Protein folding simulations with genetic algorithms and a detailed molecular description

We have explored the application of genetic algorithms (GA) to the determination of protein structure from sequence, using a full atom representation. A free energy function with point charge electrostatics and an area based solvation model is used. The method is found to be superior to previously investigated Monte Carlo algorithms. For selected fragments, up to 14 residues long, the lowest free energy structures produced by the GA are similar in conformation to the corresponding experimental structures in most cases. There are three main conclusions from these results. First, the genetic algorithm is an effective method for searching amongst the compact conformations of a polypeptide chain. Second, the free energy function is generally able to select native-like conformations. However, some deficiencies are identified, and further development is proposed. Third, the selection of native-like conformations for some protein fragments establishes that in these cases the conformation observed in the full protein structure is largely context independent. The implications for the nature of protein folding pathways are discussed.

Comparison of database potentials and molecular mechanics force fields

The advantages and disadvantages of database and molecular mechanics force fields for the study of macromolecules are compared, with emphasis on the ability to distinguish between correct and incorrect structures. Molecular mechanics force fields have the advantage of resting on a clear theoretical basis, permitting an in-depth analysis of different contributions. On the other hand, large simplifications are necessary for tractable computing, and there has so far been little effective testing at the macromolecular level. Database potentials allow greater freedom of functional form and have been shown to be effective at discriminating between correct and incorrect complete structures. The principal negative is a controversial relationship to free energy. More testing and comparison of both sorts of potential are needed.

Elimination of the hydrolytic water molecule in a class A beta-lactamase mutant: crystal structure and kinetics

Two site-directed mutant enzymes of the class A beta-lactamase from Staphylococcus aureus PC1 were produced with the goal of blocking the site that in the native enzyme is occupied by the proposed hydrolytic water molecule. The crystal structures of these two mutant enzymes, N170Q and N170M, have been determined and refined at 2.2 and 2.0 A, respectively. They reveal that the side chain of Gln 170 displaces the water molecule, whereas that of Met170 does not. In both cases, the catalytic rates with benzylpenicillin are reduced by 10(4) compared with the native enzyme. With nitrocefin, the N170Q mutant enzyme exhibits an approximately 800-fold reduced rate compared with the native enzyme and in addition, a fast initial burst with stoichiometry of 1 mol of degraded nitrocefin/mol of enzyme. Stopped-flow kinetic experiments establish that the rate constant of the burst is 250 s-1, a value comparable with the rate of acylation of the native enzyme. Two structurally based mechanisms that explain the kinetic properties of the N170Q beta-lactamase are proposed, both invoking a deacylation-impaired enzyme due to the elimination of the hydrolytic water molecule. The catalytic rate of the N170M mutant enzyme with nitrocefin is reduced by approximately 50-fold compared with the native enzyme, and the slow progressive inhibition that is revealed indicates that the hydrolysis proceeds via a branched pathway mechanism. This is consistent with the structural data that show that the water site is preserved and that Met170 occupies part of the space that is required for substrate binding. The short contacts between the substrate and the enzyme may lead to structure perturbation and inactivation.

The current state of the art in protein structure prediction

The capabilities of current protein structure prediction methods have been assessed from the outcome of a set of blind tests. In comparative modeling, many of the numerical methods did not perform as well as expected, although the resulting structures are still of great practical use. The new methods of fold identification ('threading') were partially successful, and show considerable promise for the future. Except for secondary structure data, results from traditional ab initio methods were poor. A second blind prediction experiment is underway, and progress in all areas is expected.

Local interactions dominate folding in a simple protein model

Recent computational studies of simple models of protein folding have concluded that a pronounced energy minimum (i.e. large gap in energy between low-energy states of the model) is a necessary and sufficient condition to ensure folding of a sequence to its lowest-energy conformation. Here, we show that this conclusion strongly depends on the particular temperature scheme selected to govern the simulations. On the other hand, we show that there is a dominant factor determining if a sequence is foldable. That is, the strength of possible interactions between residues close in the sequence. We show that sequences with many possible strong local interactions (either favorable or, more surprisingly, a mixture of strong favorable and unfavorable ones) are easy to fold. Progressively increasing the strength of such local interactions makes sequences easier and easier to fold. These results support the idea that initial formation of local substructures is important to the foldability of real proteins.

Genetic algorithms for protein structure prediction

Genetic algorithms are a general class of search methods that mimic natural gene-based optimization mechanisms. Mutation, cross-over and replication operations are performed on strings. When applied to structure prediction, each string describes a particular conformation of a protein molecule. There are many ways in which such search methods may be implemented. Recent results show potential for helping with protein structure prediction, but more data are needed before a complete assessment can be made.

Positive and negative cooperativities at subsequent steps of oxygenation regulate the allosteric behavior of multistate sebacylhemoglobin

Cross-linked human hemoglobin (HbA) is obtained by reaction with bis(3,5-dibromosalicyl) sebacate. Peptide maps and crystallographic analyses confirm the presence of the 10 carbon atom long sebacyl residue cross-linking the two beta82 lysines of the beta-cleft (DecHb). The Adair's constants, obtained from the oxygen binding isotherms, show that at the first step of oxygenation normal hemoglobin and DecHb have a very similar oxygen affinity. In DecHb negative binding cooperativity is present at the second step of oxygenation, which has an affinity 27 times lower than at the first step. Positive cooperativity is present at the third binding step, whose affinity is 380 times that of the second step. The fourth binding step shows a weak negative cooperativity with an affinity one-half that of the third step. Crystals of deoxy-DecHb diffracted to 1.9 angstroms resolution. The resulting atomic coordinates are very similar to those of Fermi et al. [(1984) J. Mol.Biol. 175, 159-174] and Fronticelli et al. [(1994) J. Biol Chem. 269, 23965-23969] for deoxy-HbA. The electron density map of deoxy-DecHb indicates the presence of the 10 carbon bridge between the beta82 lysines. Molecular modeling confirms that insertion of the linker into the T structure requires only slight displacement of the two beta82 lysines. Instead, insertion of the linker into the R and R2 structures [Shaanan (1983) J. Mol. Biol. 171, 31-59; Silva et al. (1992) J. Biol. Chem. 267, 17248-17256] is hindered by serious sterical restrictions. The linker primarily affects the partially and fully liganded states of hemoglobin. The data suggest in DecHb concerted conformational changes at each step of oxygenation.

The acute rise in plasma fibrinogen concentration with exercise is influenced by the G-453-A polymorphism of the beta-fibrinogen gene

We have investigated the effects of chronic physical training and acute intensive exercise on plasma fibrinogen levels and the relationship of these responses to beta-fibrinogen G-453-A polymorphism genotype. One hundred fifty-six male British Army recruits were studied at the start of their 10-week basic training, which emphasizes physical fitness. Cohorts were restudied between 0.5 and 5 days after a major 2-day strenuous military exercise (ME) undertaken in their final week of training. Changes in fibrinogen concentration were adjusted for the effects of age, body mass index, and smoking history. Compared with baseline values, fibrinogen concentrations were significantly lower (11.9%, P=.04) at day 5 after ME, consistent with the beneficial effect of training. However, they were higher on days 1 through 3 after ME (suggesting an "acute-phase" response to strenuous exercise) and were maximal on days 1 and 2 (27.2%, P<.001 and 37.1%, P<.001 respectively). Fibrinogen genotype was available in 149 individuals. As expected from previous studies, men with one or more fibrinogen gene A-453 alleles had plasma fibrinogen concentration slightly but significantly higher at baseline (4.5%, P=.11). During the acute-phase response (days 2 and 3), however, the degree of rise was strongly related to the presence of the A allele, being 26.7+/-5.4% (mean+/-SE), 36.5+/-11.0%, and 89.2+/-30.7 for the GG, GA, and AA genotypes, respectively (P=.01). These results confirm that chronic exercise training lowers plasma fibrinogen levels, that intensive exercise generates an acute-phase rise in levels, and that this acute response is strongly influenced by the G/A polymorphism of the beta-fibrinogen gene.

Crystallographic, molecular modeling, and biophysical characterization of the valine beta 67 (E11)-->threonine variant of hemoglobin

The crystal structure of the mutant deoxyhemoglobin in which the beta-globin Val67(E11) has been replaced with threonine [Fronticelli et al. (1993) Biochemistry 32, 1235-1242] has been determined at 2.2 A resolution. Prior to the crystal structure determination, molecular modeling indicated that the Thr67(E11) side chain hydroxyl group in the distal beta-heme pocket forms a hydrogen bond with the backbone carbonyl of His63(E7) and is within hydrogen-bonding distance of the N delta of His63(E7). The mutant crystal structure indicates only small changes in conformation in the vicinity of the E11 mutation confirming the molecular modeling predictions. Comparison of the structures of the mutant beta-subunits and recombinant porcine myoglobin with the identical mutation [Cameron et al. (1993) Biochemistry 32, 13061-13070] indicates similar conformations of residues in the distal heme pocket, but there is no water molecule associated with either of the threonines of the beta-subunits. The introduction of threonine into the distal heme pocket, despite having only small perturbations in the local structure, has a marked affect on the interaction with ligands. In the oxy derivative there is a 2-fold decrease in O2 affinity [Fronticelli et al. (1993) Biochemistry 32, 1235-1242], and the rate of autoxidation is increased by 2 orders of magnitude. In the CO derivative the IR spectrum shows modifications with respect to that of normal human hemoglobin, suggesting the presence of multiple CO conformers. In the nitrosyl derivative an interaction with the O gamma atom of Thr67(E11) is probably responsible for the 10-fold increase in the rate of NO release from the beta-subunits. In the aquomet derivative there is a 6-fold decrease in the rate of hemin dissociation suggesting an interaction of the Fe-coordinated water with the O gamma of Thr67(E11).

Confronting the problem of interconnected structural changes in the comparative modeling of proteins

Comparative models of three proteins have been built using a variety of computational methods, heavily supplemented by visual inspection. We consider the accuracy obtained to be worse than expected. A careful analysis of the models shows that a major reason for the poor results is the interconnectedness of the structural differences between the target proteins and the template structures they were modeled from. Side chain conformations are often determined by details of the structure remote in the sequence, and can be influenced by relatively small main chain changes. Almost all of the regions of substantial main chain conformational change interact with at least one other such region, so that they often cannot be modeled independently. Visual inspection is sometimes effective in correcting errors in sequence alignment and in spotting when an alternative template structure is more appropriate. We expect some improvements in the near future through the development of structure-based sequence alignment tools, side chain interconnectedness rotamer choice algorithms, and a better understanding of the context sensitivity of conformational features.

Ab initio structure prediction for small polypeptides and protein fragments using genetic algorithms

Ab initio folding simulations have been performed on three peptides, using a genetic algorithm-based search method which operates on a full atom representation. Conformations are evaluated with an empirical force field parameterized by a potential of mean force analysis of experimental structures. The dominant terms in the force field are local and nonlocal main chain electrostatics and the hydrophobic effect. Two of the simulated structures were for fragments of complete proteins (eosinophil-derived neurotoxin (EDN) and the subtilisin propeptide) that were identified as being likely initiation sites for folding. The experimental structure of one of these (EDN) was subsequently found to be consistent with that prediction (using local hydrophobic burial as the determinant for independent folding). The simulations of the structures of these two peptides were only partly successful. The most successful folding simulation was that of a 22-residue peptide corresponding to the membrane binding domain of blood coagulation factor VIII (Membind). Three simulations were performed on this peptide and the lowest energy conformation was found to be the most similar to the experimental structure. The conformation of this peptide was determined with a C alpha rms deviation of 4.4 A. Although these simulations were partly successful there are still many unresolved problems, which we expect to be able to address in the next structure prediction experiment.

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11-14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested.

Structure, dynamics and energetics of initiation sites in protein folding: I. Analysis of a 1 ns molecular dynamics trajectory of an early folding unit in water: the helix I/loop I-fragment of barnase

The dynamic and energetic behavior of an initiation site of protein folding (helix I/loop I fragment of barnase) isolated from the tertiary environment of the rest protein is investigated in a 1 ns molecular dynamics simulation. All atom representation, explicit solvent description, and periodic boundary conditions are applied. In the course of the simulation several steps of structural disintegration are observed, followed by events partially rebuilding the initial structure. The phase of disintegration results in a fragment conformation completely lacking hydrogen bonds, with one residue in the center of the helix changed from alpha to beta conformation. The transition state of helix disintegration is characterized by a complete i-->i + 4/i + 5 hydrogen bonding network which undergoes gradual hydrolysis starting at the solvent exposed flank and proceeding towards the interior of the fragment perpendicular to the axis of the helix. Energetic analysis of the helix transitions shows that the i-->i + 4/i-->i + 5 network of hydrogen bonds accommodates one helical residue in beta conformation with only slightly worse hydrogen bonding energy and Van der Waals packing compared to the regular alpha-helix. The stability of the fragment is primarily due to hydrophobic interactions of residues shown to be essential in mutagenesis experiments.

Role of electrostatic screening in determining protein main chain conformational preferences

Amino acids display significant variation in propensity for the alpha R-helical, beta-sheet, and other main chain conformational states in proteins and peptides. The physical reason for these preferences remains controversial. Conformational entropy, steric factors, and the hydrophobic effect have all been advanced as the dominant underlying cause. In this work, we explore the role of a fourth factor, electrostatics, in determining the main chain conformation in protein molecules. Potentials of mean force derived from experimental protein structures are used to evaluate the free energy of electrostatic and other interactions of a residue in a protein environment. The local and nonlocal electrostatic interactions of main chain polar atoms are found to be crucial for determining the preferences of residues for the alpha R-helical state and other main chain conformational states of a residue. Further, the strength of local and nonlocal electrostatic interactions is shown to depend on the electrostatic screening by solvent and protein groups. Residue specific modulation of this screening in a manner related to side chain bulk and squatness produces a model that fits the observed distribution of residue conformations in proteins and recent experimental mutagenesis data on protein stability better than any other single factor.

Comparison of systematic search and database methods for constructing segments of protein structure

Two principal methods of determining the conformation of short pieces of polypeptide backbone in proteins have been developed: using a database of known structures and systematically generating all conformations. In this paper, we compare the effectiveness of these two techniques. The completeness of the database for segments of different lengths is examined and it is found to contain most conformations for segments seven residues long, but to deteriorate rapidly for longer regions. When the database segment is to be incorporated into the rest of a structure, at least seven residues are required to build four new residues, because of the need to position the segment relative to the rest of the structure. It is found that such positioning using flanking residues results in large errors in the inserted region. We conclude that the database method is currently not effective for comparative modeling, even for short segments. The systematic search procedure is found to generate almost all structures of short segments found in proteins. In contrast to the database method, low root mean square error structures are obtained for a set of trial segments embedded in the rest of a protein structure. Thus, it should be considered the method of choice.

Finding the lowest free energy conformation of a protein is an NP-hard problem: proof and implications

The protein folding problem and the notion of NP-completeness and NP-hardness are discussed. A lattice model is suggested to capture the essence of protein folding. For this model we present a proof that finding the lowest free energy conformation belongs to the class of NP-hard problems. The implications of the proof are discussed and we suggest that the natural folding process cannot be considered as a search for the global free energy minimum. However, we suggest an explanation as to why, for many proteins, the native functional conformation may coincide with the lowest free energy conformation.

On achieving better than 1-A accuracy in a simulation of a large protein: Streptomyces griseus protease A

Computational methods are frequently used to simulate the properties of proteins. In these studies accuracy is clearly important, and the improvement of accuracy of protein simulation methodology is one of the major challenges in the application of theoretical methods, such as molecular dynamics, to structural studies of biological molecules. Much effort is being devoted to such improvements. Here, we present an analysis of a 187-ps molecular dynamics simulation of the serine protease Streptomyces griseus protease A in its crystal environment. The reproduction of the experimental structure is considerably better than has been achieved in earlier simulations--the root mean square deviation of the simulated structure from the x-ray structure being less than 1 A, a significant step toward the goal of simulating proteins to within experimental error. The use of a longer cutoff with truncation rather than a switching function, inclusion of all crystalline water and the counterions in the crystallization medium, and use of the consistent valence force field characterize the differences in this calculation.

Genetic algorithms for protein folding simulations

Genetic algorithms methods utilize the same optimization procedures as natural genetic evolution, in which a population is gradually improved by selection. We have developed a genetic algorithm search procedure suitable for use in protein folding simulations. A population of conformations of the polypeptide chain is maintained, and conformations are changed by mutation, in the form of conventional Monte Carlo steps, and crossovers in which parts of the polypeptide chain are interchanged between conformations. For folding on a simple two-dimensional lattice it is found that the genetic algorithm is dramatically superior to conventional Monte Carlo methods.

Troponin-C mutants with increased calcium affinity

Binding of two Ca2+ to the regulatory sites I and II of troponin C (TnC) induces a conformational transition believed to be responsible for the activation of muscle contraction. Based on the known crystal structure (2Ca2+ state), a model for the transition to the 4Ca2+ state has been proposed [Herzberg, O., Moult, J. & James, M. N. G. (1986) J. Biol. Chem. 261, 2638-2644]. The proposed conformational transition predicts that during Ca2+ binding a number of nonpolar residues become exposed to the solvent, creating a hydrophobic patch. Such a model implies that mutation of the hydrophobic to polar residues should increase the Ca2+ affinity at the regulatory sites and reduce the Ca2+ concentration necessary for muscle activation. To test this prediction, we have constructed and functionally characterized two troponin-C mutants (V45T and M48A mutations). Direct calcium-binding measurements in the mutants demonstrate an increase in the Ca2+ affinity for two low-affinity sites. Replacement of endogenous troponin C in skinned muscle fibers by TnC with mutations V45T or M48A increased the Ca2+ sensitivity of their tension development. These results show that the model can be used to construct mutants that regulate muscle contraction at lower Ca2+ concentrations. They provide further experimental support for the proposed calcium-induced conformational change of troponin C and suggest that the predicted transition plays a central role in the activation of the thin filament.

Construction and characterization of a spectral probe mutant of troponin C: application to analyses of mutants with increased Ca2+ affinity

A spectral probe mutant (F29W) of chicken skeletal muscle troponin C (TnC) has been prepared in which Phe-29 has been substituted by Trp. Residue 29 is at the COOH-terminal end of the A helix immediately adjacent to the Ca2+ binding loop of site I (residues 30-41) of the regulatory N domain. Since this protein is naturally devoid of Tyr and Trp, spectral features can be assigned unambiguously to the single Trp. The fluorescent quantum yield at 336 nm is increased almost 3-fold in going from the Ca(2+)-free state to the 4Ca2+ state with no change in the wavelength of maximum emission. Comparisons of the Ca2+ titration curves of the change in far-UV CD and fluorescence emission indicated that the latter was associated only with the binding of 2Ca2+ to the regulatory sites I and II. No change in fluorescence was detected by titration with Mg2+. The Ca(2+)-induced transitions of both the N and C domains were highly cooperative. Addition of Ca2+ also produced a red shift in the UV absorbance spectrum and a reduction in positive ellipticity as monitored by near-UV CD measurements. The fluorescent properties of F29W were applied to an investigation of five double mutants: F29W/V45T, F29W/M46Q, F29W/M48A, F29W/L49T, and F29W/M82Q. Ca2+ titration of their fluorescent emissions indicated in each case an increased Ca2+ affinity of their N domains. The magnitude of these changes and the decreased cooperativity observed between Ca2+ binding sites I and II for some of the mutants are discussed in terms of the environment of the mutated residues in the 2Ca2+ and modeled 4Ca2+ states.(ABSTRACT TRUNCATED AT 250 WORDS)

Docking by least-squares fitting of molecular surface patterns

Molecular surfaces are fitted to each other by a new solution to the problem of docking a ligand into the active site of a protein molecule. The procedure constructs patterns of points on the surfaces and superimposes them upon each other using a least-squares best-fit algorithm. This brings the surfaces into contact and provides a direct measure of their local complementarity. The search over the ligand surface produces a large number of dockings, of which a small fraction having the best complementarity and the least steric hindrance are evaluated for electrostatic interaction energy. When applied to molecules taken from crystallographically observed complexes, this procedure consistently assigns the lowest electrostatic energies to correct dockings. On independently determined structures, the ability of the method to discern correct dockings depends on how much conformational difference there is between the free and complexed forms of the molecules. The procedure is found to be fast enough on contemporary workstation computers to permit many conformations to be considered, and tolerant enough to make rather coarse bond dihedral sampling a practicable way to overcome the problem of structural flexibility.

Fitting electron density by systematic search

A systematic search approach to the automatic refinement of protein structures could reduce the need for manual intervention. In this approach, possible conformations for a segment of the polypeptide chain are generated systematically and the trial segments are scored for their agreement with the observed diffraction data. The sampling of conformational space is sufficiently exhaustive that reasonable conformations should be included. A number of score functions have been tested, including local electron-density correlations and global structure-factor agreements. The score functions vary in their predictive power as well as in their bias toward the conformation found in the current refined model, but the best score functions have reasonable predictive power. Related functions can be used to indicate which regions of the model fit poorly, reducing the need for manual inspection of models in electron density.

Analysis of the steric strain in the polypeptide backbone of protein molecules

The extent to which local strain is present in the polypeptide backbone of folded protein molecules has been examined. The occurrence of steric strain associated with nonproline cis peptide bonds and energetically unfavorable main chain dihedral angles can be identified reliably from the well ordered parts of high resolution, refined crystal structures. The analysis reveals that there are relatively few sterically strained features. Those that do occur are located overwhelmingly in regions concerned with function. We attribute this to the greater precision necessary for ligand binding and catalysis, compared with the requirements of satisfactory folding.