Conformational Properties of the Chemotherapeutic Drug Analogue Epothilone A: How to Model a Flexible Protein Ligand Using Scarcely Available Experimental Data.

Epothilones are among the most potent chemotherapeutic drugs used for the treatment of cancer. Epothilone A (EpoA), a natural product, is a macrocyclic molecule containing 34 non-hydrogen atoms and a thiazole side chain. NMR studies of EpoA in aqueous solution, unbound as well as bound to αß-tubulin, and unbound in dimethyl sulfoxide (DMSO) solution have delivered sets of nuclear Overhauser effect (NOE) atom-atom distance bounds, but no structures based on NMR data are present in structural data banks. X-ray diffraction of crystals has provided structures of EpoA unbound and bound to αß-tubulin. Since both crystal structures derived from X-ray diffraction intensities do not completely satisfy the three available sets of NOE distance bounds for EpoA, molecular dynamics (MD) simulations have been employed to obtain conformational ensembles in aqueous and in DMSO solution that are compatible with the respective NOE data. It was found that EpoA displays a larger conformational variability in DMSO than in water and the two conformational ensembles show little overlap. Yet, they both provide conformational scaffolds that are energetically accessible at physiological temperature and pressure.

A molecular dynamics simulation investigation of the relative stability of the cyclic peptide octreotide and its deprotonated and its (CF3)-Trp substituted analogs in different solvents.

The cyclic octa-peptide octreotide and its derivatives are used as diagnostics and therapeutics in relation to particular types of cancers. This led to investigations of their conformational properties using spectroscopic, NMR and CD, methods. A CF3-substituted derivative, that was designed to stabilize the dominant octreotide conformer responsible for receptor binding, turned out to have a lower affinity. The obtained spectroscopic data were interpreted as to show an increased flexibility of the CF3 derivative compared to the unsubstituted octreotide, which could then explain the lower affinity. In this article, we use MD simulation without and with time-averaged NOE distance and time-averaged local-elevation 3J-coupling restraining representing experimental NMR data to determine the conformational properties of the different peptides in the different solvents for which experimental data are available, that are compatible with the NOE atom-atom distance bounds and the 3JHNHα-couplings as derived from the NMR measurements. The conformational ensembles show that the CF3 substitution in combination with the change of solvent from water to methanol leads to a decrease in flexibility and a shift in the populations of the dominant conformers that are compatible with the experimental data.

A comparison of pathway-independent and pathway-dependent methods in the calculation of conformational free enthalpy differences.

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-ß-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.

Flexible Boundaries for Multiresolution Solvation: An Algorithm for Spatial Multiscaling in Molecular Dynamics Simulations.

An algorithm is proposed for performing molecular dynamics (MD) simulations of a biomolecular solute represented at atomistic resolution surrounded by a surface layer of atomistic fine-grained (FG) solvent molecules within a bulk represented by coarse-grained (CG) solvent beads. The method, called flexible boundaries for multiresolution solvation (FBMS), is based on: (i) a three-region layering of the solvent around the solute, involving an FG layer surrounded by a mixed FG-CG buffer layer, itself surrounded by a bulk CG region; (ii) a definition of the layer boundary that relies on an effective distance to the solute surface and is thus adapted to the shape of the solute as well as adjusts to its conformational changes. The effective surface distance is defined by inverse-nth power averaging over the distances to all non-hydrogen solute atoms, and the layering is enforced by means of half-harmonic distance restraints, attractive for the FG molecules and repulsive for the CG beads. A restraint-free region at intermediate distances enables the formation of the buffer layer, where the FG and CG solvents can mix freely. The algorithm is tested and validated using the GROMOS force field and the associated FG (SPC) and CG (polarizable CGW) water models. The test systems include pure-water systems, where one FG molecule plays the role of a solute, and a deca-alanine peptide with two widely different solute shapes considered, α-helical and fully extended. In particular, as the peptide unfolds, the number of FG molecules required to fill its close-range solvation layer increases, with the additional molecules being provided by the buffer layer. Further validation involves simulations of four proteins in multiresolution FG/CG mixtures. The resulting structural, energetic, and solvation properties are found to be similar to those observed in corresponding pure FG simulations.

Challenge of representing entropy at different levels of resolution in molecular simulation.

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 ß-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.

Time-averaged order parameter restraints in molecular dynamics simulations.

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.

On the use of one-step perturbation to investigate the dependence of NOE-derived atom-atom distance bound violations of peptides upon a variation of force-field parameters.

The method of one-step perturbation can be used to predict from a single molecular dynamics simulation the values of observable quantities as functions of variations in the parameters of the Hamiltonian or biomolecular force field used in the simulation. The method is used to predict violations of nuclear overhauser effect (NOE) distance bounds measured in nuclear magnetic resonance (NMR) experiments by atom-atom distances of the NOE atom pairs when varying force-field parameters. Predictions of NOE distance bound violations between different versions of the GROMOS force field for a hexa-ß-peptide in solution show that the technique works for rather large force-field parameter changes as well as for very different NOE bound violation patterns. The effect of changing individual force-field parameters on the NOE distance bound violations of the ß-peptide and an α-peptide was investigated too. One-step perturbation, which in this case is equivalent to reweighting configurations, constitutes an efficient technique to predict many values of different quantities from a single conformational ensemble for a particular system, which makes it a powerful force-field development technique that easily reduces the number of required separate simulations by an order of magnitude.

Enhanced conformational sampling using enveloping distribution sampling.

To lessen the problem of insufficient conformational sampling in biomolecular simulations is still a major challenge in computational biochemistry. In this article, an application of the method of enveloping distribution sampling (EDS) is proposed that addresses this challenge and its sampling efficiency is demonstrated in simulations of a hexa-ß-peptide whose conformational equilibrium encompasses two different helical folds, i.e., a right-handed 2.7(10∕12)-helix and a left-handed 3(14)-helix, separated by a high energy barrier. Standard MD simulations of this peptide using the GROMOS 53A6 force field did not reach convergence of the free enthalpy difference between the two helices even after 500 ns of simulation time. The use of soft-core non-bonded interactions in the centre of the peptide did enhance the number of transitions between the helices, but at the same time led to neglect of relevant helical configurations. In the simulations of a two-state EDS reference Hamiltonian that envelops both the physical peptide and the soft-core peptide, sampling of the conformational space of the physical peptide ensures that physically relevant conformations can be visited, and sampling of the conformational space of the soft-core peptide helps to enhance the transitions between the two helices. The EDS simulations sampled many more transitions between the two helices and showed much faster convergence of the relative free enthalpy of the two helices compared with the standard MD simulations with only a slightly larger computational effort to determine optimized EDS parameters. Combined with various methods to smoothen the potential energy surface, the proposed EDS application will be a powerful technique to enhance the sampling efficiency in biomolecular simulations.

Refinement of the application of the GROMOS 54A7 force field to ß-peptides.

In this study, a hexa-ß-peptide whose conformational equilibrium encompasses two different helical folds, a right-handed 2.7(10/12)-helix and a left-handed 3(14)-helix, is simulated using different GROMOS force-field parameter sets. When applying the recently developed GROMOS 54A7 force field, a significant destabilization effect on the 2.7(10/12)-helix of the peptide is observed, and the agreement with the experimental NOE distance bounds is much worse compared with the ones using previous versions of the GROMOS force field. This led us to investigate the free enthalpy difference between the two helices as a function of a variation of different subsets of force-field parameters. Both long time molecular dynamics simulations and one-step perturbation predictions suggest that the disagreement with the experimental NMR data when using the 54A7 force field is caused by the use for ß-peptides of the new backbone φ-/ψ-torsional-angle energy terms introduced in this force field which were based on conformational fitting of backbone φ/ψ angles for a large set of proteins. This means that these parameters of backbone φ- and ψ-torsional-angle terms should not be applied to non-α-peptides such as ß-peptides. This modified assignment of torsional-angle energy terms and parameters is denoted as 54A7_ß. It corrects the wrong description of the conformational ensemble of the hexa-ß-peptide obtained using the previous assignment and yields as good agreement with NMR data for other ß-peptides that adopt a single helical or a hairpin fold.

Influence of variation of a side chain on the folding equilibrium of a ß-peptide: limitations of one-step perturbation.

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94, 597), the one-step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔGF,U of six hepta-ß-peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔGF,U values obtained using one-step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft-core atoms in the side chain of the fifth residue showed an overall accuracy of about kB T for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference-state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ1 and χ2 torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔGF,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one-step perturbation technique to compute free enthalpies of folding are discussed.

Combination of Enveloping Distribution Sampling (EDS) of a Soft-Core Reference-State Hamiltonian with One-Step Perturbation to Predict the Effect of Side Chain Substitution on the Relative Stability of Right- and Left-Helical Folds of ß-Peptides.

Folding free enthalpies of many not too different polypeptides can be efficiently and accurately predicted with the one-step perturbation (OSP) method using only one or a few molecular dynamics (MD) simulations. In this article, we introduce a combination of enveloping distribution sampling (EDS) and the OSP method (EDS-OSP) and apply it to predict the free enthalpy differences between a right-handed 2.710/12-helix and a left-handed 314-helix for 16 ß-peptides with slightly different side-chain substitution patterns. An EDS simulation of a designed soft-core reference-state peptide was carried out in which both helices were sampled. Then, the soft-core atoms were perturbed into physical atoms. Thus, free enthalpy differences between the two helices for the 16 ß-peptides can be predicted from only one simulation. The results predicted by EDS-OSP and a previous OSP study are very similar, i.e., the deviations between the results of the 16 peptides are mostly within the order of kBT, and the average absolute deviation is 1.2 kJ mol(-1). Together with the EDS parameter update simulation, about 128 ns of MD simulations needed to be carried out using the EDS-OSP method, while 700 ns of MD simulations were required in the previous OSP study where two separate reference-state simulations and an additional long time MD simulation of one of the 16 ß-peptides were carried out. Thus, the computational effort was significantly reduced, i.e., by more than a factor of 5, using the EDS-OSP method. Hence, we consider this method an efficient tool to predict conformational free enthalpy differences from MD simulations.

Influence of 63Ser phosphorylation and dephosphorylation on the structure of the stathmin helical nucleation sequence: a molecular dynamics study.

Phosphorylation is an important mechanism regulating protein-protein interactions involving intrinsically disordered protein regions. Stathmin, an archetypical example of an intrinsically disordered protein, is a key regulator of microtubule dynamics in which phosphorylation of 63Ser within the helical nucleation sequence strongly down-regulates the tubulin binding and microtubule destabilizing activities of the protein. Experimental studies on a peptide encompassing the 19-residue helical nucleation sequence of stathmin (residues 55-73) indicate that phosphorylation of 63Ser destabilizes the peptide's secondary structure by disrupting the salt bridges supporting its helical conformation. In order to investigate this hypothesis at atomic resolution, we performed molecular dynamics simulations of nonphosphorylated and phosphorylated stathmin-[55-73] at room temperature and pressure, neutral pH, and explicit solvation using the recently released GROMOS force field 54A7. In the simulations of nonphosphorylated stathmin-[55-73] emerged salt bridges associated with helical configurations. In the simulations of 63Ser phosphorylated stathmin-[55-73] these configurations dispersed and were replaced by a proliferation of salt bridges yielding disordered configurations. The transformation of the salt bridges was accompanied by emergence of numerous interactions between main and side chains, involving notably the oxygen atoms of the phosphorylated 63Ser. The loss of helical structure induced by phosphorylation is reversible, however, as a final simulation showed. The results extend the hypothesis of salt bridge derangement suggested by experimental observations of the stathmin nucleation sequence, providing new insights into regulation of intrinsically disordered protein systems mediated by phosphorylation.

Using enveloping distribution sampling to compute the free enthalpy difference between right- and left-handed helices of a ß-peptide in solution.

Recently, the method of enveloping distribution sampling (EDS) to efficiently obtain free enthalpy differences between different molecular systems from a single simulation has been generalized to compute free enthalpy differences between different conformations of a system [Z. X. Lin, H. Y. Liu, S. Riniker, and W. F. van Gunsteren, J. Chem. Theory Comput. 7, 3884 (2011)]. However, the efficiency of EDS in this case is hampered if the parts of the conformational space relevant to the two end states or conformations are far apart and the conformational diffusion from one state to the other is slow. This leads to slow convergence of the EDS parameter values and free enthalpy differences. In the present work, we apply the EDS methodology to a challenging case, i.e., to calculate the free enthalpy difference between a right-handed 2.7(10∕12)-helix and a left-handed 3(14)-helix of a hexa-ß-peptide in solution from a single simulation. No transition between the two helices was detected in a standard EDS parameter update simulation, thus enhanced sampling techniques had to be applied, which included adiabatic decoupling (AD) of solute and solvent motions in combination with increasing the solute temperature, and lowering the shear viscosity of the solvent. AD was found to be unsuitable to enhance the sampling of the solute conformations in the EDS parameter update simulations. Lowering the solvent shear viscosity turned out to be useful during EDS parameter update simulations, i.e., it did speed up the conformational diffusion of the solute, more transitions between the two helices were observed. This came at the cost of more CPU time spent due to the shorter time step needed for simulations with the lower solvent shear viscosity. Using an improved EDS parameter update scheme, parameter convergence was five-fold enhanced. The resulting free enthalpy difference between the two helices calculated from EDS agrees well with the result obtained through direct counting from a long MD simulation, while the EDS technique significantly enhances the sampling of both helices over non-helical conformations.

Exploring the properties of small molecule protein binding via molecular simulations: the TRSH-p53 core domain complex.

Molecular dynamics simulations have been performed to investigate the binding of tris(hydroxymethyl)-aminomethane to the surface of the core domain of the mouse cellular tumor antigen p53 employing the GROMOS and 53A6 force field parameter sets. A close investigation of the crystal structure reported by Ho et al. revealed that the protonated form is bound to the protein, i.e. a tris(hydroxymethyl)-methylammonium ion (TRSH). Molecular Dynamics (MD) simulations indicate that the p53 protein gains stability upon binding the ligand. In addition to MD simulations of the p53 protein with and without the TRSH compound, thermodynamic integration was utilised to estimate the free enthalpy of binding of the TRSH-p53 complex, which was estimated to be -49 and -54 kJ mol(-1) utilising the and 53A6 force fields, respectively.

Reoptimized interaction parameters for the peptide-backbone model compound N-methylacetamide in the GROMOS force field: influence on the folding properties of two beta-peptides in methanol.

Considering N-methylacetamide (NMA) as a model compound, new interaction parameters are developed for the amide function in the GROMOS force field that are compatible with the recently derived 53A6(OXY) parameter set for oxygen-containing chemical functions. The resulting set, referred to as 53A6(OXY+A) , represents an improvement over earlier GROMOS force-field versions in the context of the pure-liquid properties of NMA, including the density, heat of vaporization, dielectric permittivity, self-diffusion constant and viscosity, as well as in terms of the Gibbs hydration free energy of this molecule. Assuming that NMA represents an adequate model compound for the backbone of peptides, 53A6(OXY+A) may be expected to also provide an improved description of polypeptide chains. As an initial test, simulations are reported for two ß-peptides characterized by very different folding properties in methanol. For these systems, earlier force-field versions provided good agreement with experimental NMR data, and the test shows that the improved description achieved in the context of NMA is not accompanied by any deterioration in the representation of the conformational properties of these peptides.

Calculation of relative free energies for ligand-protein binding, solvation, and conformational transitions using the GROMOS software.

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.

Using one-step perturbation to predict the folding equilibrium of differently stereochemically substituted ß-peptides.

The one-step perturbation technique is used to predict the folding equilibria for 16 peptides with different stereochemical side-chain substitutions through one or two long-time simulations, one of an unphysical reference state and another of one of the 16 peptides for which many folding events can be sampled. The accuracy of the one-step perturbation results was investigated by comparing to results available from long-time MD simulations of particular peptides. Their folding free energies were reproduced within statistical accuracy. The one-step perturbation results show that an axial substitution at either the C(α) or the C(ß) position destabilizes the 3(14)-helical conformation of the hepta-ß-peptide, which is consistent with data inferred from experimental CD spectra. The methodology reduces the number of required separate simulations by an order of magnitude.

A comparison of the different helices adopted by α- and ß-peptides suggests different reasons for their stability.

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 ß-peptides. Using molecular dynamics simulations, the properties of α-helical α-peptides and 3(14)-helical ß-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.

Using one-step perturbation to predict the effect of changing force-field parameters on the simulated folding equilibrium of a beta-peptide in solution.

Computer simulation using molecular dynamics is increasingly used to simulate the folding equilibria of peptides and small proteins. Yet, the quality of the obtained results depends largely on the quality of the force field used. This comprises the solute as well as the solvent model and their energetic and entropic compatibility. It is, however, computational very expensive to perform test simulations for each combination of force-field parameters. Here, we use the one-step perturbation technique to predict the change of the free enthalpy of folding of a beta-peptide in methanol solution due to changing a variety of force-field parameters. The results show that changing the solute backbone partial charges affects the folding equilibrium, whereas this is relatively insensitive to changes in the force constants of the torsional energy terms of the force field. Extending the cut-off distance for nonbonded interactions beyond 1.4 nm does not affect the folding equilibrium. The same result is found for a change of the reaction-field permittivity for methanol from 17.7 to 30. The results are not sensitive to the criterion, e.g., atom-positional RMSD or number of hydrogen bonds, that is used to distinguish folded and unfolded conformations. Control simulations with perturbed Hamiltonians followed by backward one-step perturbation indicated that quite large perturbations still yield reliable results. Yet, perturbing all solvent molecules showed where the limitations of the one-step perturbation technique are met. The evaluated methodology constitutes an efficient tool in force-field development for molecular simulation by reducing the number of required separate simulations by orders of magnitude.

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1.

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.