Time-trimming tricks for dynamic simulations: splitting force updates to reduce computational work

Assessment of the Sampling Performance of Multiple-Copy Dynamics versus a Unique Trajectory

The goal of the present study was to ascertain the differential performance of a long molecular dynamics trajectory versus several shorter ones starting from different points in the phase space and covering the same sampling time. For this purpose, we selected the 16-mer peptide Bak₁₆BH3 as a model for study and carried out several samplings in explicit solvent. These samplings included an 8 μs trajectory (sampling S1); two 4 μs trajectories (sampling S2); four 2 μs trajectories (sampling S3); eight 1 μs trajectories (sampling S4); 16 0.5 μs trajectories (sampling S5), and 80 0.1 μs trajectories (sampling S6). Moreover, the 8 μs trajectory was further extended to 16 μs to have reference values of the diverse properties measured. The diverse samplings were compared qualitatively and quantitatively. Among the former, we carried out a comparison of the conformational profiles of the peptide using cluster analysis. Moreover, we also gained insight into the interchange among these structures along the sampling process. Among the latter, we computed the number of new conformational patterns sampled with time using strings defined from the conformations attained by each of the residues in the peptide. We also compared the locations and depths of the obtained minima on the free energy surface using principal component analysis. Finally, we also compared the helical profiles per residue at the end of the sampling process. The results suggest that a few short molecular dynamics trajectories may provide better sampling than one unique trajectory. Moreover, this procedure can also be advantageous to avoid getting trapped in a local minimum. However, caution should be exercised since short trajectories need to be long enough to overcome local barriers surrounding the starting point and the required sampling time depends on the number of degrees of freedom of the system under study. An effective way to gain insight into the minimum MD trajectory length is to monitor the convergence of different structural features, as shown in the present work.

Combining an Elastic Network With a Coarse-Grained Molecular Force Field: Structure, Dynamics, and Intermolecular Recognition

Structure-based and physics-based coarse-grained molecular force fields have become attractive approaches to gain mechanistic insight into the function of large biomolecular assemblies. Here, we study how both approaches can be combined into a single representation, that we term ELNEDIN. In this representation an elastic network is used as a structural scaffold to describe and maintain the overall shape of a protein and a physics-based coarse-grained model (MARTINI-2.1) is used to describe both inter- and intramolecular interactions in the system. The results show that when used in molecular dynamics simulations ELNEDIN models can be built so that the resulting structural and dynamical properties of a protein, including its collective motions, are comparable to those obtained using atomistic protein models. We then evaluate the behavior of such models in (1) long, microsecond time-scale, simulations, (2) the modeling of very large macromolecular assemblies, a viral capsid, and (3) the study of a protein-protein association process, the reassembly of the ROP homodimer. The results for this series of tests indicate that ELNEDIN models allow microsecond time-scale molecular dynamics simulations to be carried out readily, that large biological entities such as the viral capsid of the cowpea mosaic virus can be stably modeled as assemblies of independent ELNEDIN models, and that ELNEDIN models show significant promise for modeling protein-protein association processes.

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution

Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.

Fast and reliable analysis of molecular motion using proximity relations and dimensionality reduction

The analysis of molecular motion starting from extensive sampling of molecular configurations remains an important and challenging task in computational biology. Existing methods require a significant amount of time to extract the most relevant motion information from such data sets. In this work, we provide a practical tool for molecular motion analysis. The proposed method builds upon the recent ScIMAP (Scalable Isomap) method, which, by using proximity relations and dimensionality reduction, has been shown to reliably extract from simulation data a few parameters that capture the main, linear and/or nonlinear, modes of motion of a molecular system. The results we present in the context of protein folding reveal that the proposed method characterizes the folding process essentially as well as ScIMAP. At the same time, by projecting the simulation data and computing proximity relations in a low-dimensional Euclidean space, it renders such analysis computationally practical. In many instances, the proposed method reduces the computational cost from several CPU months to just a few CPU hours, making it possible to analyze extensive simulation data in a matter of a few hours using only a single processor. These results establish the proposed method as a reliable and practical tool for analyzing motions of considerably large molecular systems and proteins with complex folding mechanisms.

Distinct energetics and closing pathways for DNA polymerase beta with 8-oxoG template and different incoming nucleotides

Background

8-Oxoguanine (8-oxoG) is a common oxidative lesion frequently encountered by DNA polymerases such as the repair enzyme DNA polymerase β (pol β). To interpret in atomic and energetic detail how pol β processes 8-oxoG, we apply transition path sampling to delineate closing pathways of pol β 8-oxoG complexes with dCTP and dATP incoming nucleotides and compare the results to those of the nonlesioned G:dCTP and G:dATPanalogues.

Results

Our analyses show that the closing pathways of the 8-oxoG complexes are different from one another and from the nonlesioned analogues in terms of the individual transition states along each pathway, associated energies, and the stability of each pathway's closed state relative to the corresponding open state. In particular, the closed-to-open state stability difference in each system establishes a hierarchy of stability (from high to low) as G:C > 8-oxoG:C > 8-oxoG:A > G:A, corresponding to -3, -2, 2, 9 k_BT, respectively. This hierarchy of closed state stability parallels the experimentally observed processing efficiencies for the four pairs. Network models based on the calculated rate constants in each pathway indicate that the closed species are more populated than the open species for 8-oxoG:dCTP, whereas the opposite is true for 8-oxoG:dATP.

Conclusion

These results suggest that the lower insertion efficiency (larger K_m) for dATP compared to dCTP opposite 8-oxoG is caused by a less stable closed-form of pol β, destabilized by unfavorable interactions between Tyr271 and the mispair. This stability of the closed vs. open form can also explain the higher insertion efficiency for 8-oxoG:dATP compared to the nonlesioned G:dATP pair, which also has a higher overall conformational barrier. Our study offers atomic details of the complexes at different states, in addition to helping interpret the different insertion efficiencies of dATP and dCTP opposite 8-oxoG and G.

Differing conformational pathways before and after chemistry for insertion of dATP versus dCTP opposite 8-oxoG in DNA polymerase beta

To elucidate how human DNA polymerase beta (pol beta) discriminates dATP from dCTP when processing 8-oxoguanine (8-oxoG), we analyze a series of dynamics simulations before and after the chemical step with dATP and dCTP opposite an 8-oxoG template started from partially open complexes of pol beta. Analyses reveal that the thumb closing of pol beta before chemistry is hampered when the incorrect nucleotide dATP is bound opposite 8-oxoG; the unfavorable interaction between active-site residue Tyr(271) and dATP that causes an anti to syn change in the 8-oxoG (syn):dATP complex explains this slow motion, in contrast to the 8-oxoG (anti):dCTP system. Such differences in conformational pathways before chemistry for mismatched versus matched complexes help explain the preference for correct insertion across 8-oxoG by pol beta. Together with reference studies with a nonlesioned G template, we propose that 8-oxoG leads to lower efficiency in pol beta's incorporation of dCTP compared with G by affecting the requisite active-site geometry for the chemical reaction before chemistry. Furthermore, because the active site is far from ready for the chemical reaction after partial closing or even full thumb closing, we suggest that pol beta is tightly controlled not only by the chemical step but also by a closely related requirement for subtle active-site rearrangements after thumb movement but before chemistry.

Subtle but variable conformational rearrangements in the replication cycle of Sulfolobus solfataricus P2 DNA polymerase IV (Dpo4) may accommodate lesion bypass

The possible conformational changes of DNA polymerase IV (Dpo4) before and after the nucleotidyl-transfer reaction are investigated at the atomic level by dynamics simulations to gain insight into the mechanism of low-fidelity polymerases and identify slow and possibly critical steps. The absence of significant conformational changes in Dpo4 before chemistry when the incoming nucleotide is removed supports the notion that the "induced-fit" mechanism employed to interpret fidelity in some replicative and repair DNA polymerases does not exist in Dpo4. However, significant correlated movements in the little finger and finger domains, as well as DNA sliding and subtle catalytic-residue rearrangements, occur after the chemical reaction when both active-site metal ions are released. Subsequently, Dpo4's little finger grips the DNA through two arginine residues and pushes it forward. These metal ion correlated movements may define subtle, and possibly characteristic, conformational adjustments that operate in some Y-family polymerase members in lieu of the prominent subdomain motions required for catalytic cycling in other DNA polymerases like polymerase beta. Such subtle changes do not easily provide a tight fit for correct incoming substrates as in higher-fidelity polymerases, but introduce in low-fidelity polymerases different fidelity checks as well as the variable conformational-mobility potential required to bypass different lesions.

Comparative molecular dynamics-Similar folds and similar motions?

Proteins possessing the same fold may undergo similar motions, particularly if these motions involve large conformational transitions. The increasing amounts of structural data provide a useful starting point with which to test this hypothesis. We have performed a total of 0.29 micros of molecular dynamics across a series of proteins within the same fold family (periplasmic binding proteinlike) in order to address to what extent similarity of motion exists. Analysis of the local conformational space on these timescales (10-20 ns) revealed that the behavior of the proteins could be readily distinguished between an apo-state and a ligand-bound state. Moreover, analysis of the root-mean-square fluctuations reveals that the presence of the ligand exerts a stabilizing effect on the protein, with similar motions occurring, but with reduced magnitude. Furthermore, the conformational space in the presence of the ligand appears to be dictated by sequence but not by the type of ligand present. In contrast, apo-simulations showed considerable overlap of conformational space across the fold as a result of their ability to undergo larger fluctuations. Indeed, we observed several transitions from different simulations between states corresponding to the closed-cleft and open-cleft forms of the fold, with the predominant motions being conserved across the different proteins. Thus, large-scale conformational changes do indeed appear to be conserved across this fold architecture, but smaller conformational motions appear to reflect the differences in sequence and local fold.

Highly organized but pliant active site of DNA polymerase beta: compensatory mechanisms in mutant enzymes revealed by dynamics simulations and energy analyses

To link conformational transitions noted for DNA polymerases with kinetic results describing catalytic efficiency and fidelity, we investigate the role of key DNA polymerase beta residues on subdomain motion through simulations of five single-residue mutants: Arg-283-Ala, Tyr-271-Ala, Asp-276-Val, Arg-258-Lys, and Arg-258-Ala. Since a movement toward a closed state was only observed for R258A, we suggest that Arg(258) is crucial in modulating motion preceding chemistry. Analyses of protein/DNA interactions in the mutant active site indicate distinctive hydrogen bonding and van der Waals patterns arising from compensatory structural adjustments. By comparing closed mutant complexes with the wild-type enzyme, we interpret experimentally derived nucleotide binding affinities in molecular terms: R283A (decreased), Y271A (increased), D276V (increased), and R258A (decreased). Thus, compensatory interactions (e.g., in Y271A with adjacent residues Phe(272), Asn(279), and Arg(283)) increase the overall binding affinity for the incoming nucleotide although direct interactions may decrease. Together with energetic analyses, we predict that R258G might increase the rate of nucleotide insertion and maintain enzyme fidelity as R258A; D276L might increase the nucleotide binding affinity more than D276V; and R283A/K280A might decrease the nucleotide binding affinity and increase misinsertion more than R283A. The combined observations regarding key roles of specific residues (e.g., Arg(258)) and compensatory interactions echo the dual nature of polymerase active site, namely versatility (to accommodate various basepairs) and specificity (for preserving fidelity) and underscore an organized but pliant active site essential to enzyme function.

Critical role of magnesium ions in DNA polymerase beta's closing and active site assembly

To dissect the effects of the nucleotide-binding and catalytic metal ions on DNA polymerase mechanisms for DNA repair and synthesis, aside from the chemical reaction, we investigate their roles in the conformational transitions between closed and open states and assembly/disassembly of the active site of polymerase beta/DNA complexes before and after the chemical reaction of nucleotide incorporation. Using dynamics simulations, we find that closing before chemical reaction requires both divalent metal ions in the active site while opening after the chemical reaction is triggered by release of the catalytic metal ion. The critical closing is stabilized by the interaction of the incoming nucleotide with conserved catalytic residues (Asp190, Asp192, Asp256) and the two functional magnesium ions; without the catalytic ion, other protein residues (Arg180, Arg183, Gly189) coordinate the incomer's triphosphate group through the nucleotide-binding ion. Because we also note microionic heterogeneity near the active site, Mg(2+) and Na(+) ions can diffuse into the active site relatively rapidly, we suggest that the binding of the catalytic ion itself is not a rate-limiting conformational or overall step. However, geometric adjustments associated with functional ions and proper positioning in the active site, including subtle but systematic motions of protein side chains (e.g., Arg258), define slow or rate-limiting conformational steps that may guide fidelity mechanisms. These sequential rearrangements are likely sensitively affected when an incorrect nucleotide approaches the active site. Our suggestion that subtle and slow adjustments of the nucleotide-binding and catalytic magnesium ions help guide polymerase selection for the correct nucleotide extends descriptions of polymerase pathways and underscores the importance of the delicate conformational events both before and after the chemical reaction to polymerase efficiency and fidelity mechanisms.

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.

Dynamical multiple-time stepping methods for overcoming resonance instabilities

Current molecular dynamics simulations of biomolecules using multiple time steps to update the slowly changing force are hampered by instabilities beginning at time steps near the half period of the fastest vibrating mode. These "resonance" instabilities have became a critical barrier preventing the long time simulation of biomolecular dynamics. Attempts to tame these instabilities by altering the slowly changing force and efforts to damp them out by Langevin dynamics do not address the fundamental cause of these instabilities. In this work, we trace the instability to the nonanalytic character of the underlying spectrum and show that a correct splitting of the Hamiltonian, which renders the spectrum analytic, restores stability. The resulting Hamiltonian dictates that in addition to updating the momentum due to the slowly changing force, one must also update the position with a modified mass. Thus multiple-time stepping must be done dynamically.

Effect of DNA superhelicity and bound proteins on mechanistic aspects of the Hin-mediated and Fis-enhanced inversion

Using a recently developed inhomogeneous, macroscopic model for long DNA bound to proteins, we examine topological and geometric aspects of DNA/protein structures and dynamics on various stages of the Hin inversion pathway. This biological reaction involves exchange of DNA in a synaptic complex that brings together several DNA sites bound to Hin dimers as well as Fis enhancers. Brownian dynamics simulations in the millisecond timescale allow us to follow and analyze the DNA/protein dynamics trajectories and to examine the effects of DNA superhelicity and protein binding on various reaction steps. Analysis of the generated kinetic pathways helps explain mechanistic aspects regarding the process by which two or three protein-bound DNA sites come to close spatial proximity and show that how topological selectivity (two trapped supercoils), enhancer binding, and properties of supercoiled DNA play critical roles in regulating the inversion reaction. Specifically, a critical amount of DNA superhelicity (e.g., |sigma| > 0.02) leads to an optimal interplay for the first reaction step-two-site juxtaposition-between large-scale random rearrangements of Hin-bound DNA and local slithering within branches of plectonemes. The three-site juxtaposition, the second step, is significantly accelerated by the presence of an enhancer protein that, due to severe local bending, also alters juxtaposition mechanisms, especially for superhelical density magnitude greater than around 0.04.

Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms

Multiple time step (MTS) algorithms present an effective integration approach to reduce the computational cost of dynamics simulations. By using force splitting to allow larger time steps for the more slowly varying force components, computational savings can be realized. The Particle-Mesh-Ewald (PME) method has been independently devised to provide an effective and efficient treatment of the long-range electrostatics interactions. Here we examine the performance of a combined MTS/PME algorithm previously developed for AMBER on a large polymerase beta/DNA complex containing 40,673 atoms. Our goal is to carefully combine the robust features of the Langevin/MTS (LN) methodology implemented in CHARMM-which uses position rather than velocity Verlet with stochasticity to make possible outer time steps of 150 fs-with the PME formulation. The developed MTS/PME integrator removes fast terms from the reciprocal-space Ewald component by using switch functions. We analyze the advantages and limitations of the resulting scheme by comparing performance to the single time step leapfrog Verlet integrator currently used in AMBER by evaluating different time-step protocols using three assessors for accuracy, speedup, and stability, all applied to long (i.e., nanosecond) simulations to ensure proper energy conservation. We also examine the performance of the algorithm on a parallel, distributed shared-memory computer (SGI Origin 2000 with 8 300-MHz R12000 processors). Good energy conservation and stability behavior can be demonstrated, for Newtonian protocols with outer time steps of up to 8 fs and Langevin protocols with outer time steps of up to 16 fs. Still, we emphasize the inherent limitations imposed by the incorporation of MTS methods into the PME formulation that may not be widely appreciated. Namely, the limiting factor on the largest outer time-step size, and hence speedup, is an intramolecular cancellation error inherent to PME. This error stems from the excluded-nonbonded correction term contained in the reciprocal-space component. This cancellation error varies in time and introduces artificial frequencies to the governing dynamics motion. Unfortunately, we find that this numerical PME error cannot be easily eliminated by refining the PME parameters (grid resolution and/or order of interpolating polynomial). We suggest that methods other than PME for fast electrostatics may allow users to reap the full advantages from MTS algorithms.

A Hoogsteen base pair embedded in undistorted B-DNA

Hoogsteen base pairs within duplex DNA typically are only observed in regions containing significant distortion or near sites of drug intercalation. We report here the observation of a Hoogsteen base pair embedded within undistorted, unmodified B-DNA. The Hoogsteen base pair, consisting of a syn adenine base paired with an anti thymine base, is found in the 2.1 A resolution structure of the MATalpha2 homeodomain bound to DNA in a region where a specifically and a non-specifically bound homeodomain contact overlapping sites. NMR studies of the free DNA show no evidence of Hoogsteen base pair formation, suggesting that protein binding favors the transition from a Watson-Crick to a Hoogsteen base pair. Molecular dynamics simulations of the homeodomain-DNA complex support a role for the non-specifically bound protein in favoring Hoogsteen base pair formation. The presence of a Hoogsteen base pair in the crystal structure of a protein-DNA complex raises the possibility that Hoogsteen base pairs could occur within duplex DNA and play a hitherto unrecognized role in transcription, replication and other cellular processes.

Local deformations revealed by dynamics simulations of DNA polymerase Beta with DNA mismatches at the primer terminus

Nanosecond dynamics simulations for DNA polymerase beta (pol beta)/DNA complexes with three mismatched base-pairs, namely GG, CA, or CC (primer/template) at the DNA polymerase active site, are performed to investigate the mechanism of polymerase opening and how the mispairs may affect the DNA extension step; these trajectories are compared to the behavior of a pol beta/DNA complex with the correct GC base-pair, and assessed with the aid of targeted molecular dynamics (TMD) simulations of all systems from the closed to the open enzyme state. DNA polymerase conformational changes (subdomain closing and opening) have been suggested to play a critical role in DNA synthesis fidelity, since these changes are associated with the formation of the substrate-binding pocket for the nascent base-pair. Here we observe different large C-terminal subdomain (thumb) opening motions in the simulations of pol beta with GC versus GG base-pairs. Whereas the conformation of pol beta in the former approaches the observed open state in the crystal structures, the enzyme in the latter does not. Analyses of the motions of active-site protein/DNA residues help explain these differences. Interestingly, rotation of Arg258 toward Asp192, which coordinates both active-site metal ions in the closed "active" complex, occurs rapidly in the GG simulation. We have previously suggested that this rotation is a key slow step in the closed to open transition. TMD simulations also point to a unique pathway for Arg258 rotation in the GG mispair complex. Simulations of the mismatched systems also reveal distorted geometries in the active site of all the mispair complexes examined. The hierarchy of the distortions (GG>CC>CA) parallels the experimentally deduced inability of pol beta to extend these mispairs. Such local distortions would be expected to cause inefficient DNA extension and polymerase dissociation and thereby might lead to proofreading by an extrinsic exonuclease. Thus, our studies on the dynamics of pol beta opening in mismatch systems provide structural and dynamic insights to explain experimental results regarding inefficient DNA extension following misincorporation; these details shed light on how proofreading may be invoked by the abnormal active-site geometry.

Polymerase beta simulations suggest that Arg258 rotation is a slow step rather than large subdomain motions per se

The large-scale opening motion of mammalian DNA polymerase beta is followed at atomic resolution by dynamic simulations that link crystal "closed" and "open" conformations. The closing/opening conformational change is thought to be key to the ability of polymerases to choose a correct nucleotide (through "induced fit") and hence maintain DNA repair synthesis fidelity. Corroborating available structural and kinetic measurements, our studies bridge static microscopic crystal structures with macroscopic kinetic data by delineating a specific sequence, Phe272 ring flip, large thumb movement, Arg258 rotation with release of catalytic Mg2+, together with estimated time-scales, that suggest the Arg258 rearrangement as a limiting factor of large subdomain motions. If similarly slow in the closing motion, this conformational change might be restricted further when an incorrect nucleotide binds and thus play a role in pol beta's selectivity for the correct nucleotide. These results suggest new lines of experimentation in the study of polymerase mechanisms (e.g. enzyme mutants), which should provide further insights into mechanisms of error discrimination and DNA synthesis fidelity.

Dynamic simulations of 13 TATA variants refine kinetic hypotheses of sequence/activity relationships 1 1Edited by B. Honig

The fundamental relationship between DNA sequence/deformability and biological function has attracted numerous experimental and theoretical studies. A classic prototype system used for such studies in eukaryotes is the complex between the TATA element transcriptional regulator and the TATA-box binding protein (TBP). The recent crystallographic study by Burley and co-workers demonstrated the remarkable structural similarity contrasted to different transcriptional activity of 11 TBP/DNA complexes in which the DNAs differed by single base-pairs. By simulating these TATA variants and two other single base-pair variants that were not crystallizable, we uncover sequence-dependent structural, energetic, and flexibility properties that tailor TATA elements to TBP interactions, complementing many previous studies by refining kinetic hypotheses on sequence/activity correlations. The factors that combine to produce favorable elements for TBP activity include overall flexibility; minor groove widening, as well as roll, rise, and shift increases at the ends of the TATA element; untwisting within the TATA element accompanied by large roll at the TATA element ends; and relatively low maximal water densities around the DNA. These features accompany the severe deformation induced by the minor-groove binding protein, which kinks the TATA element at the ends and displaces local water molecules to form stabilizing hydrophobic contacts. Interestingly, the preferred bending direction itself is not a significant predictor of activity disposition, although certain variants (such as wild-type AdMLP, 5'-TATA4G-3', and inactive A29, 5'-TA6G-3') exhibit large preferred bends in directions consistent with their activity or inactivity (major groove and minor groove bends, respectively). These structural, flexibility, and hydration preferences, identified here and connected to a new crystallographic study of a larger group of DNA variants than reported to date, highlight the profound influence of single base-pair DNA variations on DNA motion. Our refined kinetic hypothesis suggests the functional implications of these motions in a kinetic model of TATA/TBP recognition, inviting further theoretical and experimental research.