduced in the last decade. MAJOR CONCLUSIONS: In comparison to the original implementation of aMD, the recent variant in which all the rotatable dihedral angles are accelerated (RaMD) exhibits faster convergence rates and significant improvement in statistical accuracy of retrieved thermodynamic properties. RaMD in conjunction with accelerating diffusive degrees of freedom, i.e. dual boosting, has been rigorously tested for the most difficult conformational sampling problem, protein folding. It has been shown that RaMD with dual boosting is capable of efficiently sampling multiple folding and unfolding events in small fast folding proteins. GENERAL SIGNIFICANCE: RaMD with the dual boost approach opens exciting possibilities for sampling multiple timescales in biomolecules. While equilibrium properties can be recovered satisfactorily from aMD-based methods, directly obtaining dynamics and kinetic rates for larger systems presents a future challenge. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

The dilemma of conformational dynamics in enzyme catalysis: perspectives from theory and experiment.

The role of protein dynamics in catalysis is a contemporary issue that has stirred intense debate in the field. This chapter provides a brief overview of the approaches and findings of a wide range of experimental, computational and theoretical studies that have addressed this issue. We summarize the results of our recent atomistic molecular dynamic studies on cis-trans isomerase. Our results help to reconcile the disparate perspectives regarding the complex role of enzyme dynamics in the catalytic step and emphasize the major contribution of transition state stabilization in rate enhancement.

Achieving Rigorous Accelerated Conformational Sampling in Explicit Solvent.

Molecular dynamics simulations can provide valuable atomistic insights into biomolecular function. However, the accuracy of molecular simulations on general-purpose computers depends on the time scale of the events of interest. Advanced simulation methods, such as accelerated molecular dynamics, have shown tremendous promise in sampling the conformational dynamics of biomolecules, where standard molecular dynamics simulations are nonergodic. Here we present a sampling method based on accelerated molecular dynamics in which rotatable dihedral angles and nonbonded interactions are boosted separately. This method (RaMD-db) is a different implementation of the dual-boost accelerated molecular dynamics, introduced earlier. The advantage is that this method speeds up sampling of the conformational space of biomolecules in explicit solvent, as the degrees of freedom most relevant for conformational transitions are accelerated. We tested RaMD-db on one of the most difficult sampling problems - protein folding. Starting from fully extended polypeptide chains, two fast folding α-helical proteins (Trpcage and the double mutant of C-terminal fragment of Villin headpiece) and a designed ß-hairpin (Chignolin) were completely folded to their native structures in very short simulation time. Multiple folding/unfolding transitions could be observed in a single trajectory. Our results show that RaMD-db is a promisingly fast and efficient sampling method for conformational transitions in explicit solvent. RaMD-db thus opens new avenues for understanding biomolecular self-assembly and functional dynamics occurring on long time and length scales.

Resolving the complex role of enzyme conformational dynamics in catalytic function.

Despite growing evidence suggesting the importance of enzyme conformational dynamics (ECD) in catalysis, a consensus on how precisely ECD influences the chemical step and reaction rates is yet to be reached. Here, we characterize ECD in Cyclophilin A, a well-studied peptidyl-prolyl cis-trans isomerase, using normal and accelerated, atomistic molecular dynamics simulations. Kinetics and free energy landscape of the isomerization reaction in solution and enzyme are explored in unconstrained simulations by allowing significantly lower torsional barriers, but in no way compromising the atomistic description of the system or the explicit solvent. We reveal that the reaction dynamics is intricately coupled to enzymatic motions that span multiple timescales and the enzyme modes are selected based on the energy barrier of the chemical step. We show that Kramers' rate theory can be used to present a clear rationale of how ECD affects the reaction dynamics and catalytic rates. The effects of ECD can be incorporated into the effective diffusion coefficient, which we estimate to be about ten times slower in enzyme than in solution. ECD thereby alters the preexponential factor, effectively impeding the rate enhancement. From our analyses, the trend observed for lower torsional barriers can be extrapolated to actual isomerization barriers, allowing successful prediction of the speedup in rates in the presence of CypA, which is in notable agreement with experimental estimates. Our results further reaffirm transition state stabilization as the main effect in enhancing chemical rates and provide a unified view of ECD's role in catalysis from an atomistic perspective.

Atomic-level insights into metabolite recognition and specificity of the SAM-II riboswitch.

Although S-adenosylhomocysteine (SAH), a metabolic by-product of S-adenosylmethionine (SAM), differs from SAM only by a single methyl group and an overall positive charge, SAH binds the SAM-II riboswitch with more than 1000-fold less affinity than SAM. Using atomistic molecular dynamics simulations, we investigated the molecular basis of such high selectivity in ligand recognition by SAM-II riboswitch. The biosynthesis of SAM exclusively generates the (S,S) stereoisomer, and (S,S)-SAM can spontaneously convert to the (R,S) form. We, therefore, also examined the effects of (R,S)-SAM binding to SAM-II and its potential biological function. We find that the unfavorable loss in entropy in SAM-II binding is greater for (S,S)- and (R,S)-SAM than SAH, which is compensated by stabilizing electrostatic interactions with the riboswitch. The positively charged sulfonium moiety on SAM acts as the crucial anchor point responsible for the formation of key ionic interactions as it fits favorably in the negatively charged binding pocket. In contrast, SAH, with its lone pair of electrons on the sulfur, experiences repulsion in the binding pocket of SAM-II and is enthalpically destabilized. In the presence of SAH, similar to the unbound riboswitch, the pseudoknot structure of SAM-II is not completely formed, thus exposing the Shine-Dalgarno sequence. Unlike SAM, this may further facilitate ribosomal assembly and translation initiation. Our analysis of the conformational ensemble sampled by SAM-II in the absence of ligands and when bound to SAM or SAH reveals that ligand binding follows a combination of conformational selection and induced-fit mechanisms.

Improved Statistical Sampling and Accuracy with Accelerated Molecular Dynamics on Rotatable Torsions.

In enhanced sampling techniques, the precision of the reweighted ensemble properties is often decreased due to large variation in statistical weights and reduction in the effective sampling size. To abate this reweighting problem, here, we propose a general accelerated molecular dynamics (aMD) approach in which only the rotatable dihedrals are subjected to aMD (RaMD), unlike the typical implementation wherein all dihedrals are boosted (all-aMD). Nonrotatable and improper dihedrals are marginally important to conformational changes or the different rotameric states. Not accelerating them avoids the sharp increases in the potential energies due to small deviations from their minimum energy conformations and leads to improvement in the precision of RaMD. We present benchmark studies on two model dipeptides, Ace-Ala-Nme and Ace-Trp-Nme, simulated with normal MD, all-aMD, and RaMD. We carry out a systematic comparison between the performances of both forms of aMD using a theory that allows quantitative estimation of the effective number of sampled points and the associated uncertainty. Our results indicate that, for the same level of acceleration and simulation length, as used in all-aMD, RaMD results in significantly less loss in the effective sample size and, hence, increased accuracy in the sampling of φ-ψ space. RaMD yields an accuracy comparable to that of all-aMD, from simulation lengths 5 to 1000 times shorter, depending on the peptide and the acceleration level. Such improvement in speed and accuracy over all-aMD is highly remarkable, suggesting RaMD as a promising method for sampling larger biomolecules.

Extracting Realistic Kinetics of Rare Activated Processes from Accelerated Molecular Dynamics Using Kramers' Theory.

The cis-trans isomerization of peptide bonds is very slow, occurring in hundreds of seconds. Kinetic studies of such processes using straightforward molecular dynamics are currently not possible. Here, we use Kramers' rate theory in the high friction regime in combination with accelerated molecular dynamics in explicit solvent to successfully retrieve the normal rate of cis to trans switching in the glycyl-prolyl dipeptide. Our approach bypasses the time-reweighting problem of the hyperdynamics scheme, wherein the addition of the bias potential alters the transition state regions and avoids an accurate estimation of kinetics. By performing accelerated molecular dynamics at a few different levels of acceleration, the rate of isomerization is enhanced as much as 10(10) to 10(11) times. Remarkably, the normal rates obtained by simply extrapolating to zero bias are within an order of experimental estimates. This provides validation from a kinetic standpoint of the ω torsional parameters of the AMBER force field that were recently revised by matching to experimentally measured equilibrium properties. We also provide a comparative analysis of the performance of the widely used water models, i.e., TIP3P and SPC/E, in estimating the kinetics of cis-trans isomerization. Furthermore, we show that the dynamic properties of bulk water can be corrected by adjusting the collision frequency in a Langevin thermostat, which then allows for better reproduction of cis-trans isomerization kinetics and a closer agreement of rates between experiments and simulations.

Examining the limits of time reweighting and Kramers' rate theory to obtain correct kinetics from accelerated molecular dynamics.

Accelerated molecular dynamics simulations are routinely being used to recover the correct canonical probability distributions corresponding to the original potential energy landscape of biomolecular systems. However, the limits of time reweighting, based on transition state theory, in obtaining true kinetic rates from accelerated molecular dynamics for biomolecular systems are less obvious. Here, we investigate this issue by studying the kinetics of cis-trans isomerization of peptidic omega bond by accelerated molecular dynamics. We find that time reweighting is valid for obtaining true kinetics when the original potential is not altered at the transition state regions, as expected. When the original potential landscape is modified such that the applied boost potential alters the transition state regions, time reweighting fails to reproduce correct kinetics and the reweighted rate is much slower than the true rate. By adopting the overdamped limit of Kramers' rate theory, we are successful in recovering correct kinetics irrespective of whether or not the transition state regions are modified. Furthermore, we tested the validity of the acceleration weight factor from the path integral formalism for obtaining the correct kinetics of cis-trans isomerization. It was found that this formulation of the weight factor is not suitable for long time scale processes such as cis-trans isomerization with high energy barriers.

Water's Contribution to the Energetic Roughness from Peptide Dynamics.

Water plays a very important role in the dynamics and function of proteins. Apart from protein-protein and protein-water interactions, protein motions are accompanied by the formation and breakage of hydrogen-bonding network of the surrounding water molecules. This ordering and reordering of water also adds to the underlying roughness of the energy landscape of proteins and thereby alters their dynamics. Here, we extract the contribution of water to the ruggedness (in terms of an energy scale ε) of the energy landscape from molecular dynamics simulations of a peptide substrate analogue of prolyl cis-trans isomerases. In order to do so, we develop and implement a model based on the position space analog of the Ornstein-Uhlenbeck process and Zwanzig's theory of diffusion on a rough potential. This allows us to also probe an important property of the widely used atomistic simulation water models that directly affects the dynamics of biomolecular systems and highlights the importance of the choice of the water model in studying protein dynamics. We show that water contributes an additional roughness to the energy landscape. At lower temperatures this roughness, which becomes comparable to kBT, can considerably slow down protein dynamics. These results also have much broader implications for the function of some classes of enzymes, since the landscape topology of their substrates may change upon moving from an aqueous environment into the binding site.

Reoptimization of the AMBER force field parameters for peptide bond (Omega) torsions using accelerated molecular dynamics.

Improving the accuracy of molecular mechanics force field parameters for atomistic simulations of proteins and nucleic acids has been an ongoing effort. The availability of computer power and improved methodologies for conformational sampling has allowed the assessment of these parameters by comparing the free energies calculated from molecular dynamic (MD) simulations and those measured from thermodynamic experiments. Here, we focus on testing and optimizing the AMBER force field parameters for the omega dihedral, which represents rotation around the peptide bond of proteins. Due to the very slow isomerization rate of the peptide bond, it is not possible to sample the phase space with standard MD simulations. We therefore employed an accelerated MD method in explicit water in which the original Hamiltonian is modified to speed up conformational sampling and the correct canonical distribution is recaptured. Using well-studied model systems for the peptide and peptidyl prolyl bonds, we discovered that the AMBER omega dihedral parameters underestimated experimentally measured activation free energy barriers for cis/trans conversion as well as failed to reproduce the free energy difference between the two isomers. We reoptimized the original AMBER omega dihedral parameters and further validated their transferability on several experimentally studied dipeptides. The revised set of parameters successfully reproduced the cis/trans equilibria and free energy barriers within experimental and simulation errors. We also investigated the structures of the transition state and cis/trans isomers of prolyl peptide bonds in terms of pyramidality, a measure of the puckering of the prolyl ring. We observed, as expected from quantum mechanical studies, significant bidirectional, out-of-plane motions of prolyl nitrogen in the transition state.

Protein folding rates and stability: how much is there beyond size?

An intriguing feature of protein folding is that the overall behavior obeys simple physical rules, but the finer details show a great deal of complexity. The scaling of thermodynamic and kinetic properties with protein size is one such rule. However, it is not clear to what extent biologically relevant folding properties (i.e., rates and stabilities) depend on size and/or on other factors such as structure and amino acid sequence. Here we address this question analyzing experimental data on 52 nonmultistate folding proteins with a simple theoretical model. We find that size scaling is the primary factor in determining folding rates, and more surprisingly also protein stability. Furthermore, our analysis reveals that the experimental deviations from size predictions are due to minute differences in the fundamental parameters (e.g., less than 2% for the stability). Folding is thus highly sensitive to little changes in protein energetics, but at the same time the folding properties of natural proteins are remarkably homogeneous. These results suggest that evolution has selected a small subset of possibilities from the physically plausible folding catalog and highlight the need for highly accurate protein force fields to predict rates and stabilities beyond general trends.

Protein folding kinetics: barrier effects in chemical and thermal denaturation experiments.

Recent experimental work on fast protein folding brings about an intriguing paradox. Microsecond-folding proteins are supposed to fold near or at the folding speed limit (downhill folding), but yet their folding behavior seems to comply with classical two-state analyses, which imply the crossing of high free energy barriers. However, close inspection of chemical and thermal denaturation kinetic experiments in fast-folding proteins reveals systematic deviations from two-state behavior. Using a simple one-dimensional free energy surface approach we find that such deviations are indeed diagnostic of marginal folding barriers. Furthermore, the quantitative analysis of available fast-kinetic data indicates that many microsecond-folding proteins fold downhill in native conditions. All of these proteins are then promising candidates for an atom-by-atom analysis of protein folding using nuclear magnetic resonance.1 We also find that the diffusion coefficient for protein folding is strongly temperature dependent, corresponding to an activation energy of approximately 1 kJ.mol-1 per protein residue. As a consequence, the folding speed limit at room temperature is about an order of magnitude slower than the approximately 1 micros estimates from high-temperature T-jump experiments. Our analysis is quantitatively consistent with the available thermodynamic and kinetic data on slow two-state folding proteins and provides a straightforward explanation for the apparent fast-folding paradox.

Dynamics, energetics, and structure in protein folding.

For many decades, protein folding experimentalists have worked with no information about the time scales of relevant protein folding motions and without methods for estimating the height of folding barriers. Protein folding experiments have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiments was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (approximately 14RT for the very slow folder AcP) to nonexistent. While slow-folding (i.e., > or = 1 ms) single-domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with a marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic factors from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single-molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.

Role for the alpha-helix in aberrant protein aggregation.

Is the alpha-helix structure capable of triggering the formation of aberrant protein aggregates? To answer this question, we investigate the in vitro aggregation of tau protein in the presence of the helix-inducing agent TFE. Tau is a natively unfolded protein that binds to microtubules and forms aggregates in Alzheimer's disease. We find that full-length tau has residual alpha-helix structure, which is further enhanced by three mutations involved in genetic neurological disorders. TFE concentrations matching an alpha-helical content of 40% in full-length tau and the triple mutant induce the formation of aggregates that are morphologically and structurally heterogeneous. A simple dilution experiment reveals that heterogeneity results from the competition between alpha-helical fibrillar aggregates and more classical amyloid-like aggregates. The alpha-helical aggregates are more resilient to dilution and have the spectroscopic features of alpha-helical coiled coils. We propose a general mechanism by which intrinsically stable alpha-helices can associate into aggregates with only coarse coiled-coil symmetry. In tau, high intrinsic alpha-helix stability and coarse coiled-coil symmetry could be byproducts of its biological function.