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

History of advances in enzyme kinetic methods: From minutes to milliseconds

The last review on transient-state kinetic methods in The Enzymes was published three decades ago (Johnson, K.A., 1992. The Enzymes, XX, 1-61). In that review the foundations were laid out for the logic behind the design and interpretation of experiments. In the intervening years the instrumentation has improved mainly in providing better sample economy and shorter dead times. More significantly, in 1992 we were just introducing methods for fitting data based on numerical integration of rate equations, but the software was slow and difficult to use. Today, advances in numerical integration methods for data fitting have led to fast and dynamic software, making it easy to fit data without simplifying approximations. This approach overcomes multiple disadvantages of traditional data fitting based on equations derived by analytical integration of rate equations, requiring simplifying approximations. Mechanism-based fitting using computer simulation resolves mechanisms by accounting for the concentration dependence of the rates and amplitudes of the reaction to find a set of intrinsic rate constants that reproduce the experimental data, including details about how the experiment was performed in modeling the data. Rather than discuss how to design and interpret rapid-quench and stopped-flow experiments individually, we now focus on how to fit them simultaneously so that the quench-flow data anchor the interpretation of fluorescence signals. Computer simulation streamlines the fitting of multiple experiments globally to yield a single unifying model to account for all available data.

High fidelity DNA strand-separation is the major specificity determinant in DNA methyltransferase CcrM's catalytic mechanism

Strand-separation is emerging as a novel DNA recognition mechanism but the underlying mechanisms and quantitative contribution of strand-separation to fidelity remain obscure. The bacterial DNA adenine methyltransferase, CcrM, recognizes 5'GANTC'3 sequences through a DNA strand-separation mechanism with unusually high selectivity. To explore this novel recognition mechanism, we incorporated Pyrrolo-dC into cognate and noncognate DNA to monitor the kinetics of strand-separation and used tryptophan fluorescence to follow protein conformational changes. Both signals are biphasic and global fitting showed that the faster phase of DNA strand-separation was coincident with the protein conformational transition. Non-cognate sequences did not display strand-separation and methylation was reduced > 300-fold, providing evidence that strand-separation is a major determinant of selectivity. Analysis of an R350A mutant showed that the enzyme conformational step can occur without strand-separation, so the two events are uncoupled. A stabilizing role for the methyl-donor (SAM) is proposed; the cofactor interacts with a critical loop which is inserted between the DNA strands, thereby stabilizing the strand-separated conformation. The results presented here are broadly applicable to the study of other N6-adenine methyltransferases that contain the structural features implicated in strand-separation, which are found widely dispersed across many bacterial phyla, including human and animal pathogens, and some Eukaryotes.

Design and interpretation of experiments to establish enzyme pathway and define the role of conformational changes in enzyme specificity

We describe the experimental methods and analysis to define the role of enzyme conformational changes in specificity based on published studies using DNA polymerases as an ideal model system. Rather than give details of how to perform transient-state and single-turnover kinetic experiments, we focus on the rationale of the experimental design and interpretation. We show how initial experiments to measure k_cat and k_cat/K_m can accurately quantify specificity but do not define its underlying mechanistic basis. We describe methods to fluorescently label enzymes to monitor conformational changes and to correlate fluorescence signals with rapid-chemical-quench flow assays to define the steps in the pathway. Measurements of the rate of product release and of the kinetics of the reverse reaction complete the kinetic and thermodynamic description of the full reaction pathway. This analysis showed that the substrate-induced change in enzyme structure from an open to a closed state was much faster than rate-limiting chemical bond formation. However, because the reverse of the conformational change was much slower than chemistry, specificity is governed solely by the product of the binding constant for the initial weak substrate binding and the rate constant for the conformational change (k_cat/K_m=K₁k₂) so that the specificity constant does not include k_cat. The enzyme conformational change leads to a closed complex in which the substrate is bound tightly and is committed to the forward reaction. In contrast, an incorrect substrate is bound weakly, and the rate of chemistry is slow, so the mismatch is released from the enzyme rapidly. Thus, the substrate-induced-fit is the major determinant of specificity. The methods outlined here should be applicable to other enzyme systems.

Machines on Genes through the Computational Microscope

Macromolecular machines acting on genes are at the core of life's fundamental processes, including DNA replication and repair, gene transcription and regulation, chromatin packaging, RNA splicing, and genome editing. Here, we report the increasing role of computational biophysics in characterizing the mechanisms of "machines on genes", focusing on innovative applications of computational methods and their integration with structural and biophysical experiments. We showcase how state-of-the-art computational methods, including classical and ab initio molecular dynamics to enhanced sampling techniques, and coarse-grained approaches are used for understanding and exploring gene machines for real-world applications. As this review unfolds, advanced computational methods describe the biophysical function that is unseen through experimental techniques, accomplishing the power of the "computational microscope", an expression coined by Klaus Schulten to highlight the extraordinary capability of computer simulations. Pushing the frontiers of computational biophysics toward a pragmatic representation of large multimegadalton biomolecular complexes is instrumental in bridging the gap between experimentally obtained macroscopic observables and the molecular principles playing at the microscopic level. This understanding will help harness molecular machines for medical, pharmaceutical, and biotechnological purposes.

Leveraging intrinsic flexibility to engineer enhanced enzyme catalytic activity

Dynamic motions of enzymes occurring on a broad range of timescales play a pivotal role in all steps of the reaction pathway, including substrate binding, catalysis, and product release. However, it is unknown whether structural information related to conformational flexibility can be exploited for the directed evolution of enzymes with higher catalytic activity. Here, we show that mutagenesis of residues exclusively located at flexible regions distal to the active site of Homo sapiens kynureninase (HsKYNase) resulted in the isolation of a variant (BF-HsKYNase) in which the rate of the chemical step toward kynurenine was increased by 45-fold. Mechanistic pre–steady-state kinetic analysis of the wild type and the evolved enzyme shed light on the underlying effects of distal mutations (>10 Å from the active site) on the rate-limiting step of the catalytic cycle. Hydrogen-deuterium exchange coupled to mass spectrometry and molecular dynamics simulations revealed that the amino acid substitutions in BF-HsKYNase allosterically affect the flexibility of the pyridoxal-5′-phosphate (PLP) binding pocket, thereby impacting the rate of chemistry, presumably by altering the conformational ensemble and sampling states more favorable to the catalyzed reaction.

Structural and Molecular Kinetic Features of Activities of DNA Polymerases

DNA polymerases catalyze DNA synthesis during the replication, repair, and recombination of DNA. Based on phylogenetic analysis and primary protein sequences, DNA polymerases have been categorized into seven families: A, B, C, D, X, Y, and RT. This review presents generalized data on the catalytic mechanism of action of DNA polymerases. The structural features of different DNA polymerase families are described in detail. The discussion highlights the kinetics and conformational dynamics of DNA polymerases from all known polymerase families during DNA synthesis.

Single-molecule Taq DNA polymerase dynamics

Taq DNA polymerase functions at elevated temperatures with fast conformational dynamics-regimes previously inaccessible to mechanistic, single-molecule studies. Here, single-walled carbon nanotube transistors recorded the motions of Taq molecules processing matched or mismatched template-deoxynucleotide triphosphate pairs from 22° to 85°C. By using four enzyme orientations, the whole-enzyme closures of nucleotide incorporations were distinguished from more rapid, 20-μs closures of Taq's fingers domain testing complementarity and orientation. On average, one transient closure was observed for every nucleotide binding event; even complementary substrate pairs averaged five transient closures between each catalytic incorporation at 72°C. The rate and duration of the transient closures and the catalytic events had almost no temperature dependence, leaving all of Taq's temperature sensitivity to its rate-determining open state.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Conformational dynamics during misincorporation and mismatch extension defined using a DNA polymerase with a fluorescent artificial amino acid

High-fidelity DNA polymerases select the correct nucleotide over the structurally similar incorrect nucleotides with extremely high specificity while maintaining fast rates of incorporation. Previous analysis revealed the conformational dynamics and complete kinetic pathway governing correct nucleotide incorporation using a high-fidelity DNA polymerase variant containing a fluorescent unnatural amino acid. Here we extend this analysis to investigate the kinetics of nucleotide misincorporation and mismatch extension. We report the specificity constants for all possible misincorporations and characterize the conformational dynamics of the enzyme during misincorporation and mismatch extension. We present free energy profiles based on the kinetic measurements and discuss the effect of different steps on specificity. During mismatch incorporation and subsequent extension with the correct nucleotide, the rates of the conformational change and chemistry are both greatly reduced. The nucleotide dissociation rate, however, increases to exceed the rate of chemistry. To investigate the structural basis for discrimination against mismatched nucleotides, we performed all atom molecular dynamics simulations on complexes with either the correct or mismatched nucleotide bound at the polymerase active site. The simulations suggest that the closed form of the enzyme with a mismatch bound is greatly destabilized due to weaker interactions with active site residues, nonideal base pairing, and a large increase in the distance from the 3'-OH group of the primer strand to the α-phosphate of the incoming nucleotide, explaining the reduced rates of misincorporation. The observed kinetic and structural mechanisms governing nucleotide misincorporation reveal the general principles likely applicable to other high-fidelity DNA polymerases.

String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor

The kinetics of a dynamical system comprising two metastable states is formulated in terms of a finite-time propagator in phase space (position and velocity) adapted to the underdamped Langevin equation. Dimensionality reduction to a subspace of collective variables yields familiar expressions for the propagator, committor, and steady-state flux. A quadratic expression for the steady-state flux between the two metastable states can serve as a robust variational principle to determine an optimal approximate committor expressed in terms of a set of collective variables. The theoretical formulation is exploited to clarify the foundation of the string method with swarms-of-trajectories, which relies on the mean drift of short trajectories to determine the optimal transition pathway. It is argued that the conditions for Markovity within a subspace of collective variables may not be satisfied with an arbitrary short time-step and that proper kinetic behaviors appear only when considering the effective propagator for longer lag times. The effective propagator with finite lag time is amenable to an eigenvalue-eigenvector spectral analysis, as elaborated previously in the context of position-based Markov models. The time-correlation functions calculated by swarms-of-trajectories along the string pathway constitutes a natural extension of these developments. The present formulation provides a powerful theoretical framework to characterize the optimal pathway between two metastable states of a system.

Computer Simulations of the Dissociation Mechanism of Gleevec from Abl Kinase with Milestoning

Gleevec (a.k.a., imatinib) is an important anticancer (e.g., chronic myeloid leukemia) chemotherapeutic drug due to its inhibitory interaction with the Abl kinase. Here, we use atomically detailed simulations within the Milestoning framework to study the molecular dissociation mechanism of Gleevec from Abl kinase. We compute the dissociation free energy profile, the mean first passage time for unbinding, and explore the transition state ensemble of conformations. The milestones form a multidimensional network with average connectivity of about 2.93, which is significantly higher than the connectivity for a one-dimensional reaction coordinate. The free energy barrier for Gleevec dissociation is estimated to be ∼10 kcal/mol, and the exit time is ∼55 ms. We examined the transition state conformations using both, the committor and transition function. We show that near the transition state the highly conserved salt bridge K217 and E286 is transiently broken. Together with the calculated free energy profile, these calculations can advance the understanding of the molecular interaction mechanisms between Gleevec and Abl kinase and play a role in future drug design and optimization studies.

Catalytic Magnesium as a Door Stop for DNA Sliding

The protein HIV Reverse Transcriptase (HIV RT) synthesizes a DNA strand according to a template. During the synthesis, the polymerase slides on the double stranded DNA to allow the entry of a new nucleotide to the active site. We use Molecular Dynamics simulations to estimate the free energy profile and the time scale of the DNA-protein's relative displacement in the complex's closed state. We illustrate that the presence of the catalytic magnesium slows down the process. Upon removing the catalytic magnesium ion, the process is rapid and significantly faster than reopening the active site in preparation for the new substrate. We speculate that magnesium regulates DNA translocation. The magnesium locks the DNA into a specific orientation during the chemical addition of the nucleotide. The release of Mg²⁺ eases DNA sliding and the acceptance of a new substrate.

Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

Kinetic and thermodynamic analysis defines roles for two metal ions in DNA polymerase specificity and catalysis

Magnesium ions play a critical role in catalysis by many enzymes and contribute to the fidelity of DNA polymerases through a two-metal ion mechanism. However, specificity is a kinetic phenomenon and the roles of Mg²⁺ ions in each step in the catalysis have not been resolved. We first examined the roles of Mg²⁺ by kinetic analysis of single nucleotide incorporation catalyzed by HIV reverse transcriptase. We show that Mg.dNTP binding induces an enzyme conformational change at a rate that is independent of free Mg²⁺ concentration. Subsequently, the second Mg²⁺ binds to the closed state of the enzyme-DNA-Mg.dNTP complex (K_d = 3.7 mM) to facilitate catalysis. Weak binding of the catalytic Mg²⁺ contributes to fidelity by sampling the correctly aligned substrate without perturbing the equilibrium for nucleotide binding at physiological Mg²⁺ concentrations. An increase of the Mg²⁺ concentration from 0.25 to 10 mM increases nucleotide specificity (k_cat/K_m) 12-fold largely by increasing the rate of the chemistry relative to the rate of nucleotide release. Mg²⁺ binds very weakly (K_d ≤ 37 mM) to the open state of the enzyme. Analysis of published crystal structures showed that HIV reverse transcriptase binds only two metal ions prior to incorporation of a correct base pair. Molecular dynamics simulations support the two-metal ion mechanism and the kinetic data indicating weak binding of the catalytic Mg²⁺. Molecular dynamics simulations also revealed the importance of the divalent cation cloud surrounding exposed phosphates on the DNA. These results enlighten the roles of the two metal ions in the specificity of DNA polymerases.

Enhanced enzyme kinetics of reverse transcriptase variants cloned from animals infected with SIVmac239 lacking viral protein X

HIV Type 1 (HIV-1) and simian immunodeficiency virus (SIV) display differential replication kinetics in macrophages. This is because high expression levels of the active host deoxynucleotide triphosphohydrolase sterile α motif domain and histidine-aspartate domain-containing protein 1 (SAMHD1) deplete intracellular dNTPs, which restrict HIV-1 reverse transcription, and result in a restrictive infection in this myeloid cell type. Some SIVs overcome SAMHD1 restriction using viral protein X (Vpx), a viral accessory protein that induces proteasomal degradation of SAMHD1, increasing cellular dNTP concentrations and enabling efficient proviral DNA synthesis. We previously reported that SAMHD1-noncounteracting lentiviruses may have evolved to harbor RT proteins that efficiently polymerize DNA, even at low dNTP concentrations, to circumvent SAMHD1 restriction. Here we investigated whether RTs from SIVmac239 virus lacking a Vpx protein evolve during in vivo infection to more efficiently synthesize DNA at the low dNTP concentrations found in macrophages. Sequence analysis of RTs cloned from Vpx (+) and Vpx (-) SIVmac239-infected animals revealed that Vpx (-) RTs contained more extensive mutations than Vpx (+) RTs. Although the amino acid substitutions were dispersed indiscriminately across the protein, steady-state and pre-steady-state analysis demonstrated that selected SIVmac239 Vpx (-) RTs are characterized by higher catalytic efficiency and incorporation efficiency values than RTs cloned from SIVmac239 Vpx (+) infections. Overall, this study supports the possibility that the loss of Vpx may generate in vivo SIVmac239 RT variants that can counteract the limited availability of dNTP substrate in macrophages.

Conformational dynamics during high-fidelity DNA replication and translocation defined using a DNA polymerase with a fluorescent artificial amino acid

We address the role of enzyme conformational dynamics in specificity for a high-fidelity DNA polymerase responsible for genome replication. We present the complete characterization of the conformational dynamics during the correct nucleotide incorporation forward and reverse reactions using stopped-flow and rapid-quench methods with a T7 DNA polymerase variant containing a fluorescent unnatural amino acid, (7-hydroxy-4-coumarin-yl) ethylglycine, which provides a signal for enzyme conformational changes. We show that the forward conformational change (>6000 s⁻¹) is much faster than chemistry (300 s⁻¹) while the enzyme opening to allow release of bound nucleotide (1.7 s⁻¹) is much slower than chemistry. These parameters show that the conformational change selects a correct nucleotide for incorporation through an induced-fit mechanism. We also measured conformational changes occurring after chemistry and during pyrophosphorolysis, providing new insights into processive polymerization. Pyrophosphorolysis occurs via a conformational selection mechanism as the pyrophosphate binds to a rare pretranslocation state of the enzyme–DNA complex. Global data fitting was achieved by including experiments in the forward and reverse directions to correlate conformational changes with chemical reaction steps. This analysis provided well-constrained values for nine rate constants to establish a complete free-energy profile including the rates of DNA translocation during processive synthesis. Translocation does not follow Brownian ratchet or power stroke models invoking nucleotide binding as the driving force. Rather, translocation is rapid and thermodynamically favorable after enzyme opening and pyrophosphate release, and it appears to limit the rate of processive synthesis at 4 °C.

Engineered CRISPR/Cas9 enzymes improve discrimination by slowing DNA cleavage to allow release of off-target DNA

CRISPR/Cas9 is a programmable genome editing tool widely used for biological applications and engineered Cas9s have increased discrimination against off-target cleavage compared with wild-type Streptococcus pyogenes (SpCas9) in vivo. To understand the basis for improved discrimination against off-target DNA containing important mismatches at the distal end of the guide RNA, we performed kinetic analyses on the high-fidelity (Cas9-HF1) and hyper-accurate (HypaCas9) engineered Cas9 variants. We show that DNA cleavage is impaired by more than 100- fold for the high-fidelity variants. The high-fidelity variants improve discrimination by slowing the observed rate of cleavage without increasing the rate of DNA rewinding and release. The kinetic partitioning favors release rather than cleavage of a bound off-target substrate only because the cleavage rate is so low. Further improvement in discrimination may require engineering increased rates of dissociation of off-target DNA.

Engineered high-fidelity Cas9s have increased discrimination against off-targets. Kinetic analyses of Cas9-HF1 and HypaCas9 engineered Cas9 variants show that their DNA cleavage is impaired by more than 100- fold, which leads to release rather than cleavage of a bound off-target substrate.

A pre-catalytic non-covalent step governs DNA polymerase β fidelity

DNA polymerase β (pol β) selects the correct deoxyribonucleoside triphosphate for incorporation into the DNA polymer. Mistakes made by pol β lead to mutations, some of which occur within specific sequence contexts to generate mutation hotspots. The adenomatous polyposis coli (APC) gene is mutated within specific sequence contexts in colorectal carcinomas but the underlying mechanism is not fully understood. In previous work, we demonstrated that a somatic colon cancer variant of pol β, K289M, misincorporates deoxynucleotides at significantly increased frequencies over wild-type pol β within a mutation hotspot that is present several times within the APC gene. Kinetic studies provide evidence that the rate-determining step of pol β catalysis is phosphodiester bond formation and suggest that substrate selection is governed at this step. Remarkably, we show that, unlike WT, a pre-catalytic step in the K289M pol β kinetic pathway becomes slower than phosphodiester bond formation with the APC DNA sequence but not with a different DNA substrate. Based on our studies, we propose that pre-catalytic conformational changes are of critical importance for DNA polymerase fidelity within specific DNA sequence contexts.

Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate

Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.

ScMile: A Script to Investigate Kinetics with Short Time Molecular Dynamics Trajectories and the Milestoning Theory

Studies of complex and rare events in condensed phase systems continue to attract considerable attention. Milestoning is a useful theory and algorithm to investigate the long-time dynamics of activated molecular events. It is based on launching a large number of short trajectories and statistical analysis of the outcome. The implementation of the theory in a computer script is described that enables more efficient Milestoning calculation, reducing user time and errors, and automating a significant fraction of the algorithm. The script exploits a molecular dynamics engine, which at present is NAMD, to run the short trajectories. However, since the script is external to the engine, the script can be easily adapted to different molecular dynamics codes. The outcomes of the short trajectories are analyzed to obtain a kinetic and thermodynamic description of the entire process. While many examples of Milestoning were published in the past, we provide two simple examples (a conformational transition of alanine dipeptide in a vacuum and aqueous solution) to illustrate the use of the script.

New standards for collecting and fitting steady state kinetic data

The Michaelis-Menten equation is usually expressed in terms of k _cat and K _m values: v = k _cat[S]/(K _m + [S]). However, it is impossible to interpret K _m in the absence of additional information, while the ratio of k _cat/K _m provides a measure of enzyme specificity and is proportional to enzyme efficiency and proficiency. Moreover, k _cat/K _m provides a lower limit on the second order rate constant for substrate binding. For these reasons it is better to redefine the Michaelis-Menten equation in terms of k _cat and k _cat/K _m values: v = k _SP[S]/(1 + k _SP[S]/k _cat), where the specificity constant, k _SP = k _cat/K _m. In this short review, the rationale for this assertion is explained and it is shown that more accurate measurements of k _cat/K _m can be derived directly using the modified form of the Michaelis-Menten equation rather than calculated from the ratio of k _cat and K _m values measured separately. Even greater accuracy is achieved with fitting the raw data directly by numerical integration of the rate equations rather than using analytically derived equations. The importance of fitting to derive k _cat and k _cat/K _m is illustrated by considering the role of conformational changes in enzyme specificity where k _cat and k _cat/K _m can reflect different steps in the pathway. This highlights the pitfalls in attempting to interpret K _m, which is best understood as the ratio of k _cat divided by k _cat/K _m.

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

Efficient prediction and ranking of small molecule binders by their kinetic ( kon and koff) and thermodynamic ( Δ G) properties can be a valuable metric for drug lead optimization, as these quantities are often indicators of in vivo efficacy. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon's, koff's, and Δ G's. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, β-cyclodextrin, based on predicted kon's and koff's. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long time scale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and Δ G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish "best practices" for its future use.

Revealing the distinct folding phases of an RNA three-helix junction

Remarkable new insight has emerged into the biological role of RNA in cells. RNA folding and dynamics enable many of these newly discovered functions, calling for an understanding of RNA self-assembly and conformational dynamics. Because RNAs pass through multiple structures as they fold, an ensemble perspective is required to visualize the flow through fleetingly populated sets of states. Here, we combine microfluidic mixing technology and small angle X-ray scattering (SAXS) to measure the Mg-induced folding of a small RNA domain, the tP5abc three helix junction. Our measurements are interpreted using ensemble optimization to select atomically detailed structures that recapitulate each experimental curve. Structural ensembles, derived at key stages in both time-resolved studies and equilibrium titrations, reproduce the features of known intermediates, and more importantly, offer a powerful new structural perspective on the time-progression of folding. Distinct collapse phases along the pathway appear to be orchestrated by specific interactions with Mg ions. These key interactions subsequently direct motions of the backbone that position the partners of tertiary contacts for later bonding, and demonstrate a remarkable synergy between Mg and RNA across numerous time-scales.

Single-molecule FRET reveals proofreading complexes in the large fragment of Bacillus stearothermophilus DNA polymerase I

There is increasing interest in the use of DNA polymerases (DNA pols) in next-generation sequencing strategies. These methodologies typically rely on members of the A and B family of DNA polymerases that are classified as high-fidelity DNA polymerases. These enzymes possess the ability to selectively incorporate the correct nucleotide opposite a templating base with an error frequency of only 1 in 10⁶ insertion events. How they achieve this remarkable fidelity has been the subject of numerous investigations, yet the mechanism by which these enzymes achieve this level of accuracy remains elusive. Several smFRET assays were designed to monitor the conformational changes associated with the nucleotide selection mechanism(s) employed by DNA pols. smFRET has also been used to monitor the movement of DNA pols along a DNA substrate as well as to observe the formation of proof-reading complexes. One member among this class of enzymes, the large fragment of Bacillus stearothermophilus DNA polymerase I (Bst pol I LF), contains both 5'→3' polymerase and 3'→5' exonuclease domains, but reportedly lacks exonuclease activity. We have designed a smFRET assay showing that Bst pol I LF forms proofreading complexes. The formation of proofreading complexes at the single molecule level is strongly influenced by the presence of the 3' hydroxyl at the primer-terminus of the DNA substrate. Our assays also identify an additional state, observed in the presence of a mismatched primer-template terminus, that may be involved in the transfer of the primer-terminus from the polymerase to the exonuclease active site.

A new paradigm for atomically detailed simulations of kinetics in biophysical systems

The kinetics of biochemical and biophysical events determined the course of life processes and attracted considerable interest and research. For example, modeling of biological networks and cellular responses relies on the availability of information on rate coefficients. Atomically detailed simulations hold the promise of supplementing experimental data to obtain a more complete kinetic picture. However, simulations at biological time scales are challenging. Typical computer resources are insufficient to provide the ensemble of trajectories at the correct length that is required for straightforward calculations of time scales. In the last years, new technologies emerged that make atomically detailed simulations of rate coefficients possible. Instead of computing complete trajectories from reactants to products, these approaches launch a large number of short trajectories at different positions. Since the trajectories are short, they are computed trivially in parallel on modern computer architecture. The starting and termination positions of the short trajectories are chosen, following statistical mechanics theory, to enhance efficiency. These trajectories are analyzed. The analysis produces accurate estimates of time scales as long as hours. The theory of Milestoning that exploits the use of short trajectories is discussed, and several applications are described.

The catalytic inactivation of the N-half of human hexokinase 2 and structural and biochemical characterization of its mitochondrial conformation

The high proliferation rate of tumor cells demands high energy and metabolites that are sustained by a high glycolytic flux known as the 'Warburg effect'. The activation and further metabolism of glucose is initiated by hexokinase, a focal point of metabolic regulation. The human hexokinase 2 (HK2) is overexpressed in all aggressive tumors and predominantly found on the outer mitochondrial membrane, where interactions through its N-terminus initiates and maintains tumorigenesis. Here, we report the structure of HK2 in complex with glucose and glucose-6-phosphate (G6P). Structural and biochemical characterization of the mitochondrial conformation reveals higher conformational stability and slow protein unfolding rate (k_u) compared with the cytosolic conformation. Despite the active site similarity of all human hexokinases, the N-domain of HK2 is catalytically active but not in hexokinase 1 and 3. Helix-α₁₃ that protrudes out of the N-domain to link it to the C-domain of HK2 is found to be important in maintaining the catalytic activity of the N-half. In addition, the N-domain of HK2 regulates the stability of the whole enzyme in contrast with the C-domain. Glucose binding enhanced the stability of the wild-type (WT) enzyme and the single mutant D657A of the C-domain, but it did not increase the stability of the D209A mutant of the N-domain. The interaction of HK2 with the mitochondria through its N-half is proposed to facilitate higher stability on the mitochondria. The identification of structural and biochemical differences between HK2 and other human hexokinase isozymes could potentially be used in the development of new anticancer therapies.

The mechano-chemistry of a monomeric reverse transcriptase

Retroviral reverse transcriptase catalyses the synthesis of an integration-competent dsDNA molecule, using as a substrate the viral RNA. Using optical tweezers, we follow the Murine Leukemia Virus reverse transcriptase as it performs strand-displacement polymerization on a template under mechanical force. Our results indicate that reverse transcriptase functions as a Brownian ratchet, with dNTP binding as the rectifying reaction of the ratchet. We also found that reverse transcriptase is a relatively passive enzyme, able to polymerize on structured templates by exploiting their thermal breathing. Finally, our results indicate that the enzyme enters the recently characterized backtracking state from the pre-translocation complex.

DNA Unwinding Is the Primary Determinant of CRISPR-Cas9 Activity

Bacterial adaptive immunity utilizes RNA-guided surveillance complexes comprising Cas proteins together with CRISPR RNAs (crRNAs) to target foreign nucleic acids for destruction. Cas9, a type II CRISPR-Cas effector complex, can be programed with a single-guide RNA that base pairs with the target strand of dsDNA, displacing the non-target strand to create an R-loop, where the HNH and the RuvC nuclease domains cleave opposing strands. While many structural and biochemical studies have shed light on the mechanism of Cas9 cleavage, a clear unifying model has yet to emerge. Our detailed kinetic characterization of the enzyme reveals that DNA binding is reversible, and R-loop formation is rate-limiting, occurring in two steps, one for each of the nuclease domains. The specificity constant for cleavage is determined through an induced-fit mechanism as the product of the equilibrium binding affinity for DNA and the rate of R-loop formation.

Rock climbing: A local-global algorithm to compute minimum energy and minimum free energy pathways

The calculation of minimum energy or minimum free energy paths is an important step in the quantitative and qualitative studies of chemical and physical processes. The computations of these coordinates present a significant challenge and have attracted considerable theoretical and computational interest. Here we present a new local-global approach to study reaction coordinates, based on a gradual optimization of an action. Like other global algorithms, it provides a path between known reactants and products, but it uses a local algorithm to extend the current path in small steps. The local-global approach does not require an initial guess to the path, a major challenge for global pathway finders. Finally, it provides an exact answer (the steepest descent path) at the end of the calculations. Numerical examples are provided for the Mueller potential and for a conformational transition in a solvated ring system.

Pyrophosphate Release in the Protein HIV Reverse Transcriptase

Enzymatic reactions usually occur in several steps: a step of substrate binding to the surface of the protein, a step of protein reorganization around the substrate and conduction of a chemical reaction, and a step of product release. The release of inorganic phosphate-PPi-from the matrix of the protein HIV reverse transcriptase is investigated computationally. Atomically detailed simulations with explicit solvent are analyzed to obtain the free energy profile, mean first passage time, and detailed molecular mechanisms of PPi escape. A challenge for the computations is of time scales. The experimental time scale of the process of interest is in milliseconds, and straightforward molecular dynamics simulations are in sub-microseconds. To overcome the time scale gap, we use the algorithm of Milestoning along a reaction coordinate to compute the overall free energy profile and rate. The methods of locally enhanced sampling and steered molecular dynamics determine plausible reaction coordinates. The observed molecular mechanism couples the transfer of the PPi to positively charged lysine side chains that are found on the exit pathway and to an exiting magnesium ion. In accord with experimental findings, the release rate is comparable to the chemical step, allowing for variations in substrate (DNA or RNA template) in which the release becomes rate determining.

A Change in the Rate-Determining Step of Polymerization by the K289M DNA Polymerase β Cancer-Associated Variant

K289M is a variant of DNA polymerase β (pol β) that has previously been identified in colorectal cancer. The expression of this variant leads to a 16-fold increase in mutation frequency at a specific site in vivo and a reduction in fidelity in vitro in a sequence context-specific manner. Previous work shows that this reduction in fidelity results from a decreased level of discrimination against incorrect nucleotide incorporation at the level of polymerization. To probe the transition state of the K289M mutator variant of pol β, single-turnover kinetic experiments were performed using β,γ-CXY dGTP analogues with a wide range of leaving group monoacid dissociation constants (pK_a4), including a corresponding set of novel β,γ-CXY dCTP analogues. Surprisingly, we found that the values of the log of the catalytic rate constant (k_pol) for correct insertion by K289M, in contrast to those of wild-type pol β, do not decrease with increased leaving group pK_a4 for analogues with pK_a4 values of <11. This suggests that one of the relative rate constants differs for the K289M reaction in comparison to that of the wild type (WT). However, a plot of log(k_pol) values for incorrect insertion by K289M versus pK_a4 reveals a linear correlation with a negative slope, in this respect resembling k_pol values for misincorporation by the WT enzyme. We also show that some of these analogues improve the fidelity of K289M. Taken together, our data show that Lys289 critically influences the catalytic pathway of pol β.

A new general method for simultaneous fitting of temperature and concentration dependence of reaction rates yields kinetic and thermodynamic parameters for HIV reverse transcriptase specificity

Recent studies have demonstrated the dominant role of induced fit in enzyme specificity of HIV reverse transcriptase and many other enzymes. However, relevant thermodynamic parameters are lacking, and equilibrium thermodynamic methods are of no avail because the key parameters can only be determined by kinetic measurement. By modifying KinTek Explorer software, we present a new general method for globally fitting data collected over a range of substrate concentrations and temperatures and apply it to HIV reverse transcriptase. Fluorescence stopped-flow methods were used to record the kinetics of enzyme conformational changes that monitor nucleotide binding and incorporation. The nucleotide concentration dependence was measured at temperatures ranging from 5 to 37 °C, and the raw data were fit globally to derive a single set of rate constants at 37 °C and a set of activation enthalpy terms to account for the kinetics at all other temperatures. This comprehensive analysis afforded thermodynamic parameters for nucleotide binding (K_d , ΔG, ΔH, and ΔS at 37 °C) and kinetic parameters for enzyme conformational changes and chemistry (rate constants and activation enthalpy). Comparisons between wild-type enzyme and a mutant resistant to nucleoside analogs used to treat HIV infections reveal that the ground state binding is weaker and the activation enthalpy for the conformational change step is significantly larger for the mutant. Further studies to explore the structural underpinnings of the observed thermodynamics and kinetics of the conformational change step may help to design better analogs to treat HIV infections and other diseases. Our new method is generally applicable to enzyme and chemical kinetics.

Triphosphate Reorientation of the Incoming Nucleotide as a Fidelity Checkpoint in Viral RNA-dependent RNA Polymerases

The nucleotide incorporation fidelity of the viral RNA-dependent RNA polymerase (RdRp) is important for maintaining functional genetic information but, at the same time, is also important for generating sufficient genetic diversity to escape the bottlenecks of the host's antiviral response. We have previously shown that the structural dynamics of the motif D loop are closely related to nucleotide discrimination. Previous studies have also suggested that there is a reorientation of the triphosphate of the incoming nucleotide, which is essential before nucleophilic attack from the primer RNA 3'-hydroxyl. Here, we have used ³¹P NMR with poliovirus RdRp to show that the binding environment of the triphosphate is different when correct versus incorrect nucleotide binds. We also show that amino acid substitutions at residues known to interact with the triphosphate can alter the binding orientation/environment of the nucleotide, sometimes lead to protein conformational changes, and lead to substantial changes in RdRp fidelity. The analyses of other fidelity variants also show that changes in the triphosphate binding environment are not always accompanied by changes in the structural dynamics of the motif D loop or other regions known to be important for RdRp fidelity, including motif B. Altogether, our studies suggest that the conformational changes in motifs B and D, and the nucleoside triphosphate reorientation represent separable, "tunable" fidelity checkpoints.

A QM/QTAIM research under the magnifying glass of the DPT tautomerisation of the wobble mispairs involving 2-aminopurine

In this study, a comprehensive survey of the changes of the physico-chemical parameters at each point of the IRC for the biologically important T·2AP*(w) ↔ T*·2AP(w) and G·2AP*(w) ↔ G*·2AP(w) DPT tautomerisation reactions involved in the point mutations (transitions and transversions) induced by 2-aminopurine (2AP) in DNA is provided.

Whether 2-aminopurine induces incorporation errors at the DNA replication? A quantum-mechanical answer on the actual biological issue

In this paper, we consider the mutagenic properties of the 2-aminopurine (2AP), which has intrigued molecular biologists, biophysicists and physical chemists for a long time and been widely studied by both experimentalists and theorists. We have shown for the first time using QM calculations, that 2AP very effectively produces incorporation errors binding with cytosine (C) into the wobble (w) C·2AP(w) mispair, which is supported by the N4H⋯N1 and N2H⋯N3 H-bonds and is tautomerized into the Watson-Crick (WC)-like base mispair C*·2AP(WC) (asterisk denotes the mutagenic tautomer of the base), that quite easily in the process of the thermal fluctuations acquires enzymatically competent conformation. 2AP less effectively produces transversions forming the wobble mispair with A base - A·2AP(w), stabilized by the participation of the N6H⋯N1 and N2H⋯N1 H-bonds, followed by further tautomerization A·2AP(w) → A*·2AP(WC) and subsequent conformational transition A*·2AP(WC) → A*·2AP_syn thus acquiring enzymatically competent structure. In this case, incorporation errors occur only in those case, when 2AP belongs to the incoming nucleotide. Thus, answering the question posed in the title of the article, we affirm for certain that 2AP induces incorporation errors at the DNA replication. Obtained results are consistent well with numerous experimental data.

Path-sampling strategies for simulating rare events in biomolecular systems

Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (<10μs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.

Perspective: Computer simulations of long time dynamics

Atomically detailed computer simulations of complex molecular events attracted the imagination of many researchers in the field as providing comprehensive information on chemical, biological, and physical processes. However, one of the greatest limitations of these simulations is of time scales. The physical time scales accessible to straightforward simulations are too short to address many interesting and important molecular events. In the last decade significant advances were made in different directions (theory, software, and hardware) that significantly expand the capabilities and accuracies of these techniques. This perspective describes and critically examines some of these advances.

HIV-1 Reverse Transcriptase Polymerase and RNase H (Ribonuclease H) Active Sites Work Simultaneously and Independently

HIV reverse transcriptase plays a central role in viral replication and requires coordination of both polymerase and RNase H activities. Although this coordination is crucial in viral replication, whether a DNA/RNA hybrid can simultaneously engage both active sites has yet to be determined as structural and kinetic analyses have provided contradictory results. Single nucleotide incorporation and RNase H cleavage were examined using presteady-state kinetics with global data analysis. The results revealed three interconverting reverse transcriptase-DNA/RNA species; 43% were active for both sites simultaneously, 27% showed only polymerase activity, and the remaining 30% were nonproductive. Our data clearly demonstrated that the DNA/RNA hybrid could contact both active sites simultaneously, although the single nucleotide incorporation (105 s^-1) was ∼5-fold faster than the cleavage (23 s^-1). By using a series of primers with different lengths, we found that a string of at least 4-6 nucleotides downstream of the cleaving site was required for efficient RNA cleavage. This was corroborated by our observations that during processive nucleotide incorporation, sequential rounds of RNA cleavage occurred each time after ∼6 nucleotides were incorporated. More importantly, during processive primer extension, pyrophosphate (PP_i) release was rate-limiting so that the average rate of nucleotide incorporation (∼28 s^-1) was comparable with that of net RNA cleavage (∼27 nucleotides(s)). Although polymerization is efficient and processive, RNase H is inefficient and periodic. This combination allows the two catalytic centers of HIVRT to work simultaneously at similar speeds without being tightly coupled.

Rate-limiting Pyrophosphate Release by HIV Reverse Transcriptase Improves Fidelity

Previous measurements of the rates of polymerization and pyrophosphate release with DNA templates showed that pyrophosphate (PP_i) dissociation was fast after nucleotide incorporation so that it did not contribute to enzyme specificity (k_cat/K_m). Here, kinetic parameters governing nucleotide incorporation and PP_i release were determined using an RNA template. Compared with a DNA template of the same sequence, the rate of chemistry increased by up to 10-fold (250 versus 24 s^-1), whereas the rate of PP_i release decreased to approximately 58 s^-1 so that PP_i release became the rate-limiting step. During processive nucleotide incorporation, the first nucleotide (TTP) was incorporated at a fast rate (152 s^-1), whereas the rates of incorporation of remaining nucleotides (CGTCG) were much slower with an average rate of 24 s^-1, suggesting that sequential incorporation events were limited by the relatively slow PP_i release step. The accompanying paper shows that slow PP_i release allows polymerization and RNase H to occur at comparable rates. Although PP_i release is the rate-determining step, it is not the specificity-determining step for correct incorporation based on our current estimates of the rate of reversal of the chemistry step (3 s^-1). In contrast, during misincorporation, PP_i release became extremely slow, which we estimated to be ∼0.002 s^-1 These studies establish the mechanistic basis for DNA polymerase fidelity during reverse transcription and provide a free energy profile. We correct previous underestimates of discrimination by including the slow PP_i release step. Our current estimate of 2.4 × 10⁶ is >20-fold greater than estimated previously.

Exploring the mechanism of DNA polymerases by analyzing the effect of mutations of active site acidic groups in Polymerase β

Elucidating the catalytic mechanism of DNA polymerase is crucial for a progress in the understanding of the control of replication fidelity. This work tries to advance the mechanistic understanding by analyzing the observed effect of mutations of the acidic groups in the active site of Polymerase β as well as the pH effect on the rate constant. The analysis involves both empirical valence bond (EVB) free energy calculations and considerations of the observed pH dependence of the reaction. The combined analysis indicates that the proton transfer (PT) from the nucleophilic O3' has two possible pathways, one to D256 and the second to the bulk. We concluded based on calculations and the experimental pH profile that the most likely path for the wild-type (WT) and the D256E and D256A mutants is a PT to the bulk, although the WT may also use a PT to Asp 256. Our analysis highlights the need for very extensive sampling in the calculations of the activation barrier and also clearly shows that ab initio QM/MM calculations that do not involve extensive sampling are unlikely to give a clear quantitative picture of the reaction mechanism. Proteins 2016; 84:1644-1657. © 2016 Wiley Periodicals, Inc.

Role of Conformational Motions in Enzyme Function: Selected Methodologies and Case Studies

It is now common knowledge that enzymes are mobile entities relying on complex atomic-scale dynamics and coordinated conformational events for proper ligand recognition and catalysis. However, the exact role of protein dynamics in enzyme function remains either poorly understood or difficult to interpret. This mini-review intends to reconcile biophysical observations and biological significance by first describing a number of common experimental and computational methodologies employed to characterize atomic-scale residue motions on various timescales in enzymes, and second by illustrating how the knowledge of these motions can be used to describe the functional behavior of enzymes and even act upon it. Two biologically relevant examples will be highlighted, namely the HIV-1 protease and DNA polymerase β enzyme systems.

A Simple and Accurate Method To Calculate Free Energy Profiles and Reaction Rates from Restrained Molecular Simulations of Diffusive Processes

A method is developed to obtain simultaneously free energy profiles and diffusion constants from restrained molecular simulations in diffusive systems. The method is based on low-order expansions of the free energy and diffusivity as functions of the reaction coordinate. These expansions lead to simple analytical relationships between simulation statistics and model parameters. The method is tested on 1D and 2D model systems; its accuracy is found to be comparable to or better than that of the existing alternatives, which are briefly discussed. An important aspect of the method is that the free energy is constructed by integrating its derivatives, which can be computed without need for overlapping sampling windows. The implementation of the method in any molecular simulation program that supports external umbrella potentials (e.g., CHARMM) requires modification of only a few lines of code. As a demonstration of its applicability to realistic biomolecular systems, the method is applied to model the α-helix ↔ β-sheet transition in a 16-residue peptide in implicit solvent, with the reaction coordinate provided by the string method. Possible modifications of the method are briefly discussed; they include generalization to multidimensional reaction coordinates [in the spirit of the model of Ermak and McCammon (Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352-1360)], a higher-order expansion of the free energy surface, applicability in nonequilibrium systems, and a simple test for Markovianity. In view of the small overhead of the method relative to standard umbrella sampling, we suggest its routine application in the cases where umbrella potential simulations are appropriate.

A novel conception for spontaneous transversions caused by homo-pyrimidine DNA mismatches: a QM/QTAIM highlight

We have firstly shown that the T·T(w) and C·C(w) DNA mismatches with wobble (w) geometry stay in slow tautomeric equilibrium with short T·T*(WC) and C·C*(WC) Watson-Crick (WC) mispairs. These non-dissociative tautomeric rearrangements are controlled by the plane-symmetric, highly stable, highly polar and zwitterionic transition states. The obtained results allow us to understand in what way the T·T(w) and C·C(w) mismatches acquire enzymatically competent T·T*(WC) and C·C*(WC) conformations directly in the hydrophobic recognition pocket of a high-fidelity DNA-polymerase, thereby producing thermodynamically non-equilibrium spontaneous transversions. The simplest numerical estimation of the frequency ratio of the TT to CC spontaneous transversions satisfactorily agrees with experimental data.

Nonequilibrium Relaxation of Conformational Dynamics Facilitates Catalytic Reaction in an Elastic Network Model of T7 DNA Polymerase

Nucleotide-induced conformational closing of the finger domain of DNA polymerase is crucial for its catalytic action during DNA replication. Such large-amplitude molecular motion is often not fully accessible to either direct experimental monitoring or molecular dynamics simulations. However, a coarse-grained model can offer an informative alternative, especially for probing the relationship between conformational dynamics and catalysis. Here we investigate the dynamics of T7 DNA polymerase catalysis using a Langevin-type elastic network model incorporating detailed structural information on the open conformation without the substrate bound. Such a single-parameter model remarkably captures the induced conformational dynamics of DNA polymerase upon dNTP binding, and reveals its close coupling to the advancement toward transition state along the coordinate of the target reaction, which contributes to significant lowering of the activation energy barrier. Furthermore, analysis of stochastic catalytic rates suggests that when the activation energy barrier has already been significantly lowered and nonequilibrium relaxation toward the closed form dominates the catalytic rate, one must appeal to a picture of two-dimensional free energy surface in order to account for the full spectrum of catalytic modes. Our semiquantitative study illustrates the general role of conformational dynamics in achieving transition-state stabilization, and suggests that such an elastic network model, albeit simplified, possesses the potential to furnish significant mechanistic insights into the functioning of a variety of enzymatic systems.