Twisted hyperboloid (Strophoid) as a model of beta-barrels in proteins.

Using a least-squares fitting procedure, polypeptide backbones of one parallel and seven antiparallel beta-barrels were approximated with various curved surfaces. Although the hyperboloid gave better approximations to all the beta-barrel backbones than the ellipsoid, elliptical cylinder or catenoid, the best approximations were obtained with a novel surface, a twisted hyperboloid (strophoid). The root-mean-square errors between individual beta-barrels and the fitted strophoid surfaces ranged from 0.75 A to 1.64 A. The parameters which determine the strophoid surface allow groups of beta-barrel shapes to be defined according to their barrel twists (i.e. angles subtended by directions of the long axis of cross-section at the top and the bottom of the barrel), course of elliptical cross-sections (either monotonically increasing along the barrel axis, as in cones, or having a middle "waist", as in hyperboloids), and types of backbone curvatures (either convex or concave). The curvatures at individual points of strophoid surface are local, variable quantities related to the local helicity (coil) of the polypeptide backbone, in contrast to values of beta-sheet twist (i.e. dihedral angles subtended by adjacent beta-strands) known to be virtually identical in all the beta-sheets. The variability found in parameters such as barrel shapes and curvatures suggests that simple models (isotropically stressed surfaces, principle of minimal surface tension) proposed in the past to account for beta-barrel shapes are not sufficient. Rather, the complex nature of best-fit theoretical surfaces points to an important role played by a local variability of the forces involved.

Empirical free energy calculations: a blind test and further improvements to the method.

Empirical Gibbs functions estimate free energies of non-covalent reactions (deltaG) from atomic coordinates of reaction products (e.g. antibody-antigen complexes). The function previously developed by us has four terms that quantify the effects of hydrophobic, electrostatic and entropy changes (conformational, association) upon complexation. The function was used to calculate delta deltaG of ten lysozyme mutants affecting the stability of the HyHEL-10 antibody-lysozyme complex. The mutants were computer-modeled from the X-ray structure of the wild-type, and free energy calculations produced a correlation coefficient of 0.5 with the experimental delta deltaG data (average absolute error +/-3 kcal). The following changes were then introduced into the Gibbs function: (1) the hydrophobic force was made proportional to the molecular surface, as calculated by the GEPOL93 algorithm, with the scaling constant of 70 cal/mol/A2; (2) calculation of the electrostatics of binding was carried out by the finite difference Poisson-Boltzmann algorithm, which employed uniform grid charging, dielectric boundary smoothing and charge anti-aliasing; and (3) side-chain conformational entropy was estimated from the CONGEN sampling of torsional degrees of freedom. In the new calculations, correlation with experimental data improved to 0.6 or 0.8 if a single outlying mutant, K96M, was neglected. Analysis of the errors remaining in our calculations indicated that molecular mechanics-based modeling of the mutants, rather than the form of our amended Gibbs function, was the main factor limiting the accuracy of the free energy estimates.

Modeling the antigen combining site of an anti-dinitrophenyl antibody, ANO2.

A model structure has been constructed for a monoclonal anti-dinitrophenyl antibody. The antibody, ANO2, has been sequenced and cloned (Anglister, J., Frey, T., & McConnell, H.M., 1984, Biochemistry 23, 1138-1142). Its amino acid sequence shows striking homology with the anti-lysozyme Fab fragments HyHel5 (83%) and HyHel10 (73%). Based on this homology, a model for the ANO2 variable heavy and variable light chain framework was constructed using a hybrid of the HyHel5 light chain and the HyHel10 heavy chain backbone, omitting the hypervariable loops. These coordinates were used as scaffolds for the model building of ANO2. The CONGEN conformational sampling algorithm (Bruccoleri, R.E. & Karplus, M., 1987, Biopolymers 26, 127-196) was used to model the six hypervariable loops that contain the antigen-combining site. All the possible conformations of the loop backbones were constructed and the best loop structures were selected using a combination of the CHARMM potential energy function and evaluation of the solvent-accessible surface area of the conformers. The order in which the loops were searched was carried out based on the relative locations of the loops with reference to the framework of the beta-barrel, namely, L2-H1-L3-H2-H3-L1. The model structures thus obtained were compared to the high resolution X-ray structure (Brünger, A.T., Leahy, D.J., Hynes, T.R., & Fox, R.O., 1991, J. Mol. Biol. 221, 239-256).

Simulated annealing with restrained molecular dynamics using CONGEN: energy refinement of the NMR solution structures of epidermal and type-alpha transforming growth factors.

The new functionality of the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168; Bassolino-Klimas D et al., 1996, Protein Sci 5:593-603) has been applied for energy refinement of two previously determined solution NMR structures, murine epidermal growth factor (mEGF) and human type-alpha transforming growth factor (hTGF alpha). A summary of considerations used in converting experimental NMR data into distance constraints for CONGEN is presented. A general protocol for simulated annealing with restrained molecular dynamics is applied to generate NMR solution structures using CONGEN together with real experimental NMR data. A total of 730 NMR-derived constraints for mEGF and 424 NMR-derived constraints for hTGF alpha were used in these energy-refinement calculations. Different weighting schemes and starting conformations were studied to check and/or improve the sampling of the low-energy conformational space that is consistent with all constraints. The results demonstrate that loosened (i.e., "relaxed") sets of the EGF and hTGF alpha internuclear distance constraints allow molecules to overcome local minima in the search for a global minimum with respect to both distance restraints and conformational energy. The resulting energy-refined structures of mEGF and hTGF alpha are compared with structures determined previously and with structures of homologous proteins determined by NMR and X-ray crystallography.

Homology modeling using simulated annealing of restrained molecular dynamics and conformational search calculations with CONGEN: application in predicting the three-dimensional structure of murine homeodomain Msx-1.

We have developed an automatic approach for homology modeling using restrained molecular dynamics and simulated annealing procedures, together with conformational search algorithms available in the molecular mechanics program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168). The accuracy of the method is validated by "predicting" structures of two homeodomain proteins with known three-dimensional structures, and then applied to predict the three-dimensional structure of the homeodomain of the murine Msx-1 transcription factor. Regions of the unknown protein structure that are highly homologous to the known template structure are constrained by "homology distance constraints," whereas the conformations of nonhomologous regions of the unknown protein are defined only by the potential energy function. A full energy function (excluding explicit solvent) is employed to ensure that the calculated structures have good conformational energies and are physically reasonable. As in NMR structure determinations, information on the consistency of the structure prediction is obtained by superposition of the resulting family of protein structures. In this paper, our homology modeling algorithm is described and compared with related homology modeling methods using spatial constraints derived from the structures of homologous proteins. The software is then used to predict the DNA-bound structures of three homeodomain proteins from the X-ray crystal structure of the engrailed homeodomain protein (Kissinger CR et al., 1990, Cell 63:579-590). The resulting backbone and side-chain conformations of the modeled yeast Mat alpha 2 and D. melanogaster Antennapedia homeodomains are excellent matches to the corresponding published X-ray crystal (Wolberger C et al., 1991, Cell 67:517-528) and NMR (Billeter M et al., 1993, J Mol Biol 234:1084-1097) structures, respectively. Examination of these structures of Msx-1 reveals a network of highly conserved surface salt bridges that are proposed to play a role in regulating protein-protein interactions of homeodomains in transcription complexes.

Simulated annealing with restrained molecular dynamics using a flexible restraint potential: theory and evaluation with simulated NMR constraints.

A new functional representation of NMR-derived distance constraints, the flexible restraint potential, has been implemented in the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168) for molecular structure generation. In addition, flat-bottomed restraint potentials for representing dihedral angle and vicinal scalar coupling constraints have been introduced into CONGEN. An effective simulated annealing (SA) protocol that combines both weight annealing and temperature annealing is described. Calculations have been performed using ideal simulated NMR constraints, in order to evaluate the use of restrained molecular dynamics (MD) with these target functions as implemented in CONGEN. In this benchmark study, internuclear distance, dihedral angle, and vicinal coupling constant constraints were calculated from the energy-minimized X-ray crystal structure of the 46-amino acid polypeptide crambin (ICRN). Three-dimensional structures of crambin that satisfy these simulated NMR constraints were generated using restrained MD and SA. Polypeptide structures with extended backbone and side-chain conformations were used as starting conformations. Dynamical annealing calculations using extended starting conformations and assignments of initial velocities taken randomly from a Maxwellian distribution were found to adequately sample the conformational space consistent with the constraints. These calculations also show that loosened internuclear constraints can allow molecules to overcome local minima in the search for a global minimum with respect to both the NMR-derived constraints and conformational energy. This protocol and the modified version of the CONGEN program described here are shown to be reliable and robust, and are applicable generally for protein structure determination by dynamical simulated annealing using NMR data.

Modulation of antibody affinity by a non-contact residue.

Antibody LB4, produced by a spontaneous variant of the murine anti-digoxin monoclonal antibody 26-10, has an affinity for digoxin two orders of magnitude lower than that of the parent antibody due to replacement of serine with phenylalanine at position 52 of the heavy chain variable region (Schildbach, J.F., Panka, D.J., Parks, D.R., et al., 1991, J. Biol. Chem. 266, 4640-4647). To examine the basis for the decreased affinity, a panel of engineered antibodies with substitutions at position 52 was created, and their affinities for digoxin were measured. The antibody affinities decreased concomitantly with increasing size of the substituted side chains, although the shape of the side chains also influenced affinity. The crystal structure of the 26-10 Fab complexed with digoxin (P.D.J., R.K. Strong, L.C. Sieker, C. Chang, R.L. Campbell, G.A. Petsko, E.H., M.N.M., & S.S., submitted for publication) shows that the serine at heavy chain position 52 is not in contact with hapten, but is adjacent to a tyrosine at heavy chain position 33 that is a contact residue. The mutant antibodies were modeled by applying a conformational search procedure to position side chains, using the 26-10 Fab crystal structure as a starting point. The results suggest that each of the substituted side chains may be accommodated within the antibody without substantial structural rearrangement, and that none of these substituted side chains are able to contact hapten. These modeling results are consistent with the substituents at position 52 having only an indirect influence upon antibody affinity.(ABSTRACT TRUNCATED AT 250 WORDS)

Contribution of a single heavy chain residue to specificity of an anti-digoxin monoclonal antibody.

Two distinct spontaneous variants of the murine anti-digoxin hybridoma 26-10 were isolated by fluorescence-activated cell sorting for reduced affinity of surface antibody for antigen. Nucleotide and partial amino acid sequencing of the variant antibody variable regions revealed that 1 variant had a single amino acid substitution: Lys for Asn at heavy chain position 35. The second variant antibody had 2 heavy chain substitutions: Tyr for Asn at position 35, and Met for Arg at position 38. Mutagenesis experiments confirmed that the position 35 substitutions were solely responsible for the markedly reduced affinity of both variant antibodies. Several mutants with more conservative position 35 substitutions were engineered to ascertain the contribution of Asn 35 to the binding of digoxin to antibody 26-10. Replacement of Asn with Gln reduced affinity for digoxin 10-fold relative to the wild-type antibody, but maintained wild-type fine specificity for cardiac glycoside analogues. All other substitutions (Val, Thr, Leu, Ala, and Asp) reduced affinity by at least 90-fold and caused distinct shifts in fine specificity. The Ala mutant demonstrated greatly increased relative affinities for 16-acetylated haptens and haptens with a saturated lactone. The X-ray crystal structure of the 26-10 Fab in complex with digoxin (Jeffrey PD et al., 1993, Proc Natl Acad Sci USA 90:10310-10314) reveals that the position 35 Asn contacts hapten and forms hydrogen bonds with 2 other contact residues. The reductions in affinity of the position 35 mutants for digoxin are greater than expected based upon the small hapten contact area provided by the wild-type Asn. We therefore performed molecular modeling experiments which suggested that substitution of Gln or Asp can maintain these hydrogen bonds whereas the other substituted side chains cannot. The altered binding of the Asp mutant may be due to the introduction of a negative charge. The similarities in binding of the wild-type and Gln-mutant antibodies, however, suggest that these hydrogen bonds are important for maintaining the architecture of the binding site and therefore the affinity and specificity of this antibody. The Ala mutant eliminates the wild-type hydrogen bonding, and molecular modeling suggests that the reduced side-chain volume also provides space that can accommodate a congener with a 16-acetyl group or saturated lactone, accounting for the altered fine specificity of this antibody.

Correlation among sites of limited proteolysis, enzyme accessibility and segmental mobility.

The relationship among accessibility to an enzyme, flexibility, and limited proteolysis was explored. Regions accessible to large probes, comparable in size to proteolytic enzymes, were computed in the crystallographic structures of thermolysin, trypsinogen and ribonuclease. Positions of these accessible regions were compared with sites of autolytic/proteolytic attacks, and with locations of flexible backbone segments. All the proteolytic sites were found to be exceptionally accessible. Most of them were also flexible, but at least one prominent site in trypsinogen appeared to be rigid. Thus, surface exposure seems to be more essential to proteolysis than flexibility.

Solution conformation of a cyclic pentapeptide endothelin antagonist. Comparison of structures obtained from constrained dynamics and conformational search.

The structure of a cyclic pentapeptide, cyclo-(D-Trp-D-Asp-L-Pro-D-Val-L-Leu), that has high selectively for the endothelin ETA receptor has been determined by NMR spectroscopy using constrained molecular dynamics and conformational search procedures. Structures obtained using two methods of refinement, namely (i) constrained molecular dynamics; and (ii) systematic searches of conformational space for optimal satisfaction of distance constraints, were compared to those obtained from systematic searches of conformational space without NMR data. The two different procedures of refinement produce similar conformations that are consistent with the NMR distance constraints. Conformational searches for optimal energy without any NMR distance constraints produced several low-energy structures, two of which have essentially the same backbone as those structures derived from distance-constrained procedures and one of these even reproduces several side-chain positions well. The pentapeptide backbone consists of a linked gamma- and beta-turn conformation, with the leucine and tryptophan as corner residues of the type II beta-turn. The side chains are highly ordered both in aqueous solvent and in dimethyl sulfoxide. In aqueous media the leucine side chain is directed towards the indole ring, presumably to reduce the non-polar surface exposure, producing unusual upfield shifts for the methyls (and particularly H gamma). This structural feature was reproduced in one of the structures obtained from conformational searches performed without NMR data. Exhaustive conformational searches appear to provide an alternative method for structure generation for cyclic peptides.

Conformational sampling using high-temperature molecular dynamics.

High-temperature molecular dynamics as a method for conformational search was explored on the antigen combining site of McPC 603, a phosphorylcholine binding immunoglobulin. Simulations at temperatures of 500, 800, and 1500 K were run for 111.5, 101.7, and 76.3 ps, respectively. The effectiveness of the search was assessed using a variety of methods. For the shorter hypervariable loops, molecular dynamics explored an appreciable fraction of the conformational space as evidenced by a comparison to a simple theoretical model of the size of the conformational space. However, for the longer loops and the antigen combining site as a whole, the simulation times were too short for a complete search. The simulations at 500 and 800 K both generated conformations that minimized to energies 200 kcal/mole lower than the crystal structure. However, the 1500 K simulation produced higher energy structures, even after minimization; in addition, this highest temperature run had many cis-trans peptide isomerizations. This suggests that 1500 K is too high a temperature for unconstrained conformational sampling. Comparison of the results of high temperature molecular dynamics with a direct conformational search method, [R. E. Bruccoleri & M. Karplus (1987) Biopolymers 26, 137-168]. showed that the two methods did not overlap much in conformational space. Simple geometric measures of the conformational space indicated that the direct method covered more space than molecular dynamics at the lower temperature, but not at 1500 K. The results suggest that high-temperature molecular dynamics can aid in conformational searches.

An improved algorithm for nucleic acid secondary structure display.

An improved algorithm for the display of nucleic acid secondary structures is presented. It is particularly suitable for large sequence segments and it automatically generates an aesthetically pleasing display of the structure with very limited overlap of strands. Structural similarities in different structures are conserved in the display thus greatly aiding structural homology comparisons. Using the algorithm, we illustrate the effect of ribosome translocation on the secondary structure of a rat neuropeptide messenger RNA.

Application of a directed conformational search for generating 3-D coordinates for protein structures from alpha-carbon coordinates.

A directed conformational search algorithm using the program CONGEN (ref. 3), which samples backbone conformers, is described. The search technique uses information from the partially built structures to direct the search process and is tested on the problem of generating a full set of backbone Cartesian coordinates given only alpha-carbon coordinates. The method has been tested on six proteins of known structure, varying in size and classification, and was able to generate the original backbone coordinates with RMSs ranging from 0.30-0.87A for the alpha-carbons and 0.5-0.99A RMSs for the backbone atoms. Cis peptide linkages were also correctly identified. The procedure was also applied to two proteins available with only alpha-carbon coordinates in the Brookhaven Protein Data Bank; thioredoxin (SRX) and triacylglycerol acylhydrolase (TGL). All-atom models are proposed for the backbone of both these proteins. In addition, the technique was applied to randomized coordinates of flavodoxin to assess the effects of irregularities in the data on the final RMS. This study represents the first time a deterministic conformational search was used on such a large scale.

Stabilities of leucine zipper dimers estimated by an empirical free energy method.

The leucine zipper motif is a characteristic amino acid sequence found in dimeric DNA-binding proteins. Computer-generated models for leucine zippers were constructed as alpha-helical coiled dimers with leucine repeated every seventh residue. An empirical Gibbs free energy, delta G, function which incorporates hydrophobic force, electrostatic interactions, and conformational entropy loss as the major intermolecular interactions was used to estimate the delta G of dimer formation in fos, jun, and GCN4 zipper sequences. The calculations showed that complexes known to form stable homo- or heterodimers have favorable (negative) delta G, while other less stable complexes have unfavorable (positive) delta G. Leucines in position d of the coiled coil contribute large hydrophobic stabilization energies while residues in the a position contribute less to dimer stability. Hydrophobic contributions show little sequence specificity, however, and do not contribute significantly to homo/heterodimer preference. Charged residues in the e and g positions, on the other hand, determine homo/heterodimer specificity. In GCN4 homodimers, residues GLU el, Glu b2, Lys g2, and Lys e4 greatly contribute to dimer stability. The preferential stability of fos-jun heterodimer over the jun-jun and fos-fos homodimers is primarily due to the side chains Asp b1, Glu g1, Asp b2, Glu e2, Glu g2, Glu g3, and Lys a5 of the fos helix, and Arg c1, Lys g1, Lys b2, Lys e2, Arg e4, and Glu g4 of the jun helix.

Criteria that discriminate between native proteins and incorrectly folded models.

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.

Structure of antibody hypervariable loops reproduced by a conformational search algorithm.

The antigen-combining site of antibody molecules consists of six separate loops supported by a conserved beta-sheet framework; antibody specificity arises from length and sequence variation of these 'hypervariable' loops and can be manipulated by transferring sets of loops between different frameworks. Irregular loops are the most difficult parts of protein structure to understand and to model correctly. Here, we describe two computer experiments where all the hypervariable loops were deleted from X-ray structures of mouse immunoglobulins and reconstructed using the conformational search program CONGEN. A protocol was developed for reconstruction of the hypervariable loops in McPC 603 antibody. Calculated loop conformations were generated and a model of the combining site was built from selected low-energy conformations. We then modelled hypervariable loops in another antibody molecule, HyHEL-5. Both models agreed well with the known crystal structures. Our results hold out promise for the success of future modelling studies of complete antigen-combining sites from amino acid sequences.

Computer analysis of mutations that affect antibody specificity.

The mouse hybridoma cell line 40-150 secretes antibodies with high affinity toward the cardiac glycosides digoxin and digitoxin. A spontaneous mutant, 40-150 A2.4, produces an antibody which carries a single residue mutation, Ser----Arg, in its heavy chain (H94) and has an altered specificity. A second-order mutant, 40-150 A2.4 P.10, produces two antibody molecules, one the same as 40-150 A2.4, the other lacking two residues at the N-terminus of its H chain, and having a specificity profile approaching that of 40-150 antibody. The N-terminus and the position H94 are distant from the antigen-binding site of the antibody; thus, the structural basis of the specificity changes was not immediately clear. Approximate structures of the 40-150 antibody and its mutants were constructed in the computer, based on atomic coordinates of the homologous mouse antibody McPC 603. Using the program CONGEN, the torsional space of the polypeptide backbone and side chains around position H94 was uniformly sampled, and the lowest energy conformations were analyzed in detail. The results indicate that when Arg-H94 is substituted for Ser, Arg-H94 can hydrogen bond to side chains of Asp-H101, Arg-L46, and Asp-L55. This results in a change in the surface of the combining site which may account for the affinity changes. Deletion of the two N-terminal residues increases solvent accessibility of Arg-H94. The solvation may cause a hydrogen bond between Arg-H94 and Asp-H101 to be lost, restoring the structure to one similar to that of 40-150.

Protein antigenicity: a static surface property.

Much recent progress has been made in understanding the nature of antigenicity in the generation of antibodies. In this article Jirí Novotný and his colleagues discuss properties such as accessibility, flexibility and shape which determine the antigenicity of sites on proteins and consider the influence of these properties on the formation of immune complexes and the composition of the idiotype network.