On the dependence of molecular conformation on the type of solvent environment: a molecular dynamics study of cyclosporin A

The dependence of the conformation of cyclosporin A (CPA), a cyclic undecapeptide with potent immunosuppressive activity, on the type of solvent environment is examined using the computer simulation method of molecular dynamics (MD). Conformational and dynamic properties of CPA in aqueous solution are obtained from MD simulations of a CPA molecule dissolved in a box with water molecules. Corresponding properties of CPA in apolar solution are obtained from MD simulations of CPA in a box with carbontetrachloride. The results of these simulations in H2O and in CCl4 are compared to each other and to those of previous simulations of crystalline CPA and of an isolated CPA molecule. The conformation of the backbone of the cyclic polypeptide is basically independent of the type of solvent. In aqueous solution the beta-pleated sheet is slightly weaker and the gamma-turn is a bit less pronounced than in apolar solution. Side chains may adopt different conformations in different solvents. In apolar solution the hydrophobic side chain of the MeBmt residue is in an extended conformation with its hydroxyl group hydrogen bonded to the backbone carbonyl group. In aqueous solution this hydrophobic side chain folds over the core of the molecule and the mentioned hydrogen bond is broken in favor of hydrogen bonding to water molecules. The conformation obtained from the MD simulation in CCl4 nicely agrees with experimental atom-atom distance data as obtained from nmr experiments in chloroform. In aqueous solution the relaxation of atomic motion tends to be slower than in apolar solution.     

Folding propensity and biological activity of peptides: the effect of a single stereochemical isomerization on the conformational properties of bombinins in aqueous solution

Folding propensities of bombinins H2 and H4, two members of amphibian bombinins H, a family of 17-20 residue alpha-helical peptides, have been investigated by means of circular dichroism (CD) measurements and molecular dynamics (MD) simulations. The two peptides, with primary structure IIGPVLGLVGSALGGLLKKI-NH2 and differing only for the configuration of the second aminoacid (an L-isoleucine in H2 and a D-alloisoleucine in H4) behave rather differently in solution. In particular both CD measurements and MD simulations indicate that bombinin H2 shows a markedly higher tendency to fold. From a careful inspection of MD trajectories it emerges that the stereochemical isomerization mutation of residue 2 to D-alloisoleucine in H4 peptide, drastically decreases its ability to form intrapeptide contacts. MD simulations also indicate that the conformational sampling in both systems derives from a subtle combination of energetic and entropic effects both involving the peptide itself and the solvent. The present results have been finally paralleled with preliminary information on bombinins H2 and H4 biological activity, i.e. interaction with membrane, supporting the hypothesis of an "already folded" conformation in water rather than interfacial folding tenet.     

Measuring enzyme hydration in nonpolar organic solvents using NMR

A very sensitive NMR method has been developed for measuring deuterated water bound to proteins suspended in nonpolar solvents. This has been used to determine the amount of bound water as a function of water activity for subtilisin Carlsberg suspended in hexane, benzene, and toluene and for alpha-chymotrypsin in hexane. The adsorption isotherms for subtilisin in the three solvents are very similar showing that water activity can be usefully employed to predict the amount of water bound to proteins in nonpolar organic media. Comparison of the degree of enzyme hydration reached in nonpolar solvents with that obtained in air shows that adsorption of strongly bound water is hardly affected by the low dielectric medium, but adsorption of loosely bound water is significantly reduced. This suggests that the hydrophobic regions of the protein surface are preferentially solvated by solvent molecules, and that in a nonpolar environment formation of a complete monolayer of water over the protein surface is thermodynamically unfavorable. (c) 1995 John Wiley & Sons, Inc.     

Effects of water content on the tetrahedral intermediate of chymotrypsin - trifluoromethylketone in polar and non-polar media: observations from molecular dynamics simulation

The work uses MD simulation to study effects of five water contents (3 %, 10 %, 20 %, 50 %, 100 %?v/v) on the tetrahedral intermediate of chymotrypsin - trifluoromethyl ketone in polar acetonitrile and non-polar hexane media. The water content induced changes in the structure of the intermediate, solvent distribution and H-bonding are analyzed in the two organic media. Our results show that the changes in overall structure of the protein almost display a clear correlation with the water content in hexane media while to some extent U-shaped/bell-shaped dependence on the water content is observed in acetonitrile media with a minimum/maximum at 10–20 % water content. In contrast, the water content change in the two organic solvents does not play an observable role in the stability of catalytic hydrogen-bond network, which still exhibits high stability in all hydration levels, different from observations on the free enzyme system [Zhu L, Yang W, Meng YY, Xiao X, Guo Y, Pu X, Li M (2012) J Phys Chem B 116(10):3292–3304]. In low hydration levels, most water molecules mainly distribute near the protein surface and an increase in the water content could not fully exclude the organic solvent from the protein surface. However, the acetonitrile solvent displays a stronger ability to strip off water molecules from the protein than the hexane. In a summary, the difference in the calculated properties between the two organic solvents is almost significant in low water content (<10 %) and become to be small with increasing water content. In addition, some structural properties at 10?~?20 %?v/v hydration zone, to large extent, approach to those in aqueous solution.

Ligand migration in the apolar tunnel of Cerebratulus lacteus mini-hemoglobin

The large apolar tunnel traversing the mini-hemoglobin from Cerebratulus lacteus (CerHb) has been examined by x-ray crystallography, ligand binding kinetics, and molecular dynamic simulations. The addition of 10 atm of xenon causes loss of diffraction in wild-type (wt) CerHbO(2) crystals, but Leu-86(G12)Ala CerHbO(2), which has an increased tunnel volume, stably accommodates two discrete xenon atoms: one adjacent to Leu-86(G12) and another near Ala-55(E18). Molecular dynamics simulations of ligand migration in wt CerHb show a low energy pathway through the apolar tunnel when Leu or Ala, but not Phe or Trp, is present at the 86(G12) position. The addition of 10-15 atm of xenon to solutions of wt CerHbCO and L86A CerHbCO causes 2-3-fold increases in the fraction of geminate ligand recombination, indicating that the bound xenon blocks CO escape. This idea was confirmed by L86F and L86W mutations, which cause even larger increases in the fraction of geminate CO rebinding, 2-5-fold decreases in the bimolecular rate constants for ligand entry, and large increases in the computed energy barriers for ligand movement through the apolar tunnel. Both the addition of xenon to the L86A mutant and oxidation of wt CerHb heme iron cause the appearance of an out Gln-44(E7) conformer, in which the amide side chain points out toward the solvent and appears to lower the barrier for ligand escape through the E7 gate. However, the observed kinetics suggest little entry and escape (≤ 25%) through the E7 pathway, presumably because the in Gln-44(E7) conformer is thermodynamically favored.     

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.     

Protein extraction and activity in reverse micelles of a nonionic detergent

We describe, for the first time, the ability of a polyoxyethylene sorbitan trioleate-isopropanol microemulsion in hexane to solubilize pure proteins. The dependences of cytochrome c extraction and buffer solubilization by the reverse micellar system on ionic strength of the aqueous phase, detergent concentration, and cosurfactant concentration result in increased extraction. In addition, subtilisin (a serine protease) is shown to be active in this microemulsion. Further the activity of the enzyme can be regulated by the water content of the micelles, enabling control of enzyme activity by "solvent engineering."     

Molecular dynamics simulation of the stability of a 22-residue α-helix in water and 30% trifluoroethanol

A molecular dynamics (MD) simulation was performed on the α-helix H8-HC5, the C-terminal part of myoglobin (residue 132–153), under periodic boundary conditions in two different solutions, water and water with 30% (v/v) 2,2,2-trifluoroethanol (TFE), at 300 K to investigate the stability of the helix. In both simulations, the initial configuration was a canonical right-handed α-helix. In the course of the MD trajectory in water (200 ps), the helix clearly destabilized and began to unfold after 100 ps. In the TFE solution, two stable parts of helical regions were observed after 70 ps of a 200-ps MD simulation, supporting the notion that TFE acts as a structure-forming solvent. © 1993 John Wiley & Sons, Inc.     

Dynamics of Ca2+-saturated calmodulin D129N mutant studied by multiple molecular dynamics simulations

Fifteen independent 1-nsec MD simulations of fully solvated Ca(2+) saturated calmodulin (CaM) mutant D129N were performed from different initial conditions to provide a sufficient statistical basis to gauge the significance of observed dynamical properties. In all MD simulations the four Ca(2+) ions remained in their binding sites, and retained a single water ligand as observed in the crystal structure. The coordination of Ca(2+) ions in EF-hands I, II, and III was sevenfold. In EF-hand IV, which was perturbed by the mutation of a highly conserved Asp129, an anomalous eightfold Ca(2+) coordination was observed. The Ca(2+) binding loop in EF-hand II was observed to dynamically sample conformations related to the Ca(2+)-free form. Repeated MD simulations implicate two well-defined conformations of Ca(2+) binding loop II, whereas similar effect was not observed for loops I, III, and IV. In 8 out of 15 MD simulations Ca(2+) binding loop II adopted an alternative conformation in which the Thr62 >C=O group was displaced from the Ca(2+) coordination by a water molecule, resulting in the Ca(2+) ion ligated by two water molecules. The alternative conformation of the Ca(2+) binding loop II appears related to the "closed" state involved in conformational exchange previously detected by NMR in the N-terminal domain fragment of CaM and the C-terminal domain fragment of the mutant E140Q. MD simulations suggest that conformations involved in microsecond exchange exist partially preformed on the nanosecond time scale.     

Acetylcholinesterase: mechanisms of covalent inhibition of H447I mutant determined by computational analyses

The reaction mechanisms of two inhibitor TFK(+) and TFK(0) binding to H447I mutant mouse acetylcholinesterase (mAChE) have been investigated by using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) approach and classical molecular dynamics (MD) simulations. TFK(+) binding to the H447I mutant may proceed with a different reaction mechanism from the wild-type. A water molecule takes over the role of His447 and participates in the bond breaking and forming as a "charge relayer". Unlike in the wild-type mAChE case, Glu334, a conserved residue from the catalytic triad, acts as a catalytic base in the reaction. The calculated energy barrier for this reaction is about 8kcal/mol. These predictions await experimental verification. In the case of the neutral ligand TFK(0), however, multiple MD simulations on the TFK(0)/H447I complex reveal that none of the water molecules can be retained in the active site as a "catalytic" water. Taken together our computational studies confirm that TFK(0) is almost inactive in the H447I mutant, and also provide detailed mechanistic insights into the experimental observations.     

"Fluctuograms" reveal the intermittent intra-protein communication in subtilisin Carlsberg and correlate mechanical coupling with co-evolution

The mechanism of intra-protein communication and allosteric coupling is key to understanding the structure-property relationship of protein function. For subtilisin Carlsberg, the Ca2+-binding loop is distal to substrate-binding and active sites, yet the serine protease function depends on Ca2+ binding. The atomic molecular dynamics (MD) simulations of apo and Ca2+-bound subtilisin show similar structures and there is no direct evidence that subtilisin has alternative conformations. To model the intra-protein communication due to Ca2+ binding, we transform the sequential segments of an atomic MD trajectory into separate elastic network models to represent anharmonicity and nonlinearity effectively as the temporal and spatial variation of the mechanical coupling network. In analogy to the spectrogram of sound waves, this transformation is termed the "fluctuogram" of protein dynamics. We illustrate that the Ca2+-bound and apo states of subtilisin have different fluctuograms and that intra-protein communication proceeds intermittently both in space and in time. We found that residues with large mechanical coupling variation due to Ca2+ binding correlate with the reported mutation sites selected by directed evolution for improving the stability of subtilisin and its activity in a non-aqueous environment. Furthermore, we utilize the fluctuograms calculated from MD to capture the highly correlated residues in a multiple sequence alignment. We show that in addition to the magnitude, the variance of coupling strength is also an indicative property for the sequence correlation observed in a statistical coupling analysis. The results of this work illustrate that the mechanical coupling networks calculated from atomic details can be used to correlate with functionally important mutation sites and co-evolution.     

Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials

The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned "on" and "off." Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from approximately 25,000 to 2500. The computations are very efficient and the statistical error is small ( approximately 1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within approximately 2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining potentials can be computationally inexpensive and accurate.     

Conformational mobility of active and E-64-inhibited actinidin

Background

Actinidin, a protease from kiwifruit, belongs to the C1 family of cysteine proteases. Cysteine proteases were found to be involved in many disease states and are valid therapeutic targets. Actinidin has a wide pH activity range and wide substrate specificity, which makes it a good model system for studying enzyme–substrate interactions.

Methods

The influence of inhibitor (E-64) binding on the conformation of actinidin was examined by 2D PAGE, circular dichroism (CD) spectroscopy, hydrophobic ligand binding assay, and molecular dynamics simulations.

Results

Significant differences were observed in electrophoretic mobility of proteolytically active and E-64-inhibited actinidin. CD spectrometry and hydrophobic ligand binding assay revealed a difference in conformation between active and inhibited actinidin. Molecular dynamics simulations showed that a loop defined by amino-acid residues 88–104 had greater conformational mobility in the inhibited enzyme than in the active one. During MD simulations, the covalently bound inhibitor was found to change its conformation from extended to folded, with the guanidino moiety approaching the carboxylate.

Conclusions

Conformational mobility of actinidin changes upon binding of the inhibitor, leading to a sequence of events that enables water and ions to protrude into a newly formed cavity of the inhibited enzyme. Drastic conformational mobility of E-64, a common inhibitor of cysteine proteases found in many crystal structures stored in PDB, was also observed.

General significance

The analysis of structural changes which occur upon binding of an inhibitor to a cysteine protease provides a valuable starting point for the future design of therapeutic agents.     

Effects of organic solvents and substrate binding on trypsin in acetonitrile and hexane media

In this work, we used molecular dynamic (MD) simulation to study trypsin with and without a six-amino-acid peptide bound in three different solvents (water, acetonitrile and hexane) in order to provide molecular information for well understanding the structure and function of enzymes in non-aqueous media. The results show that the enzyme is more compact and less native-like in hexane than in the other two polar solvents. The substrate could stabilize the native protein structure in the two polar media, but not in the non-polar hexane. There are no significant differences in the conformation of the S1 pocket upon the substrate binding in water and acetonitrile media while a reverse behavior is observed in hexane media, implying a possible induced fit binding mechanism in the non-polar media. The substrate binding enhances the stability of catalytic H-bond network since it could expel the solvent molecules from the active site. The enzyme and the substrate appear to be more appropriate to the reactive conformation in the organic solvents compared with aqueous solution. There is much greater substrate binding strength in hexane media than the water and acetonitrile ones since the polar solvent significantly weakens electrostatic interactions, which are observed to be the main driving force to the binding. In addition, some residues of the S1 pocket could remain favorable contribution to the binding despite the solvent change, but with differences in the contribution extent, the number and the type of residues between the three media.

Towards more active biocatalysts in organic media: increasing the activity of salt-activated enzymes

The activation of freeze-dried subtilisin Carlsberg (SC) in hexane has been systematically studied and partially optimized with respect to the freezing method, the addition of inorganic salts and lyoprotectants, the initial concentration and final weight percent of additives, and the amount of water added to the organic solvent. Activity and water content were found to correlate directly with the kosmotropicity of the activating salt (kosmotropic salts bind water molecules strongly relative to the strength of water-water interactions in bulk solution). Combinations of kosmotropic salts with known lyoprotectants such as poly(ethylene glycol) (PEG) and sugars did not yield an appreciably more active catalyst. However, the combination of the kosmotropic sodium acetate with the strongly buffering sodium carbonate activated the enzyme more than the individual additives alone. Enzyme activity was enhanced further by the addition of small amounts of water to the organic solvent. Under optimal conditions, enzyme activity in hexane was improved over 27,000-fold relative to the salt-free enzyme, reaching a catalytic efficiency that was within one order of magnitude of k(cat)/K(m) for hydrolysis of the same substrate in aqueous buffer. Further activation to attain even higher catalytic efficiencies may be possible with additional optimization.     

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.     

Crosslinking of imprinted proteases to maintain a tailor-made substrate selectivity in aqueous solutions

A covalent method to keep imprinted properties of proteins stable in aqueous as well as in organic environment is described. To stabilize the ligand induced acceptance for D-configured substrates by alpha-chymotrypsin or subtilisin Carlsberg, each protein was first vinylated by acylation with itaconic anhydride. Then, the tailoring of the derivatized proteins by precipitation in the presence of N-acetyl-D-tryptophan from an aqueous medium with 1-propanol, and the subsequent crosslinking of the enzyme preparations with ethylene glycol dimethacrylate in cyclohexane was carried out. The crosslinked imprinted proteins (CLIPs) obtained catalyzed the hydrolysis of N-acetyl-D-tryptophan ethyl ester in phosphate buffer and the corresponding back reaction in cyclohexane, respectively. The repeated use of CLIP-alpha-chymotrypsin in D-ester hydrolysis was demonstrated. Furthermore, this particular CLIP-alpha-chymotrypsin showed no loss in activity when it subsequently was used in the synthesis of N-acetyl-D-tryptophan ethyl ester in cyclohexane again. In the case of D-ester hydrolysis the reaction rate acceleration (k(enz)/k(nonenz)) was in the same order of magnitude of about 10(4)-10(5) mM(-1) for the two CLIP-proteases. The results suggest that enzymes tailored by imprinting technique do not lose their induced "new" property in the presence of water when they are prepared according to the described vinylation/crosslinking method (CLIP technique).     

Molecular dynamic study of subtilisin Carlsberg in aqueous and nonaqueous solvents

Using molecular dynamics simulations, we have obtained an important insight into the structural and dynamical changes exerted by a nonaqueous solvent on the serine protease subtilisin Carlsberg. Our findings show that the structural properties of the subtilisin–acetonitrile (MeCN) system were sensitive to the amount of water present at the protein surface. A decrease or lack of water promoted the enzyme–MeCN interaction, which increased structural changes of the enzyme primarily at the surface loops. This effect caused variations on the secondary and tertiary structure of the protein and induced the opening of a pathway for the solvent to the protein core. Also, disturbance of the oxyanion hole was observed due to changes in the orientation in the Asn-155 side chain. The disruption of the oxyanion hole and the changes of the tertiary structure should affect the optimal activity of the enzyme.     

Effect of crown ethers on structure, stability, activity, and enantioselectivity of subtilisin Carlsberg in organic solvents.

Colyophilization or codrying of subtilisin Carlsberg with the crown ethers 18-crown-6, 15-crown-5, and 12-crown-4 substantially improved enzyme activity in THF, acetonitrile, and 1,4-dioxane in the transesterification reactions of N-acetyl-L-phenylalanine ethylester and 1-propanol and that of (+/-)-1-phenylethanol and vinylbutyrate. The acceleration of the initial rate, V(0), ranged from less than 10-fold to more than 100-fold. All crown ethers activated subtilisin substantially, which excludes a specific macrocyclic effect from being responsible. The secondary structure of subtilisin was studied by Fourier-transform infrared (FTIR) spectroscopy. 18-Crown-6 and 15-crown-5 led to a more nativelike structure of subtilisin in the organic solvents employed when compared with that of the dehydrated enzyme obtained from buffer alone. However, the high level of activation with 12-crown-4 where this effect was not observed excluded overall structural preservation from being the primary cause of the observed enzyme activation. The conformational mobility of subtilisin was investigated by performing thermal denaturation experiments in 1,4-dioxane. Although only a small effect of temperature on subtilisin structure was observed for the samples prepared with or without 12-crown-4, both 18-crown-6 and 15-crown-5 caused the enzyme to denature at quite low temperatures (38 degrees C and 56 degrees C, respectively). No relationship between this property and V(0) was evident, but increased conformational mobility of the protein decreased its storage stability. The possibility of a "molecular imprinting" effect was also tested by removing 18-crown-6 from the subtilisin-18-crown-6 colyophilizate by washing. V(0) was only halved as a result of this procedure, an effect insignificant compared with the ca. 80-fold rate enhancement observed prior to washing in THF. This suggests that molecular imprinting is likely the primary cause of subtilisin activation by crown ethers, as recently suggested.