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A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using rotational and molecule-internal configurational sampling instead of the common refinement procedure that is based on the approximation of the nonuniform rotational distribution of the molecule by a single alignment tensor representing the average nonuniformity of this distribution. Using rotational sampling, as is occurring in the experiment leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and thus the assumption that the overall rotation of the molecule is decoupled from its internal motions and that the molecule be rigid. Two simple molecules, two-united-atomic ethane and a cyclooctane molecule with eight side chains, containing 24 united atoms, serve as the so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility and force-field deficiencies on the outcome of structure refinement based on RDCs. For a molecule of a given size (number of atoms N at ), there must be a sufficiently large number N RDC of measured RDC values available to allow the restraining forces to bias the overall orientation distribution of the molecule. If the ratio N RDC / N at gets too small, the RDC-restraining forces will either not be strong enough to change the overall rotational direction of the molecule such that the target RDC values are approximated well or will be so strong that they induce a local deformation of the molecule. In the latter case, the size or inertia of the molecule hinders a restraining-induced overall rotation and the internal structure of the molecule is not strong enough to avoid local deformation due to the restraining forces.

Values of 3 J-couplings as obtained from NMR experiments on proteins cannot easily be used to determine protein structure due to the difficulty of accounting for the high sensitivity of intermediate 3 J-coupling values (4-8 Hz) to the averaging period that must cover the conformational variability of the torsional angle related to the 3 J-coupling, and due to the difficulty of handling the multiple-valued character of the inverse Karplus relation between torsional angle and 3 J-coupling. Both problems can be solved by using 3 J-coupling time-averaging local-elevation restraining MD simulation. Application to the protein hen egg white lysozyme using 213 backbone and side-chain 3 J-coupling restraints shows that a conformational ensemble compatible with the experimental data can be obtained using this technique, and that accounting for averaging and the ability of the algorithm to escape from local minima for the torsional angle induced by the Karplus relation, are essential for a comprehensive use of 3 J-coupling data in protein structure determination.

The derivation of protein structure from values of observable quantities measured in NMR experiments is a rather nontrivial task due to (i) the limited number of data compared to degrees of freedom of a protein, (ii) the uncertainty inherent to the function connecting an observable quantity to molecular structure, (iii) the finite quality of biomolecular models and force fields used in structure refinement, and (iv) the conformational freedom of a protein in aqueous solution, which requires extensive conformational sampling and appropriate conformational averaging when calculating or restraining to sets of NMR data. The protein interleukin-4 (IL-4) has been taken as a test case using NOE distances, S 2 order parameters, and 3 J-couplings as test data and the former two types of data as restraints. It is shown that, by combining sets of different, complementary NMR data as restraints in MD simulations, inconsistencies in the data or flaws in the model and procedures used to derive protein structure from NMR data can be detected. This leads to an improved structural interpretation of such data particularly in more mobile loop regions.

Deriving molecular structure from [Formula: see text]-couplings obtained from NMR experiments is a challenge due to (1) the uncertainty in the Karplus relation [Formula: see text] connecting a [Formula: see text]-coupling value to a torsional angle [Formula: see text], (2) the need to account for the averaging inherent to the measurement of [Formula: see text]-couplings, and (3) the sampling road blocks that may emerge due to the multiple-valuedness of the inverse function [Formula: see text] of the function [Formula: see text]. Ways to properly handle these issues in structure refinement of biomolecules are discussed and illustrated using the protein hen egg white lysozyme as example.

The multistep umbrella sampling method, which belongs to pathway-dependent methods to calculate conformational free enthalpy differences, is used to calculate the free enthalpy difference between a right-handed 2.710/12 -helix and a left-handed 314 -helix of a hexa-β-peptide in methanol solution. The same conformational free enthalpy difference was previously investigated using pathway-independent methods such as direct counting and enveloping distribution sampling. Our results show that the pathway-dependent simulations are sensitive to the choice of the pathway and its parameter values. A pathway based on restraining distances of hydrogen-bonding atom pairs shows poor sampling for two different values of the restraining force constant. Another pathway based on restraining backbone dihedral angles did smoothly sample the transition between the two helical conformations, but only with a proper choice of the restraining force constant. The results illustrate that if, and only if, a proper pathway and proper parameters are chosen, the multistep umbrella sampling can be almost 50 times more efficient than the pathway-independent methods in this case. The analysis illustrates the advantages and pitfalls of the much used multistep umbrella sampling methodology., (© 2015 The Protein Society.)

The role of entropic contributions in processes involving biomolecules is illustrated using the process of vaporization or condensation of the solvents water and methanol and the process of polypeptide folding in solution using molecular models at different levels of resolution: subatomic, atomic, supra-atomic, and supramolecular. For the folding process, a β-hexapeptide that adopts, as inferred from NMR experiments, both a right-handed 2.710/12-helical fold and a left-handed 314-helical fold in methanol, is used to illustrate the challenge of modeling thermodynamically driven processes at different levels of resolution.

The flavoenzyme pyranose dehydrogenase (PDH) from the litter decomposing fungus Agaricus meleagris oxidizes many different carbohydrates occurring during lignin degradation. This promiscuous substrate specificity makes PDH a promising catalyst for bioelectrochemical applications. A generalized approach to simulate all 32 possible aldohexopyranoses in the course of one or a few molecular dynamics (MD) simulations is reported. Free energy calculations according to the one-step perturbation (OSP) method revealed the solvation free energies (ΔGsolv) of all 32 aldohexopyranoses in water, which have not yet been reported in the literature. The free energy difference between β- and α-anomers (ΔGβ-α) of all d-stereoisomers in water were compared to experimental values with a good agreement. Moreover, the free-energy differences (ΔG) of the 32 stereoisomers bound to PDH in two different poses were calculated from MD simulations. The relative binding free energies (ΔΔGbind) were calculated and, where available, compared to experimental values, approximated from Km values. The agreement was very good for one of the poses, in which the sugars are positioned in the active site for oxidation at C1 or C2. Distance analysis between hydrogens of the monosaccharide and the reactive N5-atom of the flavin adenine dinucleotide (FAD) revealed that oxidation is possible at HC1 or HC2 for pose A, and at HC3 or HC4 for pose B. Experimentally detected oxidation products could be rationalized for the majority of monosaccharides by combining ΔΔGbind and a reweighted distance analysis. Furthermore, several oxidation products were predicted for sugars that have not yet been tested experimentally, directing further analyses. This study rationalizes the relationship between binding free energies and substrate promiscuity in PDH, providing novel insights for its applicability in bioelectrochemistry. The results suggest that a similar approach could be applied to study promiscuity of other enzymes.

A method is described that allows experimental S(2) order parameters to be enforced as a time-averaged quantity in molecular dynamics simulations. The two parameters that characterize time-averaged restraining, the memory relaxation time and the weight of the restraining potential energy term in the potential energy function used in the simulation, are systematically investigated based on two model systems, a vector with one end restrained in space and a pentapeptide. For the latter it is shown that the backbone N-H order parameter of individual residues can be enforced such that the spatial fluctuations of quantities depending on atomic coordinates are not significantly perturbed. The applicability to realistic systems is illustrated for the B3 domain of protein G in aqueous solution.

Starting from a nonpolarizable rigid molecular model for DMSO, a polarizable rigid model for DMSO in the liquid phase is proposed. The molecular polarizability is represented by a charge-on-spring (COS) inducible dipole at the sulfur atom and its polarization is damped for large values of the electric field strength. Some parameters of the model, the partial charge distribution, the polarizability, the value of the electric field at which damping sets in, were varied, and the overall depth and repulsion strength of the Lennard-Jones interactions were scaled with the aim of reproducing the experimental values for the molecular dipole moment, the density, heat of vaporization, and static dielectric constant of liquid DMSO at ambient temperature and pressure. The polarizable DMSO/D model well reproduces the experimental data, such as excess free energy, surface tension, translational, and rotational diffusion, for liquid DMSO. The model is further tested in mixtures with polarizable water models and in mixtures with nonpolarizable DMSO. The latter results suggest that it could serve as model for polarizable cosolvent in aqueous solutions.

The predictive power of biomolecular simulation critically depends on the quality of the force field or molecular model used and on the extent of conformational sampling that can be achieved. Both issues are addressed. First, it is shown that widely used force fields for simulation of proteins in aqueous solution appear to have rather different propensities to stabilize or destabilize α-, π-, and 3(10)- helical structures, which is an important feature of a biomolecular force field due to the omni-presence of such secondary structure in proteins. Second, the relative stability of secondary structure elements in proteins can only be computationally determined through so-called free-energy calculations, the accuracy of which critically depends on the extent of configurational sampling. It is shown that the method of enveloping distribution sampling is a very efficient method to extensively sample different parts of configurational space.

NMR experiments have shown that water molecules in the crystal of the protein Crh are still mobile at temperatures well below 273 K. In order to investigate this water anomaly, a molecular dynamics (MD) simulation study of crystalline Crh was carried out to determine the mobility of water in this crystal. The simulations were carried out at three temperatures, 150, 200, and 291 K. Simulations of bulk water at these temperatures were also done to obtain the properties of the simple point charge (SPC) water model used at these temperatures and to allow a comparison of the properties of water in the Crh crystal with those of bulk water at the same temperatures. According to the simulations, water is immobilized at 150 K both in crystal and in bulk water. As expected, at 291 K it diffuses and rotates more slowly in the protein crystal than in bulk water. However, at 200 K, the translational and rotational mobility of the water molecules is larger in the crystal than in bulk water. The enhancement of water mobility in the crystal at 200 K was further investigated by MD simulations in which the backbone or all protein atoms were positionally restrained, and in which additionally the electrostatic protein-water interactions were removed. Of these changes in the environment of the water molecules, rigidifying the protein backbones slightly enhanced water diffusion, while it slowed down rotation. In contrast, removal of electrostatic protein-water interactions did not change water diffusion but enhanced rotational motion significantly. Further investigations are required to delineate particular features of the protein crystal that induce the anomalous behavior of water at 200 K.

The enzyme chorismate mutase EcCM from Escherichia coli catalyzes one of the few pericyclic reactions in biology, the transformation of chorismate to prephenate. The isochorismate pyruvate lyase PchB from Pseudomonas aeroginosa catalyzes another pericyclic reaction, the isochorismate to salicylate transformation. Interestingly, PchB possesses weak chorismate mutase activity as well thus being able to catalyze two distinct pericyclic reactions in a single active site. EcCM and PchB possess very similar folds, despite their low sequence identity. Using molecular dynamics simulations of four combinations of the two enzymes (EcCM and PchB) with the two substrates (chorismate and isochorismate) we show that the electrostatic field due to EcCM at atoms of chorismate favors the chorismate to prephenate transition and that, analogously, the electrostatic field due to PchB at atoms of isochorismate favors the isochorismate to salicylate transition. The largest differences between EcCM and PchB in electrostatic field strengths at atoms of the substrates are found to be due to residue side chains at distances between 0.6 and 0.8 nm from particular substrate atoms. Both enzymes tend to bring their non-native substrate in the same conformation as their native substrate. EcCM and to a lower extent PchB fail in influencing the forces on and conformations of the substrate such as to favor the other chemical reaction (isochorismate pyruvate lyase activity for EcCM and chorismate mutase activity for PchB). These observations might explain the difficulty of engineering isochorismate pyruvate lyase activity in EcCM by solely mutating active site residues., (© 2013 The Protein Society.)

Various experimental studies of hen egg white lysozyme (HEWL) in water and TFE/water clearly indicate structural differences between the native state and TFE state of HEWL, e.g. the helical content of the protein in the TFE state is much higher than in the native state. However, the available detailed NMR studies were not sufficient to determine fully a structure of HEWL in the TFE state. Different molecular dynamics (MD) simulations, i.e. at room temperature, at increased temperature and using proton-proton distance restraints derived from NMR NOE data, have been used to generate configurational ensembles corresponding to the TFE state of HEWL. The configurational ensemble obtained at room temperature using atom-atom distance restraints measured for HEWL in TFE/water solution satisfies the experimental data and has the lowest protein energy. In this ensemble residues 50-58, which are part of the β-sheet in native HEWL, adopt fluctuating α-helical secondary structure.

The contemporary proteinogenic repertoire contains 20 amino acids with diverse functional groups and side chain geometries. Primordial proteins, in contrast, were presumably constructed from a subset of these building blocks. Subsequent expansion of the proteinogenic alphabet would have enhanced their capabilities, fostering the metabolic prowess and organismal fitness of early living systems. While the addition of amino acids bearing innovative functional groups directly enhances the chemical repertoire of proteomes, the inclusion of chemically redundant monomers is difficult to rationalize. Here, we studied how a simplified chorismate mutase evolves upon expanding its amino acid alphabet from nine to potentially 20 letters. Continuous evolution provided an enhanced enzyme variant that has only two point mutations, both of which extend the alphabet and jointly improve protein stability by >4 kcal/mol and catalytic activity tenfold. The same, seemingly innocuous substitutions (Ile→Thr, Leu→Val) occurred in several independent evolutionary trajectories. The increase in fitness they confer indicates that building blocks with very similar side chain structures are highly beneficial for fine-tuning protein structure and function., Competing Interests: PM is an inventor of the GM3 culturing device, which is patented under WIPO WO0034433. This patent is licensed to Heurisko USA, of which PM is the president of the board.

Water molecules in the binding pocket of a protein and their role in ligand binding have increasingly raised interest in recent years. Displacement of such water molecules by ligand atoms can be either favourable or unfavourable for ligand binding depending on the change in free enthalpy. In this study, we investigate the displacement of water molecules by an apolar probe in the binding pocket of two proteins, cyclin-dependent kinase 2 and tRNA-guanine transglycosylase, using the method of enveloping distribution sampling (EDS) to obtain free enthalpy differences. In both cases, a ligand core is placed inside the respective pocket and the remaining water molecules are converted to apolar probes, both individually and in pairs. The free enthalpy difference between a water molecule and a CH(3) group at the same location in the pocket in comparison to their presence in bulk solution calculated from EDS molecular dynamics simulations corresponds to the binding free enthalpy of CH(3) at this location. From the free enthalpy difference and the enthalpy difference, the entropic contribution of the displacement can be obtained too. The overlay of the resulting occupancy volumes of the water molecules with crystal structures of analogous ligands shows qualitative correlation between experimentally measured inhibition constants and the calculated free enthalpy differences. Thus, such an EDS analysis of the water molecules in the binding pocket may give valuable insight for potency optimization in drug design.

The protein chorismate mutase MtCM from Mycobacterium tuberculosis catalyzes one of the few pericyclic reactions known in biology: the transformation of chorismate to prephenate. Chorismate mutases have been widely studied experimentally and computationally to elucidate the transition state of the enzyme catalyzed reaction and the origin of the high catalytic rate. However, studies about substrate entry and product exit to and from the highly occluded active site of the enzyme have to our knowledge not been performed on this enzyme. Crystallographic data suggest a possible substrate entry gate, that involves a slight opening of the enzyme for the substrate to access the active site. Using multiple molecular dynamics simulations, we investigate the natural dynamic process of the product exiting from the binding pocket of MtCM. We identify a dominant exit pathway, which is in agreement with the gate proposed from the available crystallographic data. Helices H2 and H4 move apart from each other which enables the product to exit from the active site. Interestingly, in almost all exit trajectories, two residues arginine 72 and arginine 134, which participate in the burying of the active site, are accompanying the product on its exit journey from the catalytic site., (Copyright © 2012 The Protein Society.)

Atomistic molecular dynamics simulations of proteins in aqueous solution are still limited to the multinanosecond time scale and multinanometer range by computational cost. Combining atomic solutes with a supra-molecular solvent model in hybrid fine-grained/coarse-grained (FG/CG) simulations allows atomic detail in the region of interest while being computationally more efficient. A recent comparison of the properties of four proteins in CG water versus FG water showed the preservation of the secondary and tertiary structure with a computational speed-up of at least an order of magnitude. However, an increased occurrence of hydrogen bonds between side chains was observed due to a lack of hydrogen-bonding partners in the supra-molecular solvent. Here, the introduction of a FG water layer around the protein to recover the hydrogen-bonding pattern of the atomistic simulations is studied. Three layer thicknesses of 0.2, 0.4, and 0.8 nm are considered. A layer thickness of 0.8 nm is found sufficient to recover the behavior of the proteins in the atomistic simulations, whereas the hybrid simulation is still three times more efficient than the atomistic one and the cutoff radius for nonbonded interactions could be increased from 1.4 to 2.0 nm.

Understanding of the driving forces of protein folding is a complex challenge because different types of interactions play a varying role. To investigate the role of hydrogen bonding involving the backbone, the effect of thio substitutions in a protein, hen egg white lysozyme (HEWL), was investigated through molecular dynamics simulations of native as well as partly (only residues in loops) and fully thionated HEWL using the GROMOS 54A7 force field. The results of the three simulations show that the structural properties of fully thionated HEWL clearly differ from those of the native protein, while for partly thionated HEWL they only changed slightly compared with native HEWL. The analysis of the torsional-angle distributions and hydrogen bonds in the backbone suggests that the α-helical segments of native HEWL tend to show a propensity to convert to 3(10)-helical geometry in fully thionated HEWL. A comparison of the simulated quantities with experimental NMR data such as nuclear overhauser effect (NOE) atom-atom distance bounds and (3)J((H)(N)(H)(α))-couplings measured for native HEWL illustrates that the information content of these quantities with respect to the structural changes induced by thionation of the protein backbone is rather limited., (Copyright © 2012 The Protein Society.)

Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or (3) J-coupling constants on the other. The standardly used relation connecting (3) J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and (3) J (αβ)-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between (3) J (αβ)-couplings and the corresponding χ(1)-angle in proteins.

Prediction and understanding of the folding and stability of the 3D structure of proteins is still a challenge. The different atomic interactions, such as non polar contacts and hydrogen bonding, are known but their exact relative weights and roles when contributing to protein folding and stability are not identified. Initiated by a previous molecular dynamics simulation of fully ester-linked hen egg white lysozyme (HEWL), which showed a more compact fold of the ester-linked molecule compared to the native one, three variants of this protein are analyzed in the present study. These are 129-residue native HEWL, partly ester-linked HEWL, in which only 34 peptide linkages that are not involved in the helical or β-strand parts of native HEWL were replaced by ester linkages, and fully (126 residues) ester-linked HEWL. Native and partly ester-linked HEWL showed comparable behaviour, whereas fully ester-linked HEWL could not maintain the native secondary structure of HEWL in the simulation and adopted a more compact fold. The conformational changes were analyzed by comparing simulation averaged values of quantities that can be measured by NMR, such as (1)H-(15)N backbone order parameters, residual dipolar couplings, proton-proton NOE distances and (3)J-couplings with the corresponding values derived from experimental NMR data for native HEWL. The information content of the latter appeared to be insufficient to detect the local conformational rearrangements upon esterification of the loop regions of the protein. For fully ester-linked HEWL, a significantly reduced agreement was observed. Upon esterification, the backbone-side chain and side chain-side chain hydrogen-bonding pattern of HEWL changes to maintain its compactness and thus the structural stability of the ester-linked lysozymes., (© 2011 The Authors Journal compilation © 2011 FEBS.)

The calculation of the relative free energies of ligand-protein binding, of solvation for different compounds, and of different conformational states of a polypeptide is of considerable interest in the design or selection of potential enzyme inhibitors. Since such processes in aqueous solution generally comprise energetic and entropic contributions from many molecular configurations, adequate sampling of the relevant parts of configurational space is required and can be achieved through molecular dynamics simulations. Various techniques to obtain converged ensemble averages and their implementation in the GROMOS software for biomolecular simulation are discussed, and examples of their application to biomolecules in aqueous solution are given., (© 2011 American Chemical Society)

The ability to design well-folding β-peptides with a specific biological activity requires detailed insight into the relationship between the β-amino acid sequence and the dominant three-dimensional structure of such a peptide. To this end, secondary structure preferences of two sets of 16 β-peptides were investigated by means of one-step perturbation using molecular dynamics (MD) simulations. For each set of peptides, two reference-state simulations and one perturbed-state simulation were carried out to predict the secondary structure preferences for the other 15 peptides. The results show that the substitution of a methyl group in the third or fourth residue stabilizes the left-handed 3(14)-helix over the right-handed 2.7(10/12)-helix for the set of hexapeptides A; for the set of heptapeptides B, having methyl substitutions at both β- and α-carbon positions of the fourth or fifth residue stabilizes the left-handed 3(14)-helix over the right-handed 2.5(12)-helix. Not only the side-chain substitution pattern but also the side-chain composition affects the relative stability of different secondary structures. The approach described here may be of use in peptide design with an eye to obtaining peptides with particular folds and biological activities.

For the understanding of cellular processes the molecular structure of biomolecules has to be accurately determined. Initial models can be significantly improved by structure refinement techniques. Here, we present the refinement methods and analysis techniques implemented in the GROMOS software for biomolecular simulation. The methodology and some implementation details of the computation of NMR NOE data, (3)J-couplings and residual dipolar couplings, X-ray scattering intensities from crystals and solutions and neutron scattering intensities used in GROMOS is described and refinement strategies and concepts are discussed using example applications. The GROMOS software allows structure refinement combining different types of experimental data with different types of restraining functions, while using a variety of methods to enhance conformational searching and sampling and the thermodynamically calibrated GROMOS force field for biomolecular simulation., (© Springer Science+Business Media B.V. 2011)

Docking algorithms for computer-aided drug discovery and design often ignore or restrain the flexibility of the receptor, which may lead to a loss of accuracy of the relative free enthalpies of binding. In order to evaluate the contribution of receptor flexibility to relative binding free enthalpies, two host-guest systems have been examined: inclusion complexes of α-cyclodextrin (αCD) with 1-chlorobenzene (ClBn), 1-bromobenzene (BrBn) and toluene (MeBn), and complexes of DNA with the minor-groove binding ligands netropsin (Net) and distamycin (Dist). Molecular dynamics simulations and free energy calculations reveal that restraining of the flexibility of the receptor can have a significant influence on the estimated relative ligand-receptor binding affinities as well as on the predicted structures of the biomolecular complexes. The influence is particularly pronounced in the case of flexible receptors such as DNA, where a 50% contribution of DNA flexibility towards the relative ligand-DNA binding affinities is observed. The differences in the free enthalpy of binding do not arise only from the changes in ligand-DNA interactions but also from changes in ligand-solvent interactions as well as from the loss of DNA configurational entropy upon restraining.

A refined implicit aqueous solvation model is proposed for the simulation of biomolecules without the explicit inclusion of the solvent degrees of freedom. The mean force due to solvation is approximated by the derivative of a simple analytic function of the solvent accessible surface area combined with two atomic solvation parameters, as described previously, with the addition of a novel term to account for the interaction of the interior atoms of the solute with the solvent. The extended model is parametrized by comparing the structural properties and energies computed from simulations of six test proteins of varying sizes and shapes using the new solvation energy term with the corresponding values obtained from simulations in vacuum, using the original implicit solvent model and in explicit water, and from the X-ray or NMR model structures. The mean solvation model proposed here improves the structural properties relative to vacuum simulations and relative to the simpler model that neglects the volume contribution, while remaining significantly more efficient than simulations in explicit water.

Three methods to enhance the configurational sampling of ions in aqueous solution, temperature and Hamiltonian replica exchange and adiabatic decoupling with translational temperature scaling, were compared for a system of CaSO(4) in water. It took 11 replicas in the case of temperature replica exchange to make use of a diffusion coefficient that is a factor of 1.5 larger at 350 K compared to that at 300 K. Thirty replicas were required in the Hamiltonian replica exchange with charge reduction to reach uncharged ions that have a diffusion coefficient that is 2-7 times larger than the fully charged ones. The adiabatic decoupling technique with translational temperature scaling yielded a diffusion coefficient that was 15 times larger while keeping the distribution of the water molecules around the ions unaltered with respect to the standard temperature simulation. This result illustrates the efficiency of the adiabatic decoupling technique to enhance configurational sampling.

Trigger sequences are indispensable elements for coiled-coil formation. The monomeric helical trigger sequence of the yeast transcriptional activator GCN4 has been investigated recently using several solution NMR observables including nuclear Overhauser enhancement (NOE) intensities and 3J(HN, HCα)-coupling constants, and a set of 20 model structures was proposed. Constrained to satisfy the NOE-derived distance bounds, the NMR model structures do not appear to reproduce all the measured 3J(HN-HCα)-coupling constant values, indicating that the α-helical propensity is not uniform along the GCN4 trigger sequence. A recent methodological study of unrestrained and restrained molecular dynamics (MD) simulations of the GCN4 trigger sequence in solution showed that only MD simulations incorporating time-averaged NOE distance restraints and instantaneous or local-elevation 3J-coupling restraints could satisfy the entire set of the experimental data. In this report, we assess by means of cluster analyses the model structures characteristic of the two simulations that are compatible with the measured data and compare them with the proposed 20 NMR model structures. Striking characteristics of the MD model structures are the variability of the simulated configurations and the indication of entropic stability mediated by the aromatic N-terminal residues 17Tyr and 18His, which are absent in the set of NMR model structures., (Copyright © 2010 The Protein Society.)

The right-handed α-helix is the dominant helical fold of α-peptides, whereas the left-handed 3(14)-helix is the dominant helical fold of β-peptides. Using molecular dynamics simulations, the properties of α-helical α-peptides and 3(14)-helical β-peptides with different C-terminal protonation states and in the solvents water and methanol are compared. The observed energetic and entropic differences can be traced to differences in the polarity of the solvent-accessible surface area and, in particular, the solute dipole moments, suggesting different reasons for their stability.

With the aim to gain a better understanding of the various driving forces that govern sequence specific DNA minor groove binding, we performed a thermodynamic analysis of netropsin binding to an AT-containing and to a set of six mixed AT/GC-containing binding sequences in the DNA minor groove. The relative binding free energies obtained using molecular dynamics simulations and free energy calculations show significant variations with the binding sequence. While the introduction of a GC base pair in the middle or close to the middle of the binding site is unfavorable for netropsin binding, a GC base pair at the end of the binding site appears to have no negative influence on the binding. The results of the structural and energetic analyses of the netropsin-DNA complexes reveal that the differences in the calculated binding affinities cannot be explained solely in terms of netropsin-DNA hydrogen-bonding or interaction energies. In addition, solvation effects and entropic contributions to the relative binding free energy provide a more complete picture of the various factors determining binding. Analysis of the relative binding entropy indicates that its magnitude is highly sequence-dependent, with the ratio |TDeltaDeltaS|/|DeltaDeltaH| ranging from 0.07 for the AAAGA to 1.7 for the AAGAG binding sequence, respectively.

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16-31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 phi torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular alpha-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured (3)J(H(N)-H(Calpha))-coupling constants, indicating that different conformers of GCN4p16-31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and (3)J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and (3)J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16-31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16-31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.

A molecular dynamics (MD) simulation study of a cyclic 22 residue D,L-alpha-peptide is reported. The 154 experimental ROE distance bounds that determine a beta-helical fold in chloroform are all satisfied in MD simulations starting from the folded and from a refolded structure. Interestingly, the latter simulations generated structures of lower energy than the NMR model structures, thereby yielding a better conformational representation of the measured experimental data. The stability of the beta-helical fold, characterized by 16 beta-sheet hydrogen bonds, was investigated by varying the temperature and the solvent composition. Different metastable states were found and examined. Various strategies to fold the cyclic, highly hydrogen bonded peptide, starting from different nonfolded conformations of the peptide, were investigated. Due to the high barriers to (un)folding, a folding/unfolding equilibrium could not be established.

A new charge-on-spring (COS) model for water is introduced (COS/D). It includes a sublinear dependence of the induced dipole on the electric field for large field strength to include the effect of hyperpolarizability by damping the polarizability. Only two new parameters were introduced to define the damping of the polarizability. In the parametrization procedure, these two damping parameters, the two Lennard-Jones parameters, the charge on the oxygen, and the distance between the virtual site and the oxygen atom were varied to reproduce the density, the heat of vaporization, the dielectric permittivity, and the position of the first peak in the radial distribution function of liquid water at room temperature and pressure. In this way, a model was obtained that correctly describes a variety of thermodynamic, dynamic, and dielectric properties of water while still preserving the simplicity of the COS model, which allows a straightforward introduction of explicit polarization into (bio)molecular force fields.

The effects of temperature and urea denaturation (6M urea) on the dominant structures of the 20-residue Trp-cage mini-protein TC5b are investigated by molecular dynamics simulations of the protein at different temperatures in aqueous and in 6M urea solution using explicit solvent degrees of freedom and the GROMOS force-field parameter set 45A3. In aqueous solution at 278 K, TC5b is stable throughout the 20 ns of MD simulation and the trajectory structures largely agree with the NMR-NOE atom-atom distance data available. Raising the temperature to 360 K and to 400 K, the protein denatures within 22 ns and 3 ns, showing that the denaturation temperature is well below 360 K using the GROMOS force field. This is 40-90 K lower than the denaturation temperatures observed in simulations using other much used protein force fields. As the experimental denaturation temperature is about 315 K, the GROMOS force field appears not to overstabilize TC5b, as other force fields and the use of continuum solvation models seem to do. This feature may directly stem from the GROMOS force-field parameter calibration protocol, which primarily involves reproduction of condensed phase thermodynamic quantities such as energies, densities, and solvation free energies of small compounds representative for protein fragments. By adding 6M urea to the solution, the onset of denaturation is observed in the simulation, but is too slow to observe a particular side-chain side-chain contact (Trp6-Ile4) that was experimentally observed to be characteristic for the denatured state. Interestingly, using temperature denaturation, the process is accelerated and the experimental data are reproduced.

Explicit solvent molecular dynamics (MD) simulations of three beta-heptapeptides with a central beta- HAla(alpha-F) amino acid (Figure 1) in methanol are reported. They aim at an analysis of the conformational consequences of C(alpha) carbon atom bound fluoro atoms, and the particular configuration of the central fluoro-beta-amino acid: peptide 3 with an S configuration of the C(alpha) bound fluor atom, peptide 4 with an R configuration of the C(alpha) bound fluor atom, and peptide 5 with a difluoro substitution at the C(alpha) atom of residue 4. The NMR and CD spectra of these three beta-peptides were earlier (Mathad et al. Helv. Chim. Acta 2005, 88, 266-280) interpreted to indicate a decrease in propensity of 3(14)-helical structure from peptide 4 to peptide 5 to peptide 3. This result was at odds with previous experimental data for beta-heptapeptides with a central beta-HAla(alpha-Me) amino acid which showed that the beta-heptapeptide with the S,S configuration of the central beta-HAla(alpha-Me) was the most 3(14)-helical, whereas the S,R configuration did not lead to any detected helicity. The reported MD simulations resolve this paradox. The MD trajectories of all three peptides do agree with the primary, measured data: NMR nuclear Overhauser effect (NOE) atom-atom distance bounds and (3)J-coupling constants. A conformational analysis of the MD trajectory conformations shows, however, a decrease in 3(14)-helical character from peptide 3 to peptide 5 to peptide 4, which is in line with the results for the nonfluorinated peptides. It is shown that interpretation of NMR NOE data using single-structure refinement in vacuo based on local (along the sequence) and limited atom-atom distance data as in ref 1 (Mathad et al. Helv. Chim. Acta 2005, 88, 266-280) may lead to molecular structures that are not representative for the ensemble of molecular conformations.

Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, 3 J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values varphi correspond to the same 3 J-coupling constant and high-energy barriers are separating those, restraining 3 J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to 3 J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental 3 J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom-atom distance upper bounds. Afterwards the torsional angles varphi are kept restrained by the built-up local-elevation potential energies.

Schizophyllan is a beta(1-->3)-D-glucan polysaccharide with beta(1-->6)-branched lateral glucose residues that presents a very stiff triple-helical structure under most experimental conditions. Despite the remarkable stability of this structure (which persists up to 120 degrees C in aqueous solution), schizophyllan undergoes a major change of state around 7 degrees C in water that has been hypothesized to result from an order-disorder transition in the lateral residues. This hypothesis is only supported by indirect experimental evidence and detailed knowledge (at the atomic level) concerning hydrogen-bonding networks, interactions with the solvent molecules, orientational freedom of the lateral residues, and orientational correlations among them is still lacking. In this study explicit-solvent molecular dynamics simulations of a schizophyllan fragment (complemented by simulations of its tetrasaccharide monomer) are performed at three different temperatures (273 K, 350 K, and 450 K) and with two different types of boundary conditions (finite nonperiodic or infinite periodic fragment) as an attempt to provide detailed structural and dynamical information about the triple-helical conformation in solution and the mechanism of the low-temperature transition. These simulations suggest that three important driving forces for the high stability of the triple helix are i), the limited conformational work involved in its formation; ii), the formation of a dense hydrogen-bonding network at its center; and iii), the formation of interchain hydrogen bonds between main-chain and lateral glucose residues. However, these simulations evidence a moderate and continuous variation of the simulated observables upon increasing the temperature, rather than a sharp transition between the two lowest temperatures (that could be associated with the state transition). Although water-mediated hydrogen-bonded association of neighboring lateral residues is observed, this interaction is not strong enough to promote the formation of an ordered state (correlated motions of the lateral residues), even at the lowest temperature considered.

Detailed knowledge of how networks of surface salt bridges contribute to protein thermal stability is essential not only to understand protein structure and function but also to design thermostable proteins for industrial applications. Experimental studies investigating thermodynamic stability through measurements of free energy associated with mutational alterations in proteins provide only macroscopic evidence regarding the structure of salt-bridge networks and assessment of their contribution to protein stability. Using explicit-solvent molecular dynamics simulations to provide insight on the atomic scale, we investigate here the structural stability, defined in terms of root-mean-square fluctuations, of a short polypeptide designed to fold into a stable trimeric coiled coil with a well-packed hydrophobic core and an optimal number of intra- and interhelical surface salt bridges. We find that the increase of configurational entropy of the backbone and side-chain atoms and decreased pair correlations of these with increased temperature are consistent with nearly constant atom-positional root-mean-square fluctuations, increased salt-bridge occupancies, and stronger electrostatic interactions in the coiled coil. Thus, our study of the coiled coil suggests a mechanism in which well-designed salt-bridge networks could accommodate stochastically the disorder of increased thermal motion to produce thermostability.

The lack of an explicit description of electronic polarization in nonpolarizable force fields usually results in an incomplete transferability of force-field parameter sets when applied in simulations of the system of interest in either a polar or an apolar environment. For example, the use of nonpolarizable parameter sets optimized to reproduce experimental data on properties of pure liquids of polar compounds commonly yields too low solubilities in water for the corresponding compounds. The reason is that the fixed charge distributions calibrated for the pure liquid might correspond to too low molecular dipole moments in case of hydration. In the current study, we quantitatively show that explicit inclusion of electronic polarization can improve the transferability of biomolecular force-field parameter sets. With this aim, free energies of polarization, DeltaGpola, have been calculated, with DeltaGpola corresponding to the free energy difference between identical systems described by a polarizable and a nonpolarizable model. Using a nonpolarizable model and a polarizable one (based on the charge-on-spring approach) for dimethyl ether (DME), which were both parametrized to reproduce experimental values for pure liquid properties, small values were found for DeltaGpola for the pure liquid or when a DME solute was solvated in the apolar solvent cyclohexane. For the solute hydrated in water, however, DeltaGpola was found to be of the same order of magnitude as the discrepancy between the free energy of hydration from simulation using a nonpolarizable solute model and the experimental value. Thus, introducing polarizabilities clearly improves the transferability of the parameter set. Additionally, in calculations of an anion solvated in DME, DeltaGpola for the solvent adopted relatively large values. From an estimation of the errors in the calculated free energy differences, it was furthermore shown that the calculation of DeltaGpola offers an effective and accurate method to obtain differences in solvation (or excess) free energies between systems described by polarizable and nonpolarizable models when compared to a direct calculation of solvation (or excess) free energies.

A series of explicit-solvent molecular dynamics simulations of the protein ubiquitin are reported, which investigate the effect of environmental factors (presence of methanol cosolvent in the aqueous solution, neutral or low pH value, room or elevated temperature) on the structure, stability, and dynamics of the protein. The simulations are initiated either from the native structure of the protein or from a model of a partially folded state (A-state) that is known to exist at low pH in methanol-water mixtures. The main results of the simulations are: (1) The ubiquitin native structure is remarkably stable at neutral pH in water; (2) the addition of the methanol cosolvent enhances the stability of the secondary structure but weakens tertiary interactions within the protein; (3) this influence of methanol on the protein structure is enhanced at low pH, while the effect of lowering the pH in pure water is limited; and (4) the A-state of ubiquitin can be described as a set of relatively rigid secondary structure elements (a native-like beta-sheet and native-like alpha-helix plus two nonnative alpha-helices) connected by flexible linkers.

The use of time-dependent restraints in molecular simulation in order to generate a conformational ensemble for molecules that is in accordance with measured ensemble averages for particular observable quantities is investigated. Using a model system consisting of liquid butane and the cyclic peptide antamanide the reproduction of particular average (3) J-coupling constant values in a molecular dynamics simulation is analysed. It is shown that the multiple-valuedness and the sizeable gradients of the Karplus curve relating (3) J-coupling constants measured in NMR experiments to the corresponding torsional-angle values cause severe problems when trying to restrain a (3) J-coupling constant to a value close to the extrema of the Karplus curve. The introduction of a factor oscillating with time into the restraining penalty function alleviates this problem and enhances the restrained conformational sampling.

Cyclophilins are proteins that catalyze X-proline cis-trans interconversion, where X represents any amino acid. Its mechanism of action has been investigated over the past years but still generates discussion, especially because until recently structures of the ligand in the cis and trans conformations for the same system were lacking. X-ray crystallographic structures for the complex cyclophilin A and HIV-1 capsid mutants with ligands in the cis and trans conformations suggest a mechanism where the N-terminal portion of the ligand rotates during the cis-trans isomerization. However, a few years before, a C-terminal rotating ligand was proposed to explain NMR solution data. In the present study we use molecular dynamics (MD) simulations to generate a trans structure starting from the cis structure. From simulations starting from the cis and trans structures obtained through the rotational pathways, the seeming contradiction between the two sets of experimental data could be resolved. The simulated N-terminal rotated trans structure shows good agreement with the equivalent crystal structure and, moreover, is consistent with the NMR data. These results illustrate the use of MD simulation at atomic resolution to model structural transitions and to interpret experimental data.

Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.

Single-chain and single-fragment configurational entropies of lipid tails in hydrated lipid bilayers are evaluated from molecular dynamics simulations using the quasi-harmonic approximation. The entropy distribution along individual acyl tails is obtained and compared to that of corresponding hydrocarbon chains in the liquid phase. We consider pure dipalmitoylphosphatidylcholine and mixed dioleoylphosphatidylcholine/dioleoylphosphatidylethanolamine bilayers. The systems are modeled at different levels of spatial resolution: In an atomic-level (AL) model all (heavy) atoms are explicitly simulated; in a coarse-grained (CG) model particles (beads) representing groups of covalently bound atoms are used, which map approximately four non-hydrogen atoms to one interaction site. Single-chain and single-fragment entropies and correlations between the motions of (single) acyl chains are compared. A good correspondence is found between the flexibility of the AL and CG models. The loss in configurational entropy due to the reduction in the number of degrees of freedom upon coarse-graining of the model is estimated. The CG model shows about 4 times faster convergence of the chain entropies than the more detailed AL model. Corrections to the quasi-harmonic entropy estimates were found to be small for the CG model. For the AL model, the correction due to mode anharmonicities is small, but the correction due to pairwise (supralinear) mode correlations is sizable.

Explicit-solvent molecular dynamics simulations (50 ns, 300 K) of the eight reducing glucose disaccharides (kojibiose, sophorose, nigerose, laminarabiose, maltose, cellobiose, isomaltose, and gentiobiose) have been carried out using the GROMOS 45A4 force field (including a recently reoptimized carbohydrate parameter set), to investigate and compare their conformational preferences, intramolecular hydrogen-bonding patterns, torsional dynamics, and configurational entropies. The calculated average values of the glycosidic torsional angles agree well with available experimental data, providing validation for the force field and simulation methodology employed in this study. These simulations show in particular that: 1) (1-->6)-linked disaccharides are characterized by an increased flexibility, the absence of any persistent intramolecular hydrogen bond and a significantly higher configurational entropy (compared to the other disaccharides); 2) cellobiose presents a highly persistent interresidue hydrogen bond and a significantly lower configurational entropy (compared to the other disaccharides); 3) persistent hydrogen bonds are observed for all disaccharides (except (1-->6)-linked) and typically involve a hydrogen donor in the reducing residue and an acceptor in the nonreducing one; 4) the probability distributions associated with the glycosidic dihedral angles and psi are essentially unimodal for all disaccharides, and full rotation around these angles occurs at most once or twice for (never for psi) on the 50-ns timescale; and 5) the timescales associated with torsional transitions (except around and psi) range from approximately 30 ps (rotation of hydroxyl groups) to the nanosecond range (rotation of the lactol and hydroxymethyl groups, and around the omega-glycosidic dihedral angle in (1-->6)-linked disaccharides).

A method to enhance sampling of rare events is presented. It makes use of distance or dihedral-angle restraints to overcome an energy barrier separating two metastable states or to stabilize a transition state between the two metastable states. In order not to perturb these metastable end states themselves, a prefactor is introduced into the restraining energy function, which smoothly increases the weight of this function from zero to one at the transition state or on top of the separating energy barrier and then decreases the weight again to zero at the final state. The method is combined with multi-configurational thermodynamic integration and applied to two biomolecular systems, which were difficult to treat using standard thermodynamic integration. As first example the free energy difference of a cyclic alpha-aminoxy-hexapeptide-ion complex upon changing the ion from Cl- to Na+ was calculated. A large conformational rearrangement of the peptide was necessary to accommodate this change. Stabilizing the transition state by (hidden) restraints facilitates that. As a second example, the free energy difference between the 4C1 and the 1C4 conformation of beta-D-glucopyranoside was calculated. In unrestrained simulations the change from the 4C1 into the 1C4 conformation was never observed because of the high energy barrier separating the two states. Using (hidden) restraints, the transition from the 4C1 into the 1C4 state and back could be enforced without perturbing the end states. As comparison, for the same transitions the potential of mean force as obtained by using dihedral-angle constraints is provided.

Molecular liquids can be modeled at different levels of spatial resolution. In atomic-level (AL) models, all (heavy) atoms can be explicitly simulated. In coarse-grained (CG) models, particles (beads) that represent groups of covalently bound atoms are used as elementary units. Ideally, a CG model should reproduce the thermodynamic and structural properties of the corresponding AL model after mapping to the lower-resolution scale. In the present work, two such models are investigated: (i) the classical GROMOS atomic-level model; (ii) a CG model recently proposed by Marrink et al., which maps approximately four non-hydrogen atoms to one bead [J. Phys. Chem. B 2004, 108, 750]. The study is restricted to n-alkanes whose aliphatic fragments are abundantly found in lipids of biological interest. Additionally, cis-9-octadecene is included, as a template chain of the lipid dioleoylphosphatidylcholine (DOPC). The two representations of molecules in the liquid phase are compared in terms of average molecular structures, extent of configurational space sampled, and single-molecule entropies. An approximate method is used to estimate the rotational contributions to the absolute configurational entropy. Good correspondence between the AL and CG representations is found. The loss in configurational entropy due to the reduction in degrees of freedom upon coarse-graining of the model is estimated.