Physicochemical evaluation of protein folds predicted by threading

Protein structure prediction remains an unsolved problem. Since prediction of the native structure seems very difficult, one usually tries to predict the correct fold of a protein. Here the "fold" is defined by the approximate backbone structure of the protein. However, physicochemical factors that determine the correct fold are not well understood. It has recently been reported that molecular mechanics energy functions combined with effective solvent terms can discriminate the native structures from misfolded ones. Using such a physicochemical energy function, we studied the factors necessary for discrimination of correct and incorrect folds. We first selected correct and incorrect folds by a conventional threading method. Then, all-atom models of those folds were constructed by simply minimizing the atomic overlaps. The constructed correct model representing the native fold has almost the same backbone structure as the native structure but differs in side-chain packing. Finally, the energy values of the constructed models were compared with that of the experimentally determined native structure. The correct model as well as the native structure showed lower energy than misfolded models. However, a large energy gap was found between the native structure and the correct model. By decomposing the energy values into their components, it was found that solvent effects such as the hydrophobic interaction or solvent shielding and the Born energy stabilized the correct model rather than the native structure. The large energetic stabilization of the native structure was attained by specific side-chain packing. The stabilization by solvent effects is small compared to that by side-chain packing. Therefore, it is suggested that in order to confidently predict the correct fold of a protein, it is also necessary to predict correct side-chain packing.     

Electrostatic contributions to the stability of a thermophilic cold shock protein

The thermophilic Bacillus caldolyticus cold shock protein (Bc-Csp) differs from the mesophilic Bacillus subtilis cold shock protein B (Bs-CspB) in 11 of the 66 residues. Stability measurements of Schmid and co-workers have implicated contributions of electrostatic interactions to the thermostability. To further elucidate the physical basis of the difference in stability, previously developed theoretical methods that treat electrostatic effects in both the folded and the unfolded states were used in this paper to study the effects of mutations, ionic strength, and temperature. For 27 mutations that narrow the difference in sequence between Bc-Csp and Bs-CspB, calculated changes in unfolding free energy (Delta G) and experimental results have a correlation coefficient of 0.98. Bc-Csp appears to use destabilization of the unfolded state by unfavorable charge-charge interactions as a mechanism for increasing stability. Accounting for the effects of ionic strength and temperature on the electrostatic free energies in both the folded and the unfolded states, explanations for two important experimental observations are presented. The disparate ionic strength dependences of Delta G for Bc-Csp and Bs-CspB were attributed to the difference in the total charges (-2e and -6e, respectively). A main contribution to the much higher unfolding entropy of Bs-CspB was found to come from the less favorable electrostatic interactions in the folded state. These results should provide insight for understanding the thermostability of other thermophilic proteins.     

Important amino acid properties for enhanced thermostability from mesophilic to thermophilic proteins

Understanding the role of various interactions in enhancing the thermostability of proteins is important not only for clarifying the mechanism of protein stability but also for designing stable proteins. In this work, we have analyzed the thermostability of 16 different families by comparing mesophilic and thermophilic proteins with 48 various physicochemical, energetic and conformational properties. We found that the increase in shape, s (location of branch point in side chain) increases the thermostability, whereas, an opposite trend is observed for Gibbs free energy change of hydration for native proteins, GhN, in 14 families. A good correlation is observed between these two properties and the simultaneous increases of -GhN and s is necessary to enhance the thermostability from mesophile to thermophile. The increase in shape, which tends to increase with increasing number of carbon atoms both for polar and non-polar residues, may generate more packing and compactness, and the position of beta and higher order branches may be important for better packing. On the other hand, the increase in -GhN in thermophilic proteins increases the solubility of the proteins. This tendency counterbalances the increases in insolubility and unfolding heat capacity change due to the increase in the number of carbon atoms. Thus, the present results suggest that the stability of thermophilic proteins may be achieved by a balance between better packing and solubility.     

Thermodynamic differences among homologous thermophilic and mesophilic proteins.

Here, we analyze the thermodynamic parameters and their correlations in families containing homologous thermophilic and mesophilic proteins which show reversible two-state folding <--> unfolding transitions between the native and the denatured states. For the proteins in these families, the melting temperatures correlate with the maximal protein stability change (between the native and the denatured states) as well as with the enthalpic and entropic changes at the melting temperature. In contrast, the heat capacity change is uncorrelated with the melting temperature. These and additional results illustrate that higher melting temperatures are largely obtained via an upshift and broadening of the protein stability curves. Both thermophilic and mesophilic proteins are maximally stable around room temperature. However, the maximal stabilities of thermophilic proteins are considerably greater than those of their mesophilic homologues. At the living temperatures of their respective source organisms, homologous thermophilic and mesophilic proteins have similar stabilities. The protein stability at the living temperature of the source organism does not correlate with the living temperature of the protein. We tie thermodynamic observations to microscopics via the hydrophobic effect and a two-state model of the water structure. We conclude that, to achieve higher stability and greater resistance to high and low temperatures, specific interactions, particularly electrostatic, should be engineered into the protein. The effect of these specific interactions is largely reflected in an increased enthalpy change at the melting temperature.     

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.     

Empirical solvation models can be used to differentiate native from near-native conformations of bovine pancreatic trypsin inhibitor.

Several hydration models for peptides and proteins based on solvent accessible surface area have been proposed previously. We have evaluated some of these models as well as four new ones in the context of near-native conformations of a protein. In addition, we propose an empirical site-site distance-dependent correction that can be used in conjunction with any of these models. The set of near-native structures consisted of 39 conformations of bovine pancreatic trypsin inhibitor (BPTI) each of which was a local minimum of an empirical energy function (ECEPP) in the absence of solvent. Root-mean-square (rms) deviations from the crystallographically determined structure were in the following ranges: 1.06-1.94 A for all heavy atoms, 0.77-1.36 A for all backbone heavy atoms, 0.68-1.33 A for all alpha-carbon atoms, and 1.41-2.72 A for all side-chain heavy atoms. We have found that there is considerable variation among the solvent models when evaluated in terms of concordance between the solvation free energy and the rms deviations from the crystallographically determined conformation. The solvation model for which the best concordance (0.939) with the rms deviations of the C alpha atoms was found was derived from NMR coupling constants of peptides in water combined with an exponential site-site distance dependence of the potential of mean force. Our results indicate that solvation free energy parameters derived from nonpeptide free energies of hydration may not be transferrable to peptides. Parameters derived from peptide and protein data may be more applicable to conformational analysis of proteins. A general approach to derive parameters for free energy of hydration from ensemble-averaged properties of peptides in solution is described.     

A folding model of α-lactalbumin deduced from the three-state denaturation mechanism

It has been shown that α-lactalbumin undergoes a three-state denaturation, involving a helical intermediate state, on treatment with guanidine hydrochloride. The unfolding of the protein and the characteristics of the intermediate state are examined by means of circular dichroism, difference spectra and pH-jump measurements to investigate the temperature dependence and kinetic properties of the unfolding and refolding, the pH dependence of the transition between the intermediate and the fully unfolded states, and the effect of disulphide bond reduction on the stabilization of the intermediate.The results show that the long-range specific interactions such as specific electrostatic interactions and disulphide linkages are not important for stabilizing the intermediate, and that the transition between the intermediate and the fully unfolded states is extremely rapid (a relaxation time of less than one millisecond) and may correspond to the helix-coil transition of a polypeptide backbone. On the other hand, the activation parameters of the transition between the native and the intermediate states have suggested that the final stabilization by charge-pair interactions is preceded by hydrophobic interactions in the process of going from the intermediate to the native state.The mechanism of folding of the protein is discussed, and the folding process from the fully unfolded to the native state is apparently divided into at least three main steps: (1) the formation of incipient helical structures dictated by local interactions; (2) the packing of the helical segments accompanied with hydrophobic interactions; (3) the final stabilization by the electrostatic interactions. The relevance to the current theoretical results on protein folding is also discussed.     

Importance of main-chain hydrophobic free energy to the stability of thermophilic proteins

Living organisms are found in the most unexpected places, including deep-sea vents at 100 degrees C and several hundred bars pressure, in hot springs. Needless to say, the proteins found in thermophilic species are much more stable than their mesophilic counterparts. There are no obvious reasons to say that one would be more stable than others. Even examination of the amino acids and comparison of structural features of thermophiles with mesophilies cannot bring satisfactory explanation for the thermal stability of such proteins. In order to bring out the hidden information behind the thermal stabilization of such proteins in terms of energy factors and their combinations, analysis were made on good resolution structures of thermophilic and their mesophilic homologous from 23 different families. From the structural coordinates, free energy contributions due to hydrophobic, electrostatic, hydrogen bonding, disulfide bonding and van der Waals interactions are computed. In this analysis, a vast majority of thermophilic proteins adopt slightly lower free energy contribution in each energy terms than its mesophilic counterparts. The major observation noted from this study is the lower hydrophobic free energy contribution due to carbon atoms and main-chain nitrogen atoms in all the thermophilic proteins. The possible combination of different free energy terms shows majority of the thermophilic proteins have lower free energy strategy than their mesophilic homologous. The derived results show that the hydrophobic free energy due to carbon and nitrogen atoms and such combinations of free energy components play a vital role in the thermostablisation of such proteins.     

Electrostatic screening and backbone preferences of amino acid residues in urea-denatured ubiquitin

Local structures in denatured proteins may be important in guiding a polypeptide chain during the folding and misfolding processes. Existence of local structures in chemically denatured proteins is a highly controversial issue. NMR parameters [coupling constants (3) J(H(alpha),H(N)) and chemical shifts] of chemically denatured proteins in general deviate little from their values in small peptides. These peptides were presumed to be completely unstructured; therefore, it was considered that chemically denatured proteins are random coils. But recent experimental studies show that small peptides adopt relatively stable structures in aqueous solutions. Small deviations of the NMR parameters from their values in small peptides may thus actually indicate the existence of local structures in chemically denatured proteins. Using NMR data and theoretical predictions we show here that fluctuating beta-strands exist in urea-denatured ubiquitin (8 M urea at pH 2). Residues in such beta-strands populate more frequently the left side of the broad beta region of -psi space. Urea-denatured ubiquitin contains no detectable beta-sheet secondary structures; nevertheless, the fluctuating beta-strands in urea-denatured ubiquitin coincide to the beta-strands in the native state. Formation of beta-strands is in accord with the electrostatic screening model of unfolded proteins. The free energy of a residue in an unfolded protein is in this model determined by the local backbone electrostatics and its screening by backbone solvation. These energy terms introduce strong electrostatic coupling between neighboring residues, which causes cooperative formation of beta-strands in denatured proteins. We propose that fluctuating beta-strands in denatured proteins may serve as initiation sites to form fibrils.     

The dominant role of side-chain backbone interactions in structural realization of amino acid code. ChiRotor: a side-chain prediction algorithm based on side-chain backbone interactions

The basic differences between the 20 natural amino acid residues are due to differences in their side-chain structures. This characteristic design of protein building blocks implies that side-chain-side-chain interactions play an important, even dominant role in 3D-structural realization of amino acid codes. Here we present the results of a comparative analysis of the contributions of side-chain-side-chain (s-s) and side-chain-backbone (s-b) interactions to the stabilization of folded protein structures within the framework of the CHARMm molecular data model. Contrary to intuition, our results suggest that side-chain-backbone interactions play the major role in side-chain packing, in stabilizing the folded structures, and in differentiating the folded structures from the unfolded or misfolded structures, while the interactions between side chains have a secondary effect. An additional analysis of electrostatic energies suggests that combinatorial dominance of the interactions between opposite charges makes the electrostatic interactions act as an unspecific folding force that stabilizes not only native structure, but also compact random conformations. This observation is in agreement with experimental findings that, in the denatured state, the charge-charge interactions stabilize more compact conformations. Taking advantage of the dominant role of side-chain-backbone interactions in side-chain packing to reduce the combinatorial problem, we developed a new algorithm, ChiRotor, for rapid prediction of side-chain conformations. We present the results of a validation study of the method based on a set of high resolution X-ray structures.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.     

Exploiting the Link between Protein Rigidity and Thermostability for Data‐Driven Protein Engineering

Understanding and exploiting the relationship between microscopic structure and macroscopic stability is important for developing strategies to improve protein stability at high temperatures. The thermostability of proteins has been repeatedly linked to an enhanced structural rigidity of the folded native state. In the current study, the rigidity of protein structures from mesophilic and thermophilic organisms along a thermal unfolding trajectory is directly probed. In order to perform this, protein structures were modeled as constraint networks, and the rigidity in these networks was quantified using the Floppy Inclusion and Rigid Substructure Topography (FIRST) method. During the thermal unfolding, a phase transition was observed that defines the rigidity percolation threshold and corresponds to the folded‐unfolded transition in protein folding. Using concepts from percolation theory and network science, a higher phase transition temperature was observed for ca. two‐thirds of the proteins from thermophilic organisms compared to their mesophilic counterparts, when applied to a data set of 20 pairs of homologues. From both the analysis of the microstructure of the constraint networks and monitoring the macroscopic behavior during the thermal unfolding, direct evidence was found for the “corresponding states” concept, which states that mesophilic and thermophilic enzymes are in corresponding states of similar flexibility at their respective optimal temperature. Finally, the current approach facilitated the identification of structural features from which a destabilization of the structure originates upon thermal unfolding. These predictions show a good agreement with the experimental data. Therefore, the information might be exploited in data‐driven protein engineering by pointing to residues that should be varied to obtain a protein with higher thermostability.     

Origin of the sequence-dependent polyproline II structure in unfolded peptides

Recent studies have indicated that the unfolded states of polypeptides contain a substantial amount of polyproline type II (P(II)) structure. This energetically and structurally preorganized state may contribute to the reduction of the folding search, as well as to the recognition of intrinsically unstructured proteins and polyproline ligands. Using Monte Carlo simulations of natively unfolded peptides in the presence of explicit aqueous solvation, we observe that residue-specific P(II) conformational propensity is the result of the modulation of polypeptide backbone hydration by a proximal side-chain. Such a mechanism may be unique among those that contribute to the modulation of secondary structures in proteins. The calculated conformational propensities should prove useful for the development of a configurational P(II) scale necessary for the prediction and design of natural-like polypeptides.     

Selecting near-native conformations in homology modeling: the role of molecular mechanics and solvation terms

A free energy function, combining molecular mechanics energy with empirical solvation and entropic terms, is used for ranking near-native conformations that occur in the conformational search steps of homology modeling, i.e., side-chain search and loop closure calculations. Correlations between the free energy and RMS deviation from the X-ray structure are established. It is shown that generally both molecular mechanics and solvation/entropic terms should be included in the potential. The identification of near-native backbone conformations is accomplished primarily by the molecular mechanics term that becomes the dominant contribution to the free energy if the backbone is even slightly strained, as frequently occurs in loop closure calculations. Both terms become equally important if a sufficiently accurate backbone conformation is found. Finally, the selection of the best side-chain positions for a fixed backbone is almost completely governed by the solvation term. The discriminatory power of the combined potential is demonstrated by evaluating the free energies of protein models submitted to the first meeting on Critical Assessment of techniques for protein Structure Prediction (CASP1), and comparing them to the free energies of the native conformations.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.     

An analysis of incorrectly folded protein models. Implications for structure predictions

Proteins with homologous amino acid sequences have similar folds and it has been assumed that an unknown three-dimensional structure can be obtained from a known homologous structure by substituting new side-chains into the polypeptide chain backbone, followed by relatively small adjustment of the model. To examine this approach of structure prediction and, more generally, to isolate the characteristics of native proteins, we constructed two incorrectly folded protein models. Sea-worm hemerythrin and the variable domain of mouse immunoglobulin K-chain, two proteins with no sequence homology, were chosen for study; the former is composed of a bundle of four alpha-helices and the latter consists of two 4-stranded beta-sheets. Using an automatic computer procedure, hemerythrin side-chains were substituted into the immunoglobulin domain and vice versa. The structures were energy-minimized with the program CHARMM and the resulting structures compared with the correctly folded forms. It was found that the incorrect side-chains can be incorporated readily into both types of structures (alpha-helices, beta-sheets) with only small structural adjustments. After constrained energy-minimization, which led to an average atomic co-ordinate shift of no more than 0.7 to 0.9 A, the incorrectly folded models arrived at potential energy values comparable to those of the correct structures. Detailed analysis of the energy results shows that the incorrect structures have less stabilizing electrostatic, van der Waals' and hydrogen-bonding interactions. The difference is particularly pronounced when the electrostatic and van der Waals' energy terms are calculated by modified equations that include an approximate representation of solvent effects. The incorrectly folded structures also have a significantly larger solvent-accessible surface and a greater fraction of non-polar side-chain atoms exposed to solvent. Examination of their interior shows that the packing of side-chains at the secondary structure interfaces, although corresponding to sterically allowed conformations, deviates from the characteristics found in normal proteins. The analysis of incorrectly folded structures has made it clear that the absence of bad non-bonded contacts, though necessary, is not sufficient to demonstrate the validity of model-built structures and that modeling of homologous structures has to be accompanied by a thorough quantitative evaluation of the results. Further, certain features that characterize native proteins are made evident by their absence in misfolded models.     

Electrostatic contribution of surface charge residues to the stability of a thermophilic protein: benchmarking experimental and predicted pKa values

Optimization of the surface charges is a promising strategy for increasing thermostability of proteins. Electrostatic contribution of ionizable groups to the protein stability can be estimated from the differences between the pKa values in the folded and unfolded states of a protein. Using this pKa-shift approach, we experimentally measured the electrostatic contribution of all aspartate and glutamate residues to the stability of a thermophilic ribosomal protein L30e from Thermococcus celer. The pKa values in the unfolded state were found to be similar to model compound pKas. The pKa values in both the folded and unfolded states obtained at 298 and 333 K were similar, suggesting that electrostatic contribution of ionizable groups to the protein stability were insensitive to temperature changes. The experimental pKa values for the L30e protein in the folded state were used as a benchmark to test the robustness of pKa prediction by various computational methods such as H++, MCCE, MEAD, pKD, PropKa, and UHBD. Although the predicted pKa values were affected by crystal contacts that may alter the side-chain conformation of surface charged residues, most computational methods performed well, with correlation coefficients between experimental and calculated pKa values ranging from 0.49 to 0.91 (p<0.01). The changes in protein stability derived from the experimental pKa-shift approach correlate well (r = 0.81) with those obtained from stability measurements of charge-to-alanine substituted variants of the L30e protein. Our results demonstrate that the knowledge of the pKa values in the folded state provides sufficient rationale for the redesign of protein surface charges leading to improved protein stability.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.