Spectrally Resolved Estimation of Water Entropy in the Active Site of Human Carbonic Anhydrase II.

A major challenge in understanding ligand binding to biomacromolecules lies in dissecting the underlying thermodynamic driving forces at the atomic level. Quantifying the contributions of water molecules is often especially demanding, although they can play important roles in biomolecular recognition and binding processes. One example is human carbonic anhydrase II, whose active site harbors a conserved network of structural water molecules that are essential for enzymatic catalysis. Inhibitor binding disrupts this water network and changes the hydrogen-bonding patterns in the active site. Here, we use atomistic molecular dynamics simulations to compute the absolute entropy of the individual water molecules confined in the active site of hCAII using a spectrally resolved estimation (SRE) approach. The entropy decrease of water molecules that remain in the active site upon binding of a dorzolamide inhibitor is caused by changes in hydrogen bonding and stiffening of the hydrogen-bonding network. Overall, this entropy decrease is overcompensated by the gain due to the release of three water molecules from the active site upon inhibitor binding. The spectral density calculations enable the assignment of the changes to certain vibrational modes. In addition, the range of applicability of the SRE approximation is systematically explored by exploiting the gradually changing degree of immobilization of water molecules as a function of the distance to a phospholipid bilayer surface, which defines an "entropy ruler". These results demonstrate the applicability of SRE to biomolecular solvation, and we expect it to become a useful method for entropy calculations in biomolecular systems.

Estimation of Protein-Ligand Unbinding Kinetics Using Non-Equilibrium Targeted Molecular Dynamics Simulations.

We here report on nonequilibrium targeted molecular dynamics simulations as a tool for the estimation of protein-ligand unbinding kinetics. Correlating simulations with experimental data from SPR kinetics measurements and X-ray crystallography on two small molecule compound libraries bound to the N-terminal domain of the chaperone Hsp90, we show that the mean nonequilibrium work computed in an ensemble of trajectories of enforced ligand unbinding is a promising predictor for ligand unbinding rates. We furthermore investigate the molecular basis determining unbinding rates within the compound libraries. We propose ligand conformational changes and protein-ligand nonbonded interactions to impact on unbinding rates. Ligands may remain longer at the protein if they exhibit strong electrostatic and/or van der Waals interactions with the target. In the case of ligands with a rigid chemical scaffold that exhibit longer residence times, transient electrostatic interactions with the protein appear to facilitate unbinding. Our results imply that understanding the unbinding pathway and the protein-ligand interactions along this path is crucial for the prediction of small molecule ligands with defined unbinding kinetics.

Monitoring transient events in infrared spectra using local mode analysis.

Time-resolved Fourier transformed infrared (FTIR) spectroscopy of chemical reactions is highly sensitive to minimal spatiotemporal changes. Structural features are decoded and represented in a comprehensible manner by combining FTIR spectroscopy with biomolecular simulations. Local mode analysis (LMA) is a tool to connect molecular motion based on a quantum mechanics simulation with infrared (IR) spectral features and vice versa. Here, we present the python-based software tool of LMA and demonstrate the novel feature of LMA to extract transient structural details and identify the related IR spectra at the case example of malonaldehyde (MA). Deuterated MA exists in two almost equally populated tautomeric states separated by a low barrier for proton transfer so IR spectra represent a mixture of both states. By state-dependent LMA, we obtain pure spectra for each tautomeric state occurring within the quantum mechanics trajectory. By time-resolved LMA, we obtain a clear view of the transition between states in the spectrum. Through local mode decomposition and the band-pass filter, marker bands for each state are identified. Thus, LMA is beneficial to analyze the experimental spectra based on a mixture of states by determining the individual contributions to the spectrum and motion of each state.

The Second Law of Thermodynamics as a Force Law.

The second law of thermodynamics states the increase of entropy, Δ S > 0 , for real processes from state A to state B at constant energy from chemistry over biological life and engines to cosmic events. The connection of entropy to information, phase-space, and heat is helpful but does not immediately convince observers of the validity and basis of the second law. This gave grounds for finding a rigorous, but more easily acceptable reformulation. Here, we show using statistical mechanics that this principle is equivalent to a force law ⟨ ⟨ f ⟩ ⟩ > 0 in systems where mass centers and forces can be identified. The sign of this net force--the average mean force along a path from A to B--determines the direction of the process. The force law applies to a wide range of processes from machines to chemical reactions. The explanation of irreversibility by a driving force appears more plausible than the traditional formulation as it emphasizes the cause instead of the effect of motions.

Ras and GTPase-activating protein (GAP) drive GTP into a precatalytic state as revealed by combining FTIR and biomolecular simulations.

Members of the Ras superfamily regulate many cellular processes. They are down-regulated by a GTPase reaction in which GTP is cleaved into GDP and P(i) by nucleophilic attack of a water molecule. Ras proteins accelerate GTP hydrolysis by a factor of 10(5) compared to GTP in water. GTPase-activating proteins (GAPs) accelerate hydrolysis by another factor of 10(5) compared to Ras alone. Oncogenic mutations in Ras and GAPs slow GTP hydrolysis and are a factor in many cancers. Here, we elucidate in detail how this remarkable catalysis is brought about. We refined the protein-bound GTP structure and protein-induced charge shifts within GTP beyond the current resolution of X-ray structural models by combining quantum mechanics and molecular mechanics simulations with time-resolved Fourier-transform infrared spectroscopy. The simulations were validated by comparing experimental and theoretical IR difference spectra. The reactant structure of GTP is destabilized by Ras via a conformational change from a staggered to an eclipsed position of the nonbridging oxygen atoms of the γ- relative to the ß-phosphates and the further rotation of the nonbridging oxygen atoms of α- relative to the ß- and γ-phosphates by GAP. Further, the γ-phosphate becomes more positive although two of its oxygen atoms remain negative. This facilitates the nucleophilic attack by the water oxygen at the phosphate and proton transfer to the oxygen. Detailed changes in geometry and charge distribution in the ligand below the resolution of X-ray structure analysis are important for catalysis. Such high resolution appears crucial for the understanding of enzyme catalysis.

The role of magnesium for geometry and charge in GTP hydrolysis, revealed by quantum mechanics/molecular mechanics simulations.

The coordination of the magnesium ion in proteins by triphosphates plays an important role in catalytic hydrolysis of GTP or ATP, either in signal transduction or energy conversion. For example, in Ras the magnesium ion contributes to the catalysis of GTP hydrolysis. The cleavage of GTP to GDP and P(i) in Ras switches off cellular signaling. We analyzed GTP hydrolysis in water, Ras, and Ras·Ras-GTPase-activating protein using quantum mechanics/molecular mechanics simulations. By comparison of the theoretical IR-difference spectra for magnesium ion coordinated triphosphate to experimental ones, the simulations are validated. We elucidated thereby how the magnesium ion contributes to catalysis. It provides a temporary storage for the electrons taken from the triphosphate and it returns them after bond cleavage and P(i) release back to the diphosphate. Furthermore, the Ras·Mg(2+) complex forces the triphosphate into a stretched conformation in which the ß- and γ-phosphates are coordinated in a bidentate manner. In this conformation, the triphosphate elongates the bond, which has to be cleaved during hydrolysis. Furthermore, the γ-phosphate adopts a more planar structure, driving the conformation of the molecule closer to the hydrolysis transition state. GTPase-activating protein enhances these changes in GTP conformation and charge distribution via the intruding arginine finger.

Exploring the Multidimensional Free Energy Surface of Phosphoester Hydrolysis with Constrained QM/MM Dynamics.

The mechanism of the hydrolysis of phosphate monoesters, a ubiquitous biological reaction, has remained under debate. We here investigated the hydrolysis of a nonenzymatic model system, the monomethyl phosphate dianion, by hybrid quantum mechanical and molecular mechanical simulations. The solvation effects were taken into account with explicit water. Detailed free energy landscapes in two-dimensional and three-dimensional space were resolved using the multidimensional potential of mean constraint force, a newly developed method that was demonstrated to be powerful for free energy calculations along multiple coordinates. As in previous theoretical studies, the associative and dissociative pathways were indistinguishable. Furthermore, the associative pathway was investigated in great detail. We propose a rotation of an O-H bond in the transition between two pentacoordinated structures, during which an overall transition state was identified with an activation energy of 50 kcal/mol. This is consistent with experimental data. The results support a concerted proton transfer from the nucleophilic water to the phosphate group, and then to the leaving group.

The specific vibrational modes of GTP in solution and bound to Ras: a detailed theoretical analysis by QM/MM simulations.

The hydrolysis of guanosine triphosphate (GTP) in general, and especially by GTPases like the Ras protein, is in the focus of biological investigations. A huge amount of experimental data from Fourier-transformed infrared studies is currently available, and many vibrational bands of free GTP, GTP·Mg(2+), and Ras·GTP·Mg(2+) in solution have been assigned by isotopic labeling. In the Ras environment, bands between 800 cm(-1) and 1300 cm(-1) have already been assigned, but not those below 800 cm(-1). The combination of quantum and molecular mechanics (QM/MM) methods takes the quantum effects for selected relevant atoms into account. This provides structural details, vibrational frequencies and electron distributions of the region of interest. We therefore used MM and QM/MM simulations to investigate the normal vibrational modes of GTP, GTP·Mg(2+), and Ras·GTP·Mg(2+) in solution, and assigned the vibrational frequencies for each normal vibration mode. In this study, the quantum box contains the nucleoside and the Mg(2+). The comparison of calculated and experimental vibrational spectra provides a very good control for the quality of the calculations. Structurally, MM and QM/MM simulations reveal a stable tridentate coordination of the Mg(2+) by GTP in water, and a stable bidentate coordination by GTP in complex with Ras. For validation, we compare the calculated frequencies and isotopic shifts with the experimental results available in the range of 800 cm(-1) to 1300 cm(-1). For the first time we suggest band assignments of the vibrational modes below 800 cm(-1) by comparison of calculated and experimental spectra.

The structure of active opsin as a basis for identification of GPCR agonists by dynamic homology modelling and virtual screening assays.

Most of the currently available G protein-coupled receptor (GPCR) crystal structures represent an inactive receptor state, which has been considered to be suitable only for the discovery of antagonists and inverse agonists in structure-based computational ligand screening. Using the ß(2)-adrenergic receptor (B2AR) as a model system, we show that a dynamic homology model based on an "active" opsin structure without further incorporation of experimental data performs better than the crystal structure of the inactive B2AR in finding agonists over antagonists/inverse agonists. Such "active-like state" dynamic homology models can therefore be used to selectively identify GPCR agonists in in silico ligand libraries.

Simulations of a G protein-coupled receptor homology model predict dynamic features and a ligand binding site.

A computational approach to predict structures of rhodopsin-like G protein-coupled receptors (GPCRs) is presented and evaluated by comparison to the X-ray structural models. By combining sequence alignment, the rhodopsin crystal structure, and point mutation data on the beta2 adrenoreceptor (b2ar), we predict a (-)-epinephrine-bound computational model of the beta2 adrenoreceptor. The model is evaluated by molecular dynamics simulations and by comparison with the recent X-ray structures of b2ar. The overall correspondence between the predicted and the X-ray structural model is high. Especially the prediction of the ligand binding site is accurate. This shows that the proposed dynamic homology modelling approach can be used to create reasonable models for the understanding of structure and dynamics of other rhodopsin-like GPCRs.

'Dynamic Distance' Reaction Coordinate for Competing Bonds: Applications in Classical and Ab Initio Simulations.

A versatile reaction coordinate, the "dynamic distance", is introduced for the study of reactions involving the rupture and formation of a series of chemical bonds or contacts. The dynamic distance is a mass-weighted mean of selected distances. When implemented as a generalized constraint, the dynamic distance is particularly suited for driving activated processes by controlled increase during a simulation. As a single constraint acting upon multiple degrees of freedom, the sequence of events along the resulting reaction pathway is determined unambiguously by the underlying energy landscape. Free energy profiles can be readily obtained from the mean constraint force. In this paper both theoretical aspects and numerical implementation are discussed, and the unique and diverse properties of this reaction coordinate are demonstrated using three examples: In the framework of Car-Parrinello molecular dynamics, we present results for the prototypical double proton-transfer reaction in formic acid dimer and the photocycle of the guanine-cytosine DNA base pair. As a classical mechanical example, the opening of the binding pocket of the enzyme rubisco is analyzed.

Role of the arginine finger in Ras.RasGAP revealed by QM/MM calculations.

In the Ras.Ras.GAP complex, hydrolysis of guanosine triphosphate is strongly accelerated GAP as compared to Ras alone. This is largely attributed to the arginine finger R789(GAP) pointing to AlF(x) in the transition state analogue. We performed QM/MM simulations where triphosphate was treated using the quantum mechanical method of density functional theory, while the protein complex and water environment were described classically using MD. Compared to Ras, the crucial electron shift, bond stretching and distortion towards an eclipsed gamma-to-beta orientation are much more pronounced. The arginine finger is shown to act by displacing water out of the binding niche. The resulting enhanced electrostatic field catalyses the cleavage step.

Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics.

Photoinduced proton transfer in the Watson-Crick guanine (G)-cytosine (C) base pair has been studied using Car-Parrinello molecular dynamics (CP-MD). A flexible mechanical constraint acting on all three hydrogen bonds in an unbiased fashion has been devised to explore the free energy profile along the proton transfer coordinate. The lowest barrier has been found for proton transfer from G to C along the central hydrogen bond. The resulting charge transfer excited state lies energetically close to the electronic ground state suggesting the possibility of efficient radiationless decay. It is found that dynamic, finite temperature fluctuations significantly reduce the energy gap between the ground and excited states for this charge transfer product, promoting the internal conversion process. A detailed analysis of the internal degrees of freedom reveals that the energy gap is considerably reduced by out-of-plane molecular vibrations, in particular. Consequently, it appears that considering only the minimum energy path provides an upper-bound estimate of the associated energy gap compared to the full-dimension dynamical reaction coordinate. Furthermore, the first CP-MD simulations of the G-C base pair in liquid water are presented, and the effects of solvation on its electronic structure are analyzed.

Empirical rules facilitate the search for binding sites on protein surfaces.

Computational surface screening of 3D protein structures is a valuable means of finding possible docking sites for substrates, effectors and similar molecules. It can be improved by considering properties of molecules which are known to bind to protein surfaces, and thus reflect the required properties of binding sites. In-depth studies are available on drugs and lead compounds as binding partners with statistically assured properties. Here we present a simple strategy for finding binding sites, which is based on the empirical rule-of-five by Lipinski et al. for oral drugs and the rule-of-three by Congreve et al. for leads. The fast automated search with the new C-code TRIDOCK yields a preliminary set of sites, thus facilitating further investigation by visual, comparative and quantitative work. Possible binding sites are tagged by pseudo-atoms added to the structure file for molecular graphical evaluation. Usually, the strategy yields not just a few single sites, but an accumulation of several sites in known substrate binding pockets. Clusters are also found at known or putative protein-protein docking interfaces. A comparison of the activated and inactivated form of the GTPase Ras reveals clear differences and identifies a niche, which is possibly a suitable new target for compounds that bind specifically to activated Ras.

Theoretical IR spectroscopy based on QM/MM calculations provides changes in charge distribution, bond lengths, and bond angles of the GTP ligand induced by the Ras-protein.

The GTPase Ras p21 is a crucial switch in cellular signal transduction. Fourier transform infrared (FTIR) spectra of the substrate guanosine triphosphate (GTP) show remarkable changes when it binds to the enzyme. The reduced band widths indicate that the flexible GTP molecule is guided by the protein into a preferred conformation. The delocalized phosphate vibrations of unbound GTP become localized. The frequency shifts show an electron movement toward beta-phosphate, which probably contributes to catalysis by reducing the free activation energy. To quantify these qualitative observations we performed QM/MM molecular dynamics simulations of Ras.GTP and GTP in water. The triphosphate part of GTP was treated quantum mechanically using density functional theory (DFT). Vibrational spectra were calculated in harmonic approximation with an average deviation of 3% from the experimental frequencies. This provides a high confidence in the computational results as vibrational spectra are highly sensitive to conformation and charge distribution. As compared to GTP in water, Ras-bound GTP shows a shift of negative charge of approximately 0.2 e toward the beta-phosphate from gamma-phosphate and from alpha-phosphate due to the positive charge of the magnesium ion, to a lesser extent of Lys-16, and surprisingly without any effect of the P-loop backbone. Magnesium and Gly-13 twist and bend the gamma-O-beta bonds such that the crucial bond is stretched before cleaving.

Water dynamics simulation as a tool for probing proton transfer pathways in a heptahelical membrane protein.

The proton transfer pathway in a heptahelical membrane protein, the light-driven proton pump bacteriorhodopsin (BR), is probed by a combined approach of structural analysis of recent X-ray models and molecular dynamics (MD) simulations that provide the diffusion pathways of internal and external water molecules. Analyzing the hydrogen-bond contact frequencies of the water molecules with protein groups, the complete proton pathway through the protein is probed. Beside the well-known proton binding sites in the protein interior-the protonated Schiff base, Asp85 and Asp96, and the H(5)O(2) (+) complex stabilized by Glu204 and Glu194-the proton release and uptake pathways to the protein surfaces are described in great detail. Further residues were identified, by mutation of which the proposed pathways can be verified. In addition the diffusion pathway of water 502 from Lys216 to Asp96 is shown to cover the positions of the intruding waters 503 and 504 in the N-intermediate. The transiently established water chain in the N-state provides a proton pathway from Asp96 to the Schiff base in the M- to N-transition in a Grotthus-like mechanism, as concluded earlier from time-resolved Fourier transform infrared experiments [le Coutre et al., Proc Nat Acad Sci USA 1995;92:4962-4966].

Dynamics of water molecules in the bacteriorhodopsin trimer in explicit lipid/water environment.

Protonated networks of internal water molecules appear to be involved in proton transfer in various integral membrane proteins. High-resolution x-ray studies of protein crystals at low temperature deliver mean positions of most internal waters, but only limited information about fluctuations within such H-bonded networks formed by water and residues. The question arises as to how water molecules behave inside and on the surface of a fluctuating membrane protein under more physiological conditions. Therefore, as an example, long-time molecular dynamics simulations of bacteriorhodopsin were performed with explicit membrane/water environment. Based on a recent x-ray model the bacteriorhodopsin trimer was inserted in a fully solvated 16 x 16 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)-bilayer patch, resulting in a system of approximately 84,000 atoms. Unrestrained molecular dynamics calculations of 5 ns were performed using the GROMACS package and force field. Mean water densities were computed to describe the anisotropic distribution of internal water molecules. In the whole protein two larger areas of higher water density are identified. They are located between the central proton binding site, the Schiff base, and the extracellular proton release site. Separated by Arg-82 these water clusters could provide a proton release pathway in a Grotthus-like mechanism as indicated by a continuum absorbance change observed during the photocycle by time-resolved Fourier transform infrared spectroscopy. Residues are identified which are H-bonded to the water clusters and are therefore facilitating proton conduction. Their influence on proton transfer via the H-bonded network as indicated by the continuum absorbance change is predicted. This may explain why several site-directed mutations alter the proton release kinetics without a direct involvement in proton transfer.

MD simulation of protein-ligand interaction: formation and dissociation of an insulin-phenol complex.

Complexes of proteins with small ligands are of utmost importance in biochemistry, and therefore equilibria, formation, and decay have been investigated extensively by means of biochemical and biophysical methods. Theoretical studies of the molecular dynamics of such systems in solution are restricted to 10 ns, i.e., to fast processes. Only recently new theoretical methods have been developed not to observe the process in real time, but to explore its pathway(s) through the energy landscape. From the profiles of free energy, equilibrium and kinetic quantities can be determined using transition-state theory. This study is dedicated to the pharmacologically relevant insulin-phenol complex. The distance of the center of mass chosen as a reaction coordinate allows a reasonable description over most of the pathway. The analysis is facilitated by analytical expressions we recently derived for distance-type reaction coordinates. Only the sudden onset of rotations at the very release of the ligand cannot be parameterized by a distance. They obviously require a particular treatment. Like a preliminary study on a peptide, the present case emphasizes the contribution of internal friction inside a protein, which can be computed from simulation data. The calculated equilibrium constant and the friction-corrected rates agree well with experimental data.

Does F1-ATPase subunit gamma turn in the wrong direction?

Analyzing the direction of F1-ATPase subunit gamma rotation, its shape and non-random distribution of surface residues, a mechanism is proposed for how gamma induces the closing/opening of the catalytic sites at beta/alpha interfaces: by keeping contact with the mobile domain of subunits beta at the 'jaw' (D386, the seven consecutive hydrophobic residues and D394/E395), rotating gamma works as a screw conveyer within the barrel of (alpha,beta)3. Mutations of the conveyer contacts are predicted to inhibit. Rotating wheel cartoons illustrate enzyme turnover and conformational changes. Steric clashes, polar interactions and also substrate limitations lead to specific stops. Because it is constructed as a stepper, gamma prevents uncoupling at high energy charge.