How conformational dynamics of DNA polymerase select correct substrates: experiments and simulations

A MATHEMATICAL FRAMEWORK FOR EXACT MILESTONING

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.

Tautomeric transition between wobble A·C DNA base mispair and Watson-Crick-like A·C* mismatch: microstructural mechanism and biological significance

Here, we use MP2/DFT quantum-chemical methods combined with Quantum Theory of Atoms in Molecules to study the tautomeric transition between wobble A·C(w) mismatch and Watson-Crick-like A·C*(WC) base mispair, proceeding non-dissociatively via sequential proton transfer between bases through the planar, highly stable and zwitterionic TS(A∙C-)(A∙C(W)<-->A∙C&(WC)) transition state joined by the participation of (A)N6(+)H∙∙∙N4(-)(C), (A)N1(+)H∙∙∙N4(-)(C) and (A)C2(+)H∙∙∙N3(-)(C) H-bonds. Notably, the A·C(w) ↔ A·C*(WC) tautomerization reaction is accompanied by 10 unique patterns of the specific intermolecular interactions that consistently replace each other. Our data suggest that biologically significant A·C(w) → A·C*(WC) tautomerization is a kinetically controlled pathway for formation of the enzymatically competent Watson-Crick-like A·C*(WC) DNA base mispair in the essentially hydrophobic recognition pocket of the high-fidelity DNA-polymerase, responsible for the occurrence of spontaneous point AC/CA incorporation errors during DNA biosynthesis.

Thumb Site 2 Inhibitors of Hepatitis C Viral RNA-dependent RNA Polymerase Allosterically Block the Transition from Initiation to Elongation

Replication of the hepatitis C viral genome is catalyzed by the NS5B (nonstructural protein 5B) RNA-dependent RNA polymerase, which is a major target of antiviral drugs currently in the clinic. Prior studies established that initiation of RNA replication could be facilitated by starting with a dinucleotide (pGG). Here we establish conditions for efficient initiation from GTP to form the dinucleotide and subsequent intermediates leading to highly processive elongation, and we examined the effects of four classes of nonnucleoside inhibitors on each step of the reaction. We show that palm site inhibitors block initiation starting from GTP but not when starting from pGG. In addition we show that nonnucleoside inhibitors binding to thumb site-2 (NNI2) lead to the accumulation of abortive intermediates three-five nucleotides in length. Our kinetic analysis shows that NNI2 do not significantly block initiation or elongation of RNA synthesis; rather, they block the transition from initiation to elongation, which is thought to proceed with significant structural rearrangement of the enzyme-RNA complex including displacement of the β-loop from the active site. Direct measurement in single turnover kinetic studies show that pyrophosphate release is faster than the chemistry step, which appears to be rate-limiting during processive synthesis. These results reveal important new details to define the steps involved in initiation and elongation during viral RNA replication, establish the allosteric mechanisms by which NNI2 inhibitors act, and point the way to the design of more effective allosteric inhibitors that exploit this new information.

FRET-based assay to screen inhibitors of HIV-1 reverse transcriptase and nucleocapsid protein

During HIV-1 reverse transcription, the single-stranded RNA genome is converted into proviral double stranded DNA by Reverse Transcriptase (RT) within a reverse transcription complex composed of the genomic RNA and a number of HIV-1 encoded proteins, including the nucleocapsid protein NCp7. Here, we developed a one-step and one-pot RT polymerization assay. In this in vitro assay, RT polymerization is monitored in real-time by Förster resonance energy transfer (FRET) using a commercially available doubly-labeled primer/template DNA. The assay can monitor and quantify RT polymerization activity as well as its promotion by NCp7. Z-factor values as high as 0.89 were obtained, indicating that the assay is suitable for high-throughput drug screening. Using Nevirapine and AZT as prototypical RT inhibitors, reliable IC50 values were obtained from the changes in the RT polymerization kinetics. Interestingly, the assay can also detect NCp7 inhibitors, making it suitable for high-throughput screening of drugs targeting RT, NCp7 or simultaneously, both proteins.

Wobble↔Watson-Crick tautomeric transitions in the homo-purine DNA mismatches: a key to the intimate mechanisms of the spontaneous transversions

The intrinsic capability of the homo-purine DNA base mispairs to perform wobble↔Watson-Crick/Topal-Fresco tautomeric transitions via the sequential intrapair double proton transfer was discovered for the first time using QM (MP2/DFT) and QTAIM methodologies that are crucial for understanding the microstructural mechanisms of the spontaneous transversions.

Exact milestoning

A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.

Enzyme Selectivity of HIV Reverse Transcriptase: Conformations, Ligands, and Free Energy Partition

Atomically detailed simulations of HIV RT are performed to investigate the contributions of the conformational transition to the overall rate and specificity of enzyme catalysis. A number of different scenarios are considered within Milestoning theory to provide a more complete picture of the process of opening and closing the enzyme. We consider the open to closed transition in the absence of and with the correct and incorrect substrates. We also consider the free energy profile and the kinetics of the conformational change after the chemistry step in which a new base was added to the DNA, but the DNA was not yet displaced. We partition the free energy along the reaction coordinate and analyze the importance of different protein domains. Strikingly, significant influence on the free energy profile is detected for amino acids far from the active site. The overall long-range impact is about 50 percent of the total. We also illustrate that the overall rate is not necessarily determined by the highest free energy barrier along the reaction path (with respect to the free enzyme and substrate) and that the specificity is not necessarily determined by the same reaction step that determines the rate.

How many tautomerization pathways connect Watson-Crick-like G*·T DNA base mispair and wobble mismatches?

In this study, we have theoretically demonstrated the intrinsic ability of the wobble G·T(w)/G*·T*(w)/G·T(w1)/G·T(w2) and Watson-Crick-like G*·T(WC) DNA base mispairs to interconvert into each other via the DPT tautomerization. We have established that among all these transitions, only one single G·T(w) ↔ G*·T(WC) pathway is eligible from a biological perspective. It involves short-lived intermediate - the G·T*(WC) base mispair - and is governed by the planar, highly stable, and zwitterionic [Formula: see text] transition state stabilized by the participation of the unique pattern of the five intermolecular O6(+)H⋯O4(-), O6(+)H⋯N3(-), N1(+)H⋯N3(-), N1(+)H⋯O2(-), and N2(+)H⋯O2(-) H-bonds. This non-dissociative G·T(w) ↔ G*·T(WC) tautomerization occurs without opening of the pair: Bases within mispair remain connected by 14 different patterns of the specific intermolecular interactions that successively change each other along the IRC. Novel kinetically controlled mechanism of the thermodynamically non-equilibrium spontaneous point GT/TG incorporation errors has been suggested. The mutagenic effect of the analogues of the nucleotide bases, in particular 5-bromouracil, can be attributed to the decreasing of the barrier of the acquisition by the wobble pair containing these compounds of the enzymatically competent Watson-Crick's geometry via the intrapair mutagenic tautomerization directly in the essentially hydrophobic recognition pocket of the replication DNA-polymerase machinery. Proposed approaches are able to explain experimental data, namely growth of the rate of the spontaneous point incorporation errors during DNA biosynthesis with increasing temperature.

Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.

Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase

During DNA replication replicative polymerases move in discrete mechanical steps along the DNA template. To address how the chemical cycle is coupled to mechanical motion of the enzyme, here we use optical tweezers to study the translocation mechanism of individual bacteriophage Phi29 DNA polymerases during processive DNA replication. We determine the main kinetic parameters of the nucleotide incorporation cycle and their dependence on external load and nucleotide (dNTP) concentration. The data is inconsistent with power stroke models for translocation, instead supports a loose-coupling mechanism between chemical catalysis and mechanical translocation during DNA replication. According to this mechanism the DNA polymerase works by alternating between a dNTP/PPi-free state, which diffuses thermally between pre- and post-translocated states, and a dNTP/PPi-bound state where dNTP binding stabilizes the post-translocated state. We show how this thermal ratchet mechanism is used by the polymerase to generate work against large opposing loads (∼50 pN).

DPT tautomerisation of the G·A(syn) and A*·G*(syn) DNA mismatches: a QM/QTAIM combined atomistic investigation

By applying a combined QM and QTAIM atomistic computational approach we have established for the first time that the G·A(syn) and A*·G*(syn) DNA mismatches (rare tautomers are marked with an asterisk), causing spontaneous transversions with substantially various probabilities, radically differ from each other in their ability to tautomerise through the double proton transfer (DPT). The A*·G*(syn) mismatch tautomerises quite easily (ΔΔG(TS) ≈ 4·kT at room temperature) into the A·G*(syn) mismatch through the asynchronous concerted mechanism, whereas the G·A(syn) base mispair does not tautomerise via the DPT at all, since there is no local minimum corresponding to the tautomerised G*·A*(syn) mismatch on the potential energy surface. It was established that the A·G*(syn) base mispair is a dynamically unstable H-bonded complex with an extremely short lifetime of 2.17 × 10(-13) s. Consequently, the obtained results allow us to believe that spontaneous or forced dissociation of both the G·A(syn) and A*·G*(syn) DNA mismatches by the DNA-polymerase occurs with the preservation of the tautomeric status of the bases.

Molecular dynamics studies of modular polyketide synthase ketoreductase stereospecificity

Ketoreductases (KRs) from modular polyketide synthases (PKSs) can perform stereospecific catalysis, selecting a polyketide with a D- or L-α-methyl substituent for NADPH-mediated reduction. In this report, molecular dynamics (MD) simulations were performed to investigate the interactions that control stereospecificity. We studied the A1-type KR from the second module of the amphotericin PKS (A1), which is known to be stereospecific for a D-α-methyl-substituted diketide substrate (dkD). MD simulations of two ternary complexes comprised of the enzyme, NADPH, and either the correct substrate, dkD, or its enantiomer (dkL) were performed. The coordinates for the A1/NADPH binary complex were obtained from a crystal structure (PDB entry 3MJS), and substrates were modeled in the binding pocket in conformations appropriate for reduction. Simulations were intended to reproduce the initial weak binding of the polyketide substrate to the enzyme. Long (tens of nanoseconds) MD simulations show that the correct substrate is retained in a conformation closer to the reactive configuration. Many short (up to a nanosecond) MD runs starting from the initial structures display evidence that Q364, three residues N-terminal to the catalytic tyrosine, forms a hydrogen bond to the incorrect dkL substrate to yield an unreactive conformation that is more favorable than the reactive configuration. This interaction is not as strong for dkD, as the D-α-methyl substituent is positioned between the glutamine and the reactive site. This result correlates with experimental findings [Zheng, J., et al. (2010) Structure 18, 913-922] in which a Q364H mutant was observed to lose stereospecificity.

Mechanism of substrate translocation by a ring-shaped ATPase motor at millisecond resolution

Ring-shaped, hexameric ATPase motors fulfill key functions in cellular processes, such as genome replication, transcription, or protein degradation, by translocating a long substrate through their central pore powered by ATP hydrolysis. Despite intense research efforts, the atomic-level mechanism transmitting chemical energy from hydrolysis into mechanical force that translocates the substrate is still unclear. Here we employ all-atom molecular dynamics simulations combined with advanced path sampling techniques and milestoning analysis to characterize how mRNA substrate is translocated by an exemplary homohexameric motor, the transcription termination factor Rho. We find that the release of hydrolysis product (ADP + Pi) triggers the force-generating process of Rho through a 0.1 millisecond-long conformational transition, the time scale seen also in experiment. The calculated free energy profiles and kinetics show that Rho unidirectionally translocates the single-stranded RNA substrate via a population shift of the conformational states of Rho; upon hydrolysis product release, the most favorable conformation shifts from the pretranslocation state to the post-translocation state. Via two previously unidentified intermediate states, the RNA chain is seen to be pulled by six K326 side chains, whose motions are induced by highly coordinated relative translation and rotation of Rho's six subunits. The present study not only reveals in new detail the mechanism employed by ring-shaped ATPase motors, for example the use of loosely bound and tightly bound hydrolysis reactant and product states to coordinate motor action, but also provides an effective approach to identify allosteric sites of multimeric enzymes in general.

Computation of transit times using the milestoning method with applications to polymer translocation

Milestoning is an efficient approximation for computing long-time kinetics and thermodynamics of large molecular systems, which are inaccessible to brute-force molecular dynamics simulations. A common use of milestoning is to compute the mean first passage time (MFPT) for a conformational transition of interest. However, the MFPT is not always the experimentally observed timescale. In particular, the duration of the transition path, or the mean transit time, can be measured in single-molecule experiments, such as studies of polymers translocating through pores and fluorescence resonance energy transfer studies of protein folding. Here we show how to use milestoning to compute transit times and illustrate our approach by applying it to the translocation of a polymer through a narrow pore.

Conformational selection in protein binding and function

Protein binding and function often involves conformational changes. Advanced nuclear magnetic resonance (NMR) experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may "select" protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and temporal ordering of binding/unbinding events and conformational changes. We propose that conformational-selection and induced-change processes (such as induced fit) are two sides of the same coin, because the temporal ordering is reversed in binding and unbinding direction. Conformational-selection processes can be characterized by a conformational excitation that occurs prior to a binding or unbinding event, while induced-change processes exhibit a characteristic conformational relaxation that occurs after a binding or unbinding event. We discuss how the ordering of events can be determined from relaxation rates and effective on- and off-rates determined in mixing experiments, and from the conformational exchange rates measured in advanced NMR or single-molecule fluorescence resonance energy transfer experiments. For larger ligand molecules such as peptides, conformational changes and binding events can be intricately coupled and exhibit aspects of conformational-selection and induced-change processes in both binding and unbinding direction.

Conformational dynamics of Thermus aquaticus DNA polymerase I during catalysis

Despite the fact that DNA polymerases have been investigated for many years and are commonly used as tools in a number of molecular biology assays, many details of the kinetic mechanism they use to catalyze DNA synthesis remain unclear. Structural and kinetic studies have characterized a rapid, pre-catalytic open-to-close conformational change of the Finger domain during nucleotide binding for many DNA polymerases including Thermus aquaticus DNA polymerase I (Taq Pol), a thermostable enzyme commonly used for DNA amplification in PCR. However, little has been performed to characterize the motions of other structural domains of Taq Pol or any other DNA polymerase during catalysis. Here, we used stopped-flow Förster resonance energy transfer to investigate the conformational dynamics of all five structural domains of the full-length Taq Pol relative to the DNA substrate during nucleotide binding and incorporation. Our study provides evidence for a rapid conformational change step induced by dNTP binding and a subsequent global conformational transition involving all domains of Taq Pol during catalysis. Additionally, our study shows that the rate of the global transition was greatly increased with the truncated form of Taq Pol lacking the N-terminal domain. Finally, we utilized a mutant of Taq Pol containing a de novo disulfide bond to demonstrate that limiting protein conformational flexibility greatly reduced the polymerization activity of Taq Pol.

Investigations of α-helix↔β-sheet transition pathways in a miniprotein using the finite-temperature string method

A parallel implementation of the finite-temperature string method is described, which takes into account the invariance of coordinates with respect to rigid-body motions. The method is applied to the complex α-helix↔β-sheet transition in a β-hairpin miniprotein in implicit solvent, which exhibits much of the complexity of conformational changes in proteins. Two transition paths are considered, one derived from a linear interpolant between the endpoint structures and the other derived from a targeted dynamics simulation. Two methods for computing the conformational free energy (FE) along the string are compared, a restrained method, and a tessellation method introduced by E. Vanden-Eijnden and M. Venturoli [J. Chem. Phys. 130, 194103 (2009)]. It is found that obtaining meaningful free energy profiles using the present atom-based coordinates requires restricting sampling to a vicinity of the converged path, where the hyperplanar approximation to the isocommittor surface is sufficiently accurate. This sampling restriction can be easily achieved using restraints or constraints. The endpoint FE differences computed from the FE profiles are validated by comparison with previous calculations using a path-independent confinement method. The FE profiles are decomposed into the enthalpic and entropic contributions, and it is shown that the entropy difference contribution can be as large as 10 kcal/mol for intermediate regions along the path, compared to 15-20 kcal/mol for the enthalpy contribution. This result demonstrates that enthalpic barriers for transitions are offset by entropic contributions arising from the existence of different paths across a barrier. The possibility of using systematically coarse-grained representations of amino acids, in the spirit of multiple interaction site residue models, is proposed as a means to avoid ad hoc sampling restrictions to narrow transition tubes.

RB69 DNA polymerase structure, kinetics, and fidelity

This review will summarize our structural and kinetic studies of RB69 DNA polymerase (RB69pol) as well as selected variants of the wild-type enzyme that were undertaken to obtain a deeper understanding of the exquisitely high fidelity of B family replicative DNA polymerases. We discuss how the structures of the various RB69pol ternary complexes can be used to rationalize the results obtained from pre-steady-state kinetic assays. Our main findings can be summarized as follows. (i) Interbase hydrogen bond interactions can increase catalytic efficiency by 5000-fold; meanwhile, base selectivity is not solely determined by the number of hydrogen bonds between the incoming dNTP and the templating base. (ii) Minor-groove hydrogen bond interactions at positions n – 1 and n – 2 of the primer strand and position n – 1 of the template strand in RB69pol ternary complexes are essential for efficient primer extension and base selectivity. (iii) Partial charge interactions among the incoming dNTP, the penultimate base pair, and the hydration shell surrounding the incoming dNTP modulate nucleotide insertion efficiency and base selectivity. (iv) Steric clashes between mismatched incoming dNTPs and templating bases with amino acid side chains in the nascent base pair binding pocket (NBP) as well as weak interactions and large gaps between the incoming dNTPs and the templating base are some of the reasons that incorrect dNTPs are incorporated so inefficiently by wild-type RB69pol. In addition, we developed a tC°–tC_nitro Förster resonance energy transfer assay to monitor partitioning of the primer terminus between the polymerase and exonuclease subdomains.

C(α) torsion angles as a flexible criterion to extract secrets from a molecular dynamics simulation

Given the increasing complexity of simulated molecular systems, and the fact that simulation times have now reached milliseconds to seconds, immense amounts of data (in the gigabyte to terabyte range) are produced in current molecular dynamics simulations. Manual analysis of these data is a very time-consuming task, and important events that lead from one intermediate structure to another can become occluded in the noise resulting from random thermal fluctuations. To overcome these problems and facilitate a semi-automated data analysis, we introduce in this work a measure based on C(α) torsion angles: torsion angles formed by four consecutive C(α) atoms. This measure describes changes in the backbones of large systems on a residual length scale (i.e., a small number of residues at a time). Cluster analysis of individual C(α) torsion angles and its fuzzification led to continuous time patches representing (meta)stable conformations and to the identification of events acting as transitions between these conformations. The importance of a change in torsion angle to structural integrity is assessed by comparing this change to the average fluctuations in the same torsion angle over the complete simulation. Using this novel measure in combination with other measures such as the root mean square deviation (RMSD) and time series of distance measures, we performed an in-depth analysis of a simulation of the open form of DNA polymerase I. The times at which major conformational changes occur and the most important parts of the molecule and their interrelations were pinpointed in this analysis. The simultaneous determination of the time points and localizations of major events is a significant advantage of the new bottom-up approach presented here, as compared to many other (top-down) approaches in which only the similarity of the complete structure is analyzed.

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

Optimal and variant metal-ion routes in DNA polymerase β's conformational pathways

To interpret recent structures of the R283K mutant of human DNA repair enzyme DNA polymerase β (pol β) differing in the number of Mg(2+) ions, we apply transition path sampling (TPS) to assess the effect of differing ion placement on the transition from the open one-metal to the closed two-metal state. We find that the closing pathway depends on the initial ion position, both in terms of the individual transition states and associated energies. The energy barrier of the conformational pathway varies from 25 to 58 kJ/mol, compared to the conformational energy barrier of 42 kJ/mol for the wild-type pol β reported previously. Moreover, we find a preferred ion route located in the center of the enzyme, parallel to the DNA. Within this route, the conformational pathway is similar to that of the overall open to closed transition of pol β, but outside it, especially when the ion starts near active site residues Arg258 and Asp190, the conformational pathway diverges significantly. Our findings should apply generally to pol β, since R283K is relatively far from the active site; further experimental and computational work are required to confirm this. Our studies also underscore the common feature that less active mutants have less stable closed states than their open states, in marked contrast to the wild-type enzyme, where the closed state is significantly more stable than the open form.

Comparison between Mean Forces and Swarms-of-Trajectories String Methods

The original formulation of the string method in collective variable space is compared with a recent variant called string method with swarms-of-trajectories. The assumptions made in the original method are revisited and the significance of the minimum free energy path (MFEP) is discussed in the context of reactive events. These assumptions are compared to those made in the string method with swarms-of-trajectories, and shown to be equivalent in a certain regime: in particular an expression for the path identified by the swarms-of-trajectories method is given and shown to be closely related to the MFEP. Finally, the algorithmic aspects of both methods are compared.

Increasing occurrences and functional roles for high energy purine-pyrimidine base-pairs in nucleic acids

There are a growing number of studies reporting the observation of purine-pyrimidine base-pairs that are seldom observed in unmodified nucleic acids because they entail the loss of energetically favorable interactions or require energetically costly base ionization or tautomerization. These high energy purine-pyrimidine base-pairs include G•C(+) and A•T Hoogsteen base-pairs, which entail ∼180° rotation of the purine base in a Watson-Crick base-pair, protonation of cytosine N3, and constriction of the C1'-C1' distance by ∼2.5Å. Other high energy pure-pyrimidine base-pairs include G•T, G•U, and A•C mispairs that adopt Watson-Crick like geometry through either base ionization or tautomerization. Although difficult to detect and characterize using biophysical methods, high energy purine-pyrimidine base-pairs appear to be more common than once thought. They further expand the structural and functional diversity of canonical and non-canonical nucleic acid base-pairs.

Computational study of peptide permeation through membrane: Searching for hidden slow variables

Atomically detailed molecular dynamics trajectories in conjunction with Milestoning are used to analyze the different contributions of coarse variables to the permeation process of a small peptide (N-acetyl-L-tryptophanamide, NATA) through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane. The peptide reverses its overall orientation as it permeates through the biological bilayer. The large change in orientation is investigated explicitly but is shown to impact the free energy landscape and permeation time only moderately. Nevertheless, a significant difference in permeation properties of the two halves of the membrane suggests the presence of other hidden slow variables. We speculate, based on calculation of the potential of mean force, that a conformational transition of NATA makes significant contribution to these differences. Other candidates for hidden slow variables may include water permeation and collective motions of phospholipids.

Evidence of ternary complex formation in Trypanosoma cruzi trans-sialidase catalysis

Trypanosoma cruzi trans-sialidase (TcTS) is a key target protein for Chagas disease chemotherapy. In this study, we investigated the implications of active site flexibility on the biochemical mechanism of TcTS. Molecular dynamics studies revealed remarkable plasticity in the TcTS catalytic site, demonstrating, for the first time, how donor substrate engagement with the enzyme induces an acceptor binding site in the catalytic pocket that was not previously captured in crystal structures. Furthermore, NMR data showed cooperative binding between donor and acceptor substrates, supporting theoretical results. In summary, our data put forward a coherent dynamic framework to understand how a glycosidase evolved its highly efficient trans-glycosidase activity.

Biophysical Insights into the Inhibitory Mechanism of Non-Nucleoside HIV-1 Reverse Transcriptase Inhibitors

HIV-1 reverse transcriptase (RT) plays a central role in HIV infection. Current United States Federal Drug Administration (USFDA)-approved antiretroviral therapies can include one of five approved non-nucleoside RT inhibitors (NNRTIs), which are potent inhibitors of RT activity. Despite their crucial clinical role in treating and preventing HIV-1 infection, their mechanism of action remains elusive. In this review, we introduce RT and highlight major advances from experimental and computational biophysical experiments toward an understanding of RT function and the inhibitory mechanism(s) of NNRTIs.

Vaccine-derived mutation in motif D of poliovirus RNA-dependent RNA polymerase lowers nucleotide incorporation fidelity

All viral RNA-dependent RNA polymerases (RdRps) have a conserved structural element termed motif D. Studies of the RdRp from poliovirus (PV) have shown that a conformational change of motif D leads to efficient and faithful nucleotide addition by bringing Lys-359 into the active site where it serves as a general acid. The RdRp of the Sabin I vaccine strain has Thr-362 changed to Ile. Such a drastic change so close to Lys-359 might alter RdRp function and contribute in some way to the attenuated phenotype of Sabin type I. Here we present our characterization of the T362I RdRp. We find that the T362I RdRp exhibits a mutator phenotype in biochemical experiments in vitro. Using NMR, we show that this change in nucleotide incorporation fidelity correlates with a change in the structural dynamics of motif D. A recombinant PV expressing the T362I RdRp exhibits normal growth properties in cell culture but expresses a mutator phenotype in cells. For example, the T362I-containing PV is more sensitive to the mutagenic activity of ribavirin than wild-type PV. Interestingly, the T362I change was sufficient to cause a statistically significant reduction in viral virulence. Collectively, these studies suggest that residues of motif D can be targeted when changes in nucleotide incorporation fidelity are desired. Given the observation that fidelity mutants can serve as vaccine candidates, it may be possible to use engineering of motif D for this purpose.

Intermediate state trapping of a voltage sensor

Voltage sensor domains (VSDs) regulate ion channels and enzymes by undergoing conformational changes depending on membrane electrical signals. The molecular mechanisms underlying the VSD transitions are not fully understood. Here, we show that some mutations of I241 in the S1 segment of the Shaker Kv channel positively shift the voltage dependence of the VSD movement and alter the functional coupling between VSD and pore domains. Among the I241 mutants, I241W immobilized the VSD movement during activation and deactivation, approximately halfway between the resting and active states, and drastically shifted the voltage activation of the ionic conductance. This phenotype, which is consistent with a stabilization of an intermediate VSD conformation by the I241W mutation, was diminished by the charge-conserving R2K mutation but not by the charge-neutralizing R2Q mutation. Interestingly, most of these effects were reproduced by the F244W mutation located one helical turn above I241. Electrophysiology recordings using nonnatural indole derivatives ruled out the involvement of cation-Π interactions for the effects of the Trp inserted at positions I241 and F244 on the channel’s conductance, but showed that the indole nitrogen was important for the I241W phenotype. Insight into the molecular mechanisms responsible for the stabilization of the intermediate state were investigated by creating in silico the mutations I241W, I241W/R2K, and F244W in intermediate conformations obtained from a computational VSD transition pathway determined using the string method. The experimental results and computational analysis suggest that the phenotype of I241W may originate in the formation of a hydrogen bond between the indole nitrogen atom and the backbone carbonyl of R2. This work provides new information on intermediate states in voltage-gated ion channels with an approach that produces minimum chemical perturbation.

A century of enzyme kinetic analysis, 1913 to 2013

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.

Structures of intermediates along the catalytic cycle of terminal deoxynucleotidyltransferase: dynamical aspects of the two-metal ion mechanism

Terminal deoxynucleotidyltransferase (Tdt) is a non-templated eukaryotic DNA polymerase of the polX family that is responsible for the random addition of nucleotides at the V(D)J junctions of immunoglobulins and T-cell receptors. Here we describe a series of high-resolution X-ray structures that mimic the pre-catalytic state, the post-catalytic state and a competent state that can be transformed into the two other ones in crystallo via the addition of dAMPcPP and Zn(2+), respectively. We examined the effect of Mn(2+), Co(2+) and Zn(2+) because they all have a marked influence on the kinetics of the reaction. We demonstrate a dynamic role of divalent transition metal ions bound to site A: (i) Zn(2+) (or Co(2+)) in Metal A site changes coordination from octahedral to tetrahedral after the chemical step, which explains the known higher affinity of Tdt for the primer strand when these ions are present, and (ii) metal A has to leave to allow the translocation of the primer strand and to clear the active site, a typical feature for a ratchet-like mechanism. Except for Zn(2+), the sugar puckering of the primer strand 3' terminus changes from C2'-endo to C3'-endo during catalysis. In addition, our data are compatible with a scheme where metal A is the last component that binds to the active site to complete its productive assembly, as already inferred in human pol beta. The new structures have potential implications for modeling pol mu, a closely related polX implicated in the repair of DNA double-strand breaks, in a complex with a DNA synapsis.

"Gate-keeper" residues and active-site rearrangements in DNA polymerase μ help discriminate non-cognate nucleotides

Incorporating the cognate instead of non-cognate substrates is crucial for DNA polymerase function. Here we analyze molecular dynamics simulations of DNA polymerase μ (pol μ) bound to different non-cognate incoming nucleotides including A:dCTP, A:dGTP, A(syn):dGTP, A:dATP, A(syn):dATP, T:dCTP, and T:dGTP to study the structure-function relationships involved with aberrant base pairs in the conformational pathway; while a pol μ complex with the A:dTTP base pair is available, no solved non-cognate structures are available. We observe distinct differences of the non-cognate systems compared to the cognate system. Specifically, the motions of active-site residue His329 and Asp330 distort the active site, and Trp436, Gln440, Glu443 and Arg444 tend to tighten the nucleotide-binding pocket when non-cognate nucleotides are bound; the latter effect may further lead to an altered electrostatic potential within the active site. That most of these “gate-keeper” residues are located farther apart from the upstream primer in pol μ, compared to other X family members, also suggests an interesting relation to pol μ's ability to incorporate nucleotides when the upstream primer is not paired. By examining the correlated motions within pol μ complexes, we also observe different patterns of correlations between non-cognate systems and the cognate system, especially decreased interactions between the incoming nucleotides and the nucleotide-binding pocket. Altered correlated motions in non-cognate systems agree with our recently proposed hybrid conformational selection/induced-fit models. Taken together, our studies propose the following order for difficulty of non-cognate system insertions by pol μ: T:dGTP<A(syn):dATP<T:dCTP<A:dGTP<A(syn):dGTP<A:dCTP<A:dATP. This sequence agrees with available kinetic data for non-cognate nucleotide insertions, with the exception of A:dGTP, which may be more sensitive to the template sequence. The structures and conformational aspects predicted here are experimentally testable.

DNA polymerase μ (pol μ) is an enzyme that participates in DNA repair and thus has a central role in maintaining the integrity of genetic information. To efficiently repair the DNA, discriminating the cognate instead of non-cognate nucleotides (“fidelity-checking”) is required. Here we analyze molecular dynamics simulations of pol μ bound to different non-cognate nucleotides to study the structure-function relationships involved in the fidelity-checking mechanism of pol μ on the atomic level. Our results suggest that His329, Asp330, Trp436, Gln440, Glu443, and Arg444 are of great importance for pol μ's fidelity-checking mechanism. We also observe altered patterns of correlated motions within pol μ complex when non-cognate instead of cognate nucleotides are bound, which agrees with our recently proposed hybrid conformational selection/induced-fit models. Taken together, our studies help interpret the available kinetic data of various non-cognate nucleotide insertions by pol μ. We also suggest experimentally testable predictions; for example, a point mutation like E443M may reduce the ability of pol μ to insert the cognate more than of non-cognate nucleotides. Our studies suggest an interesting relation to pol μ's unique ability to incorporate nucleotides when the upstream primer is not paired.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Molecular machines

Molecular machines (MM) are essential components of living cells. They conduct mechanical work, transport materials into and out of cells, assist in processing enzymatic reactions, and more. Their operations are frequently combined with significant conformational transitions. Computational studies of these conformational transitions and their coupling to molecular functions are discussed. It is argued that coarse descriptions of these molecules which are based on mass density and shape provide useful information on directions of action. It is further argued that MM are likely to have well focused and narrow reaction pathways. The proposal for such pathways is supported by evolutionary analyses of homologous machines. Finally, these observations are used to build atomically detailed models of these systems that are making the link from structure to functions (kinetics and thermodynamics). For that purpose enhanced sampling techniques are required.

DNA mismatch synthesis complexes provide insights into base selectivity of a B family DNA polymerase

Current hypotheses that attempt to rationalize the high degree of base selectivity exhibited by replicative DNA polymerases (pols) concur that ternary complexes formed with incorrect dNTPs are destabilized. Knowing what accounts for this destabilization is likely to be the key to understanding base discrimination. To address this issue, we have determined crystal structures of ternary complexes with all 12 mismatches using an engineered RB69 pol quadruple mutant (qm, L415A/L561A/S565G/Y567A) that enabled us to capture nascent mispaired dNTPs. These structures show that mismatches in the nascent base-pair binding pocket (NBP) of the qm pol differ markedly from mismatches embedded in binary pol-DNA complexes. Surprisingly, only 3 of 12 mismatches clash with the NBP when they are modeled into the wild-type (wt) pol. The remaining can fit into a wt pol ternary complex but deviate from normal Watson-Crick base-pairs. Repositioning of the templating nucleotide residue and the enlarged NBP in qm ternary complex play important roles in accommodating incorrect incoming dNTPs. From these structures, we propose additional reasons as to why incorrect dNTPs are incorporated so inefficiently by wt RB69 pol: (i) steric clashes with side chains in the NBP after Fingers closing; (ii) weak interactions or large gaps between the incoming dNTP and the templating base; and (iii) burying a protonated base in the hydrophobic environment of the NBP. All of these possibilities would be expected to destabilize the closed ternary complex so that incorporation of incorrect dNTP would be a rare event.

Perspective: pre-chemistry conformational changes in DNA polymerase mechanisms

In recent papers, there has been a lively exchange concerning theories for enzyme catalysis, especially the role of protein dynamics/pre-chemistry conformational changes in the catalytic cycle of enzymes. Of particular interest is the notion that substrate-induced conformational changes that assemble the polymerase active site prior to chemistry are required for DNA synthesis and impact fidelity (i.e., substrate specificity). High-resolution crystal structures of DNA polymerase β representing intermediates of substrate complexes prior to the chemical step are available. These structures indicate that conformational adjustments in both the protein and substrates must occur to achieve the requisite geometry of the reactive participants for catalysis. We discuss computational and kinetic methods to examine possible conformational change pathways that lead from the observed crystal structure intermediates to the final structures poised for chemistry. The results, as well as kinetic data from site-directed mutagenesis studies, are consistent with models requiring pre-chemistry conformational adjustments in order to achieve high fidelity DNA synthesis. Thus, substrate-induced conformational changes that assemble the polymerase active site prior to chemistry contribute to DNA synthesis even when they do not represent actual rate-determining steps for chemistry.

Revisiting Molecular Dynamics on a CPU/GPU system: Water Kernel and SHAKE Parallelization

We report Graphics Processing Unit (GPU) and Open-MP parallel implementations of water-specific force calculations and of bond constraints for use in Molecular Dynamics simulations. We focus on a typical laboratory computing-environment in which a CPU with a few cores is attached to a GPU. We discuss in detail the design of the code and we illustrate performance comparable to highly optimized codes such as GROMACS. Beside speed our code shows excellent energy conservation. Utilization of water-specific lists allows the efficient calculations of non-bonded interactions that include water molecules and results in a speed-up factor of more than 40 on the GPU compared to code optimized on a single CPU core for systems larger than 20,000 atoms. This is up four-fold from a factor of 10 reported in our initial GPU implementation that did not include a water-specific code. Another optimization is the implementation of constrained dynamics entirely on the GPU. The routine, which enforces constraints of all bonds, runs in parallel on multiple Open-MP cores or entirely on the GPU. It is based on Conjugate Gradient solution of the Lagrange multipliers (CG SHAKE). The GPU implementation is partially in double precision and requires no communication with the CPU during the execution of the SHAKE algorithm. The (parallel) implementation of SHAKE allows an increase of the time step to 2.0fs while maintaining excellent energy conservation. Interestingly, CG SHAKE is faster than the usual bond relaxation algorithm even on a single core if high accuracy is expected. The significant speedup of the optimized components transfers the computational bottleneck of the MD calculation to the reciprocal part of Particle Mesh Ewald (PME).

Molecular dynamics simulation in virus research

Virus replication in the host proceeds by chains of interactions between viral and host proteins. The interactions are deeply influenced by host immune molecules and anti-viral compounds, as well as by mutations in viral proteins. To understand how these interactions proceed mechanically and how they are influenced by mutations, one needs to know the structures and dynamics of the proteins. Molecular dynamics (MD) simulation is a powerful computational method for delineating motions of proteins at an atomic-scale via theoretical and empirical principles in physical chemistry. Recent advances in the hardware and software for biomolecular simulation have rapidly improved the precision and performance of this technique. Consequently, MD simulation is quickly extending the range of applications in biology, helping to reveal unique features of protein structures that would be hard to obtain by experimental methods alone. In this review, we summarize the recent advances in MD simulations in the study of virus–host interactions and evolution, and present future perspectives on this technique.