The crystal structure of Escherichia coli heat shock protein YedU reveals three potential catalytic active sites

The mRNA of Escherichia coli yedU gene is induced 31-fold upon heat shock. The 31-kD YedU protein, also calls Hsp31, is highly conserved in several human pathogens and has chaperone activity. We solved the crystal structure of YedU at 2.2 A resolution. YedU monomer has an alpha/beta/alpha sandwich domain and a small alpha/beta domain. YedU is a dimer in solution, and its crystal structure indicates that a significant amount of surface area is buried upon dimerization. There is an extended hydrophobic patch that crosses the dimer interface on the surface of the protein. This hydrophobic patch is likely the substrate-binding site responsible for the chaperone activity. The structure also reveals a potential protease-like catalytic triad composed of Cys184, His185, and Asp213, although no enzymatic activity could be identified. YedU coordinates a metal ion using His85, His122, and Glu90. This 2-His-1-carboxylate motif is present in carboxypeptidase A (a zinc enzyme), and a number of dioxygenases and hydroxylases that utilize iron as a cofactor, suggesting another potential function for YedU.     

Crystal structure of proteolytic fragments of the redox-sensitive Hsp33 with constitutive chaperone activity

Heat shock protein 33 (Hsp33) inhibits aggregation of partially denatured proteins during oxidative stress. The chaperone activity of Hsp33 is unique among heat shock proteins because the activity is reversibly regulated by cellular redox status. We report here the crystal structure of the N-terminal region of Hsp33 fragments with constitutive chaperone activity. The structure reveals that the N-terminal portion of Hsp33 forms a tightly associated dimer formed by a domain crossover. A concave groove on the dimeric surface contains an elongated hydrophobic patch that could potentially bind denatured protein substrates. The termini of the subunits are located near the hydrophobic patch, indicating that the cleaved C-terminal domain may shield the hydrophobic patch in an inactive state. Two of the four conserved zinc-coordinating cysteines are in the end of the N-terminal domain, and the other two are in the cleaved C-terminal domain. The structural information and subsequent biochemical characterizations suggest that the redox switch of Hsp33 occurs by a reversible dissociation of the C-terminal regulatory domain through oxidation of zinc-coordinating cysteines and zinc release.     

The 2.2 A crystal structure of Hsp33: a heat shock protein with redox-regulated chaperone activity

BACKGROUND: One strategy that cells employ to respond to environmental stresses (temperature, oxidation, and pathogens) is to increase the expression of heat shock proteins necessary to maintain viability. Several heat shock proteins function as molecular chaperones by binding unfolded polypeptides and preventing their irreversible aggregation. Hsp33, a highly conserved bacterial heat shock protein, is a redox-regulated molecular chaperone that appears to protect cells against the lethal effects of oxidative stress. RESULTS: The 2.2 A crystal structure of a truncated E. coli Hsp33 (residues 1-255) reveals a domain-swapped dimer. The core domain of each monomer (1-178) folds with a central helix that is sandwiched between two beta sheets. The carboxyl-terminal region (179-235), which lacks the intact Zn binding domain of Hsp33, folds into three helices that pack on the other subunit. The interface between the two core domains is comprised of conserved residues, including a rare Glu-Glu hydrogen bond across the dyad axis. Two potential polypeptide binding sites that span the dimer are observed: a long groove containing pockets of conserved and hydrophobic residues, and an intersubunit 10-stranded beta sheet "saddle" with a largely uncharged or hydrophobic surface. CONCLUSIONS: Hsp33 is a dimer in the crystal structure. Solution studies confirmed that this dimer reflects the structural changes that occur upon activation of Hsp33 as a molecular chaperone. Patterns of conserved residues and surface charges suggest that two grooves might be potential binding sites for protein folding intermediates.     

Crystal structure of the catalytic domain of human bile salt activated lipase

Bile-salt activated lipase (BAL) is a pancreatic enzyme that digests a variety of lipids in the small intestine. A distinct property of BAL is its dependency on bile salts in hydrolyzing substrates of long acyl chains or bulky alcoholic motifs. A crystal structure of the catalytic domain of human BAL (residues 1-538) with two surface mutations (N186D and A298D), which were introduced in attempting to facilitate crystallization, has been determined at 2.3 A resolution. The crystal form belongs to space group P2(1)2(1)2(1) with one monomer per asymmetric unit, and the protein shows an alpha/beta hydrolase fold. In the absence of bound bile salt molecules, the protein possesses a preformed catalytic triad and a functional oxyanion hole. Several surface loops around the active site are mobile, including two loops potentially involved in substrate binding (residues 115-125 and 270-285).     

High affinity binding of Hsp90 is triggered by multiple discrete segments of its kinase clients

The 90 kDa heat shock protein (Hsp90) cooperates with its co-chaperone Cdc37 to provide obligatory support to numerous protein kinases involved in the regulation of cellular signal transduction pathways. In this report, crystal structures of protein kinases were used to guide the dissection of two kinases [the Src-family tyrosine kinase, Lck, and the heme-regulated eIF2alpha kinase (HRI)], and the association of Hsp90 and Cdc37 with these constructs was assessed. Hsp90 interacted with both the N-terminal (NL) and C-terminal (CL) lobes of the kinases' catalytic domains. In contrast, Cdc37 interacted only with the NL. The Hsp90 antagonist molybdate was necessary to stabilize the interactions between isolated subdomains and Hsp90 or Cdc37, but the presence of both lobes of the kinases' catalytic domain generated a stable salt-resistant chaperone-client heterocomplex. The Hsp90 co-chaperones FKBP52 and p23 interacted with the catalytic domain and the NL of Lck, whereas protein phosphatase 5 demonstrated unique modes of kinase binding. Cyp40 was a salt labile component of Hsp90 complexes formed with the full-length, catalytic domains, and N-terminal catalytic lobes of Lck and HRI. Additionally, dissections identify a specific kinase motif that triggers Hsp90's conformational switching to a high-affinity client binding state. Results indicate that the Hsp90 machine acts as a versatile chaperone that recognizes multiple regions of non-native proteins, while Cdc37 binds to a more specific kinase segment, and that concomitant recognition of multiple client segments is communicated to generate or stabilize high-affinity chaperone-client heterocomplexes.     

Farnesylation of the SNARE protein Ykt6 increases its stability and helical folding

The evolutionarily conserved soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins are involved in the fusion of vesicles with their target membranes. While most SNAREs are permanently anchored to membranes by their transmembrane domains, the vesicle-associated SNARE Ykt6 has been found both in soluble and in membrane-bound pools. The R-SNARE Ykt6 is thought to mediate interactions between various Q-SNAREs by a reversible membrane-targeting cycle. Membrane attachment of Ykt6 is achieved by its C-terminal prenylation and palmitoylation motif succeeding the SNARE motif. In this study, we have analyzed full-length farnesylated Ykt6 from yeast and humans by biochemical and structural means. In vitro farnesylation of the C-terminal CAAX box of recombinant full-length Ykt6 resulted in stabilization of the native protein and a more compactly folded structure, as shown by size exclusion chromatography and limited proteolysis. Circular dichroism spectroscopy indicated a specific increase in the helical content of the farnesylated Ykt6 compared to the nonlipidated form or the single-longin domain, which correlated with a marked increase in stability as observed by heat denaturation experiments. Although highly soluble, farnesylated Ykt6 is capable of lipid membrane binding independent of the membrane charge, as shown by surface plasmon resonance. The crystal structure of the N-terminal longin domain of yeast Ykt6 (1-140) was determined at 2.5 Å resolution. As similarly found in a previous NMR structure, the Ykt6 longin domain contains a hydrophobic patch at its surface that may accommodate the lipid moiety. In the crystal structure, this hydrophobic surface is buried in a crystallographic homomeric dimer interface. Together, these observations support a previously suggested closed conformation of cytosolic Ykt6, where the C-terminal farnesyl moiety folds onto a hydrophobic groove in the N-terminal longin domain.     

Crystal Structures of α-Crystallin Domain Dimers of αB-Crystallin and Hsp20

Small heat shock proteins (sHsps) are a family of large and dynamic oligomers highly expressed in long-lived cells of muscle, lens and brain. Several family members are upregulated during stress, and some are strongly cytoprotective. Their polydispersity has hindered high-resolution structure analyses, particularly for vertebrate sHsps. Here, crystal structures of excised α-crystallin domain from rat Hsp20 and that from human αB-crystallin show that they form homodimers with a shared groove at the interface by extending a β sheet. However, the two dimers differ in the register of their interfaces. The dimers have empty pockets that in large assemblies will likely be filled by hydrophobic sequence motifs from partner chains. In the Hsp20 dimer, the shared groove is partially filled by peptide in polyproline II conformation. Structural homology with other sHsp crystal structures indicates that in full-length chains the groove is likely filled by an N-terminal extension. Inside the groove is a symmetry-related functionally important arginine that is mutated, or its equivalent, in family members in a range of neuromuscular diseases and cataract. Analyses of residues within the groove of the αB-crystallin interface show that it has a high density of positive charges. The disease mutant R120G α-crystallin domain dimer was found to be more stable at acidic pH, suggesting that the mutation affects the normal dynamics of sHsp assembly. The structures provide a starting point for modelling higher assembly by defining the spatial locations of grooves and pockets in a basic dimeric assembly unit. The structures provide a high-resolution view of a candidate functional state of an sHsp that could bind non-native client proteins or specific components from cytoprotective pathways. The empty pockets and groove provide a starting model for designing drugs to inhibit those sHsps that have a negative effect on cancer treatment.     

Structure and interactions of the helical and U-box domains of CHIP, the C terminus of HSP70 interacting protein

The heat-shock proteins Hsp70 and Hsp90 play a crucial role in regulating protein quality control both by refolding and by preventing the aggregation of misfolded proteins. It has recently been shown that Hsp70 and Hsp90 act not only in protein refolding but also cooperate with the C terminus of Hsp70 interacting protein (CHIP), a multidomain ubiquitin ligase, to mediate the degradation of unfolded proteins. We present the crystal structure of the helical linker domain and U-box domain of zebrafish CHIP (DrCHIP-HU). The structure of DrCHIP-HU shows a symmetric homodimer. The conformation of the helical linker domains and the relative positions of the helical and U-box domains differ substantially in DrCHIP-HU from those in a recently published structure of an asymmetric dimer of mammalian (mouse) CHIP. We used an in vitro ubiquitination assay to identify residues, located on two long loops and a central alpha helix of the CHIP U-box domain, that are important for interacting with the ubiquitin-conjugating enzyme UbcH5b. In addition, we used NMR spectroscopy to define a complementary interaction surface located on the N-terminal alpha helix and the L4 and L7 loops of UbcH5b. Our results provide insights into conformational variability in the domain arrangement of CHIP and into U-box-mediated recruitment of UbcH5b for the ubiquitination of Hsp70 and Hsp90 substrates.     

Structure of the Alkalohyperthermophilic Archaeoglobus fulgidus Lipase Contains a Unique C-Terminal Domain Essential for Long-Chain Substrate Binding

Several crystal structures of AFL, a novel lipase from the archaeon Archaeoglobus fulgidus, complexed with various ligands, have been determined at about 1.8 Å resolution. This enzyme has optimal activity in the temperature range of 70-90 °C and pH 10-11. AFL consists of an N-terminal α/β-hydrolase fold domain, a small lid domain, and a C-terminal β-barrel domain. The N-terminal catalytic domain consists of a 6-stranded β-sheet flanked by seven α-helices, four on one side and three on the other side. The C-terminal lipid binding domain consists of a β-sheet of 14 strands and a substrate covering motif on top of the highly hydrophobic substrate binding site. The catalytic triad residues (Ser136, Asp163, and His210) and the residues forming the oxyanion hole (Leu31 and Met137) are in positions similar to those of other lipases. Long-chain lipid is located across the two domains in the AFL-substrate complex. Structural comparison of the catalytic domain of AFL with a homologous lipase from Bacillus subtilis reveals an opposite substrate binding orientation in the two enzymes. AFL has a higher preference toward long-chain substrates whose binding site is provided by a hydrophobic tunnel in the C-terminal domain. The unusually large interacting surface area between the two domains may contribute to thermostability of the enzyme. Two amino acids, Asp61 and Lys101, are identified as hinge residues regulating movement of the lid domain. The hydrogen-bonding pattern associated with these two residues is pH dependent, which may account for the optimal enzyme activity at high pH. Further engineering of this novel lipase with high temperature and alkaline stability will find its use in industrial applications.     

X-ray crystallographic analysis of the sulfur carrier protein SoxY from Chlorobium limicola f. thiosulfatophilum reveals a tetrameric structure

Dissimilatory oxidation of thiosulfate in the green sulfur bacterium Chlorobium limicola f. thiosulfatophilum is carried out by the ubiquitous sulfur-oxidizing (Sox) multi-enzyme system. In this system, SoxY plays a key role, functioning as the sulfur substrate-binding protein that offers its sulfur substrate, which is covalently bound to a conserved C-terminal cysteine, to another oxidizing Sox enzyme. Here, we report the crystal structures of a stand-alone SoxY protein of C. limicola f. thiosulfatophilum, solved at 2.15 A and 2.40 A resolution using X-ray diffraction data collected at 100 K and room temperature, respectively. The structure reveals a monomeric Ig-like protein, with an N-terminal alpha-helix, that oligomerizes into a tetramer via conserved contact regions between the monomers. The tetramer can be described as a dimer of dimers that exhibits one large hydrophobic contact region in each dimer and two small hydrophilic interface patches in the tetramer. At the tetramer interface patch, two conserved redox-active C-terminal cysteines form an intersubunit disulfide bridge. Intriguingly, SoxY exhibits a dimer/tetramer equilibrium that is dependent on the redox state of the cysteines and on the type of sulfur substrate component bound to them. Taken together, the dimer/tetramer equilibrium, the specific interactions between the subunits in the tetramer, and the significant conservation level of the interfaces strongly indicate that these SoxY oligomers are biologically relevant.     

Molecular basis for bre5 cofactor recognition by the ubp3 deubiquitylating enzyme

Yeast Ubp3 and its co-factor Bre5 form a deubiquitylation complex to regulate protein transport between the endoplasmic reticulum and Golgi compartments of the cell. A novel N-terminal domain of the Ubp3 catalytic subunit forms a complex with the NTF2-like domain of the Bre5 regulatory subunit. Here, we report the X-ray crystal structure of an Ubp3-Bre5 complex and show that it forms a symmetric hetero-tetrameric complex in which the Bre5 NTF2-like domain dimer interacts with two L-shaped beta-strand-turn-alpha-helix motifs of Ubp3. The Ubp3 N-terminal domain binds within a hydrophobic cavity on the surface of the Bre5 NTF2-like domain subunit with conserved residues within both proteins interacting predominantly through antiparallel beta-sheet hydrogen bonds and van der Waals contacts. Structure-based mutagenesis and functional studies confirm the significance of the observed interactions for Ubp3-Bre5 association in vitro and Ubp3 function in vivo. Comparison of the structure to other protein complexes with NTF2-like domains shows that the Ubp3-Bre5 interface is novel. Together, these studies provide new insights into Ubp3 recognition by Bre5 and into protein recognition by NTF2-like domains.     

Biochemical and structural studies of the interaction of Cdc37 with Hsp90

The heat shock protein Hsp90 plays a key, but poorly understood role in the folding, assembly and activation of a large number of signal transduction molecules, in particular kinases and steroid hormone receptors. In carrying out these functions Hsp90 hydrolyses ATP as it cycles between ADP- and ATP-bound forms, and this ATPase activity is regulated by the transient association with a variety of co-chaperones. Cdc37 is one such co-chaperone protein that also has a role in client protein recognition, in that it is required for Hsp90-dependent folding and activation of a particular group of protein kinases. These include the cyclin-dependent kinases (Cdk) 4/6 and Cdk9, Raf-1, Akt and many others. Here, the biochemical details of the interaction of human Hsp90 beta and Cdc37 have been characterised. Small angle X-ray scattering (SAXS) was then used to study the solution structure of Hsp90 and its complexes with Cdc37. The results suggest a model for the interaction of Cdc37 with Hsp90, whereby a Cdc37 dimer binds the two N-terminal domain/linker regions in an Hsp90 dimer, fixing them in a single conformation that is presumably suitable for client protein recognition.     

Structural and functional analysis of the middle segment of hsp90: implications for ATP hydrolysis and client protein and cochaperone interactions

Activation of client proteins by the Hsp90 molecular chaperone is dependent on binding and hydrolysis of ATP, which drives a molecular clamp via transient dimerization of the N-terminal domains. The crystal structure of the middle segment of yeast Hsp90 reveals considerable evolutionary divergence from the equivalent regions of other GHKL protein family members such as MutL and GyrB, including an additional domain of new fold. Using the known structure of the N-terminal nucleotide binding domain, a model for the Hsp90 dimer has been constructed. From this structure, residues implicated in the ATPase-coupled conformational cycle and in interactions with client proteins and the activating cochaperone Aha1 have been identified, and their roles functionally characterized in vitro and in vivo.     

Structural alteration of Escherichia coli Hsp31 by thermal unfolding increases chaperone activity

Escherichia coli Hsp31, encoded by hchA, is a heat-inducible molecular chaperone. We found that Hsp31 undergoes a conformational change via temperature-induced unfolding, generating a high molecular weight (HMW) form with enhanced chaperone activity. Although it has previously been reported that some subunits of the Hsp31 crystal structure show structural heterogeneity with increased hydrophobic surfaces, Hsp31 basically forms a dimer. We found that a C-terminal deletion (CΔ19) of Hsp31 exhibited structurally and functionally similar characteristics to that of the HMW form. Both the CΔ19 and HMW forms achieved a structure with considerably more β-sheets and less α-helices than the native dimeric form, exposing a portion of its hydrophobic surfaces. The structural alterations were determined from its spectral changes in circular dichroism, intrinsic fluorescence of tryptophan residues, and fluorescence of bis-ANS binding to a hydrophobic surface. Interestingly, during thermal transition, the dimeric Hsp31 undergoes a conformational change to the HMW species via the CΔ19 structure, as monitored with near-UV CD spectrum, implying that the CΔ19 resembles an intermediate state between the dimer and the HMW form. From these results, we propose that Hsp31 transforms itself into a fully functional chaperone by altering its tertiary and quaternary structures.     

The crystal structure of calcium- and integrin-binding protein 1: insights into redox regulated functions

Calcium- and integrin-binding protein 1 (CIB1) is involved in the process of platelet aggregation by binding the cytoplasmic tail of the alpha(IIb) subunit of the platelet-specific integrin alpha(Iib)beta(3). Although poorly understood, it is widely believed that CIB1 acts as a global signaling regulator because it is expressed in many tissues that do not express integrin alpha(Iib)beta(3). We report the structure of human CIB1 to a resolution of 2.3 A, crystallized as a dimer. The dimer interface includes an extensive hydrophobic patch in a crystal form with 80% solvent content. Although the dimer form of CIB1 may not be physiologically relevant, this intersub-unit surface is likely to be linked to alpha(IIb) binding and to the binding of other signaling partner proteins. The C-terminal domain of CIB1 is structurally similar to other EF-hand proteins such as calmodulin and calcineurin B. Despite structural homology to the C-terminal domain, the N-terminal domain of CIB1 lacks calcium-binding sites. The structure of CIB1 revealed a complex with a molecule of glutathione in the reduced state bond to the N-terminal domain of one of the two subunits poised to interact with the free thiol of C35. Glutathione bound in this fashion suggests CIB1 may be redox regulated. Next to the bound GSH, the orientation of residues C35, H31, and S48 is suggestive of a cysteine-type protein phosphatase active site. The potential enzymatic activity of CIB1 is discussed and suggests a mechanism by which it regulates a wide variety of proteins in cells in addition to platelets.     

Structural and Mechanical Hierarchies in the α-Crystallin Domain Dimer of the Hyperthermophilic Small Heat Shock Protein Hsp16.5

In biological systems, proteins rarely act as isolated monomers. Association to dimers or higher oligomers is a commonly observed phenomenon. As an example, small heat shock proteins form spherical homo-oligomers of mostly 24 subunits, with the dimeric α-crystallin domain as the basic structural unit. The structural hierarchy of this complex is key to its function as a molecular chaperone. In this article, we analyze the folding and association of the basic building block, the α-crystallin domain dimer, from the hyperthermophilic archaeon Methanocaldococcus jannaschii Hsp16.5 in detail. Equilibrium denaturation experiments reveal that the α-crystallin domain dimer is highly stable against chemical denaturation. In these experiments, protein dissociation and unfolding appear to follow an “all-or-none” mechanism with no intermediate monomeric species populated. When the mechanical stability was determined by single-molecule force spectroscopy, we found that the α-crystallin domain dimer resists high forces when pulled at its termini. In contrast to bulk denaturation, stable monomeric unfolding intermediates could be directly observed in the mechanical unfolding traces after the α-crystallin domain dimer had been dissociated by force. Our results imply that for this hyperthermophilic member of the small heat shock protein family, assembly of the spherical 24mer starts from folded monomers, which readily associate to the dimeric structure required for assembly of the higher oligomer.     

The crystal structure of the reduced, Zn2+-bound form of the B. subtilis Hsp33 chaperone and its implications for the activation mechanism

The bacterial heat shock protein Hsp33 is a redox-regulated chaperone activated by oxidative stress. In response to oxidation, four cysteines within a Zn2+ binding C-terminal domain form two disulfide bonds with concomitant release of the metal. This leads to the formation of the biologically active Hsp33 dimer. The crystal structure of the N-terminal domain of the E. coli protein has been reported, but neither the structure of the Zn2+ binding motif nor the nature of its regulatory interaction with the rest of the protein are known. Here we report the crystal structure of the full-length B. subtilis Hsp33 in the reduced form. The structure of the N-terminal, dimerization domain is similar to that of the E. coli protein, although there is no domain swapping. The Zn2+ binding domain is clearly resolved showing the details of the tetrahedral coordination of Zn2+ by four thiolates. We propose a structure-based activation pathway for Hsp33.     

Crystal structure of the human carboxypeptidase N (kininase I) catalytic domain

Human carboxypeptidase N (CPN), a member of the CPN/E subfamily of "regulatory" metallo-carboxypeptidases, is an extracellular glycoprotein synthesized in the liver and secreted into the blood, where it controls the activity of vasoactive peptide hormones, growth factors and cytokines by specifically removing C-terminal basic residues. Normally, CPN circulates in blood plasma as a hetero-tetramer consisting of two 83 kDa (CPN2) domains each flanked by a 48 to 55 kDa catalytic (CPN1) domain. We have prepared and crystallized the recombinant C-terminally truncated catalytic domain of human CPN1, and have determined and refined its 2.1 A crystal structure. The structural analysis reveals that CPN1 has a pear-like shape, consisting of a 319 residue N-terminal catalytic domain and an abutting, cylindrically shaped 79 residue C-terminal beta-sandwich transthyretin (TT) domain, more resembling CPD-2 than CPM. Like these other CPN/E members, two surface loops surrounding the active-site groove restrict access to the catalytic center, offering an explanation for why some larger protein carboxypeptidase inhibitors do not inhibit CPN. Modeling of the Pro-Phe-Arg C-terminal end of the natural substrate bradykinin into the active site shows that the S1' pocket of CPN1 might better accommodate P1'-Lys than Arg residues, in agreement with CPN's preference for cleaving off C-terminal Lys residues. Three Thr residues at the distal TT edge of CPN1 are O-linked to N-acetyl glucosamine sugars; equivalent sites in the membrane-anchored CPM are occupied by basic residues probably involved in membrane interaction. In tetrameric CPN, each CPN1 subunit might interact with the central leucine-rich repeat tandem of the cognate CPN2 subunit via a unique hydrophobic surface patch wrapping around the catalytic domain-TT interface, exposing the two active centers.     

Structural Redesign of Lipase B from Candida antarctica by Circular Permutation and Incremental Truncation

Circular permutation of Candida antarctica lipase B yields several enzyme variants with substantially increased catalytic activity. To better understand the structural and functional consequences of protein termini reorganization, we have applied protein engineering and x-ray crystallography to cp283, one of the most active hydrolase variants. Our initial investigation has focused on the role of an extended surface loop, created by linking the native N- and C-termini, on protein integrity. Incremental truncation of the loop partially compensates for observed losses in secondary structure and the permutants' temperature of unfolding. Unexpectedly, the improvements are accompanied by quaternary-structure changes from monomer to dimer. The crystal structures of one truncated variant (cp283Δ7) in the apo-form determined at 1.49 Å resolution and with a bound phosphonate inhibitor at 1.69 Å resolution confirmed the formation of a homodimer by swapping of the enzyme's 35-residue N-terminal region. Separately, the new protein termini at amino acid positions 282/283 convert the narrow access tunnel to the catalytic triad into a broad crevice for accelerated substrate entry and product exit while preserving the native active-site topology for optimal catalytic turnover.