Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

Transfer free energies of peptide backbone unit from water to aqueous electrolyte solutions at 298.15 K

Transfer free energies (ΔG_tr) of amino acids from water to aqueous electrolyte solutions have been determined from the solubility measurements, as a function of salt concentration at 298.15 K under atmospheric pressure. The investigated aqueous systems contain amino acids of zwitterionic glycine peptides: glycine (Gly), diglycine (Gly₂), triglycine (Gly₃), and tetraglycine (Gly₄) and cyclic glycylglycine (c(GG)) with an electrolyte compound of potassium chloride (KCl), potassium bromide (KBr) or potassium acetate (KAc). The solubilities of glycine and diglycine in aqueous solution decrease with increasing the concentration of salts (salting-out effect), whereas those of triglycine and tetraglycine increase with increasing the concentration of salts (salting-in effect). Furthermore, salting-in effect was found in aqueous c(GG)/KBr system, while salting-out effect was observed in aqueous c(GG)/KCl or c(GG)/KAc system. The experimental results were used to estimate the transfer free energies (Δg_tr) of the peptide backbone unit (–CH₂CONH–) from water to the aqueous electrolyte solutions. We developed a new trail to determine the activity coefficients (γ) for aqueous and aqueous electrolyte solutions using an activity coefficient model, with which the total contribution of transfer free energy between solute and the solvent was calculated. We compared the difference between neglecting and using the activity coefficients term in predicting ΔG_tr. Since the transfer free energy contribution is negative, interactions between the ionic salts and the peptide backbone unit of zwitterionic glycine peptides are favorable and thus the ionic salts destabilize these amino acids. It was also found that KBr stabilizes c(GG), whereas KCl and KAc destabilize c(GG). These results provide evidence for the existence of interactions between the amide unit and ionic salts, in aqueous solution, which may be of importance in maintaining protein structure as well as in protein–solute and protein–solvent interactions.     

Osmolyte effects on protein stability and solubility: a balancing act between backbone and side-chains

In adaptation biology the discovery of intracellular osmolyte molecules that in some cases reach molar levels, raises questions of how they influence protein thermodynamics. We've addressed such questions using the premise that from atomic coordinates, the transfer free energy of a native protein (ΔG_tr, N) can be predicted by summing measured water-to-osmolyte transfer free energies of the protein's solvent exposed side chain and backbone component parts. ΔG_tr, D is predicted using a self avoiding random coil model for the protein, and ΔG_tr, D − ΔG_tr, N, predicts the m-value, a quantity that measures the osmolyte effect on the N ? D transition. Using literature and newly measured m-values we show 1:1 correspondence between predicted and measured m-values covering a range of 12 kcal/mol/M in protein stability for 46 proteins and 9 different osmolytes. Osmolytes present a range of side chain and backbone effects on N and D solubility and protein stability key to their biological roles.     

Solvation free energies of nucleic acid bases in ionic liquids

The solvation free energies of five nucleic acid bases in [C_nbim]Br (where n = 2, 4, 6) ionic liquids (ILs) were computed using the Bennett acceptance ratio (BAR) method employing molecular dynamics simulations. The computed free energies using BAR were in agreement with other methods. The large and negative predicted free energies of the bases in ILs indicated that the bases were better solvated in the ILs rather than in water. Hydrogen bonding interactions between polar sites of the bases and ILs’ ions significantly contributed to the solvation mechanism.     

Microsolvation of Mg2+, Ca2+: strong influence of formal charges in hydrogen bond networks

A stochastic exploration of the quantum conformational spaces in the microsolvation of divalent cations with explicit consideration of up to six solvent molecules [Mg (H ₂ O) _n )]²⁺, (n?=?3, 4, 5, 6) at the B3LYP, MP2, CCSD(T) levels is presented. We find several cases in which the formal charge in Mg²⁺ causes dissociation of water molecules in the first solvation shell, leaving a hydroxide ion available to interact with the central cation, the released proton being transferred to outer solvation shells in a Grotthus type mechanism; this particular finding sheds light on the capacity of Mg²⁺ to promote formation of hydroxide anions, a process necessary to regulate proton transfer in enzymes with exonuclease activity. Two distinct types of hydrogen bonds, scattered over a wide range of distances (1.35–2.15 Å) were identified. We find that in inner solvation shells, where hydrogen bond networks are severely disturbed, most of the interaction energies come from electrostatic and polarization+charge transfer, while in outer solvation shells the situation approximates that of pure water clusters.

Polyproline II helix is the preferred conformation for unfolded polyalanine in water

Does aqueous solvent discriminate among peptide conformers? To address this question, we computed the solvation free energy of a blocked, 12‐residue polyalanyl‐peptide in explicit water and analyzed its solvent structure. The peptide was modeled in each of 4 conformers: α‐helix, antiparallel β‐strand, parallel β‐strand, and polyproline II helix (P_II). Monte Carlo simulations in the canonical ensemble were performed at 300 K using the CHARMM 22 forcefield with TIP3P water. The simulations indicate that the solvation free energy of P_II is favored over that of other conformers for reasons that defy conventional explanation. Specifically, in these 4 conformers, an almost perfect correlation is found between a residue's solvent‐accessible surface area and the volume of its first solvent shell, but neither quantity is correlated with the observed differences in solvation free energy. Instead, solvation free energy tracks with the interaction energy between the peptide and its first‐shell water. An additional, previously unrecognized contribution involves the conformation‐dependent perturbation of first‐shell solvent organization. Unlike P_II, β‐strands induce formation of entropically disfavored peptide:water bridges that order vicinal water in a manner reminiscent of the hydrophobic effect. The use of explicit water allows us to capture and characterize these dynamic water bridges that form and dissolve during our simulations. Proteins 2004. © 2004 Wiley‐Liss, Inc.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Thermodynamics of solvation for methylproline peptides

We have determined thermodynamic parameters for transfer of N-acetyl,N′-methylamide derivatives of proline and methylprolines from carbon tetrachloride and from chloroform to water. The hydrophilic nature of the diamide model peptides is demonstrated by the negative free energies and enthalpies for transfer. Chloroform solvates the peptides considerably better than carbon tetrachloride. Heats of dilution in carbon tetrachloride arise from disruption of intermolecular peptide–peptide hydrogen bonds. After extrapolation to dilute solution, differences in thermodynamic parameters among the isomeric mono-methylproline peptides are correlated with the population of the intramolecularly hydrogen-bonded C₇ conformer in the nonpolar solvent. However, the thermodynamic parameters aslo reflect differences in solvation due to the proximity of the two peptide groups and the side chain.     

Pentacycloundecane lactam vs lactone norstatine type protease HIV inhibitors: binding energy calculations and DFT study

Background

Novel pentacycloundecane (PCU)-lactone-CO-EAIS peptide inhibitors were designed, synthesized, and evaluated against wild-type C-South African (C-SA) HIV-1 protease. Three compounds are reported herein, two of which displayed IC₅₀ values of less than 1.00 μM. A comparative MM-PB(GB)SA binding free energy of solvation values of PCU-lactam and lactone models and their enantiomers as well as the PCU-lactam-NH-EAIS and lactone-CO-EAIS peptide inhibitors and their corresponding diastereomers complexed with South African HIV protease (C-SA) was performed. This will enable us to rationalize the considerable difference between inhibitory concentration (IC₅₀) of PCU-lactam-NH-EAIS and PCU-lactone-CO-EAIS peptides.

Results

The PCU-lactam model exhibited more negative calculated binding free energies of solvation than the PCU-lactone model. The same trend was observed for the PCU-peptide inhibitors, which correspond to the experimental activities for the PCU-lactam-NH-EAIS peptide (IC₅₀ = 0.076 μM) and the PCU-lactone-CO-EAIS peptide inhibitors (IC₅₀ = 0.850 μM). Furthermore, a density functional theory (DFT) study on the natural atomic charges of the nitrogen and oxygen atoms of the three PCU-lactam, PCU-lactim and PCU-lactone models were performed using natural bond orbital (NBO) analysis. Electrostatic potential maps were also used to visualize the electron density around electron-rich regions. The asymmetry parameter (η) and quadrupole coupling constant (χ) values of the nitrogen and oxygen nuclei of the model compounds were calculated at the same level of theory. Electronic molecular properties including polarizability and electric dipole moments were also calculated and compared. The Gibbs theoretical free solvation energies of solvation (∆G_solv) were also considered.

Conclusions

A general trend is observed that the lactam species appears to have a larger negative charge distribution around the heteroatoms, larger quadrupole constant, dipole moment and better solvation energy, in comparison to the PCU-lactone model. It can be argued that these characteristics will ensure better eletronic interaction between the lactam and the receptor, corresponding to the observed HIV protease activities in terms of experimental IC₅₀ data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12929-015-0115-5) contains supplementary material, which is available to authorized users.     

The importance of the membrane interface as the reference state for membrane protein stability

The insertion of nascent polypeptide chains into lipid bilayer membranes and the stability of membrane proteins crucially depend on the equilibrium partitioning of polypeptides. For this, the transfer of full sequences of amino-acid residues into the bilayer, rather than individual amino acids, must be understood. Earlier studies have revealed that the most likely reference state for partitioning very hydrophobic sequences is the membrane interface. We have used μs-scale simulations to calculate the interface-to-transmembrane partitioning free energies ΔG_S→TM for two hydrophobic carrier sequences in order to estimate the insertion free energy for all 20 amino acid residues when bonded to the center of a partitioning hydrophobic peptide. Our results show that prior single-residue scales likely overestimate the partitioning free energies of polypeptides. The correlation of ΔG_S→TM with experimental full-peptide translocon insertion data is high, suggesting an important role for the membrane interface in translocon-based insertion. The choice of carrier sequence greatly modulates the contribution of each single-residue mutation to the overall partitioning free energy. Our results demonstrate the importance of quantifying the observed full-peptide partitioning equilibrium, which is between membrane interface and transmembrane inserted, rather than combining individual water-to-membrane amino acid transfer free energies.     

Deciphering the crucial residues involved in heterodimerization of Bak peptide and anti-apoptotic proteins for apoptosis

B-cell lymphoma 2 (Bcl-2) family proteins are the central regulators of apoptosis, functioning via mitochondrial outer membrane permeabilization. The family members are involved in several stages of apoptosis regulation. The overexpression of the anti-apoptotic proteins leads to several cancer pathological conditions. This overexpression is modulated or inhibited by heterodimerization of pro-apoptotic BH3 domain or BH3-only peptides to the hydrophobic groove present at the surface of anti-apoptotic proteins. Additionally, the heterodimerization displayed differences in binding affinity profile among the pro-apoptotic peptides binding to anti-apoptotic proteins. In light of discovering the novel peptide/drug molecules that contain the potential to inhibit specific anti-apoptotic protein, it is necessary to understand the molecular basis of recognition between the protein and its binding partner (peptide or ligand) along with its binding energies. Therefore, the present work focused on deciphering the molecular basis of recognition between pro-apoptotic Bak peptide binding to different anti-apoptotic (Bcl-xL, Bfl-1, Bcl-W, Mcl-1, and Bcl-2) proteins using advanced Molecular Dynamics (MD) approach such as Molecular Mechanics-Generalized Born Solvent Accessible. The results from our investigation revealed that the predicted binding free energies showed excellent correlation with the experimental values (r² = .95). The electrostatic (ΔG_ele) contributions are the major component that drives the interaction between Bak peptides and different anti-apoptotic peptides. Additionally, van der Waals (ΔG_vdw) energies also play an indispensible role in determining the binding free energy. Furthermore, the decomposition analysis highlighted the comprehensive information about the energy contributions of hotspot residues involved in stabilizing the interaction between Bak peptide and different anti-apoptotic proteins.     

α/310-Helix transitions in α-methylalanine homopeptides: Conformational transition pathway and potential of mean force

The conformational transition between the α- and 3₁₀-helical states of α-methylalanine homopeptides is studied with molecular mechanics. Conformational transition pathways for Ace-(MeA)_n-NMe with n = 7, 9, and 11 are obtained with the algorithms of Elber and co-workers [R. Czerminski & R. Elber (1990) International Journal of Quantum Chemistry, Vol. 24, pp. 167–186; A. Ulitsky & R. Elber (1990) Journal of Chemical Physics, Vol. 92, pp. 1510–1511]. The free energy surface, or potential of mean force, for the conformational transition of Ace-(MeA)₉-NMe is calculated from molecular dynamics simulations, and a method is presented for the decomposition of the free energy surface into the constituent energetic and entropic terms, via the calculation of the required temperature derivatives in situ. For the AMBER/OPLS model employed here, the conformational transition pathways each contain a single 3₁₀-helical-like transition state, and the transition state potential energy relative to the 3₁₀-conformation is 3 kcal/mol, independent of peptide length. Entropic stabilization in the barrier region significantly lowers the activation free energies for the forward and reverse transitions from the estimates of the barrier heights based simply on potential energy alone. © 1994 John Wiley & Sons, Inc.     

Accurate Aqueous Proton Dissociation Constants Calculations for Selected Angiotensin-Converting Enzyme Inhibitors

Abstract

Studies that allow computing values of aqueous proton dissociation constants (pK_a), gas phase proton affinities, and the free energy of solvation have been performed for six members of angiotensin-I-converting enzyme (ACE) inhibitor family (captopril, enalaprilat, imidaprilat, ramiprilat, perindoprilat, and spiraprilat). Density functional theory (DFT) calculations using PBE1PBE functional on optimized molecular geometries have been carried out to investigate the thermodynamics of gas-phase protonation. The conductor-like polarizable continuum model (CPCM) solvation method at various levels of theory was applied to calculate the free energy of solvation for the ACE inhibitors and their respective anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. The combination of gas-phase and solvation energies according to the thermodynamic cycle enabled us to compute accurate pK_a values for the all studied molecules.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

A solvent model for simulations of peptides in bilayers. I. Membrane-promoting alpha-helix formation

We describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting alpha-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides-poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation-were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of alpha-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed.     

Co-oligopeptides of aromatic amino acids and glycine with a variable distance between the aromatic residues. III. Co-oligopeptides of L-phenylalanine, L-tryptophan, and Glycine: synthesis and ultraviolet absorption properties.

The preparation of the co-oligopeptides of the series H-Gly-Phe-(Gly)_n-Trp-Gly-OH (n = 0, 1, 2) and of other free peptides of glycine, L -tryptophan, and L -phenylalanine is reported. The syntheses have been carried out by conventional methods, using N-hydroxysuccinimide esters for the coupling steps. The ultraviolet absorption properties of the free peptides have been investigated in water. No hypo- or hyperchromicity was found for the aromatic chromophores, with the exception of H-Gly-Phe-Trp-OH, which shows a small but significant hypochromicity. The contribution of the peptide bond to the molar absorptivity in the far ultraviolet has been separated from that of the side chain plus the ? COO^? group by plotting the measured molar absorptivity ? of the farthest accessible uv maximum as a function of the number of peptide bonds (n_A). The peptide bond contribution proved to be independent of n_A in the range n_A = 1–5, thus ruling out the onset of helical conformations in the longer chain peptides.     

A semi-empirical conformational analysis of the interaction of n-alkanols with dipalmitoylphosphatidylcholine

The interaction of a homologous series of saturated aliphatic n-alkanols (containing 1–13 carbon atoms) with dipalmitoylphosphatidylcholine was studied by a semi-empirical conformational analysis. The minimal conformational energy of the isolated molecule at the hydrocarbon-water interface was calculated as the sum of the contributions resulting from the Van der Waals, torsional, electrostatic and transfer energies. From the conformers of minimal energies were calculated the hydrophilic-hydrophobic balance, the distance between hydrophilic and hydrophobic centres and the energies of interaction between homologous alkanols and between alkanols and lipids. Using these parameters, different modes of conformation, orientation and interaction of n-alkanols and dipalmitoylphosphatidylcholine were described. For methanol, ethanol and n-propanol, the gauche conformers were the most probable interacting only with the lipid polar heads. Only all-trans conformers were obtained for alkanols with longer acyl chains. n-Butanol to n-octanol form clusters in the lipid matrix. Longer n-alkanols are randomly distributed in the lipid layer. However, due to the increase in hydrocarbon chain-length, n-nonanol and higher alkanols have an interaction energy identical or superior to that found in a pure lipid monolayer, leading to a more ordered alkanol-lipid organization.     

Peptides and Peptoids - A Systematic Structure Comparison

A systematic analysis of the conformational space of the basic structure unit of peptoids in comparison to the corresponding peptide unit was performed based on ab initio MO theory and complemented by molecular mechanics (MM) and molecular dynamics (MD) calculations both in the gas phase and in aqueous solution.The calculations show three minimum conformations denoted as C_7ß, a_D and a that do not correspond to conformers on the gas phase peptide potential energy hypersurface. The influence of aqueous solvation was estimated by means of continuum models. The MD simulations indicate the a_D form as the preferred conformation in solution both in cis and trans peptide bond orientations.     

Spontaneous and promoted association of linear oligoglycines

Linear oligoglycines of various lengths bearing a carboxyl or an amide group at their C-termini and also their poly(acrylamide) conjugates were synthesized. No self-assembly into supramolecular structures was observed for free oligoglycines H-(Gly)_m-OH (m = 3–5). At the same time, oligoglycylamides H-(Gly)_m-NH₂ (m = 3–5) demonstrated ability for both self-assembly in aqueous solution and assembly promoted by an additional interaction with surface. In the case of polymer-bound oligoglycines (and their amides), no intramolecular clustering of peptide chains, as expected, was observed. This means that the presence of several oligoglycine chains bound to each other in one center is not a necessary prerequisite for polyglycine II-type association.     

On the lack of correlation between bond lengths, dissociation energies, and force constants: the fluorine-substituted ethane homologues

Accurate ab initio coupled-cluster (CCSD) calculations have been used to evaluate systematically the E-E bond lengths, homonuclear dissociation energies, and force constants of a series of fluorine-substituted ethane homologues H_3 − nF_nE-EH_3 − nF_n (n=0-3), H₃E-EF₃, and H₃E-EH₂F (E=C, Si, Ge, Sn) in their staggered ethane-like conformations. The pronounced lack of correlation between bond lengths, dissociation energies, and force constants observed previously with E=Sn has also been found for the lighter group 14 homologues. However, each element in the group exhibits a different behavior. Attempts are made to interpret the findings in the context of electronegativity, hybridization defects, as well as negative and geminal hyperconjugation.