All-atom empirical potential for molecular modeling and dynamics studies of proteins

Electric susceptibility of unsolvated glycine-based peptides

The DC electric susceptibilities of unsolvated glycine-based peptides, WGn (W = tryptophan and G = glycine) with n = 1-5, have been measured by deflection of a molecular beam in an electric field. These are the first electric deflection measurements performed on peptides. At 300 K the susceptibilities are in the range of 200-400 A(3). By far the largest contribution to the susceptibilities is from the permanent dipole moment of the peptides. The results indicate that the peptides do not have rigid conformations with fixed dipoles. Instead the dipole is averaged as the peptides explore their energy landscape. For a given WGn peptide, all molecules have almost the same average dipole, which suggests that they all explore a similar energy landscape on the microsecond time scale of the measurement. The measured susceptibilities are in good overall agreement with values calculated from the average dipole moment deduced from Monte Carlo simulations.

Water rotational relaxation and diffusion in hydrated lysozyme

This paper is concerned with the dynamics of water around a small globular protein. Dipolar second-rank relaxation time and diffusion properties of surface water were computed by extensive molecular dynamics simulations of lysozyme in water which lasted a total of 28 ns. Our results indicate that the rotational relaxation of water in the vicinity of lysozyme is 3-7 times slower than that in the bulk depending on how the hydration shell is defined in the calculation. We have also verified that the dynamics of water translational diffusion in the vicinity of lysozyme have retardations similar to rotational relaxation. This is a common assumption in nuclear magnetic relaxation dispersion (NMRD) studies to derive residence times. In contrast to bulk water dynamics, surface water is in a dispersive diffusion regime or subdiffusion. Very good agreement of dipolar second-rank relaxation time with NMRD estimates is obtained by using appropriate dimensions of the hydration shell. Although our computed second-rank dipolar retardations are independent of the water model, SPC/E describes more realistically the time scale of the water dynamics around lysozyme than does TIP3P.

Flexibility of the murine prion protein and its Asp178Asn mutant investigated by molecular dynamics simulations

Inherited forms of transmissible spongiform encephalopathy, e.g. familial Creutzfeldt-Jakob disease, Gerstmann-Sträussler-Scheinker syndrome and fatal familial insomnia, segregate with specific point mutations of the prion protein. It has been proposed that the pathologically relevant Asp178Asn (D178N) mutation might destabilize the structure of the prion protein because of the loss of the Arg164-Asp178 salt bridge. Molecular dynamics simulations of the structured C-terminal domain of the murine prion protein and the D178N mutant were performed to investigate this hypothesis. The D178N mutant did not deviate from the NMR conformation more than the wild type on the nanosecond time scale of the simulations. In agreement with CD spectroscopy experiments, no major structural rearrangement could be observed for the D178N mutant, apart from the N-terminal elongation of helix 2. The region of structure around the disulfide bridge deviated the least from the NMR conformation and showed the smallest fluctuations in all simulations in agreement with hydrogen exchange data of the wild type prion protein. Large deviations and flexibility were observed in the segments which are ill-defined in the NMR conformation. Moreover, helix 1 showed an increased degree of mobility, especially at its N-terminal region. The dynamic behavior of the D178N mutant and its minor deviation from the folded conformation suggest that the salt bridge between Arg164 and Asp178 might not be crucial for the stability of the prion protein.

Domain movements in human fatty acid synthase by quantized elastic deformational model

This paper reports the results of applying a computational method called the quantized elastic deformational model, to the determination of conformational flexibility of the supermolecular complex of human fatty acid synthase. The essence of this method is the ability to model large-scale conformational changes such as domain movements by treating the protein as an elastic object without the knowledge of protein primary sequence and atomic coordinates. The calculation was based on the electron density maps of the synthase at 19 A. The results suggest that the synthase is a very flexible molecule. Two types of flexible hinges in the structure were identified. One is an intersubunit hinge formed by the intersubunit connection and the other is an intrasubunit hinge located between domains I and II. Despite the fact that the dimeric synthase has a chemically symmetric structure, large domain movements around the hinge region occur in various directions and allow the molecule to adopt a wide range of conformations. These domain movements are likely to be important in facilitating and regulating the entire palmitate synthesis by coordinating the communication between components of the molecule, for instance, adjusting the distance between various active sites inside the catalytic reaction center. Finally, the ability to describe protein motions of a supermolecular complex, without the information of protein sequence and atomic coordinates, is a major advance in computational modeling of protein dynamics. The method provides an unprecedented ability to model protein motions at such a low resolution of structure.

Novel CD8+ T cell antagonists based on beta 2-microglobulin

The CD8 coreceptor of cytotoxic T lymphocytes binds to a conserved region of major histocompatibility complex class I molecules during recognition of peptide-major histocompatibility complex (MHC) class I antigens on the surface of target cells. This event is central to the activation of cytotoxic T lymphocyte (CTL) effector functions. The contribution of the MHC complex class I light chain, beta(2)-microglobulin, to CD8alphaalpha binding is relatively small and is mediated mainly through the lysine residue at position 58. Despite this, using molecular modeling, we predict that its mutation should have a dramatic effect on CD8alphaalpha binding. The predictions are confirmed using surface plasmon resonance binding studies and human CTL activation assays. Surprisingly, the charge-reversing mutation, Lys(58) --> Glu, enhances beta(2)m-MHC class I heavy chain interactions. This mutation also significantly reduces CD8alphaalpha binding and is a potent antagonist of CTL activation. These results suggest a novel approach to CTL-specific therapeutic immunosuppression.

Conformational polymorphism of wild-type and mutant prion proteins: Energy landscape analysis

Conformational transitions are thought to be the prime mechanism of prion diseases. In this study, the energy landscapes of a wild-type prion protein (PrP) and the D178N and E200K mutant proteins were mapped, enabling the characterization of the normal isoforms (PrP(C)) and partially unfolded isoforms (PrP(PU)) of the three prion protein analogs. It was found that the three energy landscapes differ in three respects: (i) the relative stability of the PrP(C) and the PrP(PU) states, (ii) the transition pathways from PrP(C) to PrP(PU), and (iii) the relative stability of the three helices in the PrP(C) state. In particular, it was found that although helix 1 (residues 144-156) is the most stable helix in wild-type PrP, its stability is dramatically reduced by both mutations. This destabilization is due to changes in the charge distribution that affects the internal salt bridges responsible for the greater stability of this helix in wild-type PrP. Although both mutations result in similar destabilization of helix 1, they a have different effect on the overall stability of PrP(C) and of PrP(PU) isoforms and on structural properties. The destabilization of helix 1 by mutations provides additional evidences to the role of this helix in the pathogenic transition from the PrP(C) to the pathogenic isoform PrP(SC).

The incorporation of quantum effects in enzyme kinetics modeling

We present an overview of new procedures for including quantum mechanical effects in enzyme kinetics. Quantum effects are included in three ways: (1) The electronic structure of the atoms in the catalytic center is treated quantum mechanically in order to calculate a realistic potential energy surface for the bond rearrangement process. (2) The discrete nature of quantum mechanical vibrational energies is incorporated in the treatment of nuclear motion for computing the potential of mean force. (3) Multidimensional tunneling contributions are included. These procedures are illustrated by applications to proton abstractions catalyzed by enolase and methylamine dehydrogenase and hydride-transfer reactions by alcohol dehydrogenase and xylose isomerase.

Evolution and physics in comparative protein structure modeling

From a physical perspective, the native structure of a protein is a consequence of physical forces acting on the protein and solvent atoms during the folding process. From a biological perspective, the native structure of proteins is a result of evolution over millions of years. Correspondingly, there are two types of protein structure prediction methods, de novo prediction and comparative modeling. We review comparative protein structure modeling and discuss the incorporation of physical considerations into the modeling process. A good starting point for achieving this aim is provided by comparative modeling by satisfaction of spatial restraints. Incorporation of physical considerations is illustrated by an inclusion of solvation effects into the modeling of loops.

An improved hydrogen bond potential: impact on medium resolution protein structures

A new semi-empirical force field has been developed to describe hydrogen-bonding interactions with a directional component. The hydrogen bond potential supports two alternative target angles, motivated by the observation that carbonyl hydrogen bond acceptor angles have a bimodal distribution. It has been implemented as a module for a macromolecular refinement package to be combined with other force field terms in the stereochemically restrained refinement of macromolecules. The parameters for the hydrogen bond potential were optimized to best fit crystallographic data from a number of protein structures. Refinement of medium-resolution structures with this additional restraint leads to improved structure, reducing both the free R-factor and over-fitting. However, the improvement is seen only when stringent hydrogen bond selection criteria are used. These findings highlight common misconceptions about hydrogen bonding in proteins, and provide explanations for why the explicit hydrogen bonding terms of some popular force field sets are often best switched off.

Electrostatic properties of the anion selective porin Omp32 from Delftia acidovorans and of the arginine cluster of bacterial porins

The functional properties of the anion-selective porin Omp32 from the bacterium Delftia acidovorans, formerly Comamonas acidovorans, are determined by the particularly narrow channel constriction and the electrostatic field inside and outside the pore. A cluster of arginines (Arg 38, Arg 75, and Arg 133) determines the electrostatic field close to the constriction zone. Stacked amino acids carrying charges are prone to drastic pK(a) shifts. However, optimized calculations of the titration behavior of charged groups, based on the finite-difference Poisson-Boltzmann technique, suggest that all the arginines are charged at physiological pH. Protonation of the clustered arginines is stabilized by one buried glutamate residue (Glu 58), which is strongly interacting with Arg 75 and Arg 38. This functional arrangement of three charged amino acid residues is of general significance because it is found in the constriction zones of all known 16-stranded porins from the alpha-, beta-, and gamma-proteobacteria.

Evaluating conformational free energies: the colony energy and its application to the problem of loop prediction

In this paper, we introduce a method to account for the shape of the potential energy curve in the evaluation of conformational free energies. The method is based on a procedure that generates a set of conformations, each with its own force-field energy, but adds a term to this energy that favors conformations that are close in structure (have a low rmsd) to other conformations. The sum of the force-field energy and rmsd-dependent term is defined here as the "colony energy" of a given conformation, because each conformation that is generated is viewed as representing a colony of points. The use of the colony energy tends to select conformations that are located in broad energy basins. The approach is applied to the ab initio prediction of the conformations of all of the loops in a dataset of 135 nonredundant proteins. By using an rmsd from a native criterion based on the superposition of loop stems, the average rmsd of 5-, 6-, 7-, and 8-residue long loops is 0.85, 0.92, 1.23, and 1.45 A, respectively. For 8-residue loops, 60 of 61 predictions have an rmsd of less than 3.0 A. The use of the colony energy is found to improve significantly the results obtained from the potential function alone. (The loop prediction program, "Loopy," can be downloaded at http://trantor.bioc.columbia.edu.)

Increasing the precision of comparative models with YASARA NOVA--a self-parameterizing force field

One of the conclusions drawn at the CASP4 meeting in Asilomar was that applying various force fields during refinement of template-based models tends to move predictions in the wrong direction, away from the experimentally determined coordinates. We have derived an all-atom force field aimed at protein and nucleotide optimization in vacuo (NOVA), which has been specifically designed to avoid this problem. NOVA resembles common molecular dynamics force fields but has been automatically parameterized with two major goals: (i) not to make high resolution X-ray structures worse and (ii) to improve homology models built by WHAT IF. Force-field parameters were not required to be physically correct; instead, they were optimized with random Monte Carlo moves in force-field parameter space, each one evaluated by simulated annealing runs of a 50-protein optimization set. Errors inherent to the approximate force-field equation could thus be canceled by errors in force-field parameters. Compared with the optimization set, the force field did equally well on an independent validation set and is shown to move in silico models closer to reality. It can be applied to modeling applications as well as X-ray and NMR structure refinement. A new method to assign force-field parameters based on molecular trees is also presented. A NOVA server is freely accessible at http://www.yasara.com/servers

Molecular dynamics simulations of the acyl-enzyme and the tetrahedral intermediate in the deacylation step of serine proteases

Despite the availability of many experimental data and some modeling studies, questions remain as to the precise mechanism of the serine proteases. Here we report molecular dynamics simulations on the acyl-enzyme complex and the tetrahedral intermediate during the deacylation step in elastase catalyzed hydrolysis of a simple peptide. The models are based on recent crystallographic data for an acyl-enzyme intermediate at pH 5 and a time-resolved study on the deacylation step. Simulations were carried out on the acyl enzyme complex with His-57 in protonated (as for the pH 5 crystallographic work) and deprotonated forms. In both cases, a water molecule that could provide the nucleophilic hydroxide ion to attack the ester carbonyl was located between the imidazole ring of His-57 and the carbonyl carbon, close to the hydrolytic position assigned in the crystal structure. In the "neutral pH" simulations of the acyl-enzyme complex, the hydrolytic water oxygen was hydrogen bonded to the imidazole ring and the side chain of Arg-61. Alternative stable locations for water in the active site were also observed. Movement of the His-57 side-chain from that observed in the crystal structure allowed more solvent waters to enter the active site, suggesting that an alternative hydrolytic process directly involving two water molecules may be possible. At the acyl-enzyme stage, the ester carbonyl was found to flip easily in and out of the oxyanion hole. In contrast, simulations on the tetrahedral intermediate showed no significant movement of His-57 and the ester carbonyl was constantly located in the oxyanion hole. A comparison between the simulated tetrahedral intermediate and a time-resolved crystallographic structure assigned as predominantly reflecting the tetrahedral intermediate suggests that the experimental structure may not precisely represent an optimal arrangement for catalysis in solution. Movement of loop residues 216-223 and P3 residue, seen both in the tetrahedral simulation and the experimental analysis, could be related to product release. Furthermore, an analysis of the geometric data obtained from the simulations and the pH 5 crystal structure of the acyl-enzyme suggests that since His-57 is protonated, in some aspects, this crystal structure resembles the tetrahedral intermediate.

Energetics of glycerol conduction through aquaglyceroporin GlpF

Aquaglyceroporin GlpF selectively conducts water and linear polyalcohols, such as glycerol, across the inner membrane of Escherichia coli. We report steered molecular dynamics simulations of glycerol conduction through GlpF, in which external forces accelerate the transchannel conduction in a manner that preserves the intrinsic conduction mechanism. The simulations reveal channel-glycerol hydrogen bonding interactions and the stereoselectivity of the channel. Employing Jarzynski's identity between free energy and irreversible work, we reconstruct the potential of mean force along the conduction pathway through a time series analysis of molecular dynamics trajectories. This potential locates binding sites and barriers inside the channel; it also reveals a low energy periplasmic vestibule suited for efficient uptake of glycerol from the environment.

Structure-based design of mutant Methanococcus jannaschii tyrosyl-tRNA synthetase for incorporation of O-methyl-L-tyrosine

Although incorporation of amino acid analogs provides a powerful means of producing new protein structures with interesting functions, many amino acid analogs cannot be incorporated easily by using the wild-type aminoacyl-tRNA synthetase (aaRS). To be able to incorporate specific amino acid analogs site-specifically, it is useful to build a mutant aaRS that preferentially activates the analog compared with the natural amino acids. Experimental combinatorial studies to find such mutant aaRSs have been successful but can easily become costly and time-consuming. In this article, we describe the clash opportunity progressive (COP) computational method for designing a mutant aaRS to preferentially take up the analog compared with the natural amino acids. To illustrate this COP procedure, we apply it to the design of mutant Methanococcus jannaschii tyrosyl-tRNA synthetase (M.jann-TyrRS). Because the three-dimensional structure for M.jann-TyrRS was not available, we used the STRUCTFAST homology modeling procedure plus molecular dynamics with continuum solvent forces to predict the structure of wild-type M.jann-TyrRS. We validate this structure by predicting the binding site for tyrosine and calculating the binding energies of the 20 natural amino acids, which shows that tyrosine binds the strongest. With the COP design algorithm we then designed a mutant tyrosyl tRNA synthetase to activate O-methyl-l-tyrosine preferentially compared with l-tyrosine. This mutant [Y32Q, D158A] is similar to the mutant designed with combinatorial experiments, [Y32Q, D158A, E107T, L162P], by Wang et al. [Wang, L., Brock, A., Herberich, B. & Schultz, P. G. (2001) Science 292, 498-500]. We predict that the new one will have much greater activity while retaining significant discrimination between O-methyl-l-tyrosine and tyrosine.

Gaussian fluctuations and linear response in an electron transfer protein

In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme-octapeptide complex. We obtain a reorganization free energy that is only half that for heme-octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.

Constant normal pressure, constant surface tension, and constant temperature molecular dynamics simulation of hydrated 1,2-dilignoceroylphosphatidylcholine monolayer

A constant normal pressure, constant surface tension, and constant temperature (NP(N)gammaT) molecular dynamics (MD) simulation of the liquid condensed phase of a 1,2-dilignoceroylphosphatidylcholine (DLGPC) monolayer has been performed at 293.15 K. A DLGPC molecule has two saturated 24-carbon acyl chains, giving the hydrocarbon core thickness of the monolayer approximately 28 A, which is close to the hydrocarbon core thickness of a membrane of a living system. NP(N)gammaT ensemble was used to reproduce the experimental observations, such as area/lipid, because surface tension is an essential factor in determining the monolayer structure. Data analysis on DLGPC/water monolayer shows that various liquid condensed-phase properties of the monolayer have been well reproduced from the simulation, indicating that surface tension 22.9 mN/M used in the simulation is an appropriate condition for the condensed-phase NP(N)gammaT simulation. The simulation results suggest that this long-chain phospholipid monolayer shares many structural characteristics with typical short-chain 1,2-diacylphosphatidylcholine systems, such as DPPC/water monolayer in the condensed phase and DPPC/water bilayer in the gel phase. Furthermore, it was found that DLGPC/water monolayer has almost completely rotationally disordered acyl chains, which have not been observed so far in short-chain 1,2-diacylphosphatidylcholine/water bilayers. This study indicates the good biological relevance of the DLGPC/water monolayer which might be useful in protein/lipid studies to reveal protein structure and protein/lipid interactions in a membrane environment.

Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel

The conduction of protons in the hydrogen-bonded chain of water molecules (or "proton wire") embedded in the lumen of gramicidin A is studied with molecular dynamics free energy simulations. The process may be described as a "hop-and-turn" or Grotthuss mechanism involving the chemical exchange (hop) of hydrogen nuclei between hydrogen-bonded water molecules arranged in single file in the lumen of the pore, and the subsequent reorganization (turn) of the hydrogen-bonded network. Accordingly, the conduction cycle is modeled by two complementary steps corresponding respectively to the translocation 1) of an ionic defect (H+) and 2) of a bonding defect along the hydrogen-bonded chain of water molecules in the pore interior. The molecular mechanism and the potential of mean force are analyzed for each of these two translocation steps. It is found that the mobility of protons in gramicidin A is essentially determined by the fine structure and the dynamic fluctuations of the hydrogen-bonded network. The translocation of H+ is mediated by spontaneous (thermal) fluctuations in the relative positions of oxygen atoms in the wire. In this diffusive mechanism, a shallow free-energy well slightly favors the presence of the excess proton near the middle of the channel. In the absence of H+, the water chain adopts either one of two polarized configurations, each of which corresponds to an oriented donor-acceptor hydrogen-bond pattern along the channel axis. Interconversion between these two conformations is an activated process that occurs through the sequential and directional reorientation of water molecules of the wire. The effect of hydrogen-bonding interactions between channel and water on proton translocation is analyzed from a comparison to the results obtained previously in a study of model nonpolar channels, in which such interactions were missing. Hydrogen-bond donation from water to the backbone carbonyl oxygen atoms lining the pore interior has a dual effect: it provides a coordination of water molecules well suited both to proton hydration and to high proton mobility, and it facilitates the slower reorientation or turn step of the Grotthuss mechanism by stabilizing intermediate configurations of the hydrogen-bonded network in which water molecules are in the process of flipping between their two preferred, polarized states. This mechanism offers a detailed molecular model for the rapid transport of protons in channels, in energy-transducing membrane proteins, and in enzymes.

Atomistic simulations of competition between substrates binding to an enzyme

Although the idea that electrostatic potentials generated by enzymes can guide substrates to active sites is well established, it is not always appreciated that the same potentials can also promote the binding of molecules other than the intended substrate, with the result that such enzymes might be sensitive to the presence of competing molecules. To provide a novel means of studying such "electrostatic competition" effects, computer simulation methodology has been developed to allow the diffusion and association of many solute molecules around a single enzyme to be simulated. To demonstrate the power of the methodology, simulations have been conducted on an artificial fusion protein of citrate synthase (CS) and malate dehydrogenase (MDH) to assess the chances of oxaloacetate being channeled between the MDH and CS active sites. The simulations demonstrate that the probability of channeling is strongly dependent on the concentration of the initial substrate (malate) in the solution. In fact, the high concentrations of malate used in experiments appear high enough to abolish any channeling of oxaloacetate. The simulations provide a resolution of a serious discrepancy between previous simulations and experiments and raise important questions relating to the observability of electrostatically mediated substrate channeling in vitro and in vivo.

General framework for studying the dynamics of folded and nonfolded proteins by NMR relaxation spectroscopy and MD simulation

A general framework is presented for the interpretation of NMR relaxation data of proteins. The method, termed isotropic reorientational eigenmode dynamics (iRED), relies on a principal component analysis of the isotropically averaged covariance matrix of the lattice functions of the spin interactions responsible for spin relaxation. The covariance matrix, which is evaluated using a molecular dynamics (MD) simulation, is diagonalized yielding reorientational eigenmodes and amplitudes that reveal detailed information about correlated protein dynamics. The eigenvalue distribution allows one to quantitatively assess whether overall and internal motions are statistically separable. To each eigenmode belongs a correlation time that can be adjusted to optimally reproduce experimental relaxation parameters. A key feature of the method is that it does not require separability of overall tumbling and internal motions, which makes it applicable to a wide range of systems, such as folded, partially folded, and unfolded biomolecular systems and other macromolecules in solution. The approach was applied to NMR relaxation data of ubiquitin collected at multiple magnetic fields in the native form and in the partially folded A-state using MD trajectories with lengths of 6 and 70 ns. The relaxation data of native ubiquitin are well reproduced after adjustment of the correlation times of the 10 largest eigenmodes. For this state, a high degree of separability between internal and overall motions is present as is reflected in large amplitude and collectivity gaps between internal and overall reorientational modes. In contrast, no such separability exists for the A-state. Residual overall tumbling motion involving the N-terminal beta-sheet and the central helix is observed for two of the largest modes only. By adjusting the correlation times of the 10 largest modes, a high degree of consistency between the experimental relaxation data and the iRED model is reached for this highly flexible biomolecule.

Control of the selectivity of the aquaporin water channel family by global orientational tuning

Aquaporins are transmembrane channels found in cell membranes of all life forms. We examine their apparently paradoxical property, facilitation of efficient permeation of water while excluding protons, which is of critical importance to preserving the electrochemical potential across the cell membrane. We have determined the structure of the Escherichia coli aquaglyceroporin GlpF with bound water, in native (2.7 angstroms) and in W48F/F200T mutant (2.1 angstroms) forms, and carried out 12-nanosecond molecular dynamics simulations that define the spatial and temporal probability distribution and orientation of a single file of seven to nine water molecules inside the channel. Two conserved asparagines force a central water molecule to serve strictly as a hydrogen bond donor to its neighboring water molecules. Assisted by the electrostatic potential generated by two half-membrane spanning loops, this dictates opposite orientations of water molecules in the two halves of the channel, and thus prevents the formation of a "proton wire," while permitting rapid water diffusion. Both simulations and observations revealed a more regular distribution of channel water and an increased water permeability for the W48F/F200T mutant.

On the role of electrostatic interactions in the design of protein-protein interfaces

Here, the methods of continuum electrostatics are used to investigate the contribution of electrostatic interactions to the binding of four protein-protein complexes; barnase-barstar, human growth hormone and its receptor, subtype N9 influenza virus neuraminidase and the NC41 antibody, the Ras binding domain (RBD) of kinase cRaf and a Ras homologue Rap1A. In two of the four complexes electrostatics are found to strongly oppose binding (hormone-receptor and neuraminidase-antibody complexes), in one case the net effect is close to zero (barnase-barstar) and in one case electrostatics provides a significant driving force favoring binding (RBD-Rap1A). In order to help understand the wide range of electrostatic contributions that were calculated, the electrostatic free energy was partitioned into contributions of individual charged and polar residues, salt bridges and networks involving salt bridges and hydrogen bonds. Although there is no one structural feature that accounts for the differences between the four interfaces, the extent to which the desolvation of buried charges is compensated by the formation of hydrogen bonds and ion pairs appears to be an important factor. Structural features that are correlated with contribution of an individual residue to stability are also discussed. These include partial burial of a charged group in the free monomer, the formation of networks involving charged and polar amino acids, and the formation of partially exposed ion-pairs. The total electrostatic contribution to binding is found to be inversely correlated with buried total and non-polar surface area. This suggests that different interfaces can be designed to exploit electrostatic and hydrophobic forces in very different ways.

Is the first hydration shell of lysozyme of higher density than bulk water?

Characterization of the physical properties of protein surface hydration water is critical for understanding protein structure and folding. Here, using molecular dynamics simulation, we provide an explanation of recent x-ray and neutron solution scattering data that indicate that the density of water on the surface of lysozyme is significantly higher than that of bulk water. The simulation-derived scattering profiles are in excellent agreement with the experiment. In the simulation, the 3-A-thick first hydration layer is 15% denser than bulk water. About two-thirds of this increase is the result of a geometric contribution that would also be present if the water was unperturbed from the bulk. The remaining third arises from modification of the water structure and dynamics, involving approximately equal contributions from shortening of the average water-water O-O distance and an increase in the coordination number. Variation in the first hydration shell density is shown to be determined by topographical and electrostatic properties of the protein surface. On average, denser water is found in depressions on the surface in which the water dipoles tend to be aligned parallel to each other by the electrostatic field generated by the protein atoms.

Calculation of the free energy of solvation for neutral analogs of amino acid side chains

The ability of the GROMOS96 force field to reproduce partition constants between water and two less polar solvents (cyclohexane and chloroform) for analogs of 18 of the 20 naturally occurring amino acids has been investigated. The estimations of the solvation free energies in water, in cyclohexane solution, and chloroform solution are based on thermodynamic integration free energy calculations using molecular dynamics simulations. The calculations show that while the force field reproduces the experimental solvation free energies of nonpolar analogs with reasonable accuracy the solvation free energies of polar analogs in water are systematically overestimated (too positive). The dependence of the calculated free energies on the atomic partial charges was also studied.

Energetics of radical transfer in DNA photolyase

Charge separation and radical transfer in DNA photolyase from Escherichia coli is investigated by computing electrostatic free energies from a solution of the Poisson-Boltzmann equation. For the initial charge separation 450 meV are available. According to recent experiments [Aubert et al. Nature 2000, 405, 586-590] the flavin receives an electron from the proximal tryptophan W382, which consequently forms a cationic radical WH(*)(+)382. The radical state is subsequently transferred along the triad W382-W359-W306 of conserved tryptophans. The radical transfer to the intermediate tryptophan W359 is nearly isoenergetic (58 meV uphill); the radical transfer from the intermediate W359 to the distal W306 is 200 meV downhill in energy, funneling and stabilizing the radical state at W306. The resulting cationic radical WH(*)(+)306 is further stabilized by deprotonation, yielding the neutral radical W(*)306, which is 214 meV below WH(*)(+)306. The time scale of the charge recombination process yielding back the resting enzyme with FADH(*) is governed by reprotonation of W306, with a calculated lifetime of 1.2 ms that correlates well with the measured lifetime of 17 ms. In photolyase from Anacystis nidulans the radical state is partially transferred to a tyrosine [Aubert et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 5423-5427]. In photolyase from Escherichia coli, there is a tyrosine (Y464) close to the distal tryptophan W306 that could play this role. We show that this tyrosine cannot be involved in radical transfer, because the electron transfer from tyrosine to W306 is much too endergonic (750 meV) and a direct hydrogen transfer is likely too slow. Coupling of specific charge states of the tryptophan triad with protonation patterns of titratable residues of photolyase is small.

Molecular dynamics simulations of conformational behavior of linear RGD peptidomimetics and cyclic prodrugs in aqueous and octane solutions

Conformations available to a class of cyclic prodrugs and corresponding linear RGD peptidomimetics were explored using 1 ns length molecular dynamics simulations performed with the program CHARMM. Water and octane, modeled explicitly, were used as solvents to mimic the change of the environment experienced by the solutes upon partition from water to membrane in the trans-cellular transport process. In water, the linear peptidomimetics tended to populate extended-like structures, characterized by strong favorable interactions with solvent and low intrinsic stability. In these extended conformations the charged termini are able to assume large distances, above 15 A for the longest systems. These linear peptidomimetics have been found to exhibit the highest potency in experimental studies, in accord with the trends experimentally observed for RGD peptides. In contrast, in octane compact conformers of the linear peptidomimetics were favored, with all charged groups aggregated and shielded from solvent, exhibiting high intrinsic stability and weak solute-solvent interactions. Our calculations predict a large unfavorable energy change for transferring the linear systems from water to octane, in agreement with experimental findings that these compounds are not transported via the trans-cellular pathway. The cyclic prodrugs did not exhibit major structural differences between the simulations in water and octane, adopting turn-like conformations in both solvents. The limited response of the cyclic structures to changes in the environment leads to energies of transfer from water to octane that are also unfavorable, but much less so than for the linear molecules. This effect is in accord with the observed enhanced passive trans-cellular transport of the cyclic prodrugs.

Molecular dynamics simulations of calcium-free calmodulin in solution

A 4-ns molecular dynamics simulation of calcium-free calmodulin in solution has been performed, using Ewald summation to treat electrostatic interactions. Our simulation results were mostly consistent with solution experimental studies, including NMR, fluorescence and x-ray scattering. The secondary structures within the N- and C-terminal domains were conserved in the simulation, with trajectory structures similar to the NMR-derived model structure 1CFD. However, the relative orientations of the domains, for which there are no NMR restraints, differed in details between the simulation and the 1CFD model. The most interesting information provided by the simulations is that the dynamics of calcium-free calmodulin in solution is dominated by slow rigid body reorientations of the domains. The interdomain distance fluctuated between 29 and 39 A, and interdomain orientation angle, defined as the pseudo-dihedral formed by the four calcium binding sites, varied between -2 degrees and 108 degrees. Similarly, the domain linker region also exhibited significant fluctuations, with its length varying in the 34-45 A range and its bend angle in the 10-100 degrees range. The simulations are in accord with fluorescence results suggesting that calcium-free calmodulin is more compact and more flexible than the calcium activated form. Surprisingly, quite similar solvent accessibilities of the hydrophobic patches were seen in the calcium-free trajectory described in this work and previously generated calcium-loaded calmodulin simulations. Thus, our simulations suggest a reexamination of the standard model of the structural change of calmodulin upon calcium binding, involving exposure of the hydrophobic patches to solvent.

A divide and conquer approach to fast loop modeling

We describe a fast ab initio method for modeling local segments in protein structures. The algorithm is based on a divide and conquer approach and uses a database of precalculated look-up tables, which represent a large set of possible conformations for loop segments of variable length. The target loop is recursively decomposed until the resulting conformations are small enough to be compiled analytically. The algorithm, which is not restricted to any specific loop length, generates a ranked set of loop conformations in 20-180 s on a desktop PC. The prediction quality is evaluated in terms of global RMSD. Depending on loop length the top prediction varies between 1.06 A RMSD for three-residue loops and 3.72 A RMSD for eight-residue loops. Due to its speed the method may also be useful to generate alternative starting conformations for complex simulations.

Role of protein-water hydrogen bond dynamics in the protein dynamical transition

The role of water in protein dynamics has been investigated using molecular dynamics simulations of crystals and a dehydrated powder. On the 100 ps time scale, the anharmonic and diffusive motions involved in the protein structural relaxation are correlated with the protein-water hydrogen bond dynamics. The complete structural relaxation of the protein requires relaxation of the hydrogen bond network via solvent translational displacement. Inhibiting the solvent translational mobility, and therefore the protein-water hydrogen bond dynamics, has an effect on the protein relaxation similar to dehydration.

Factors governing loss and rescue of DNA binding upon single and double mutations in the p53 core domain

The mutation of R273-->H in the p53 core domain (p53-CD) is one of the most common mutations found in human cancers. Although the 273H p53-CD retains the wild-type conformation and stability, it lacks sequence-specific DNA binding, a transactivation function and growth suppression. However, mutating T284-->R in the 273H p53-CD restores the DNA binding affinity, and transactivation and tumour suppressor functions. Since X-ray/NMR structures of DNA-free or DNA-bound mutant p53-CD molecules are unavailable, the factors governing the loss and rescue of sequence-specific DNA binding in the 273H and 273H+284R p53-CD, respectively, are unclear. Hence, we have carried out molecular dynamics (MD) simulations of the wild-type, single mutant and double mutant p53-CD, free and DNA bound, in the presence of explicit water molecules. Based on the MD structures, the DNA-binding free energy of each p53 molecule has been computed and decomposed into component energies and contributions from the interface residues. The wild-type and mutant p53-CD MD structures were found to be consistent with the antibody-binding, X-ray and NMR data. The predicted DNA binding affinity and specificity of both mutant p53-CDs were also in accord with experimental data. The non-detectable DNA binding of the 273H p53-CD is due mainly to the disruption of a hydrogen-bonding network involving R273, D281 and R280, leading to a loss of major groove binding by R280 and K120. The restoration of DNA binding affinity and specificity of the 273H+284R p53-CD is due mainly to the introduction of another DNA-binding site at position 284, leading to a recovery of major groove binding by R280 and K120. The important role of water molecules and the DNA major groove conformation as well as implications for structure-based linker rescue of the 273H p53-CD DNA-binding affinity are discussed.

A critical analysis of continuum electrostatics: the screened Coulomb potential--implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins

An analysis of the screened Coulomb potential--implicit solvent model (SCP--ISM) is presented showing that general equations for both the electrostatic and solvation free energy can be derived in a continuum approach, using statistical averaging of the polarization field created by the solvent around the molecule. The derivation clearly shows how the concept of boundary, usually found in macroscopic approaches, is eliminated when the continuum model is obtained from a microscopic treatment using appropriate averaging techniques. The model is used to study the alanine dipeptide in aqueous solution, as well as the discrimination of native protein structures from misfolded conformations. For the alanine dipeptide the free energy surface in the phi--psi space is calculated and compared with recently reported results of a detailed molecular dynamics simulation using an explicit representation of the solvent, and with other available data. The study showed that the results obtained using the SCP--ISM are comparable to those of the explicit water calculation and compares favorably to the FDPB approach. Both transition states and energy minima show a high correlation (r > 0.98) with the results obtained in the explicit water analysis. The study of the misfolded structures of proteins comprised the analysis of three standard decoy sets, namely, the EMBL, Park and Levitt, and Baker's CASP3 sets. In all cases the SCP--ISM discriminated well the native structures of the proteins, and the best-predicted structures were always near-native (cRMSD approximately 2 A).

Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: effect of geometry and tunneling on proton-transfer rate constants

The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Calpha in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examined in the gas phase and in solution. Variational transition-state theory with semiclassical ground-state tunneling was used for the calculation with potential energy surface determined by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temperature; the tunneling becomes more important at lower temperature, as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 A of the substrate. This suggests that only a small number of atoms that are close to the substrate and their motions (e.g., donor-acceptor vibration) directly determine the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramolecular proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in solution than in the gas phase and enzyme; the broader solution barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent molecules. Analysis of isotope effects showed that the conventional Arrenhius parameters are more useful as experimental criteria for determining the magnitude of tunneling than the widely used Swain-Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calculated magnitudes of tunneling and the SSE. Also, the temperature dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temperature is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the "coupled motion" between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temperature; i.e., the tunneling factor of 10 is "small" relative to the overall rate acceleration by 10(9). For the intramolecular proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in solution.

High pressure simulations of biomolecules

Pressure is a thermodynamic variable which is particularly suitable for exploration of the properties of biological macromolecules. For proteins, in particular, denaturation induced by pressure is different from that induced by temperature or denaturants. The response of proteins to pressure changes can provide information on properties of their native and non-native states. This review focuses on molecular dynamics studies of the effect of pressure on detailed atomic models of proteins. It also reports on other theoretical approaches, such as Monte Carlo simulations, which have been used to study simplified models. Another purpose of this review is to try to point out potential future studies that may be both interesting and feasible, with constantly increasing computing power.

An inverting basket model for AE1 transport

We describe an "inverting basket" model for transport in the erythrocyte anion exchanger, AE1. The inverting basket is formed by the side chains of three putative key residues, two positively (Lys 826 and Arg 730) and one negatively (Glu 681) charged residue. We have tentatively chosen seven transmembrane helices, TM1, TM2, TM4, TM8, TM10, TM12 and TM13 to form a conical channel using the well-established Glu 681 of TM8 and candidates Lys 826 and Arg 730 of TM12-13 and TM10, respectively, to form the inverting basket. We assume that these residues bind to an anion and shift from outward facing (C(o)) to inward facing (C(i)) conformation without significant backbone movements to transport an anion across the membrane. The transition of the complex (residues and ion) from outward facing (C(o)) to inward facing (C(i)) constitutes one "basket" inversion. The barrier to inversion is composed of two major components: that of the anhydrous complex, which we refer to as a steric energy barrier and a dehydration effect due to the removal of charges in the complex from water in the channel. The steric barrier is dependent on the side chain charge and configuration and on the ion charge and size. The dehydration effect, for our model, ameliorates the steric barrier, in the case of the empty complex but less so for the monovalent and divalent ions. We conclude, that it is possible for a seven-helix bundle to have a steric barrier to basket inversion, but that hydration effects in thin hydrophobic barrier models may be more complex than usually envisioned.

Mechanical force generation by G proteins

GTP-hydrolyzing G proteins are molecular switches that play a critical role in cell signaling processes. Here we use molecular dynamics simulations to show that Ras, a monomeric G protein, can generate mechanical force upon hydrolysis. The generated force levels are comparable to those produced by ATP-hydrolyzing motor proteins, consistent with the structural similarities of the catalytic region of motor proteins and G proteins. The force transduction mechanism is based on an irreversible structural change, produced by the hydrolysis, which triggers thermal switching between force-generating substates through changes in the configurational space of the protein.

Using novel variable transformations to enhance conformational sampling in molecular dynamics

One of the computational "grand challenges" is to develop methodology capable of sampling conformational equilibria in systems with rough energy landscapes. Here, a significant step forward is made by combining molecular dynamics with a novel variable transformation designed to enhance sampling by reducing barriers without introducing bias and, thus, to preserve, perfectly, equilibrium properties.

Mechanism for antibody catalysis of the oxidation of water by singlet dioxygen

Wentworth et al. [Wentworth, P., Jones, L. H., Wentworth, A. D., Zhu, X. Y., Larsen, N. A., Wilson, I. A., Xu, X., Goddard, W. A., Janda, K. D., Eschenmoser, A. & Lerner, R. A. (2001) Science 293, 1806-1811] recently reported the surprising result that antibodies and T cell receptors efficiently catalyze the conversion of molecular singlet oxygen (1O2) plus water to hydrogen peroxide (HOOH). Recently, quantum mechanical calculations were used to delineate a plausible mechanism, involving reaction of 1O2 with two waters to form HOOOH (plus H2O), followed by formation of HOOOH dimer, which rearranges to form HOO-HOOO + H2O, which rearranges to form two HOOH plus 1O2 or 3O2. For a system with 18O H2O, this mechanism leads to a 2.2:1 ratio of 16O:18O in the product HOOH, in good agreement with the ratio 2.2:1 observed in isotope experiments by Wentworth et al. In this paper we use docking and molecular dynamics techniques (HierDock) to search various protein structures for sites that stabilize these products and intermediates predicted from quantum mechanical calculations. We find that the reaction intermediates for production of HOOH from 1O2 are stabilized at the interface of light and heavy chains of antibodies and T cell receptors. This inter Greek key domain interface structure is unique to antibodies and T cell receptors, but is not present in beta2-microglobulin, which does not show any stabilization in our docking studies. This result is consistent with the experimentally observed lack of HOOH production in this system. Our results provide a plausible mechanism for the reactions and provide an explanation of the specific structural character of antibodies responsible for this unexpected chemistry.

Development and current status of the CHARMM force field for nucleic acids

The CHARMM27 all-atom force field for nucleic acids represents a highly optimized model for investigations of nucleic acids via empirical force field calculations. The force field satisfactorily treats the A, B, and Z forms of DNA as well as RNA, and it also useful for nucleosides and nucleotides. In addition, it is compatible with the CHARMM force fields for proteins and lipids, allowing for simulation studies of heterogeneous systems.

Calibration of force-field dependency in free energy landscapes of peptide conformations by quantum chemical calculations

The free energy landscapes of peptide conformations were calibrated by ab initio quantum chemical calculations, after the enhanced conformational diversity search using the multicanonical molecular dynamics simulations. Three different potentials of mean force for an isolated dipeptide were individually obtained by the multicanonical molecular dynamics simulations using the conventional force fields, AMBER parm94, AMBER parm96, and CHARMm22. Each potential of mean force was then calibrated based upon the umbrella sampling algorithm from the adiabatic energy map that was calculated separately by the ab initio molecular orbital method, and all of the calibrated potentials of mean force coincided well. The calibration method was also applied to the simulations of a peptide dimer in explicit water models, and it was shown that the calibrated free energy landscapes did not depend on the force field used in the classical simulations, as far as the conformational space was sampled well. The current calibration method fuses the classical free energy calculation with the quantum chemical calculation, and it should generally make simulations for biomolecular systems much more reliable when combining with enhanced conformational sampling.