Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.     

Conformational free energy of armadillo metmyoglobin

The conformational free energy of armadillo metmyoglobin was examined over a pH range of 4.4-8.0 and a guanidinium chloride concentration of 0-2.3 M. For isothermal unfolding at 25 degrees essentially the same value was obtained for the conformational free energy from all the data: 27 +/- 2 kJ/mol. These data suggest that the armadillo has the least stable metmyoglobin of any mammal thus far examined. The cooperativity of the unfolding with respect to denaturant is considerably less than for other mammalian myoglobins. On unfolding only three to four side chains with a pKA of 6 in the unfolded protein are protonated instead of the six found for horse and sperm whale myoglobins.     

Conformational energy analysis of melanostatin

Conformational energy calculations were carried out on the hypothalamic hormone melanostatin, a tripeptide with the primary structure H-L-Pro-L-Leu-Gly-NH2. The calculated lowest energy conformation was a type II beta bend, very similar to that reported in an X-ray crystal study. This conformation, however, was only one of 109 low-energy structures (less than or equal to 3 kcal/mol above the global minimum), indicating that the molecule in solution exists as an ensemble of conformations and is very flexible, in agreement with relaxation data from n.m.r. measurements. A statistical analysis yielded an average end-to-end distance of 6.8 A and a bend probability of 0.62, suggesting that, in nonpolar solvents, bend structures predominate within the statistical ensemble. The statistical analysis, however, also yielded a probability of only 0.11 for the occurrence of a 4 leads to 1 hydrogen bond. Hence, the calculations show that, although bend conformations predominate, bends would be difficult to observe in solution if the experiments were designed only to detect 4 leads to 1 hydrogen bonds.     

Inclusion of solvation free energy with molecular mechanics energy: alanyl dipeptide as a test case.

A combined force field of molecular mechanics and solvation free energy is tested by carrying out energy minimization and molecular dynamics on several conformations of the alanyl dipeptide. Our results are qualitatively consistent with previous experimental and computational studies, in that the addition of solvation energy stabilizes the C5 conformation of the alanyl dipeptide relative to the C7.     

Conformational energy analysis of retro-all-Dmethionine enkephalin

Empirical conformational energy calculations have been carried out on the molecule retro-all-D -methionine enkephalin. Low-energy conformers were found by energy minimization and conformational search procedures. The lowest energy conformers wee found toi have some stereochemical relationship to the calculated normal met-enkephalin conformers, but they were not retro-all-D -equivalent to the Met-enkephalin structures. The retro-all-D -equivalent conformations were ～10 kcal/mol higher energy than the low-energy conformers found here. A structural comparison between the retro-all-D -conformers and the met-enkephalin conformers shows hat one cannot rely solely on topochemical analysis to predict biological activity for linear retro-all-D -peptides.     

Conformational energy analysis of the pentapeptide Ac-Arg-Asn-Cys-Tyr-Asn-NMA from alpha 1-purothionin

Conformational energy analyses were carried out on the pentapeptide RNCYN (Ac-Arg-Asn-Cys-Tyr-Asn-NMA) and on related peptides. RNCYN is a highly conserved amino acid sequence in thionins and viscotoxins. The conformation of the pentapeptide was calculated to be an amphipathic alpha-helix, with the tyrosine and cysteine on the nonpolar side of the helix and the arginine and both asparagines on the polar side. Our results are inconsistent with the conformation determined using the Chou-Fasman prediction method, but are consistent with the conformation determined experimentally (using n.m.r.) for this pentapeptide sequence in alpha 1-purothionin.     

Conformational free energy of alkylsilanes by nonequilibrium-pulling Monte Carlo simulation

The stationary phase in supercritical fluid chromatography includes alkylsilanes, bearing typically 18-carbon alkane chains, bonded to silica. The silanes are in contact with supercritical carbon dioxide. Interaction of the stationary phase with analytes from the mobile phase depends on conformation of the silanes, whether they form a collapsed layer between the silica and the carbon dioxide or are extended into the carbon dioxide. Although equilibrium conformation of alkylsilanes can be determined by equilibrium Monte Carlo (MC) simulation, that is hampered by slow relaxation of the chains. An alternative is to pull alkylsilanes from collapsed to extended conformations, then calculate free energy change from the Jarzynski equality. This work compares conformational results from equilibrium MC simulation to free energies from nonequilibrium pulling simulations. Because both equilibrium and nonequilibrium simulations are faster for shorter silanes, this work also compares results from 8-carbon and 18-carbon silanes. Free energies from nonequilibrium pulling predict that alkylsilanes tend to bend over and form a layer between silica and carbon dioxide. Results from equilibrium simulations are qualitatively consistent with results from nonequilibrium pulling. Longer-chain silanes have greater tendency to extend slightly into the carbon dioxide.     

Conformational analysis of biologically active truncated linear analogs of endothelin-1 using NMR and molecular modeling.

Some linear truncated analogs of endothelin-1 display potent agonistic activity at the ET(B) receptor, especially when the side chain of Trp21 is N-formylated. Then, the three-dimensional arrangements of six structurally reduced linear analogs, three formylated and three nonformylated, have been investigated by high resolution NMR spectroscopy and molecular modeling, in order to pinpoint the conformational features related to the biological activity. Two-dimensional double-quantum-filtered correlation spectroscopy (DQFCOSY), total correlation spectroscopy (TOCSY) and nuclear Overhauser enhancement spectroscopy (NOESY) were recorded and analyzed for each molecule. Interspatial distance constraints were derived from the intensity of the NOESY connectivities. The formation of hydrogen bonding was monitored from the temperature dependence of the NH chemical shifts. Molecular models calculated by means of distance geometry, simulated annealing and energy minimization, using the NMR constraints, strongly suggested a global elongated structure for the formylated analogs exhibiting biological activity, and a folded arrangement for the unformylated derivatives. Homology comparisons allowed the identification of a beta-turn-like folding of the C-terminal segment Asp18-Trp21 as a probable key-factor for activity.     

Conformational analysis of phosphatides: Mapping and minimization of the intramolecular energy

Empirical intramolecular energy calculations were carried out on molecular fragments related to phosphatides in order to find the preferred conformations. The energy was mapped as a function of several pairs of torsional angles in progressively larger molecular fragments, with energy minimization being carried out at each map point with respect to other significant variables. The energy mapping results were used as starting points for energy minimization on diheptanoyl L-α-phosphatidic acid-C, which consisted of the named molecule plus a carbon atom attached to one of the phosphate oxygens. It was found that there are 6 pairs of values for 2 of the torsional angles at the 3-way branch point in the glyceryl group which give sterically acceptable conformations; only 4 of these are compatible with lipid bilayer structure in that they can give a parallel arrangement of the acyl chains. The several acceptable conformations of the phosphate and acyl ester groups within each of these conformational classes are enumerated. The results obtained may be used as a guide for further experimental and theoretical work on phosphatide structures.     

Position-resolved free energy of solvation for amino acids in lipid membranes from molecular dynamics simulations

Studies of insertion and interactions of amino acids in lipid membranes are pivotal to our understanding of membrane protein structure and function. Calculating the insertion cost as a function of transmembrane helix sequence is thus an important step towards improved membrane protein prediction and eventually drug design. Here, we present position-dependent free energies of solvation for all amino acid analogs along the membrane normal. The profiles cover the entire region from bulk water to hydrophobic core, and were produced from all-atom molecular dynamics simulations. Experimental differences corresponding to mutations and costs for entire segments match experimental data well, and in addition the profiles provide the spatial resolution currently not available from experiments. Polar side-chains largely maintain their hydration and assume quite ordered conformations, which indicates the solvation cost is mainly entropic. The cost of solvating charged side-chains is not only significantly lower than for implicit solvation models, but also close to experiments, meaning these could well maintain their protonation states inside the membrane. The single notable exception to the experimental agreement is proline, which is quite expensive to introduce in vivo despite its hydrophobicity--a difference possibly explained by kinks making it harder to insert helices in the translocon.     

Thrombin inhibitors with novel P1 binding pocket functionality: free energy of binding analysis

The high incidence of thrombembolic diseases justifies the development of new antithrombotics. The search for a direct inhibitor has resulted in the synthesis of a considerable number of low molecular weight molecules that inhibit human α-thrombin potently. However, efforts to develop an orally active drug remain in progress as the most active inhibitors with a highly basic P1 moiety exhibit an unsatisfactory bioavailability profile. In our previous work we solved several X-ray structures of human α-thrombin in complexes with (1) novel bicyclic arginine mimetics attached to the glycylproline amide and pyridinone acetamide scaffold and (2) inhibitors with a novel aza scaffold and with charged or neutral P1 moieties. In the present contribution, we correlate the structures of the complex between these inhibitors and the protein with the calculated free energy of binding. The energy of solvation was calculated using the Poisson–Boltzmann approach. In particular, the requirements for successful recognition of an inhibitor at the protein’s active site pocket S1 are discussed. Figure We report here on free energy of binding analysis of thrombin inhibitors with novel aza scaffold and novel bicyclic arginine mimetics in S1 pocket of thrombin     

Conformational equilibria and free energy profiles for the allosteric transition of the ribose-binding protein

The ribose-binding protein (RBP) is a sugar-binding bacterial periplasmic protein whose function is associated with a large allosteric conformational change from an open to a closed conformation upon binding to ribose. The crystal structures of RBP in open and closed conformations have been solved. It has been hypothesized that the open and closed conformations exist in a dynamic equilibrium in solution, and that sugar binding shifts the population from open conformations to closed conformations. Here, we study by computer simulations the thermodynamic changes that accompany this conformational change, and model the structural changes that accompany the allosteric transition, using umbrella sampling molecular dynamics and the weighted histogram analysis method. The open state is comprised of a diverse ensemble of conformations; the open ribose-free X-ray crystal conformations being representative of this ensemble. The unligated open form of RBP is stabilized by conformational entropy. The simulations predict detectable populations of closed ribose-free conformations in solution. Additional interdomain hydrogen bonds stabilize this state. The predicted shift in equilibrium from the open to the closed state on binding to ribose is in agreement with experiments. This is driven by the energetic stabilization of the closed conformation due to ribose-protein interactions. We also observe a significant population of a hitherto unobserved ribose-bound partially open state. We believe that this state is the one that has been suggested to play a role in the transfer of ribose to the membrane-bound permease complex.     

Effects of endothelin-1 and conversion of big endothelin-1 in the isolated perfused rabbit lung.

We examined the effects of endothelin-1 (ET-1) on pulmonary hemodynamic and transvascular fluid filtration and the conversion of big endothelin-1 (big ET-1), a precursor of ET-1, in isolated perfused rabbit lungs at constant vascular and airway pressures. Furthermore we examined whether ET-1 contributes to cyclooxygenase metabolism. The perfusate flow decreased significantly after bolus administration of 1 or 0.1 nmol of ET-1. Lung weight did not increase throughout the experimental period. Big ET-1- (1 nmol) induced decrease in the flow was slow in developing, although the maximum response was comparable to that induced by the same dose of ET-1. The concentration of bit ET-1 in the perfusate progressively decreased, while that of ET-1 increased in a time-dependent manner. Phosphoramidon, an inhibitor of metalloproteinase, suppressed the pressor effect of big ET-1 (P less than 0.01) and the increase in the concentration of ET-1 in the perfusate (P less than 0.05). The present findings provide the first evidence suggesting that the potent vasocontractile effect of big ET-1 in pulmonary circulation can be attributed to the production of ET-1 by the conversion from big ET-1 in the vascular bed. ET-1-induced perfusate flow changes were not affected by indomethacin, and the concentration of 6-ketoprostaglandin F1 alpha, a metabolite of prostacyclin, did not increase after ET-1 administration.     

Effect of methylation on the stability and solvation free energy of amylose and cellulose fragments: a molecular dynamics study

Molecular dynamics (MD) simulations were used to study the stability and solvation of amylose and cellulose fragments. The recently developed gromos carbohydrate force field was further tested by simulating maltose, cellobiose, and maltoheptaose. The MD simulations reproduced fairly well the favorable conformations of disaccharides defined by the torsional angles related with the glycosidic bond and the radius gyration of maltoheptaose. The effects of methylation at different hydroxyl groups on the stability of amylose and cellulose fragments were investigated. The methylations of O-2 and O-3 reduce the stability of a single helix more than methylation at O-6, while the latter reduces the stability of a double helix more. Solvation free-energy differences between the unsubstituted amylose and cellulose fragments and the methylated species were studied using the single-step perturbation method. It was found that methylation at O-2 has the biggest effect, in agreement with experiment.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

Dissecting the free energy of formation of the 1:1 actomyosin complex

The behaviour of solutions of pure myosin, of pure F-actin and of the equimolar mixture of myosin and of F-actin is studied. It is found that the chemical potential of the two proteins, in separate solutions, increases monotonically with the increase of protein osmotic pressure. A method is presented to determine the chemical potential of the 1:1 actin-myosin complex formed from equimolar solutions of myosin and of F-actin (as monomer).This is the first evaluation of the chemical potential of actomyosin under conditions similar to those of skeletal muscle. It is found that the filament suspensions of myosin and of the 1:1 actin-myosin complex display a high non-ideal behavior as well as distinctly different energy profiles as a function of protein osmotic pressure. This supports the hypothesis that, in muscle: (a) detached cross-bridge change significantly their free energy when sarcomere is shifting from the relaxed to the active or to the rigor state; and (b) the cross-bridge attachment-detachment process is accompanied by changes of muscle protein osmotic pressure.     

Unfolding of an α-helix in peptide crystals by solvation: Conformational fragility in a heptapeptide

The structure of the peptide Boc-Val-Ala-Leu-Aib-Val-Ala-Leu-OMe has been determined in crystals obtained from a dimethylsulfoxide–isopropanol mixture. Crystal parameters are as follows: C₃₈H₆₉N₇O₁₀ · H₂O · 2C₃H₇OH, space group P2₁, a = 10.350 (2) Å, b = 26.084 (4) Å, c = 10.395(2) Å, β = 96.87(12), Z = 2, R = 8.7% for 2686 reflections observed > 3.0 σ (F). A single 5 → 1 hydrogen bond is observed at the N-terminus, while two 4 → 1 hydrogen bonds characteristic of a 3₁₀-helix are seen in the central segment. The C-terminus residues, Ala(6) and Leu(7) are expended, while Val(5) is considerably distorted from a helical conformation. Two isopropanol molecules make hydrogen bonds to the C-terminal segment, while a water molecule interacts with the N-terminus. The structure is in contrast to that obtained for the same peptide in crystals from methanol-water [ I. L. Karle, J. L. Flippen-Anderson, K. Uma, and P. Balaram (1990) Proteins: Structure, Function and Genetics, Vol. 7, pp. 62–73] in which two independent molecules reveal an almost perfect α-helix and a helix penetrated by a water molecule. A comparison of the three structures provides a snapshot of the progressive effects of solvation leading to helix unwinding. The fragility of the heptapeptide helix in solution is demonstrated by nmr studies in CDC1₃ and (CD₃)₂SO. A helical conformation is supported in the apolar solvent CDCl₃, whereas almost complete unfolding is observed in the strongly solvating medium (CD₃)₂SO. © 1993 John Wiley & Sons, Inc.     

Conformational energy analysis of the chemotactic tripeptide formyl-Met-Leu-Phe and three analogs

Conformational energy analyses were carried out on the chemotactic tripeptide fMLF (CHO-Met-Leu-Phe) and three analogs fALF (CHO-Ala-Leu-Phe). fMF (CHO-Met-Phe), and MLF (H-Met-Leu-Phe). A near-folded or puckered conformation predominates in all four peptides. The calculated average end-to-end distance R of each of the peptides is 7.4 A, 7.6 A, 7.0 A, and 7.3 A, respectively (where bends have R less than or equal to 7 A and extended structures have R approximately 10.5 A). The puckered conformation calculated for fMLF is similar to that determined experimentally for fMLF in nonpolar solvents and in the protein receptor. The results suggest that maximum chemotactic activity of the peptides depends on a combination of the chemical structure (the presence of N-formyl-methionine) and backbone conformation (C7conformation of the first amino acid residue).