Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins

Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the method's explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).     

Prediction of the structure of the Y+.R-.R(+)-type DNA triple helix by molecular modelling.

Molecular mechanics has been used to predict the structure of the Y+.R-.R(+)-type DNA triple helix, in which a second polypurine strand binds antiparallel to the homopurine strand of a homopurine/homopyrimidine stretch of duplex DNA. From calculations on the sequence d(C)10.d(G)10.d(G)10, two likely structures emerge. One has the glycosidic torsions of the third strand bases in the anti-conformation and Hoogsteen hydrogen-bonds to the purine strand of the duplex, the other has the third strand purines in the syn orientation and uses a reverse-Hoogsteen hydrogen-bonding pattern. Despite the large structural differences between these two types of triplex, calculations performed in vacuo with a distance-dependent dielectric constant to mimic the shielding effect of solvent show them to be energetically very similar, with the latter (syn) slightly preferred. However, if explicit solvent molecules are included in the calculation, the anti conformation is found to be much preferred. This difference in the results seems to stem from an underestimation of short-range electrostatic interactions in the in vacuo simulations. When TAA or TAT base triples are substituted for the sixth CGG triple in the sequence, it is found that, for the solvated model, the third strand base of the TAA triple prefers the syn orientation while that in the TAT triple retains a preference, though reduced, for the anti conformation.     

Molecular dynamics simulations of small peptides: dependence on dielectric model and pH

There has been much interest recently in the structure of small peptides in solution. A recent study by Bradley and co-workers [(1989) in Techniques of Protein Chemistry, Hugli, T.E., Ed., Academic Press, Orlando, FL, pp. 531-546; (1990) Journal of Molecular Biology, 215, pp. 607-622] describes a 17-residue peptide that is stable as a monomeric helix in aqueous solution at low pH, as determined by two-dimensional nmr and CD spectroscopy. They also have determined the helix content of the peptide as a function of pH using CD. We performed molecular dynamics simulations, with an empirical force field, of this peptide at low pH, with three different dielectric models: a linear distance-dependent dielectric function (epsilon = R); a modified form [J. Ramstein and R. Lavery (1988) Proceedings of the National Academy of Science, USA, Vol. 85, pp. 7231-7235] of the sigmoidal distance-dependent dielectric function of Hingerty and co-workers [(1985) Biopolymers, Vol. 24, pp. 427-439]; and epsilon = 1 with the peptide immersed in a bath of water molecules. We found that simulations with the sigmoidal dielectric function and the model with explicit water molecules resulted in average distances for particular interactions that were consistent with the experimental nmr results, with the sigmoidal function best representing the data. However, these models exhibited very different helix-stabilizing interactions. We also performed simulations using the sigmoidal function at moderate and high pH to compare to experimental determinations of the pH dependence of helix content. Helix content did not decrease with increases in pH, as shown experimentally. We did, however, observe changes in a specific side chain-helix dipole interaction that was implicated in determining the pH-dependent behavior of this peptide. Overall, the sigmoidal dielectric function was a reasonable alternative to adding explicit water molecules. In comparing 100 ps molecular dynamics simulations, the sigmoidal function was much less computer intensive and sampled more of conformational space than the treatment using explicit water molecules. Sampling is especially important for this system since the peptide has been shown experimentally to populate both helical and nonhelical conformations.     

Molecular dynamics simulations of the cytochrome c3-rubredoxin complex from Desulfovibrio vulgaris.

Molecular dynamics simulations have been carried out on the complex formed between the tetraheme cytochrome c3 and the iron protein rubredoxin from the sulfate-reducing bacterium Desulfovibrio vulgaris. These simulations were performed both with explicit solvent water molecules included, and without solvent molecules using a distance-dependent dielectric constant to approximate the screening effects of solvent. The results of both simulations are strikingly different, indicating that the representation of environmental effects is important in such simulations. For example, a striking adaptation of the two proteins seen in the nonsolvated simulation is not seen when explicit solvent water is included; in fact, the complex appears to become weaker in the solvated simulation. Nonetheless, the iron-iron distance decreases more significantly in the solvated simulation than in the nonsolvated simulation. It was found that in both cases molecular dynamics optimized the structures further than energy minimization alone.     

Solvent Dielectric Effect and Side Chain Mutation on the Structural Stability of Burkholderia cepacia Lipase Active Site: A Quantum Mechanical/Molecular Mechanics Study

Quantum mechanical and molecular dynamics methods were used to analyze the structure and stability of neutral and zwitterionic configurations of the extracted active site sequence from a Burkholderia cepacia lipase, histidyl-seryl-glutamin (His86-Ser87-Gln88) and its mutated form, histidyl-cysteyl-glutamin (His86-Cys87-Gln88) in vacuum and different solvents. The effects of solvent dielectric constant, explicit and implicit water molecules and side chain mutation on the structure and stability of this sequence in both neutral and zwitterionic forms are represented. The quantum mechanics computations represent that the relative stability of zwitterionic and neutral configurations depends on the solvent structure and its dielectric constant. Therefore, in vacuum and the considered non-polar solvents, the neutral form of the interested sequences is more stable than the zwitterionic form, while their zwitterionic form is more stable than the neutral form in the aqueous solution and the investigated polar solvents in most cases. However, on the potential energy surfaces calculated, there is a barrier to proton transfer from the positively charged ammonium group to the negatively charged carboxylat group or from the ammonium group to the adjacent carbonyl oxygen and or from side chain oxygen and sulfur to negatively charged carboxylat group. Molecular dynamics simulations (MD) were also performed by using periodic boundary conditions for the zwitterionic configuration of the hydrated molecules in a box of water molecules. The obtained results demonstrated that the presence of explicit water molecules provides the more compact structures of the studied molecules. These simulations also indicated that side chain mutation and replacement of sulfur with oxygen leads to reduction of molecular flexibility and packing.     

Comparison of dielectric response models for simulating electrostatic effects in proteins

Two recent approaches for calculating pK shifts in proteins are compared. The first of these uses Coulomb's law with a distance-dependent dielectric permittivity, epsilon (r), to model the screening effects of the environment, and the second uses a finite difference approach to solve Poisson's equation. It is shown that an explicit form of epsilon (r) which has been fitted to experimentally determined values of the dielectric permittivity in a range from 1 to 21 A can be approximated by a linear form in the functionally significant range of charge separations of approximately 3-10 A, but for distances greater than 10 A the effective permittivity is strongly nonlinear. A statistical analysis of the errors in calculated pK shifts due to electrostatic interactions between charges with separations greater than 10 A shows that there are only marginal differences in reliability between using Coulomb's law with an appropriate form of epsilon (r) or the finite difference approach for solving Poisson's equation. Thus it is concluded that pK shifts can be calculated just as well, and with considerably less effort, using Coulomb's law.     

Distance dependence and salt sensitivity of pairwise, coulombic interactions in a protein

Histidine pK(a) values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by (1)H-NMR spectroscopy. Energies of interaction between pairs of charges (DeltaG(ij)) were obtained from the shifts in pK(a) values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental DeltaG(ij) when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The DeltaG(ij) when r(ij) < or = 10 A were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of DeltaG(ij) as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (r(ij)) approximately 5 A interacted with DeltaG(ij) approximately 0.6 kcal/mole in 0.01 M KCl, but DeltaG(ij) decayed to < or =0.10 kcal/mole when r(ij) = 20 A. In 0.10 M KCl, DeltaG(ij) approximately 0.10 kcal/mole when r(ij) = 10 A. In 1.5 M KCl, only short-range interactions with r(ij) < or = 5 A persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 A are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.     

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.     

Explicit solvent models in protein pKa calculations.

Continuum methods for calculation of protein electrostatics treat buried and ordered water molecules by one of two approximations; either the dielectric constant of regions containing ordered water molecules is equal to the bulk solvent dielectric constant, or it is equal to the protein dielectric constant though no fixed atoms are used to represent water molecules. A method for calculating the titration behavior of individual residues in proteins has been tested on models of hen egg white lysozyme containing various numbers of explicit water molecules. Water molecules were included based on hydrogen bonding, solvent accessibility, and/or proximity to titrating groups in the protein. Inclusion of water molecules significantly alters the calculated titration behavior of individual titrating sites, shifting calculated pKa values by up to 0.5 pH unit. Our results suggest that approximately one water molecule within hydrogen-bonding distance of each charged group should be included in protein electrostatics calculations.     

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.     

Molecular dynamics studies of a DNA-binding protein: 2. An evaluation of implicit and explicit solvent models for the molecular dynamics simulation of the Escherichia coli trp repressor.

Although aqueous simulations with periodic boundary conditions more accurately describe protein dynamics than in vacuo simulations, these are computationally intensive for most proteins. Trp repressor dynamic simulations with a small water shell surrounding the starting model yield protein trajectories that are markedly improved over gas phase, yet computationally efficient. Explicit water in molecular dynamics simulations maintains surface exposure of protein hydrophilic atoms and burial of hydrophobic atoms by opposing the otherwise asymmetric protein-protein forces. This properly orients protein surface side chains, reduces protein fluctuations, and lowers the overall root mean square deviation from the crystal structure. For simulations with crystallographic waters only, a linear or sigmoidal distance-dependent dielectric yields a much better trajectory than does a constant dielectric model. As more water is added to the starting model, the differences between using distance-dependent and constant dielectric models becomes smaller, although the linear distance-dependent dielectric yields an average structure closer to the crystal structure than does a constant dielectric model. Multiplicative constants greater than one, for the linear distance-dependent dielectric simulations, produced trajectories that are progressively worse in describing trp repressor dynamics. Simulations of bovine pancreatic trypsin were used to ensure that the trp repressor results were not protein dependent and to explore the effect of the nonbonded cutoff on the distance-dependent and constant dielectric simulation models. The nonbonded cutoff markedly affected the constant but not distance-dependent dielectric bovine pancreatic trypsin inhibitor simulations. As with trp repressor, the distance-dependent dielectric model with a shell of water surrounding the protein produced a trajectory in better agreement with the crystal structure than a constant dielectric model, and the physical properties of the trajectory average structure, both with and without a nonbonded cutoff, were comparable.     

Accurate representation of B-DNA double helical structure with implicit solvent and counterions

High-resolution nuclear magnetic resonance (NMR) and crystallographic data have been taken to refine the force field used in the torsion angle space nucleic acids molecular mechanics program DUPLEX. The population balance deduced from NMR studies of two carcinogen-modified DNA conformers in equilibrium was used to fine tune a sigmoidal, distance-dependent dielectric function so that reasonable relative energies could be obtained. In addition, the base-pair and backbone geometry from high-resolution crystal structures of the Dickerson-Drew dodecamer was used to re-evaluate the deoxyribose pseudorotation profile and the Lennard-Jones nonbonded energy terms. With a modified dielectric function that assumes a very steep distance-dependent form, a deoxyribose pseudorotation profile with reduced energy barriers between C2'- and C3'-endo minima, and a shift of the Lennard-Jones potential energy minimum to a distance approximately 0.4 A greater than the sum of the van der Waals' radii, the sequence-dependent conformational features of the Dickerson-Drew dodecamer in both the solid state and the aqueous liquid crystalline phase are well reproduced. The robust performance of the revised force field, in conjunction with its efficiency through implicit treatment of solvent and counterions, provides a valuable tool for elucidating conformations and structure-function relationships of DNA, including those of molecules modified by carcinogens and other ligands.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (epsilon) in the vicinity of electron carriers along the membrane normal was calculated. The value of epsilon was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined epsilon values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

Conformational free energy maps for globobiose (alpha-D-Galp-(1-->4)-beta-D-Galp) in implicit and explicit aqueous solution

Four Ramachandran maps of the conformational potential of mean force (PMF) for the galactose disaccharide globobiose (alpha-D-Galp-(1-->4)-beta-D-Galp) were calculated in vacuum, explicit water, with a simple high dielectric constant and a distance-dependent dielectric coefficient, respectively. This simple model of the galactan alpha-(1-->4)-linkage is shown to be conformationally restricted, with only a small range of syn-phi/syn-psi conformations predominating at standard temperature and pressure. This has implications for the preferred conformation and chain dynamics of alpha-galactosides. In addition, comparison of the relevant PMF surfaces reveals the substitution of a high dielectric constant for explicit water solution to be a valid approximation for reproducing the minimum energy conformation of this glycosidic linkage.     

Experimental pK(a) values of buried residues: analysis with continuum methods and role of water penetration

Lys-66 and Glu-66, buried in the hydrophobic interior of staphylococcal nuclease by mutagenesis, titrate with pK(a) values of 5.7 and 8.8, respectively (Dwyer et al., Biophys. J. 79:1610-1620; García-Moreno E. et al., Biophys. Chem. 64:211-224). Continuum calculations with static structures reproduced the pK(a) values when the protein interior was treated with a dielectric constant (epsilon(in)) of 10. This high apparent polarizability can be rationalized in the case of Glu-66 in terms of internal water molecules, visible in crystallographic structures, hydrogen bonded to Glu-66. The water molecules are absent in structures with Lys-66; the high polarizability cannot be reconciled with the hydrophobic environment surrounding Lys-66. Equilibrium thermodynamic experiments showed that the Lys-66 mutant remained folded and native-like after ionization of the buried lysine. The high polarizability must therefore reflect water penetration, minor local structural rearrangement, or both. When in pK(a) calculations with continuum methods, the internal water molecules were treated explicitly, and allowed to relax in the field of the buried charged group, the pK(a) values of buried residues were reproduced with epsilon(in) in the range 4-5. The calculations show that internal waters can modulate pK(a) values of buried residues effectively, and they support the hypothesis that the buried Lys-66 is in contact with internal waters even though these are not seen crystallographically. When only the one or two innermost water molecules were treated explicitly, epsilon(in) of 5-7 reproduced the pK(a) values. These values of epsilon(in) > 4 imply that some conformational reorganization occurs concomitant with the ionization of the buried groups.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Coincident Recombination during Mitosis in Saccharomyces: Distance-Dependent and -Independent Components

In mitosis, coincident recombination events between widely separated markers occur more frequently than expected for two independent acts. Several different mechanisms have been proposed to account for this phenomenon. It has been argued that coincident recombination could be due to either an extensive region of heteroduplex DNA or some other distance-dependent mechanism. Alternately, it has been suggested that at least some is due to subpopulations of cells which undergo recombination at very high frequencies. The purpose of these experiments is to evaluate the possible contribution of distance-dependent and distance-independent components. By comparing the coincident recombination frequencies for markers on the same homolog as well as pairs of unlinked sites, we show that there is a strong distance-dependent component for at least 8.8-35-kbp, depending on the type of recombination event (conversion or intrachromosomal exchange). For larger distances separating sites, a distance-independent mechanism(s) results in higher than expected frequencies.     

Optimization of solvation models for predicting the structure of surface loops in proteins

A novel procedure for optimizing the atomic solvation parameters (ASPs) sigma(i) developed recently for cyclic peptides is extended to surface loops in proteins. The loop is free to move, whereas the protein template is held fixed in its X-ray structure. The energy is E(tot) = E(FF)(epsilon = nr) + summation operator sigma(i)A(i), where E(FF)(epsilon = nr) is the force-field energy of the loop-loop and loop-template interactions, epsilon = nr is a distance-dependent dielectric constant, and n is an additional parameter to be optimized. A(i) is the solvent-accessible surface area of atom i. The optimal sigma(i) and n are those for which the loop structure with the global minimum of E(tot)(n, sigma(i)) becomes the experimental X-ray structure. Thus, the ASPs depend on the force field and are optimized in the protein environment, unlike commonly used ASPs such as those of Wesson and Eisenberg (Protein Sci 1992;1:227-235). The latter are based on the free energy of transfer of small molecules from the gas phase to water and have been traditionally combined with various force fields without further calibration. We found that for loops the all-atom AMBER force field performed better than OPLS and CHARMM22. Two sets of ASPs [based on AMBER (n = 2)], optimized independently for loops 64-71 and 89-97 of ribonuclease A, were similar and thus enabled the definition of a best-fit set. All these ASPs were negative (hydrophilic), including those for carbon. Very good (i.e., small) root-mean-square-deviation values from the X-ray loop structure were obtained with the three sets of ASPs, suggesting that the best-fit set would be transferable to loops in other proteins as well. The structure of loop 13-24 is relatively stretched and was insensitive to the effect of the ASPs.     

Energetics of charge-charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson-Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate of rhodanese is analyzed, with attention to the influence of alpha-helices. Finally, relationships between electrostatic potential and charge-charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance-dependent dielectric constant (epsilon = R) and a fixed dielectric constant (epsilon = 2), and Tanford-Kirkwood theory. The primary conclusions are as follows: 1) The Poisson-Boltzmann model agrees with the subtilisin data over a range of ionic strengths; 2) two alpha-helices generate a large potential in the active site of rhodanese; 3) epsilon = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; 4) Tanford-Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson-Boltzmann equation in globular proteins; and 5) the modified Tanford-Kirkwood theory over-screens the measured electrostatic interactions in subtilisin.