Analysis of the code relating sequence to conformation in globular proteins. Theory and application of expected information

1. An information theory analysis of the folding of a globular protein is proposed. 2. The folding is seen as a transfer of information between two messages, the primary sequence and the biologically active conformation. 3. It is shown how the information transferred was estimated by inspection of proteins of known primary sequence and conformation. 4. In this estimation, concerted use of subjective (Bayesian) probabilities leads to a more robust approach which can be employed whether the number of proteins of known sequence and conformation is large or small. 5. Further, it is demonstrated that the problem then becomes a very simple algebraic formulation for information estimates. 6. Finally, it is shown how this process of information theory analysis can be reversed to predict the conformation of a protein by using its primary sequence and the above information estimates obtained from other proteins. 7. The present paper provides the theoretical basis for the derivation and application of a stereochemical alphabet (Robson & Pain, 1974a,c), and for an investigation of the effects of residues on the conformations of their neighbours (Robson & Pain, 1974b).     

Analysis of the code relating sequence to conformation in globular proteins. The distribution of residue pairs in turns and kinks in the backbone chain

1. The residue pair is considered as the fundamental unit which differentiates alpha-helix, beta-pleated sheet and the various turns and kink structures of the protein backbone. 2. The HPLG alphabet (Robson & Pain, 1974) is used to group pairs of residues, giving 16 possible conformational pairs, all of which are found with differing frequencies in the nine proteins examined. 3. The frequencies of occurrence of the 16 different types of turn or kink are analysed in relation to the constituent amino acids. Those containing the L or G conformation are of low frequency and are grouped for purposes of this analysis. 4. The distribution of amino acids within all the conformational pairs is non-random, with distinct preferences shown by certain residues. 5. All pairs containing an L or G conformation require the presence of a glycine or a proton-donor side chain. 6. The results are discussed in terms of the determination of these ;random' structures by local interactions.     

Analysis of the code relating sequence to conformation in globular proteins. An informational analysis of the role of the residue in determining the conformation of its neighbours in the primary sequence

1. The effect exerted by a residue on the conformation of neighbouring residues was analysed by using data from nine globular proteins of known sequence and conformation. 2. An information measure was used which estimated the role of a residue in influencing neighbouring conformations and also its tendency to influence the lengths of runs of residues in that conformation. This measure was estimated for each residue in all conformations defined by domains on the varphi, psi diagram. 3. Plots of the information measure yielded an intercept, which was a measure of intra-residue information for a residue. The slope was a measure of the statistical co-operativity or tendency of the residue to influence the occurrence of its neighbours in runs of a particular conformation. Both parameters are a function of the residue type. Statistical co-operativity is found in the alpha(1)-helical (H(1)) and beta-pleated-sheet (P(2)) conformations and, to a lesser extent, in their distorted variants H(2) and P(1). 4. The directional nature of these influences for H(1) and P(2) conformations is illustrated by plots of the information measure against the distance m from the residue, for m=-10 to +10. 5. The results for statistical co-operativity are discussed in relation to theories of helix-coil and pleated-sheet-coil transitions. The value of the information-theory-derived parameters in obtaining s parameters for the Zimm & Bragg (1959) equations is illustrated. 6. Directional effects are discussed with particular relation to mechanisms of the termination of helices and the involvement of the alpha(II) conformation and also to discontinuities in pleated-sheet conformations.     

A code relating sequence to structure in nucleic acids

Nucleic acids are elucidated in configuration space. An algorithm relating sequence to stability in A and B helical secondary structures, is stated to incorporate NMR conformational and optical melting data. This made possible a classification of elementary sequences in terms of configuration forces driving between A and B states, a finding useful in prediction of structural behavior of different sequences of DNA, RNA and their hybrids.     

Left-handed helix conformation of poly-L-proline II type in globular proteins. Statistics of incidence and a role of sequence]

Regions of left-handed polyproline II type conformation in globular proteins were studied throughout the PDB bank. The length and sequence of corresponding fragments were analyzed. It was found that a lot of tetrapeptides (from combinatorial possible ones) show the tendency to be included in the left-handed helices. Much more tetrapeptides do not occur in this structure type.     

Analysis of the relationship between side-chain conformation and secondary structure in globular proteins

The relationship between the preferred side-chain dihedral angles and the secondary structure of a residue was examined. The structures of 61 proteins solved to a resolution of 2.0 A (1 A = 0.1 nm) or better were analysed using a relational database to store the information. The strongest feature observed was that the chi 1 distribution for most side-chains in an alpha-helix showed an absence of the g- conformation and a shift towards the t conformation when compared to the non-alpha/beta structures. The exceptions to this tendency were for short polar side-chains that form hydrogen bonds with the main-chain which prefer g+. Shifts in the chi 1 preferences for residues in the beta-sheet were observed. Other side-chain dihedral angles (chi 2, chi 3, chi 4) were found to be influenced by the main-chain. This paper presents more accurate distributions for the side-chain dihedral angles which were obtained from the increased number of proteins determined to high resolution. The means and standard deviations for chi 1 and chi 2 angles are presented for all residues according to the secondary structure of the main-chain. The means and standard deviations are given for the most popular conformations for side-chains in which chi 3 and chi 4 rotations affect the position of C atoms.     

Influence of solvent molecules on the stereochemical code of glycyl residues in proteins

The Ramachandran steric map and energy diagrams of the glycyl residue are symmetric. A plot of (phi,psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the right-handed alpha-helical region, the "equivalent" cluster is clearly shifted to in and around the (phi,psi) values of (90 degrees, 0 degrees ) instead of being centered at the left-handed alpha-helical region of (60 degrees, 40 degrees ). This lack of symmetry exists even in the (phi,psi) distribution of residues from non-alpha-helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical and sheet regions, shows that glycyl residues prefer to adopt conformations around (+/-90 degrees, 0 degrees ) instead of right- and left-handed alpha-helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central C(alpha) atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to (+/-90 degrees, 0 degrees ) are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 A or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to (+/-90 degrees, 0 degrees ). It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations in proteins.     

Extracting information on folding from the amino acid sequence: consensus regions with preferred conformation in homologous proteins.

It is investigated whether protein segments predicted to have a well-defined conformational preference in the absence of tertiary interactions are conserved in families of homologous proteins. The prediction method follows the procedures of Rooman, M., Kocher, J.-P., and Wodak, S. (preceding paper in this issue). It uses a knowledge-based force field that incorporates only local interactions along the sequence and identifies segments whose lowest energy structure displays a sizable energy gap relative to other computed conformations. In 13 of the protein families and subfamilies considered that are sufficiently homologous to have similar 3D structures, at least one region is consistently predicted as having the same preferred conformation in virtually all family members. These regions are between 4 and 26 residues long. They are often located at chain ends and correspond primarily to segments of secondary structure heavily involved in interactions with the rest of the protein, suggesting that they could act as nuclei around which other parts of the structure would assemble. Experimental data on early folding intermediates or on protein fragments with appreciable structure in aqueous solution are available for more than half of the protein families. Comparison of our results with these data is quite favorable. They reveal that each of the experimentally identified early formed, or independently stable, substructures harbors at least one of the segments consistently predicted as having a preferred conformation by our procedure. The implications of our findings for the conservation of folding pathways in homologous proteins are discussed.     

Maps of preferential conformation of dipeptides in the structural regions of globular proteins

According to X-ray crystallographic analysis of 46 globular proteins the probability of dipeptides frequency in alpha-helical beta-sheet and random coil conformations has been studied on the basis of which the maps of preferentially conformational state of dipeptide in different elements of secondary structure of proteins have been obtained.     

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.     

Structural and sequence characteristics of long alpha helices in globular proteins.

Elucidation of the detailed structural features and sequence requirements for alpha helices of various lengths could be very important in understanding secondary structure formation in proteins and, hence, in the protein folding mechanism. An algorithm to characterize the geometry of an alpha helix from its C(alpha) coordinates has been developed and used to analyze the structures of long alpha helices (number of residues > or = 25) found in globular proteins, the crystal structure coordinates of which are available from the Brookhaven Protein Data Bank. All long alpha helices can be unambiguously characterized as belonging to one of three classes: linear, curved, or kinked, with a majority being curved. Analysis of the sequences of these helices reveals that the long alpha helices have unique sequence characteristics that distinguish them from the short alpha helices in globular proteins. The distribution and statistical propensities of individual amino acids to occur in long alpha helices are different from those found in short alpha helices, with amino acids having longer side chains and/or having a greater number of functional groups occurring more frequently in these helices. The sequences of the long alpha helices can be correlated with their gross structural features, i.e., whether they are curved, linear, or kinked, and in case of the curved helices, with their curvature.     

Structural principles of the globular organization of protein chains. A stereochemical theory of globular protein secondary structure

The paper reveals the types of amino acid sequences of polypeptide chain regions of globular protein which form a regular (α or β) or irregular conformation in the native globule. The study was made taking into account general “architectural” principles of packing of polypeptide chains in globular proteins and considering the interactions of proteins with water molecules. An a priori theory is developed which permits the identification, in good agreement with experiment, of α-helical and β-structural regions in globular proteins from their primary structure.     

Structural changes and fluctuations of proteins. II. Analysis of the denaturation of globular proteins.

The statistical thermodynamic model of protein structure proposed in paper I is developed with special attention to the hydrophobic interaction. Calorimetric measurements of the thermal denaturation of five globular proteins, ribonuclease A, lysozyme, alpha-chymotrypsin, cytochrome c, and myoglobin, are quantitatively analyzed using the model. The thermodynamic parameters obtained by the least squares method reflect the global, average properties of proteins and are in good agreement with the expected values estimated from experimental and theoretical studies for model peptides. The average bond energy epsilon is well related to the tertiary structure of each protein. However, the difference in the parameters between different proteins is not observed for the cooperative energy ZJ and the chain entropy alpha. The individuality of a protein as far as its structural stability is concerned, is mainly reflected by the parameter gamma specifying the hydrophobic nature of a protein. The model is further applied in the analysis of several aspects of the structural stability of globular proteins. Denaturation induced by denaturants, salts, and pH are also explained by the model in a unified manner.     

Information and redundancy in the burial folding code of globular proteins within a wide range of shapes and sizes

Recent ab initio folding simulations for a limited number of small proteins have corroborated a previous suggestion that atomic burial information obtainable from sequence could be sufficient for tertiary structure determination when combined to sequence‐independent geometrical constraints. Here, we use simulations parameterized by native burials to investigate the required amount of information in a diverse set of globular proteins comprising different structural classes and a wide size range. Burial information is provided by a potential term pushing each atom towards one among a small number L of equiprobable concentric layers. An upper bound for the required information is provided by the minimal number of layers L^min still compatible with correct folding behavior. We obtain L^min between 3 and 5 for seven small to medium proteins with 50 ≤ N_r ≤ 110 residues while for a larger protein with N_r = 141 we find that L ≥ 6 is required to maintain native stability. We additionally estimate the usable redundancy for a given L ≥ L^min from the burial entropy associated to the largest folding‐compatible fraction of “superfluous” atoms, for which the burial term can be turned off or target layers can be chosen randomly. The estimated redundancy for small proteins with L = 4 is close to 0.8. Our results are consistent with the above‐average quality of burial predictions used in previous simulations and indicate that the fraction of approachable proteins could increase significantly with even a mild, plausible, improvement on sequence‐dependent burial prediction or on sequence‐independent constraints that augment the detectable redundancy during simulations. Proteins 2016; 84:515–531. © 2016 Wiley Periodicals, Inc.     

Molecular orbital calculations on the conformation of polypeptides and proteins. II. Conformational energy maps and stereochemical rotational states of aromatic residues

Our previous quantum-mechanical calculations, by an all-valence-electrons method (PCILO) taking into account simultaneously the σ and π electrons of the system, on the conformation energy maps of the glycyl and alanyl residues are extended to the evaluation of these maps and of the stereochemical rotational states of the aromatic residues, phenylalanyl, tyrosyl, histidyl, and tryptophanyl in dipeptides. Calculations on model compounds are used for the predetermination of the side-chain rotational angles χ₁ and χ₂ which are then used as selected parameters for the evaluation of the conformational energy maps as function of the backbone rotational angles Φ and ψ. The theory predicts that the most stable conformation for these aromatic residues should occur in the same region, around Φ = 200, ψ = 140°, in which it was predicted to occur for the glycyl and alanyl residues and which was completely overlooked by most of the previous “empirical” computations. Recent experimental work by a group of Russian authors using NMR and infrared techniques seems to confirm the theoretical result for the alanyl and phenylalanyl residues. The paper indicates also the secondary local minima which appear for the different residues. The theoretically allowed general conformational area for the four aromatic residues, within the reasonable value of 5 kcal/mole above the deepest minimum, is somewhat larger than the similar area allowed by the “hard sphere” empirical calculations. Practically all available representative experimental points from the study of small molecules and of the proteins lysozyme and myoglobin fall within the allowed area, the agreement being better with the results of the quantum mechanical calculations than with those of the “hard sphere” approximation. The values of the side-chain rotational angles χ₁ and χ₂ and of their allowed combinations agree less satisfactorily with experiment, the experimentally observed combinations being more varied than the theoretically allowed ones. These last ones having, however, been predetermined on studies with model compounds, this situation is not astonishing. It is proposed to refine these results by a minimization with respect to the four parameters Φ, ψ, χ₁, and χ₂ involved.     

Molecular orbital calculations on the conformation of polypeptides and proteins. V. Conformational energy maps and stereochemical rotational states of aliphatic residues

The quantum-mechanical calculations by the PCILO method on the conformation of amino acid residues of proteins have been extended to the valyl, leucyl, and isoleucyl residues. In distinction to the earlier “empirical” computations, the quantum-mechanical results indicate very similar energy contours for the stable conformations of the three residues. Their general outline is also similar to that of the alanyl residue, although reduced by about 25%. Contrary to the “empirical” computations, the present results predict that the region corresponding to the α-helix should be one of great stability for the three residues and in particular for the valyl residue. The quantum-mechanical results are in excellent agreement with the experimental conformations of the aliphatic residues in lysozyme and myoglobin. Their prediction as to the ready availability of the valyl residue in the α-helical conformation agrees moreover with Ptitsyn's statistical evaluation of the participation of this residue in the inner turns of the helical regions in six globular proteins. The maximum conformational space allowed for the aliphatic residues is somewhat smaller than that allowed for the aromatic ones, while the minimum conformational space (region of stability common to all the residues) is similar in both groups.     

The prediction of the conformation of membrane proteins from the sequence of amino acids.

The methods of Chou & Fasman [Biochemistry (1974) 13, 211-222, 222-245] and of Lim [J. Mol. Biol. (1974)88, 857-872, 873-894] for predicting secondary structure from amino acid sequence have been applied to five predominantly helical membrane-associated peptides. The predictions from the method of Lim (1974a,b) are consistent with the experimental observations, whereas those from Chou & Fasman (1974a,b), although not inconsistent with alpha-helix, favour a beta-structure for several very hydrophobic regions. The results may be rationalized in terms of the effect of the solvent on the conformation of a polypeptide.     

Prediction of the structural class of globular proteins from their amino acid sequence

Two-dimensional representation of consequence of 32 proteins with known three-dimensional structure has been obtained on 20 X 20 matrix of the distribution of amino acid pairs (nearest neighbours). Prediction algorithm of the structural class of globular proteins has been worked out on the basis of the comparison of 20 X 20 matrix of the distribution of amino acid pairs for the proteins of different structural classes. The accuracy of structural class predictions of 32 proteins has been carried out (all the proteins are taken from numerous ones used to obtain the algorithm).