Computer-aided discrimination between active and inactive mutants of the N-terminal domain of the bacteriophage lambda repressor.

Binding of the N-terminal domain of the lambda repressor to DNA is coupled to dimerization. Hydrophobic interactions between helix-5 and helix-5' drive the packing at the dimer interface. We have carried out computations of the conformational energy of packing of the fifth helices (and of the helix-4-loop-helix-5 portions) of variants of the lambda repressor operator binding domain, using an ECEPP/3-based packing algorithm. Here, we report the results for 26 mutants chosen among those that hve been characterized experimentally. We find that the relative orientation of the fifth helices for active mutants is very similar to the wild-type. The fifth helices of the inactive mutants have a significantly different relative orientation. This result illustrates that a unique specific orientation pattern of helix-5 relative to helix-5' is required for dimerization-coupled DNA binding activity. This finding is further supported by computational studies of the whole N-terminal domain of ten variants that showed that the active mutants, including the wild-type protein, have similar values of the number of contacts between the two monomers in the dimer, involving two amino acid residues of the fifth helices (positions 84 and 87 in each monomer). A decrease in the number of such contacts abolishes DNA-binding activity. Furthermore, all active mutants have their "DNA-recognition helices", numbers 3 and 3' positioned so that they can fit in the DNA operator like those of the wild-type protein, while some inactive mutants exhibit a substantial change in the relative orientation of their recognition helices.

Effects on protein structure and function of replacing tryptophan with 5-hydroxytryptophan: single-tryptophan mutants of the N-terminal domain of the bacteriophage lambda repressor.

Conformational energy computations have been carried out on the N-acetyl-N'-methylamide of 5-hydroxytryptophan (5OH-Trp) using ECEPP/3. As observed with tryptophan (Trp), the most preferred conformation about the C alpha-C beta bond of the side chain is g+ or t. This preference is reduced to only the t conformational state when 5-hydroxyTrp is in the middle of a right-handed poly(L-alanine) alpha-helix. A similar result has been obtained with Trp [Piela et al. (1987), Biopolymers 1987, 1273-1286]. These results suggest that replacement of Trp by its analog 5-hydroxyTrp may be tolerated in an alpha-helix. To test this hypothesis, we have replaced Trp by 5OH-Trp in the fifth helices of two functionally active mutants of the N-terminal domain of the bacteriophage lambda repressor. Computations on the packing of these helices have shown that no significant structural changes results from the replacement of Trp by 5OH-Trp. The DNA-binding activity of these mutants, as assessed indirectly through geometrical parameters, is also unaltered.

The energy of formation of internal loops in triple-helical collagen polypeptides.

The sequence-dependent local destabilization in the interior of the collagen triple helix has been evaluated by means of conformational energy computations. Using a model poly(Gly-Pro-Pro) triple helix as the reference state, a method was developed for generating local loops, i.e., internal deformations, and analyzing their conformations. A seven-residue Gly-Pro-Pro- Gly-Pro-Pro-Gly fragment was replaced by the Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in one, two, or all three of the strands of the loop region. A set of loop conformations was generated in which the ends of the loop were initially fixed in the triple-helical structure. The potential energy of the entire deformed triple helix was then minimized, resulting in a variety of structures that contained deformed loops. The conformations of the triple helices at the two ends of the loops remained essentially unchanged in many of the low-energy conformations. In numerous high-energy conformations, however, the triple-helical segments were also partially or totally disrupted. The minimum-energy conformations of the whole structures were compared in terms of rms deviations of atomic coordinates with respect to the original triple helix, and of the shapes of the loops (using a distance function derived from differential geometry). Three new geometrical parameters-stretch S, kink K, and unwinding U-were defined to describe the changes in the overall orientation of the triple helices at the two ends of the loop. It is shown that, when the number of Pro residues in a short fragment is reduced, the triple helical structure can accomodate internal loops (i.e., distortions) within a 5 kcal/mol cutoff from the essentially unperturbed triple helical structure. For structures with a Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in all three strands, the probability of finding conformations with internal loops is small, i.e., 0.06. Internal loops affect the overall orientation of these structures, as measured by the helix-distortion parameters S, K, and U.

Structure of the type I collagen molecule based on conformational energy computations: the triple-stranded helix and the N-terminal telopeptide.

Various studies have implicated a crucial role for the non-helical ends (telopeptides) of the collagen molecule during fibrillogenesis. In this paper, the first extensive conformational analysis of the type I collagen N-terminal telopeptide is reported. The commonly used "build-up" procedure for peptides and proteins has been used, with relevant modifications to take account of all the stereochemical constraints affecting the telopeptide. In particular, consideration was given not only to the interactions among the three chains that constitute the telopeptide, but also to the interactions between the telopeptide and the covalently linked triple helix. The computations led to a limited number of different structures within an energy range of 25 kcal/mol. Comparison of these models clearly shows that the portion of the telopeptide linked to the triple helix is rather rigid whereas its N terminus is more flexible. Furthermore, the lowest-energy structure has an energy that is markedly lower (by 7.75 kcal/mol) than that of other conformations with different structural features. The lowest-energy model of the N-terminal telopeptide, which differs from previous proposed models, has a contracted conformation compared to the triple helix region, in agreement with X-ray and neutron diffraction data on collagen fibers. Finally, the side-chains of the lysine residues of the telopeptide, involved in intermolecular cross-links in mature collagen fibers, are oriented to protrude to the exterior, in positions to interact with adjacent collagen molecules.

The effect of the l-azetidine-2-carboxylic acid residue on protein conformation. IV. Local substitutions in the collagen triple helix.

The properties of collagen are affected by the replacement of Pro by imino acid analogues. The structural effect of the low-level local substitution of L-azetidine-2-carboxylic acid (Aze) has been analyzed by computing the energy of CH3CO-(Gly-Pro-Pro)4-NHCH3 triple helices in which a single residue of one strand has been replaced by Aze. When Aze is in position Y of a (Gly-X-Y) unit, low-energy local deformations are introduced in the triple helix, i.e., it becomes more flexible. On the other hand, the flexibility of the triple helix is not increased with Aze in position X. The energy of the triple helix to coil transition is not changed significantly by this amount of substitution. In an earlier study, we have demonstrated that the regular substitution of Aze in every tripeptide distorts or destabilizes the triple helix to a large extent [A. Zagari, G. Némethy, & H. A. Scheraga (1990) Biopolymers, Vol. 30, pp. 967-974]. Thus, it appears that a high level of substitution is required to cause the observed chemical and biological effects of Aze on collagen.

Stabilization of the triple-helical structure of natural collagen by side-chain interactions.

Conformational energy computations have been used to demonstrate that side-chain-backbone interactions contribute substantially to the stabilization of the triple-helical structure of collagen with a natural sequence. The minimum-energy conformation has been determined for a short triple-helical segment from the N-terminus of type I bovine skin collagen, containing 12 residues in each strand. In this conformation, the side chains of three Arg and four Met residues fold tightly against the triple-helical backbone, forming numerous atomic contacts with the neighboring strand. In addition, the polar groups of the three Arg and two Ser residues form hydrogen bonds with backbone carbonyl groups. The estimated total stabilization due to the side-chain interactions is about -50 kcal/mol out of a total interchain energy of -193.5 kcal/mol. The study presented here is the first application of conformational energy computations to a real sequence in the collagen molecule.

Conformational energy studies of beta-sheets of model silk fibroin peptides. I. Sheets of poly(Ala-Gly) chains.

A new model structure is proposed for the silk I form of the crystalline domains of Bombyx mori silk fibroin and the corresponding crystal form of poly(L-Ala-Gly). It was deduced from conformational energy computations on stacked sheet structures of poly(L-Ala-Gly). The novel sheet structure contains interstrand hydrogen bonds but is composed of anti-parallel polypeptide chains whose conformation differs from that of the antiparallel beta-sheets that constitute the silk II structure. The strands of the new sheet have a two-residue repeat, in which the Ala residues adopt a right-handed and the Gly residues a left-handed sheet-like conformation. The computed unit cell is orthorhombic, with cell dimensions a = 8.94 A, b = 6.46 A, and c = 11.26 A. The model accounts for most spacings in the observed fiber x-ray diffraction patterns of silk I and of the silk-I-like form of poly(L-Ala-Gly), and it is consistent with nmr and ir spectroscopic data. As a test of the computations, the well-established beta-sheet structure of silk II and the corresponding form of poly(L-Ala-Gly) have been reproduced. The computed energies for the two forms of poly(L-Ala-Gly) indicate that the silk-II-like form is more stable, by about 1.0 kcal/mol per residue. The main difference between the two structures is the orientation of the Ala side chains of neighboring strands in each sheet. In the Pauling-Corey beta-sheet and in the silk II form, referred to as an "in-register" structure, the Ala side chains of every strand point to the same side of a sheet. In the silk I structure, referred to as "out-of-register," the side chains of Ala residues in adjacent strands point to opposite sides of the sheet.

Theoretical studies of protein conformation by means of energy computations.

In this review we describe fundamental concepts and applications of conformational energy computations, with emphasis on some recent advances and problems being investigated. The formulation of potential energy functions is described, including the nature of the intramolecular force field, the representation of interactions with the solvent, and considerations of entropy contributions. Approaches to the search for the optimal potential energy are summarized. Examples cited among applications of conformational energy computations include refinement of X-ray crystallographic structures, the use of computations in conjunction with NMR data, prediction of the structures of proteins based on either homology or on other procedures that surmount the multiple-minima problem, the analysis of hierarchical levels of structure and assembly, and interactions in enzyme-substrate complexes.

Energetics of the structure and chain tilting of antiparallel beta-barrels in proteins.

The preferred structural pattern of antiparallel beta-barrels in proteins, described as the right-handed tilting of the peptide strands with respect to the axis of the barrel, is accounted for in terms of intra- and interchain interaction energies. It is related to the preference of beta-sheets for right-handed twisting. Conformational energy computations have been carried out on three eight-stranded antiparallel beta-barrels composed of six-residue strands, in which L-Val and Gly alternate, and having a right-handed, a left-handed, or no tilt. After energy minimization, the relative energies of these structures were 0.0, 8.6, and 46.1 kcal/mol, respectively; i.e., the right-tilted beta-barrel is favored energetically, in agreement with anti-parallel beta-barrels observed in proteins. Tilting of the barrel is favored, relative to the nontilted structure, by both intra- and interstrand interactions, because tilting allows better packing of the bulky side chains. On the other hand, the energy difference between the left- and right-tilted barrels arises essentially from intrachain interactions. This is a consequence of the preference of beta-sheets for a right-handed twist. Space limitations inside the barrel are satisfied if there is an alternation of bulky residues and residues with small or no side chain (preferably Gly) in neighboring positions on adjacent strands. Such a pattern is seen frequently in antiparallel beta-barrels of globular proteins. The computations indicate that a structure with Val...Gly pairs can be accommodated in a beta-barrel with no distortion.

The effect of the L-azetidine-2-carboxylic acid residue on protein conformation. I. Conformations of the residue and of dipeptides.

The L-azetidine-2-carboxylic acid (Aze) residue can be incorporated into proteins in the place of L-proline, of which it is the lower homologue. This substitution alters the properties of proteins, especially of collagen. Conformational constraints in N-acetyl-Aze-N'-methylamide and in several dipeptides containing Aze have been analyzed by means of energy computations. They have been compared with peptides containing Pro. The overall conformational preferences of Aze and Pro are similar, but several significant differences occur between them. In general, peptides containing Aze are somewhat more flexible than corresponding peptides containing Pro, because of a decrease in constraints caused by repulsive nonconvalent interactions of the atoms of the ring with neighboring residues. This results in an entropic effect that lessens the stability of ordered polypeptide conformations with respect to the disordered statistical coil. The collagen-like near-extended conformation is energetically less favorable for Aze than for Pro in the single residue and in dipeptides. This effect also contributes to a destabilization of the collagen triple helix. The influence of Aze on the conformation of polypeptides is discussed in the accompanying papers.

The effect of the L-azetidine-2-carboxylic acid residue on protein conformation. II. Homopolymers and copolymers.

The alteration of polymer conformational properties caused by the replacement of L-proline by L-azetidine-2-carboxylic acid (Aze) has been studied by means of conformational energy computations. In addition to poly(Aze), two sequential copolymers, poly(Pro-Aze) and poly(Aze3-Pro3), have been investigated. All polymers containing Aze are more flexible than poly(Pro). This is a consequence of an increased number of permitted conformational states for the Aze residue, as compared to Pro, when they are incorporated into a polypeptide, as well as of a lessened cooperativity of the trans-cis transition. The results of the computation can be used to interpret the observed physical properties of poly(Aze) and of its copolymers.

The effect of the L-azetidine-2-carboxylic acid residue on protein conformation. III. Collagen-like poly(tripeptide)s.

The chemical and biological properties of collagen are altered by the biosynthetic substitution of the L-azetidine-2-carboxylic acid(Aze) residue in the place of proline. The reasons for this alteration have been studied by means of conformational energy computations on single- and triple-stranded structures formed by poly(Gly-X-Y) poly(tripeptide)s, where X and Y can be Pro or Aze. The most stable triple helix formed by Poly(Gly-Pro-Aze) is collagen-like, but all low-energy triple helices that can be formed by poly(Gly-Aze-Pro) and poly(Gly-Aze-Aze) are very different from collagen. Thus, the regular substitution of Aze for Pro in position X is not compatible with the collagen structure. In the absence of solvent effects, all of these triple helices are stable, relative to the statistical coil, but the substitutions reduce the stability of the collagen-like triple helix, as compared with poly(Gly-Pro-Pro).

Free energy of hydration of collagen models and the enthalpy of the transition between the triple-helical coiled-coil and single-stranded conformations.

Interactions with water make an important contribution to the free energy of stabilization of the collagen triple helix, but they do not alter the structure of the triple helix, i.e., the packing geometry of the three strands. Conformational energy computations have been carried out on poly(tripeptide) analogues of collagen, with the introduction of a newly developed form of a hydration shell model to compute the free energy of hydration. The most stable triple helix formed by poly(Gly-Pro-Pro), obtained earlier from conformational energy computations [M. H. Miller & H. A. Scheraga (1976) J. Polym. Sci. Polym. Symp. 54, 171], with a structure that is very closely similar to the observed structure, is strongly favored over other three-strand complexes, both in the absence and the presence of hydration. The hydration shell model does not provide an explanation for the increased stability of the poly(Gly-Pro-Hyp) triple helix as compared to poly(Gly-Pro-Pro). It appears that the difference should be attributed to specific binding of water, and effect that is not yet included in the present version of the hydration shell model. On the other hand, this model accounts for the observed enthalpy of unfolding of a poly(Gly-Pro-Pro) triple helix to isolated single chains in solution in terms of intramolecular noncovalent interactions and the free energy of hydration.

Energy of stabilization of the right-handed beta alpha beta crossover in proteins.

An explanation in terms of conformational energies is provided for the observed nearly exclusive preference of the beta alpha beta structure for forming a right-handed, rather than a left-handed, crossover connection. Conformational energy computations have been carried out on a model beta alpha beta structure, consisting of two six-residue Val beta-strands and of a 12-residue Ala alpha-helix, connected by two flexible four-residue Ala links to the strands. The energy of the most favorable right-handed crossover is 15.51 kcal/mol lower than that of the corresponding left-handed cross-over. The right-handed crossover is a strain-free structure. Its energy of stabilization arises largely from the interactions of the two beta-strands with one another and with the alpha-helix. On the other hand, the left-handed crossover is either disrupted after energy minimization or it remains conformationally strained, as indicated by an energetically unfavorable left twisting of the beta-sheet and by the presence of high-energy local residue conformations. In the energetically most favorable right-handed crossover, the right twisting of the beta-sheet and its manner of interacting with the alpha-helix are identical with those computed earlier for isolated beta-sheets and for packed alpha/beta structures. This result supports a proposed principle that it is possible to account for the main features of frequently occurring structural arrangements in globular proteins in terms of the properties of their component structural elements.

Prediction of the packing arrangement of strands in beta-sheets of globular proteins.

A method is proposed for predicting the adjacency order in which strands pack in a beta-sheet in a protein, on the basis of its amino acid sequence alone. The method is based on the construction of a predicted contact map for the protein, in which the probability that various residue pairs are close to each other is computed from statistically determined average distances of residue pairs in globular proteins of known structure. Compact regions, i.e., portions of the sequence with many interresidue contacts, are determined on the map by using an objective search procedure. The proximity of strands in a beta-sheet is predicted from the density of contacts in compact regions associated with each pair of strands. The most probable beta-sheet structures are those with the highest density of contacts. The method has been tested by computing the probable strand arrangements in a five-strand beta-sheet in five proteins or protein domains, containing 62-138 residues. Of the theoretically possible 60 strand arrangements, the method selects two to eight arrangements as most probable; i.e., it leads to a large reduction in the number of possibilities. The native strand arrangement is among those predicted for three of the five proteins. For the other two, it would be included in the prediction by a slight relaxation of the cutoff criteria used to analyze the density of contacts.

Prediction of probable pathways of folding in globular proteins.

A method is described for the prediction of probable folding pathways of globular proteins, based on the analysis of distance maps. It is applicable to proteins of unknown spatial structure but known amino acid sequence as well as to proteins of known structure. It is based on an objective procedure for the determination of the boundary of compact regions that contain high densities of interresidue contacts on the distance map of a globular protein. The procedure can be used both with contact maps derived from a known three-dimensional protein structure and with predicted contact maps computed by means of a statistical procedure from the amino acid sequence alone. The computed contact map can also be used to predict the location of compact short-range structures, viz. alpha-helices and beta-turns, thereby complementing other statistical predictive procedures. The method provides an objective basis for the derivation of a theoretically predicted pathway of protein folding, proposed by us earlier [Tanaka and Scheraga (1977) Macromolecules 10, 291-304; Némethy and Scheraga (1979) Proc. Natl. Acad. Sci., U.S.A. 76, 6050-6054].

Prediction of the location of structural domains in globular proteins.

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation [i-j[ in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.

Energetics of the structure of the four-alpha-helix bundle in proteins.

The main features of the four-alpha-helix bundle, one of the characteristic structural elements of many proteins, can be explained in terms of noncovalent interactions between the constituent helices. Conformational energy computations have been carried out on four types of four-alpha-helix bundles, each consisting of four CH3CO-(L-Ala)10-NHCH3 polypeptide chains, with various combinations of parallel and antiparallel orientations of the helices. In the bundle with the most favorable energy, all pairs of neighboring helices are oriented antiparallel--i.e., in the orientation that is favored by electrostatic interactions between the helices. In this structure, the orientation angle between neighboring helix axes is -168 degrees, within +/- 7 degrees, in close agreement with the orientation angles observed in proteins and with the value that we computed earlier for the most favorable packing of pairs of interacting alpha-helices. This orientation corresponds to a left-handed twisting of the helical bundle. The preferred handedness of this twisting arises as a result of favorable nonbonded interactions between the alpha-helices.