Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase

PcrA helicase, a prototype ATP-driven molecular motor

Despite extensive studies, the mechanisms underlying molecular motor function are still poorly understood. Key to the mechanisms is the coupling of ATP hydrolysis to conformational changes of the motor protein. To investigate this coupling, we have conducted combined quantum mechanical/molecular mechanical simulations of PcrA helicase, a strikingly simple motor that translocates unidirectionally along single-stranded DNA (ssDNA). Our results reveal a close similarity in catalytic site structure and reaction pathway to those of F1-ATPase, and these similarities include a proton relay mechanism important for efficient ATP hydrolysis and an "arginine finger" residue that is key to the coupling of the chemical reaction to protein conformational changes. By means of in silico mutation studies, we identified the residue Q254 as being crucial for the coupling of ssDNA translocation to the actual catalytic event. Based on the present result for PcrA helicase and previous findings for F1-ATPase, we propose a general mechanism of ATP-driven molecular motor function.

Entropy of Water in the Hydration Layer of Major and Minor Grooves of DNA

Transport properties (translational and rotational) of water in the two grooves of the B-DNA duplex are known to be different from those in the bulk. Here, we use a recently developed theoretical scheme to compute the entropies of water molecules in both of the grooves of DNA and compare them with that in the bulk. The scheme requires as input both translational and rotational velocity autocorrelation function (C(V)(t) and C(omega)(t), respectively) data. These velocity autocorrelation functions were computed from an atomistic MD simulation of a B-DNA duplex (36 base pairs long) in explicit water (TIP3P). The average values of the entropy of water at 300 K in both of the grooves of DNA (the TS value in the major groove is 6.71 kcal/mol and that in the minor groove is 6.41 kcal/mol) are found to be significantly lower than that in bulk water (the TS value is 7.27 kcal/mol). Thus, the entropic contribution to the free energy change (TDeltaS) of transferring a minor groove water molecule to the bulk is 0.86 kcal/mol and of transferring a major groove water to the bulk is 0.56 kcal/mol at 300 K, which is to be compared with 1.44 kcal/mol for melting of ice at 273 K. We also calculate the energy of interaction of each water molecule with the rest of the atoms in the system and hence calculate the chemical potential (Helmholtz free energy per water molecule, A = E - TS) in the different domains. The identical free energy value of water molecules in the different domains proves the robustness of the scheme. We propose that the configurational entropy of water in the grooves can be used as a measure of the mobility (or microviscosity) of water molecules in a given domain.

Calculations of solute and solvent entropies from molecular dynamics simulations

The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Docking interactions induce exposure of activation loop in the MAP kinase ERK2

MAP kinases bind activating kinases, phosphatases, and substrates through docking interactions. Here, we report a 1.9 A crystallographic analysis of inactive ERK2 bound to a "D motif" docking peptide (pepHePTP) derived from hematopoietic tyrosine phosphatase, a negative regulator of ERK2. In this complex, the complete D motif interaction defined by mutagenic analysis is observed, including extensive electrostatic interactions with the "CD" site of the kinase. Large conformational changes occur in the activation loop where the dual phosphorylation sites, which are buried in the inactive form of ERK2, become exposed to solvent in the complex. Similar conformational changes occur in a complex between ERK2 and a MEK2 (MAP/ERK kinase-2)-derived D motif peptide (pepMEK2). D motif peptides are known to bind homologous loci in the MAP kinases p38alpha and JNK1, also inducing conformational changes in these enzymes. However, the binding interactions and conformational changes are unique to each, thus contributing to specificity among MAP kinases.

Zooming in on ATP hydrolysis in F1

We summarize our current view of the reaction mechanism in F(1)-ATPase as it has emerged from experiment, theory, and computational studies over the last several years. ATP catalysis in the catalytic binding pockets of F(1) takes place without the release of any significant free energy and is efficiently driven by the combined action of two water molecules utilizing a so-called protein-relay mechanism. The chemical reaction itself is controlled by the spatial position of a key arginine residue.

One-Electron Reduction Potential for Oxygen- and Sulfur-Centered Organic Radicals in Protic and Aprotic Solvents

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.

On possible pitfalls in ab initio quantum mechanics/molecular mechanics minimization approaches for studies of enzymatic reactions

Reliable studies of enzymatic reactions by combined quantum mechanics/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a very large computer time for the evaluation of the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. A seemingly reasonable alternative is to perform energy minimization studies of the type used in gas-phase ab initio studies. However, it is hard to see why such an approach should give reliable results in protein active sites. To examine the problems with energy minimization QM/MM approaches, we chose the hypothetical reaction of a metaphosphate ion with water in the Ras.GAP complex. This hypothetical reaction served as a simple benchmark reaction. The possible problems with the QM/MM minimization were explored by generating several protein configurations from long MD simulations and using energy minimization and scanning of the reaction coordinates to evaluate the corresponding potential energy surfaces of the reaction for each of these different protein configurations. Comparing these potential energy surfaces, we found major variations of the corresponding minima. Furthermore, the reaction energies and activation energies also varied significantly even for similar protein configurations. The specific coordination of a magnesium ion, present in the active center of the protein complex, turned out to influence the energetics of the reaction in a major way, where a direct coordination to the reactant leads to an increase of the activation energy by 17 kcal/mol. Apparently, using energy minimization to generate potential surfaces for an enzymatic reaction, while starting from a single protein structure, could lead to major errors in calculations of activation free energies and binding free energies. Thus we believe that extensive samplings of the configurational space of the protein are essential for meaningful determination of the energetics of enzymatic reactions. The possible relevance of our conclusion with regard to a recent study of the RasGAP reaction is discussed.

Biomolecular motors: the F1-ATPase paradigm

The realization that many essential functions of living cells are performed by nanoscale motors consisting of protein complexes has given rise to an intense effort to understand their mechanisms. Considerable progress has been made in the past two years by a combination of biophysical techniques and theoretical analysis. Single-molecule studies have played a spectacular role for a variety of motors including kinesin, myosin, and polymerases. The understanding of F(1)-ATPase, the smallest biomolecular rotary motor, has made particular progress by the interplay of experimental and theoretical studies; the latter have provided information not available from experiment.

Computer simulations of protein functions: searching for the molecular origin of the replication fidelity of DNA polymerases

The use of computers to simulate the functions of complex biological macromolecules is essential to achieve a microscopic description of biological processes and to model and interpret experimental data. Here we apply theoretical computational approaches to investigate the fidelity of T7 DNA polymerase, divided into discrete steps that include contributions from substrate binding, pK(a) shifts, and rate constants for the PO bond-breaking and bond-making processes. We begin by defining the discrimination between right and wrong nucleotides in terms of the free energy landscape for the dNMP incorporation reaction. We then use the linear response approximation and the empirical valence bond methods to obtain converging results for the contribution of the binding and chemical steps to the overall fidelity. These approaches are successful in reproducing general trends in the observed polymerase incorporation fidelity. The calculations demonstrate the potential for further integration of theoretical and experimental studies to analyze high- and low-fidelity DNA polymerases.

Computer simulations of membrane proteins

Computer simulations are rapidly becoming a standard tool to study the structure and dynamics of lipids and membrane proteins. Increasing computer capacity allows unbiased simulations of lipid and membrane-active peptides. With the increasing number of high-resolution structures of membrane proteins, which also enables homology modelling of more structures, a wide range of membrane proteins can now be simulated over time spans that capture essential biological processes. Longer time scales are accessible by special computational methods. We review recent progress in simulations of membrane proteins.

Relationship of Leffler (Bronsted) alpha values and protein folding Phi values to position of transition-state structures on reaction coordinates

The positions of transition states along reaction coordinates (r++) for simple chemical reactions are often estimated from Leffler alpha values, the slope of plots of DeltaG++ (activation energy) versus DeltaG(0) (equilibrium free energy) for a series of structural variants. Protein folding is more complex than simple chemical reactions and has a multitude of reaction coordinates. Phi-Value analysis measures degree of structure formation at individual residues in folding transition states from the ratio DeltaDeltaG++/DeltaDeltaG(0) for mutations. alpha values are now being used to analyze protein folding by lumping series of Phi values into single plots. But, there are discrepancies in the values of alpha for folding with more classical measures of the extent of structure formation, which I rationalize here. I show for chemical reactions with just a single reaction coordinate that alpha = r++ only for limiting cases, such as for reactants and products being in parabolic energy wells of identical curvature. Otherwise, alpha can differ radically from r++, with alpha being determined just by the angles of intersection of reactant and product energy surfaces. Phi is an index of the progress of a local, energy-based reaction coordinate at the global transition state: Phi <0.5 corresponds to <50% progress of the local coordinate at the global transition state and Phi >0.5 means >50%. Protein Leffler plots can force different local indexes to a single fit and give skewed underestimates of the extent of global structure formation in transition states that differ from other measures of structure formation.

Structure and binding of Mg(II) ions and di-metal bridge complexes with biological phosphates and phosphoranes

Divalent Mg(2+) ions often serve as cofactors in enzyme or ribozyme-catalyzed phosphoryl transfer reactions. In this work, the interaction of Mg(2+) ions and di-metal bridge complexes with phosphates, phosphoranes, and other biological ligands relevant to RNA catalysis are characterized with density functional methods. The effect of bulk solvent is treated with two continuum solvation methods (PCM and COSMO) for comparison. The relative binding affinity for different biological ligands to Mg(2+) are quantified in different protonation states. The structure and stability of the single-metal and di-metal complexes are characterized, and the changes in phosphate and phosphorane geometry induced by metal ion binding are discussed. Di-metal bridge complexes are a ubiquitous motif and the key factors governing their electrostatic stabilization are outlined. The results presented here provide quantitative characterization of metal ion binding to ligands of importance to RNA catalysis, and lay the groundwork for design of new generation quantum models that can be applied to the full biological enzymatic systems.

ATP hydrolysis in the betaTP and betaDP catalytic sites of F1-ATPase

The enzyme F1-adenosine triphosphatase (ATPase) is a molecular motor that converts the chemical energy stored in the molecule adenosine triphosphate (ATP) into mechanical rotation of its gamma-subunit. During steady-state catalysis, the three catalytic sites of F1 operate in a cooperative fashion such that at every instant each site is in a different conformation corresponding to a different stage along the catalytic cycle. Notwithstanding a large amount of biochemical and, recently, structural data, we still lack an understanding of how ATP hydrolysis in F1 is coupled to mechanical motion and how the catalytic sites achieve cooperativity during rotatory catalysis. In this publication, we report combined quantum mechanical/molecular mechanical simulations of ATP hydrolysis in the betaTP and betaDP catalytic sites of F1-ATPase. Our simulations reveal a dramatic change in the reaction energetics from strongly endothermic in betaTP to approximately equienergetic in betaDP. The simulations identify the responsible protein residues, the arginine finger alphaR373 being the most important one. Similar to our earlier study of betaTP, we find a multicenter proton relay mechanism to be the energetically most favorable hydrolysis pathway. The results elucidate how cooperativity between catalytic sites might be achieved by this remarkable molecular motor.

Modeling loop reorganization free energies of acetylcholinesterase: A comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.