A propensity scale for type II polyproline helices (PPII): aromatic amino acids in proline-rich sequences strongly disfavor PPII due to proline-aromatic interactions

Type II polyproline helices (PPII) are a fundamental secondary structure of proteins, common in globular and nonglobular regions and important in cellular signaling. We developed a propensity scale for PPII using a host-guest system with sequence Ac-GPPXPPGY-NH(2), where X represents any amino acid. We found that proline has the highest PPII propensity, but most other amino acids display significant PPII propensities. The PPII propensity of leucine was the highest of all propensities of non-proline residues. Alanine and residues with linear side chains displayed the next highest PPII propensities. Three classes of residues displayed lower PPII propensities: β-branched amino acids (Thr, Val, and Ile), short amino acids with polar side chains (Asn, protonated Asp, Ser, Thr, and Cys), and aromatic amino acids (Phe, Tyr, and Trp). tert-Leucine particularly disfavored PPII. The basis of the low PPII propensities of aromatic amino acids in this context was significant cis-trans isomerism, with proline-rich peptides containing aromatic residues exhibiting 45-60% cis amide bonds, due to Pro-cis-Pro-aromatic and aromatic-cis-Pro amide bonds.     

Theory of protein molecule self-organization. I. Thermodynamic parameters of local secondary structures in the unfolded protein chain

This paper presents the results of a stereochemical analysis of local interactions in unfolded protein chains (sterical repulsions, hydrogen, and hydrophobic bonds, etc.) by means of space-filling modeles. On the basis of this analysis, an evaluation is made of thermodynamic parameters controlling the building-in of all the 20 natural amino acid residues in all the physically possible position of local secondary structures (α-helices, including α-helices with short fragments of helices 3₁₀ at the C-terminus; β-bends of different types, helices 3₁₀, and their combinations) as well as thermodynamic parameters of separate hydrogen bonds of polar side groups with the neighbor peptide groups (“local contacts”). The accuracy of the obtained results is discussed.     

The molecular basis of the temperature- and pH-induced conformational transitions in elastin-based peptides

Elastin undergoes an inverse temperature transition and collapses at high temperatures in both simulation and experiment. We investigated a pH-dependent modification of this transition by simulating a glutamic acid (Glu)-substituted elastin at varying pHs and temperatures. The Glu-substituted peptide collapsed at higher temperature than the unsubstituted elastin when Glu was charged. The charge effects could be reversed by neutralization of the Glu carboxyl groups at low pH, and in that case the peptide collapsed at a lower temperature. The collapse was accompanied by the formation of beta-turns and short distorted beta-sheets. Formation of contacts between hydrophobic side chains drives the collapse at high temperature, but interactions between water and polar groups (Glu and main chain) can attenuate this effect at high pH. The overall competition and balance of the polar and nonpolar groups determined the conformational states of the peptide. Water hydration contributed to the conformational transition, and the peptide and its hydration shell must be considered. Structurally, waters near polar residues mainly formed hydrogen bonds with the protein atoms, while waters around the hydrophobic side chains tended to be parallel to the peptide groups to maximize water-water interactions.     

Patterns in ionizable side chain interactions in protein structures

In a selected set of 44 high-resolution, non-homologous protein structures, the intramolecular hydrogen bonds or salt bridges formed by ionizable amino acid side chains were identified and analyzed. The analysis was based on the investigation of several properties of the involved residues such as their solvent exposure, their belonging to a certain secondary structural element, and their position relative to the N- and C-termini of their respective structural element. It was observed that two-thirds of the interactions made by basic or acidic side chains are hydrogen bonds to polar uncharged groups. In particular, the majority (78%) of the hydrogen bonds between ionizable side chains and main chain polar groups (sch:mch bonds) involved at least one buried atom, and in 42% of the cases both interacting atoms were buried. In α-helices, the sch:mch bonds observed in the proximity of the C- and N-termini show a clear preference for acidic and basic side chains, respectively. This appears to be due to the partial charges of peptide group atoms at the termini of α-helices, which establish energetically favorable electrostatic interactions with side chain carrying opposite charge, at distances even greater than 4.5 Å. The sch:mch interactions involving ionizable side chains that belong either to β-strands or to the central part of α-helices are based almost exclusively on basic residues. This results from the presence of main chain carbonyl oxygen atoms in the protein core which have unsatisfied hydrogen bonding capabilities.     

Thermostability of membrane protein helix-helix interaction elucidated by statistical analysis

A prerequisite for the survival of (micro)organisms at high temperatures is an adaptation of protein stability to extreme environmental conditions. In contrast to soluble proteins, where many factors have already been identified, the mechanisms by which the thermostability of membrane proteins is enhanced are almost unknown. The hydrophobic membrane environment constrains possible stabilizing factors for transmembrane domains, so that a difference might be expected between soluble and membrane proteins. Here we present sequence analysis of predicted transmembrane helices of the genomes from eight thermophilic and 12 mesophilic organisms. A comparison of the amino acid compositions indicates that more polar residues can be found in the transmembrane helices of thermophilic organisms. Particularly, the amino acids aspartic acid and glutamic acid replace the corresponding amides. Cysteine residues are found to be significantly decreased by about 70% in thermophilic membrane domains suggesting a non-specific function of most cysteine residues in transmembrane domains of mesophilic organisms. By a pair-motif analysis of the two sets of transmembrane helices, we found that the small residues glycine and serine contribute more to transmembrane helix-helix interactions in thermophilic organisms. This may result in a tighter packing of the helices allowing more hydrogen bond formation.     

Modular design of synthetic protein mimics. Characterization of the helical conformation of a 13-residue peptide in crystals

The incorporation of alpha-aminoisobutyryl (Aib) residues into peptide sequences facilitates helical folding. Aib-containing sequences have been chosen for the design of rigid helical segments in a modular approach to the construction of a synthetic protein mimic. The helical conformation of the synthetic peptide Boc-Aib-(Val-Ala-Leu-Aib)3-OMe in crystals is established by X-ray diffraction. The 13-residue apolar peptide adopts a helical form in the crystal with seven alpha-type hydrogen bonds in the middle and 3(10)-type hydrogen bonds at either end. The helices stack in columns, zigzag rather than linear, by means of direct NH...OC head to tail hydrogen bonds. Leucyl side chains are extended on one side of the helix and valyl side chains on the other side. Water molecules form hydrogen bonds with several backbone carbonyl oxygens that also participate in alpha-helix hydrogen bonds. There is no apparent distortion of the helix caused by hydration. The space group is P2(1)2(1)2(1), with a = 9.964 (3) A, b = 20.117 (3) A, c = 39.311 (6) A, Z = 4, and dx = 1.127 g/cm3 for C64H106N13O16.1.33H2O. The final agreement factor R was 0.089 for 3667 data observed greater than 3 sigma(F) with a resolution of 0.9 A.     

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.     

Polar residues in membrane domains of proteins: molecular basis for helix-helix association in a mutant CFTR transmembrane segment

Polar side chains constitute over 20% of residues in the transmembrane (TM) helices of membrane proteins, where they may serve as hydrogen bond interaction sites for phenotypic polar mutations that arise in membrane protein-related diseases. To systematically explore the structural consequences of H-bonds between TM helices, we focused on TM4 of the cystic fibrosis conductance regulator (CFTR) and its cystic fibrosis- (CF-) phenotypic mutation, V232D, as a model system. Synthetic peptides corresponding to wild-type (TM4-wt) (residues 219-242: LQASAFCGLGFLIVLALFQAGLGR) and mutant (TM4-V232D) sequences both adopt helical structures in SDS micelles and display dimer bands on SDS-PAGE arising from disulfide bond formation via wild-type residue Cys-225. However, the TM4-V232D peptide additionally forms a ladder of noncovalent oligomers, including tetramers, hexamers, and octamers, mediated by a hydrogen bond network involving Asp-Gln side chain-side chain interactions. Ala-scanning mutagenesis of the TM4 sequence indicated that ladder formation minimally required the simultaneous presence of the Cys-225, Asp-232, and Gln-237 residues. As random hydrophobic sequences containing these three residues at TM4 equivalent positions did not oligomerize, specific van der Waals packing interactions between helix side chains were also shown to play a crucial role. Overall, the results suggest that polar mutations in membrane domains, in conjunction with critically positioned polar partner residues, potentially constitute a source of aberrant helix interactions that could contribute to loss of function when they arise in protein transmembrane domains.     

Structure-based statistical analysis of transmembrane helices

Recent advances in determination of the high-resolution structure of membrane proteins now enable analysis of the main features of amino acids in transmembrane (TM) segments in comparison with amino acids in water-soluble helices. In this work, we conducted a large-scale analysis of the prevalent locations of amino acids by using a data set of 170 structures of integral membrane proteins obtained from the MPtopo database and 930 structures of water-soluble helical proteins obtained from the protein data bank. Large hydrophobic amino acids (Leu, Val, Ile, and Phe) plus Gly were clearly prevalent in TM helices whereas polar amino acids (Glu, Lys, Asp, Arg, and Gln) were less frequent in this type of helix. The distribution of amino acids along TM helices was also examined. As expected, hydrophobic and slightly polar amino acids are commonly found in the hydrophobic core of the membrane whereas aromatic (Trp and Tyr), Pro, and the hydrophilic amino acids (Asn, His, and Gln) occur more frequently in the interface regions. Charged amino acids are also statistically prevalent outside the hydrophobic core of the membrane, and whereas acidic amino acids are frequently found at both cytoplasmic and extra-cytoplasmic interfaces, basic amino acids cluster at the cytoplasmic interface. These results strongly support the experimentally demonstrated biased distribution of positively charged amino acids (that is, the so-called the positive-inside rule) with structural data.     

Correlation of sequence and tertiary structure in globular proteins

The x-ray crystal structures of 19 selected proteins are examined empirically for correlations between the amino acid sequence and long-range, tertiary conformation. There is clear evidence for preferential associations of certain types of amino acids, particularly among the hydrophobic aliphatic, aromatic, and cysteine residues. However, the likelihoods of forming these residue-pair contacts are all less than 12%, so packing and geometric requirements must often take precedent over energetic considerations. The prediction of long-range contacts is not substantially improved by taking into account the sequentially previous residues. The analysis of atom–atom contacts shows a similar lack of predictive ability, but the results show that a good approximation to the interresidue energy function must include different types of interactions at two or three different sites on some amino acids. Backbone–backbone long-range interactions are relatively rare and nonspecific, whereas some “polar” side chains form hydrogen bonds from the polar groups while occasionally forming hydrophobic contacts with the remainder of the chain.     

Stabilizing nonpolar/polar side-chain interactions in the alpha-helix.

A simplistic, yet often used, view of protein stability is that amino acids attract other amino acids with similar polarity, whereas nonpolar and polar side chains repel. Here we show that nonpolar/polar interactions, namely Val or Ile bonding to Lys or Arg in alpha-helices, can in fact be stabilizing. Residues spaced i, i + 4 in alpha-helices are on the same face of the helix, with potential to favorably interact and stabilize the structure. We observe that the nonpolar/polar pairs Ile-Lys, Ile-Arg, and Val-Lys occur in protein helices more often than expected when spaced i, i + 4. Partially helical peptides containing pairs of nonpolar/polar residues were synthesized. Controls with i, i + 5 spacing have the residues on opposite faces of the helix and are less helical than the test peptides with the i, i + 4 interactions. Experimental circular dichroism results were analyzed with helix-coil theory to calculate the free energy for the interactions. All three stabilize the helix with DeltaG between -0.14 and -0.32 kcal x mol(-1). The interactions are hydrophobic with contacts between Val or Ile and the alkyl groups in Arg or Lys. Side chains such as Lys and Arg can thus interact favorably with both polar and nonpolar residues.     

Distribution of amino acids in a lipid bilayer from computer simulations

We have calculated the distribution in a lipid bilayer of small molecules mimicking 17 natural amino acids in atomistic detail by molecular dynamics simulation. We considered both charged and uncharged forms for Lys, Arg, Glu, and Asp. The results give detailed insight in the molecular basis of the preferred location and orientation of each side chain as well the preferred charge state for ionizable residues. Partitioning of charged and polar side chains is accompanied by water defects connecting the side chains to bulk water. These water defects dominate the energetic of partitioning, rather than simple partitioning between water and a hydrophobic phase. Lys, Glu, and Asp become uncharged well before reaching the center of the membrane, but Arg may be either charged or uncharged at the center of the membrane. Phe has a broad distribution in the membrane but Trp and Tyr localize strongly to the interfacial region. The distributions are useful for the development of coarse-grained and implicit membrane potentials for simulation and structure prediction. We discuss the relationship between the distribution in membranes, bulk partitioning to cyclohexane, and several amino acid hydrophobicity scales.     

Invariant features of globin primary structure and coding of their secondary structure

Invariant features of the primary structure of 67 globins are analysed. These features may be responsible for the formation of the secondary structure of these proteins at the first stage of self-organization (in the unfolded chain). It is shown that in primary structures of globins there are 11 sites or regions of one to four residues in which at least one of the residues Asn, Asp, His, Pro, Ser or Thr is located in every globin (haem-linking His residues are excluded from these sites). An unambiguous correlation exists between the position of these regions and the secondary structure of globins: all these regions (except one) are located near the ends of helices in globins whose three-dimensional structure is known and the ends of all helices (except for the helix F) are coded by such regions. A decrease in the set of residues listed above leads to a sharp drop in the number of regions invariantly occupied by the residues, while an addition of residues such as Tyr and Gly to this set does not eventually increase the number of invariant regions. Five residues (Asn, Asp, His, Ser and Thr) of the six that code the ends of helical regions have polar side groups with a small number of degrees of freedom capable of forming hydrogen bonds with atoms of the backbone with a relatively small loss of entropy. One residue (Pro) has no NH-group and, therefore, has less chance of participating in the formation of hydrogen bonds between atoms of the backbone. This corroborates the hypothesis that competition between hydrogen bonds of short polar side groups and hydrogen bonds in the backbone is essential for the formation of the secondary structure in unfolded protein chains. Amino acid replacements in hydrophobic cores of the 67 globins are considered in the Appendix.     

Anchoring of a monotopic membrane protein: the binding of prostaglandin H2 synthase-1 to the surface of a phospholipid bilayer

Prostaglandin H₂ synthases (PGHS-1 and -2) are monotopic peripheral membrane proteins that catalyse the synthesis of prostaglandins in the arachidonate cascade. Picot et al. (1994) proposed that the enzyme is anchored to one leaflet of the bilayer by a membrane anchoring domain consisting of a right-handed spiral of amphipathic helices (residues 73–116) forming a planar motif. Two different computational approaches are used to examine the association of the PGHS-1 membrane anchoring domain with a membrane via the proposed mechanism. The electrostatic contribution to the free energy of solvation is obtained by solving numerically the finite-difference Poisson equation for the protein attached to a membrane represented as a planar slab of low dielectric. The nonpolar cavity formation and van der Waals contributions to the solvation free energy are assumed to be proportional to the water accessible surface area. Based on the optimum position determined from the continuum solvent model, two atomic models of the PGHS-1 anchoring domain associated with an explicit dimyristoylphosphatidylcholine (DMPC) bilayer differing by the thickness of the membrane bilayer were constructed. A total of 2 ns molecular dynamics simulation were performed to study the details of lipid- protein interactions at the microscopic level. In the simulations the lipid hydrocarbon chains interacting with the anchoring domain assume various shapes, suggesting that the plasticity of the membrane is significant. The hydrophobic residues in the membrane side of the helices interact with the hydrophobic membrane core, while the positively charged residues interact with the lipid polar headgroups to stabilize the anchoring of the membrane domain to the upper half of the bilayer. The phosphate headgroup of one DMPC molecule disposed at the center of the spiral formed by helices A, B, C and D interacts strongly with Arg120, a residue on helix D that has previously been identified as being important in the activity of PGHS-1. In the full enzyme structure, this position corresponds to the entrance of a long hydrophobic channel leading to the cyclooxygenase active site. These observations provide insights into the association of the arachidonic acid substrate to the cyclooxygenase active site of PGHS-1. Received: 20 December 1999 / Revised version: 26 March 2000 / Accepted: 26 March 2000     

Geometry of interaction of the histidine ring with other planar and basic residues

Among the aromatic residues in protein structures, histidine (His) is unique, as it can exist in the neutral or positively charged form at the physiological pH. As such, it can interact with other aromatic residues as well as form hydrogen bonds with polar and charged (both negative and positive) residues. We have analyzed the geometry of interaction of His residues with nine other planar side chains containing aromatic (residues Phe, Tyr, Trp, and His), carboxylate (Asp and Glu), carboxamide (Asn and Gln) and guanidinium (Arg) groups in 432 polypeptide chains. With the exception of the aspartic (Asp) and glutamic (Glu) acid side-chains, all other residues prefer to interact in a face-to-face or offset-face-stacked orientation with the His ring. Such a geometry is different from the edge-to-face relative orientation normally associated with the aromatic-aromatic interaction. His-His pair prefers to interact in a face-to-face orientation; however, when both the residues bind the same metal ion, the interplanar angle is close to 90 degrees. The occurrence of different interactions (including the nonconventional N-H...pi and C-H...pi hydrogen bonds) have been correlated with the relative orientations between the interacting residues. Several structural motifs, mostly involved in binding metal ions, have been identified by considering the cases where His residues are in contact with four other planar moieties. About 10% of His residues used here are also found in sequence patterns in PROSITE database. There are examples of the amino end of the Lys side chain interacting with His residues in such a way that it is located on an arc around a ring nitrogen atom.     

Intra-Helical Salt Bridge Contribution to Membrane Protein Insertion

Salt bridges between negatively (D, E) and positively charged (K, R, H) amino acids play an important role in protein stabilization. This has a more prevalent effect in membrane proteins where polar amino acids are exposed to a hydrophobic environment. In transmembrane (TM) helices the presence of charged residues can hinder the insertion of the helices into the membrane. It is possible that the formation of salt bridges could decrease the cost of membrane integration. However, the presence of intra-helical salt bridges in TM domains and their effect on insertion has not been properly studied yet. In this work, we show that potentially salt-bridge forming pairs are statistically over-represented in TM-helices. We then selected some candidates to experimentally determine the contribution of these electrostatic interactions to the translocon-assisted membrane insertion process. Using both in vitro and whole cell systems, we confirm the presence of intra-helical salt bridges in TM segments during biogenesis and determined that they contribute ～0.5 kcal/mol to the apparent free energy of membrane insertion (ΔG_app). Our observations suggest that salt bridge interactions can be stabilized during translocon-mediated insertion and thus could be relevant to consider for the future development of membrane protein prediction software.     

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.     

A survey of left-handed polyproline II helices

Left-handed polyproline II helices (PPII) are contiguous elements of protein secondary structure in which the phi and psi angles of constituent residues are restricted to around -75 degrees and 145 degrees, respectively. They are important in structural proteins, in unfolded states and as ligands for signaling proteins. Here, we present a survey of 274 nonhomologous polypeptide chains from proteins of known structure for regions that form these structures. Such regions are rare, but the majority of proteins contain at least one PPII helix. Most PPII helices are shorter than five residues, although the longest found contained 12 amino acids. Proline predominates in PPII, but Gln and positively charged residues are also favored. The basis of Gln's prevalence is its ability to form an i, i + 1 side-chain to main-chain hydrogen bond with the backbone carbonyl oxygen of the proceeding residue; this helps to fix the psi angle of the Gln and the phi and psi of the proceeding residue in PPII conformations and explains why Gln is favored at the first position in a PPII helix. PPII helices are highly solvent exposed, which explains why apolar amino acids are disfavored despite preferring this region of phi/psi space when in isolation. PPII helices have perfect threefold rotational symmetry and within these structures we find significant correlation between the hydrophobicity of residues at i and i + 3; thus, PPII helices in globular proteins can be considered to be amphipathic.     

Structural basis for the unusual specificity of Escherichia coli aminopeptidase N

Aminopeptidase N from Escherichia coli is a M1 class aminopeptidase with the active-site region related to that of thermolysin. The enzyme has unusual specificity, cleaving adjacent to the large, nonpolar amino acids Phe and Tyr but also cleaving next to the polar residues Lys and Arg. To try to understand the structural basis for this pattern of hydrolysis, the structure of the enzyme was determined in complex with the amino acids L-arginine, L-lysine, L-phenylalanine, L-tryptophan, and L-tyrosine. These amino acids all bind with their backbone atoms close to the active-site zinc ion and their side chain occupying the S1 subsite. This subsite is in the form of a cylinder, about 10 A in cross-section and 12 A in length. The bottom of the cylinder includes the zinc ion and a number of polar side chains that make multiple hydrogen-bonding and other interactions with the alpha-amino group and the alpha-carboxylate of the bound amino acid. The walls of the S1 cylinder are hydrophobic and accommodate the nonpolar or largely nonpolar side chains of Phe and Tyr. The top of the cylinder is polar in character and includes bound water molecules. The epsilon-amino group of the bound lysine side chain and the guanidinium group of arginine both make multiple hydrogen bonds to this part of the S1 site. At the same time, the hydrocarbon part of the lysine and arginine side chains is accommodated within the nonpolar walls of the S1 cylinder. This combination of hydrophobic and hydrophilic binding surfaces explains the ability of ePepN to cleave Lys, Arg, Phe, and Tyr. Another favored substrate has Ala at the P1 position. The short, nonpolar side chain of this residue can clearly be bound within the hydrophobic part of the S1 cylinder, but the reason for its facile hydrolysis remains uncertain.     

Extension of the fragment method to calculate amino acid zwitterion and side chain partition coefficients

The fragment method of calculating partition coefficients (P) has been extended to include the common amino acids (AAs). The results indicate that polar and charged side chains influence the hydrophobicity of atoms in the side chain in a predictable manner. Field effects, as evidenced through polar proximity factors and bond factors, need to be considered for accurate estimation of transfer phenomena. The calculated log P and delta G degree ' values of the 20 AAs agree well with the observed values. Pro calculates to be more hydrophilic than the observed log P. Hydrophobicity scales for peptide side chain residues are compared and evaluated in terms of suitability. Calculated pi values for nonpolar side chain residues agree well with the observed values; calculated values for uncharged polar side chain residues deviate by about 0.6 log units except for Gln and Cys; and polar side chain residues with charged side chains calculate as too hydrophilic. Reasons for the differences are explored. We also suggest that tightly bound water to polar moieties in amino acids and peptides may be transferred into the octanol phase during partitioning experiments. A quantitative methodology is presented which characterizes the thermodynamic partitioning of groups and individual atoms in amino acids and proteins.