New theoretical methodology for elucidating the solution structure of peptides from NMR data. II. Free energy of dominant microstates of Leu-enkephalin and population-weighted average nuclear Overhauser effects intensities

Exploring Conformational Preferences of Leu-enkephalin Using the Conformational Search and Double-Hybrid DFT Energy Calculations

The conformational preferences of Leu-enkephalin (Leu-Enk) were explored by the conformational search and density functional theory (DFT) calculations. By a combination of low-energy conformers of each residue, the initial structures of the neutral Leu-Enk were generated and optimized using the ECEPP3 force field in the gas phase. These structures were reoptimized at the HF/3-21G(d) and M06-2X levels of theory with 6-31G(d) and 6-31+G(d) basis functions. We finally located the 139 structures with the relative energy <10 kcal mol-1 in the gas phase, from which the structures of the corresponding zwitterionic Leu-Enk were generated and reoptimized at the M06-2X/6-31+G(d) level of theory using the implicit solvation model based on density (SMD) in water. The conformational preferences of Leu-Enk were analyzed using Gibbs free energies corrected by single-point energies calculated at the double-hybrid DSD-PBEP86-D3BJ/def2-TZVP level of theory in the gas phase and in water. The neutral Leu-Enk dominantly adopted a folded structure in the gas phase stabilized by three H-bonds with a βII'-bend-like motif at the Gly3-Phe4 sequence and a close contact between the side chains of Phe4 and Leu5. The zwitterionic Leu-Enk exhibited a folded structure in water stabilized by three H-bonds with double β-bends such as a βII' bend at the Gly2-Gly3 sequence and a βI bend at the Gly3-Phe4 sequence. The calculated ensemble-averaged distance between CGly2 α and CLeu5 α of the zwitterionic Leu-Enk in water is consistent with the value estimated from the simulated annealing using the distance constraints derived from nuclear Overhauser effect spectroscopy (NOESY) spectra in water. Interestingly, the preferred conformations of the neutral and zwitterionic Leu-Enk are new folded structures not predicted by earlier computational studies. According to the refined model of the zwitterionic Leu-Enk bound to δ-opioid receptor (δOR), there were favorable interactions of the terminal charged groups of Leu-Enk with the side chains of charged residues of δOR as well as a favorable CAryl···H interaction of the Phe4 residue of Leu-Enk with Trp284 of δOR. Hence, these favorable interactions would induce the folded structure of the zwitterionic Leu-Enk with double β-bends isolated in water into the "bioactive conformation" like an extended structure when binding to δOR.

The conformation of enkephalin bound to its receptor: an "elusive goal" becoming reality

The availability of solid state structures of opioid receptors has prompted us to reconsider a crucial question concerning bioactive peptides: can their conformation be studied without any knowledge of the structure of their receptors? The possibility of giving a meaningful answer to this query rests ultimately on the ease of dealing with the flexibility of bioactive peptides, and amongst them one of the most flexible bioactive peptides, enkephalin. All solution studies of enkephalin hint at an inextricable mixture of quasi isoenergetic conformers. In this study we refer to the only NMR work that yielded inter-residue NOEs, performed at very low temperature. In the present work, we have used the simplest possible docking methods to check the consistency of the main conformers of enkephalin with the steric requirements of the active site of the receptor, as provided by the crystal structure of its complex with naltrindole, a rigid antagonist. We show that the conformers found in the equilibrium mixture at low temperature are indeed compatible with a good fit to the receptor active site. The possible uncertainties linked to the different behavior of agonists and antagonists do not diminish the relevance of the finding.

Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics

The commonly used simulation techniques, Metropolis Monte Carlo (MC) and molecular dynamics (MD) are of a dynamical type which enables one to sample system configurations i correctly with the Boltzmann probability, P(i)(B), while the value of P(i)(B) is not provided directly; therefore, it is difficult to obtain the absolute entropy, S approximately -ln P(i)(B), and the Helmholtz free energy, F. With a different simulation approach developed in polymer physics, a chain is grown step-by-step with transition probabilities (TPs), and thus their product is the value of the construction probability; therefore, the entropy is known. Because all exact simulation methods are equivalent, i.e. they lead to the same averages and fluctuations of physical properties, one can treat an MC or MD sample as if its members have rather been generated step-by-step. Thus, each configuration i of the sample can be reconstructed (from nothing) by calculating the TPs with which it could have been constructed. This idea applies also to bulk systems such as fluids or magnets. This approach has led earlier to the "local states" (LS) and the "hypothetical scanning" (HS) methods, which are approximate in nature. A recent development is the hypothetical scanning Monte Carlo (HSMC) (or molecular dynamics, HSMD) method which is based on stochastic TPs where all interactions are taken into account. In this respect, HSMC(D) can be viewed as exact and the only approximation involved is due to insufficient MC(MD) sampling for calculating the TPs. The validity of HSMC has been established by applying it first to liquid argon, TIP3P water, self-avoiding walks (SAW), and polyglycine models, where the results for F were found to agree with those obtained by other methods. Subsequently, HSMD was applied to mobile loops of the enzymes porcine pancreatic alpha-amylase and acetylcholinesterase in explicit water, where the difference in F between the bound and free states of the loop was calculated. Currently, HSMD is being extended for calculating the absolute and relative free energies of ligand-enzyme binding. We describe the whole approach and discuss future directions.

Redox-Active Tyrosine Residues in Pentapeptides

Tyrosyl radicals are important in long-range electron transfer in several enzymes, but the protein environmental factors that control midpoint potential and electron-transfer rate are not well understood. To develop a more detailed understanding of the effect of protein sequence on their photophysical properties, we have studied the spectroscopic properties of tyrosyl radicals at 85 K. Tyrosyl radical was generated by UV-photolysis of pentapeptides in polycrystalline samples. The sequence of the pentapeptides was chosen to mimic peptide sequences found in redox-active tyrosine containing enzymes, ribonucleotide reductase and photosystem II. From EPR studies, we report that the EPR line shape of the tyrosyl radical depends on peptide sequence. We also present the first evidence for a component of the tyrosyl radical EPR signal, which decays on the seconds time scale at 85 K. We suggest that this transient results from a spontaneous, small conformational rearrangement in the radical. From FT-IR studies, we show that amide I vibrational bands (1680-1620 cm(-1)) and peptide bond skeletal vibrations (1230-1090 cm(-1)) are observed in the photolysis spectra of tyrosine-containing pentapeptides. From these data, we conclude that oxidation of the tyrosine aromatic ring perturbs the electronic structure of the peptide bond in tyrosine-containing oligopeptides. We also report sequence-dependent alterations in these bands. These results support the previous suggestion (J. Am. Chem. Soc. 2002, 124, 5496) that spin delocalization can occur from the tyrosine aromatic ring into the peptide bond. We hypothesize that these sequence-dependent effects are mediated either by electrostatics or by changes in conformer preference in the peptides. Our findings suggest that primary structure influences the functional properties of redox-active tyrosines in enzymes.

Conformational search of peptides and proteins: Monte Carlo minimization with an adaptive bias method applied to the heptapeptide deltorphin

The energy function of a protein consists of a tremendous number of minima. Locating the global energy minimum (GEM) structure, which corresponds approximately to the native structure, is a severe problem in global optimization. Recently we have proposed a conformational search technique based on the Monte Carlo minimization (MCM) method of Li and Scheraga, where trial dihedral angles are not selected at random within the range [-180 degrees,180 degrees ] (as with MCM) but with biased probabilities depending on the increased structure-energy correlations as the GEM is approached during the search. This method, called the Monte Carlo minimization with an adaptive bias (MCMAB), was applied initially to the pentapeptide Leu-enkephalin. Here we study its properties further by applying it to the larger peptide with bulky side chains, deltorphin (H-Tyr-D-Met-Phe-His-Leu-Met-Asp-NH(2)). We find that on average the number of energy minimizations required by MCMAB to locate the GEM for the first time is smaller by a factor of approximately three than the number required by MCM-in accord with results obtained for Leu-enkephalin.

Cross-checking of nanoelectrospray ionization mass spectrometry and computer simulation for the evaluation of the interaction strength of non-covalently bound enkephalins in solution

Nanoelectrospray ionization mass spectrometry (nanoESI-MS) and computer simulation were applied to the characterization of non-covalent interactions of [Leu5]-enkephalin (LE) and its optical isomers, [D-Tyr1, Leu5]-enkephalin (Y-LE), [D-Phe4, Leu5]-enkephalin (F-LE) and [D-Tyr1, D-Phe4, Leu5]-enkephalin (YF-LE). The dimer formation tendencies of the optical isomers of LE were evaluated by nanoESI-MS using quadruply deuterated LE (H2N-Tyr-(2,2-d2)Gly-(2,2-d2)Gly-Phe-Leu-COOH, d4-LE) as an internal standard. The relative interaction strengths of the optical isomers of LE were estimated to be Y-LE < F-LE < LE < YF-LE. Geometry optimization calculations were performed for interactions in vacuo and in water using a semi-empirical SCF method (PM3). The initial coordinate of the dimer structure of LE was taken from that obtained from single-crystalline x-ray diffraction analysis. Estimates of the interaction strengths of the dimer complexes were based on the heats of formation of a dimer complex (Hd) and the corresponding monomers (Hm) using the equation DeltaH = Hd - 2Hm. The values of DeltaH obtained from the calculations for interactions in water decreased in the order Y-LE > F-LE > LE > YF-LE. Since the smaller values of DeltaH correspond to stronger interactions between peptides, the results from computer simulations were qualitatively consistent with those obtained from the nanoESI experiments. The possibility of cross-checking these independent techniques was demonstrated using medium-sized molecules of biological importance. The agreement of the results from the two techniques suggested that nanoESI experiments, at least qualitatively, reflected the relative interaction strengths of non-covalently bound enkephalins in aqueous solution.

On the transferability of atomic solvation parameters: Ab initio structural prediction of cyclic heptapeptides in DMSO

A statistical mechanics methodology for predicting the solution structures and populations of peptides developed recently is based on a novel method for optimizing implicit solvation models, which was applied initially to a cyclic hexapeptide in DMSO (C. Baysal and H. Meirovitch, Journal of American Chemical Society, 1998, vol. 120, pp. 800-812). Thus, the molecule has been described by the simplified energy function E(tot) = E(GRO) + summation operator(k) sigma(k)A(k), where E(GRO) is the GROMOS force-field energy, sigma(k) and A(k) are the atomic solvation parameter (ASP) and the solvent accessible surface area of atom k, respectively. In a more recent study, these ASPs have been found to be transferable to the cyclic pentapeptide cyclo(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) in DMSO (C. Baysal and H. Meirovitch, Biopolymers, 2000, vol. 53, pp. 423-433). In the present paper, our methodology is applied to the cyclic heptapeptides axinastatin 2 [cyclo(Asn(1)-Pro(2)-Phe(3)-Val(4)-Leu(5)-Pro(6)-Val(7))] and axinastatin 3 [cyclo(Asn(1)-Pro(2)-Phe(3)-Ile(4)-Leu(5)-Pro(6)-Val(7))], in DMSO, which were studied by nmr by Mechnich et al. (Helvetica Chimica Acta, 1997, vol. 80, pp. 1338-1354). The calculations for axinastatin 2 show that special ASPs should be optimized for the partially charged side-chain atoms of Asn while the rest of the atoms take their values derived in our previous work; this suggests that similar optimization might be needed for other side chains as well. The solution structures of these peptides are obtained ab initio (i.e., without using experimental restraints) by an extensive conformational search based on E(GRO) alone and E(*)(tot), which consists of the new set of ASPs. For E(*)(tot), the theoretical values of proton-proton distances, (3)J coupling constants, and other properties are found to agree very well with the nmr results, and they are always better than those based on E(GRO).

Ab initio prediction of the solution structures and populations of a cyclic pentapeptide in DMSO based on an implicit solvation model

Using a recently developed statistical mechanics methodology, the solution structures and populations of the cyclic pentapeptide cyclo(D-Pro(1)-Ala(2)-Ala(3)-Ala(4)-Ala(5)) in DMSO are obtained ab initio, i.e., without using experimental restraints. An important ingredient of this methodology is a novel optimization of implicit solvation parameters, which in our previous publication [Baysal, C.; Meirovitch, H. J Am Chem Soc 1998, 120, 800-812] has been applied to a cyclic hexapeptide in DMSO. The molecule has been described by the simplified energy function E(tot) = E(GRO) + summation operator(k) sigma(k)A(k), where E(GRO) is the GROMOS force-field energy, sigma(k) and A(k) are the atomic solvation parameter (ASP) and the solvent accessible surface area of atom k. This methodology, which relies on an extensive conformational search, Monte Carlo simulations, and free energy calculations, is applied here with E(tot) based on the ASPs derived in our previous work, and for comparison also with E(GRO) alone. For both models, entropy effects are found to be significant. For E(tot), the theoretical values of proton-proton distances and (3)J coupling constants agree very well with the NMR results [Mierke, D. F.; Kurz, M.; Kessler, H. J Am Chem Soc 1994, 116, 1042-1049], while the results for E(GRO) are significantly worse. This suggests that our ASPs might be transferrable to other cyclic peptides in DMSO as well, making our methodology a reliable tool for an ab initio structure prediction; obviously, if necessary, parts of this methodology can also be incorporated in a best-fit analysis where experimental restraints are used.

Free energy based populations of interconverting microstates of a cyclic peptide lead to the experimental NMR data

Analysis of nuclear Overhauser enhancement (NOE) intensities data of interconverting microstates of a peptide is a difficult problem in nmr. A new statistical mechanics methodology has been proposed recently, consisting of several steps: (1) potential energy wells on the energy surface of the molecule are identified (the corresponding regions are called wide microstates); (2) each wide microstate is then spanned by a Monte Carlo (MC) or molecular dynamics simulation starting from a representative structure, and the corresponding relative populations are obtained from the free energy calculated with the local states method; and (3) the overall NOEs and 3J coupling constants are obtained as averages over the corresponding contributions of the samples, weighted by the populations. Extending this methodology to cyclic peptides, we are treating here the hexapeptide cyclo(D-Pro1-Phe2-Ala3-Ser4-Phe5-Phe6) in DMSO, which was studied by Kessler et al. using nmr (Journal of the American Chemical Society, 1992, Vol. 114, pp. 4805-4818). They found that at least two structures are required to explain their NOE data, a conclusion also corroborated by our analysis (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800-812) and led to a novel derivation of atomic solvation parameters (ASPs) for DMSO. Thus, the overall interactions within the peptide-solvent system are described approximately by Etot = EGRO + summation operator sigmaiAi, where EGRO is the energy of the GROMOS force field, Ai is the solvent-accessible surface area of atom i, and sigmai is the ASP. In the present paper the validity of these ASPs within the framework of the entire methodology is verified. This requires taking into account 23 microstates. A very good agreement is obtained between experimental and calculated NOEs and 3J coupling constants. The free energy based populations lead to the best results, which means that entropic effects should not be ignored. We have also studied the behavior of the internal angular fluctuations of the proton-proton vectors and discovered that they have a negligible effect on the calculated NOEs; this is due to the relatively concentrated wide microstates spanned by the MC simulations. The applicability of our ASPs to other cyclic peptides in DMSO is being studied in another work and preliminary results are discussed.