Design of potent selective zinc-mediated serine protease inhibitors

Many serine proteases are targets for therapeutic intervention because they often play key roles in disease. Small molecule inhibitors of serine proteases with high affinity are especially interesting as they could be used as scaffolds from which to develop drugs selective for protease targets. One such inhibitor is bis(5-amidino-2-benzimidazolyl)methane (BABIM), standing out as the best inhibitor of trypsin (by a factor of over 100) in a series of over 60 relatively closely related analogues. By probing the structural basis of inhibition, we discovered, using crystallographic methods, a new mode of high-affinity binding in which a Zn2+ ion is tetrahedrally coordinated between two chelating nitrogens of BABIM and two active site residues, His57 and Ser 195. Zn2+, at subphysiological levels, enhances inhibition by over 10(3)-fold. The distinct Zn2+ coordination geometry implies a strong dependence of affinity on substituents. This unique structural paradigm has enabled development of potent, highly selective, Zn2+-dependent inhibitors of several therapeutically important serine proteases, using a physiologically ubiquitous metal ion.

A novel dCMP methylase by engineering thymidylate synthase

X-ray crystal structures of binary complexes of dUMP or dCMP with the Lactobacillus caseiTS mutant N229D, a dCMP methylase, revealed that there is a steric clash between the 4-NH2 of dCMP and His 199, a residue which normally H-bonds to the 4-O of dUMP but is not essential for activity. As a result, the cytosine moiety of dCMP is displaced from the active site and the catalytic thiol is moved from the C6 of the substrate about 0.5 A further than in the wild-type TS-dUMP complex. We reasoned that combining the N229D mutation with mutations at residue 199 which did not impinge on the 4-NH2 of dCMP should correct the displacements and further favor methylation of dCMP. We therefore prepared several TS N229D mutants and characterized their steady state kinetic parameters. TS H199A/N229D showed a 10(11) change in specificity for methylation of dCMP versus dUMP. The structures of TS H199A/N229D in complex with dCMP and dUMP confirmed that the position and orientation of bound dCMP closely approaches that of dUMP in wild-type TS, whereas dUMP was displaced from the optimal catalytic binding site.

A designed four helix bundle protein with native-like structure

A 108 amino acid protein was designed and constructed from a reduced alphabet of seven amino acids. The 2.9 A resolution X-ray crystal structure confirms that the protein is a four helix bundle, as it was designed to be. Hydrogen/deuterium exchange experiments reveal buried amide protons with protection factors in excess of 1 x 10(6) in the range characteristic of well protected protons in functional folded proteins (10(3)-10(8)) rather than protons in rapid exchange (0-10(2)). The protein is monomeric at 1 mM, the concentration at which the exchange experiments were undertaken, indicating that the exchange factors are due to a unique stable tertiary structure fold, and not due to any higher order quaternary structure. Thermodynamic analysis provides an estimate of the free energy of folding of -9.3 kcal mole-1 at 25 degrees C, consistent with the free energy of folding derived from the protection factors of the most protected protons, indicating that global unfolding is required for exchange of the most protected protons.

Access to phosphorylation in isocitrate dehydrogenase may occur by domain shifting

To clarify further the mechanism of regulation by phosphorylation of isocitrate dehydrogenase, cocrystallization of isocitrate dehydrogenase and isocitrate dehydrogenase kinase/phosphatase in the presence of an ATP analog was attempted. Although cocrystallization was unsuccessful, a new crystal form of isocitrate dehydrogenase was obtained which provides insight into the phosphorylation mechanism. The new, orthorhombic crystal form of isocitrate dehydrogenase is related to the previously reported tetragonal form largely by an approximately 16 degrees shift of a large domain relative to the small domain and clasp region within each subunit of the dimeric enzyme. The NADP+ cofactor binding surface is significantly disrupted by the shift to the open conformation. The solvent-accessible surface area and surface-enclosed volume increase by 2% relative to the dimeric tetragonal form. Most of the increase results from expansion of the active site cleft such that the distance across its opening increases from approximately 5 to 13 A, significantly increasing accessibility to Ser-113. The conformation of isocitrate dehydrogenase in the orthorhombic crystal form more closely resembles that of the crystal structure of the homologous enzyme 3-isopropylmalate dehydrogenase than does the tetragonal isocitrate dehydrogenase conformation. Since the crystal lattice forces are fairly weak, it appears that isocitrate dehydrogenase is a flexible molecule that can easily undergo domain shifts and possibly other induced fit conformational changes, to accommodate binding to isocitrate dehydrogenase kinase/phosphatase.

The discovery, characterization and crystallographically determined binding mode of an FMOC-containing inhibitor of HIV-1 protease

A pharmacophore derived from the structure of the dithiolane derivative of haloperidol bound in the active site of the HIV-1 protease (HIV-1 PR) has been used to search a three-dimensional database for new inhibitory frameworks. This search identified an FMOC-protected N-tosyl arginine as a lead candidate. A derivative in which the arginine carboxyl has been converted to an amide has been crystallized with HIV-1 PR and the structure has been determined to a resolution of 2.5 A with a final R-factor of 18.5%. The inhibitor binds in an extended conformation that results in occupancy of the S2, S1', and S3' subsites of the active site. Initial structure-activity studies indicate that: (1) the FMOC fluorenyl moiety interacts closely with active site residues and is important for binding; (2) the N(G)-tosyl group is necessary to suppress protonation of the arginine guanidinyl terminus; and (3) the arginine carboxamide function is involved in interactions with the water coordinated to the catalytic aspartyl groups. FMOC-protected arginine derivatives, which appear to be relatively specific and nontoxic, offer promise for the development of useful HIV-1 protease inhibitors.

Crystal structure of colicin Ia

The ion-channel forming colicins A, B, E1, Ia, Ib and N all kill bacterial cells selectively by co-opting bacterial active-transport pathways and forming voltage-gated ion conducting channels across the plasma membrane of the target bacterium. The crystal structure of colicin Ia reveals a molecule 210 A long with three distinct functional domains arranged along a backbone of two extraordinarily long alpha-helices. A central domain at the bend of the hairpin-like structure mediates specific recognition and binding to an outer-membrane receptor. A second domain mediates translocation across the outer membrane via the TonB transport pathway; the TonB-box recognition element of colicin Ia is on one side of three 80 A-long helices arranged as a helical sheet. A third domain is made up of 10 alpha-helices which form a voltage-activated and voltage-gated ion conducting channel across the plasma membrane of the target cell. The two 160 A-long alpha-helices that link the receptor-binding domain to the other domains enable the colicin Ia molecule to span the periplasmic space and contact both the outer and plasma membranes simultaneously during function.

Structure of the conserved GTPase domain of the signal recognition particle

The signal-recognition particle (SRP) and its receptor (SR) function in the co-translational targeting of nascent protein-ribosome complexes to the membrane translocation apparatus. The SRP protein subunit (termed Ffh in bacteria) that recognizes the signal sequence of nascent polypeptides is a GTPase, as is the SR-alpha subunit (termed FtsY). Ffh and FtsY interact directly, each stimulating the GTP hydrolysis activity of the other. The sequence of Ffh suggests three domains: an amino-terminal N domain of unknown function, a central GTPase G domain, and a methionine-rich M domain that binds both SRP RNA and signal peptides. Sequence conservation suggests that structurally similar N and G domains are present in FtsY. Here we report the structure of the nucleotide-free form of the NG fragment of Ffh. Consistent with a role for apo Ffh in protein targeting, the side chains of the empty active-site pocket form a tight network of interactions which may stabilize the nucleotide-free protein. The structural relationship between the two domains suggests that the N domain senses or controls the nucleotide occupancy of the GTPase domain. A structural subdomain unique to these evolutionarily conserved GTPases constitutes them as a distinct subfamily in the GTPase superfamily.

An essential role for water in an enzyme reaction mechanism: the crystal structure of the thymidylate synthase mutant E58Q

A water-mediated hydrogen bond network coordinated by glutamate 60(58) appears to play an important role in the thymidylate synthase (TS) reaction mechanism. We have addressed the role of glutamate 60(58) in the TS reaction by cocrystalizing the Escherichia coli TS mutant E60(58)Q with dUMP and the cofactor analog CB3717 and have determined the X-ray crystal structure to 2.5 A resolution with a final R factor of 15.2% (Rfree = 24.0%). Using difference Fourier analysis, we analyzed directly the changes that occur between wild-type and mutant structures. The structure of the mutant enzyme suggests that E60(58) is not required to properly position the ligands in the active site and that the coordinated hydrogen bond network has been disrupted in the mutant, providing an atomic resolution explanation for the impairment of the TS reaction by the E60(58)Q mutant and confirming the proposal that E60(58) coordinates this conserved hydrogen bond network. The structure also provides insight into the role of specific waters in the active site which have been suggested to be important in the TS reaction. Finally, the structure shows a unique conformation for the cofactor analog, CB3717, which has implications for structure-based drug design and sheds light on the controversy surrounding the previously observed enzymatic nonidentity between the chemically identical monomers of the TS dimer.

Binding of the anticancer drug ZD1694 to E. coli thymidylate synthase: assessing specificity and affinity

BACKGROUND

Thymidylate synthase (TS) catalyzes the reductive methylation of deoxyuridine monophosphate (dUMP) by 5, 10-methylenetetrahydrofolate (CH2H4folate) to form deoxythymidine monophosphate (dTMP) and dihydrofolate (H2folate). The essential role of TS in the cell life cycle makes it an attractive target for the development of substrate and cofactor-based inhibitors that may find efficacy as anticancer and antiproliferative drugs. Antifolates that compete specifically with the binding of CH2H4 folate include the cofactor analog CB3717 (10-propargyl-5,8-dideazafolate). However, the development of potent cofactor analog inhibitors of TS, such as CB3717, as drugs has been slowed by their toxicity, which often becomes apparent as hepatic and renal toxicity mediated by the specific chemistry of the compound. Attempts to abolish toxicity in human patients while preserving potency against the target enzyme, have led to the development of ZD1694, which has already shown significant activity against colorectal tumours.

RESULTS

The three dimensional crystallographic structure of ZD1694 in complex with dUMP and Escherichia coli TS has been determined to a resolution of 2.2 . This was used to evaluate the specific structural determinants of ZD1694 potency and to correlate structure/activity relationships between it and the closely related ligand, CB3717. ZD1694 binds to TS in the same manner as CB3717 and H2 folate, but a methyl group on its quinazoline ring, its thiophene ring and the methyl group at N10 are compensated for by plastic accommodation of the enzyme active site coupled with specific rearrangement in the solvent structure. A specific hydrogen bond between the protein and the inhibitor CB3717 is absent in the case of ZD1694 whose monoglutamate tail is reoriented and more well ordered.

CONCLUSIONS

The binding mode of ZD1694 to thymidylate synthase has been determined at atomic resolution. ZD1694 forms a ternary complex with dUMP and participates in the multi-step TS reaction through the covalent bond formation between dUMP and Cys146 thereby competing with CH2H4 folate at the active site. Analysis of this inhibitor ternary complex structure and comparison with that of CB3717 reveals that the enzyme accommodates the differences between the two inhibitors with small shifts in the positions of key active site residues and by repositioning an active site water molecule, thereby preserving a general binding mode of these inhibitors.

Three-dimensional structures of HIV-1 and SIV protease product complexes

Strain is eliminated as a factor in hydrolysis of the scissile peptide bond by human immunodeficiency virus (HIV)-1 and simian immunodeficiency virus (SIV), based on the first eight complexes of products of hydrolysis with the enzymes. The carboxyl group generated at the scissile bond interacts with both catalytic aspartic acids. The structures directly suggest the interactions of the gemdiol intermediate with the active site. Based on the structures, the nucleophilic water is displaced stereospecifically by substrate binding toward one catalytic aspartic acid, while the scissile carbonyl becomes hydrogen bonded to the other catalytic aspartic acid in position for hydrolysis. Crystal structures for two N-terminal (P) products and two C-terminal (Q) products provide unambiguous density for the ligands at 2.2-2.6 A resolution and 17-21% R factors. The N-terminal product, Ac-S-L-N-F/, overlaps closely with the N-terminal sequences of peptidomimetic inhibitors bound to the protease. Comparison of the two C-terminal products, /F-L-E-K and /F(NO2)-E-A-Nle-S, indicates that the P2' residue is highly constrained, while the positioning of the P1' and P3' residues are sequence dependent.

A new class of HIV-1 protease inhibitor: the crystallographic structure, inhibition and chemical synthesis of an aminimide peptide isostere

The essential role of HIV-1 protease (HIV-1 PR) in the viral life cycle makes it an attractive target for the development of substrate-based inhibitors that may find efficacy as anti-AIDS drugs. However, resistance has arisen to potent peptidomimetic drugs necessitating the further development of novel chemical backbones for diversity based chemistry focused on probing the active site for inhibitor interactions and binding modes that evade protease resistance. AQ148 is a potent inhibitor of HIV-1 PR and represents a new class of transition state analogues incorporating an aminimide peptide isostere. A 3-D crystallographic structure of AQ148, a tetrapeptide isostere, has been determined in complex with its target HIV-1 PR to a resolution of 2.5 A and used to evaluate the specific structural determinants of AQ148 potency and to correlate structure-activity relationships within the class of related compounds. AQ148 is a competitive inhibitor of HIV-1 PR with a Ki value of 137 nM. Twenty-nine derivatives have been synthesized and chemical modifications have been made at the P1, P2, P1', and P2' sites. The atomic resolution structure of AQ148 bound to HIV-1 PR reveals both an inhibitor binding mode that closely resembles that of other peptidomimetic inhibitors and specific protein/inhibitor interactions that correlate with structure-activity relationships. The structure provides the basis for the design, synthesis and evaluation of the next generation of hydroxyethyl aminimide inhibitors. The aminimide peptide isostere is a scaffold with favorable biological properties well suited to both the combinatorial methods of peptidomimesis and the rational design of potent and specific substrate-based analogues.

Partitioning roles of side chains in affinity, orientation, and catalysis with structures for mutant complexes: asparagine-229 in thymidylate synthase

Thymidylate synthase (TS) methylates only dUMP, not dCMP. The crystal structure of TS.dCMP shows sCMP 4-NH2 excluded from the space between Asn-229 and His-199 by the hydrogen bonding and steric properties and Asn-229. Consequently, 6-C of dCMP is over 4 A from the active site sulfhydryl. The Asn-229 side chain is prevented from flipping 180 degrees to and orientation the could hydrogen bond to dCMP by a hydrogen bond network between conserved residues. Thus, the specific binding of dUMP by TS results from occlusion of competing substrates by steric and electronic effects of residues in the active site cavity. When Asn-229 is replaced by a cysteine, the Cys-229 S gamma rotates out of the active site, and the mutant enzyme binds both dCMP and dUMP tightly but does not methylate dCMP. Thus simply admitting dCMP into the dUMP binding site of TS is not sufficient for methylation of dCMP. Structures of nucleotide complexes of TS N229D provide a reasonable explanation for the preferential methylation of dCMP instead of dUMP by this mutant. In TS N229D.dCMP, Asp-229 forms hydrogen bonds to 3-N and 40NH2 of dCMP. Neither the Asp-229 carboxyl moiety nor ordered water appears to hydrogen bond to 4-O of dUMP. Hydrogen bonds to 4-O (or 4-NH2) have been proposed to stabilize reaction intermediates. If their absence in TS N229D.dUMP persists in the ternary complex, it could explain the 10(4)-fold decrease in kcat/Km for dUMP.

Asparagine 229 mutants of thymidylate synthase catalyze the methylation of 3-methyl-2'-deoxyuridine 5'-monophosphate

The conserved Asn 229 of thymidylate synthase (TS) forms a cyclic hydrogen bond network with the 3-NH and 4-O of the nucleotide substrate 2'-deoxyuridine 5'-monophosphate (dUMP). Asn 229 is not essential for substrate binding or catalysis [Liu, l., & Santi, D. B. (1993) Proc. Natl. Acad. Sci. U.S.A. 90, 8604-8608] but is a major determinant in substrate specificity [Liu, l., & Santi, D. V. (1993) Biochemistry 32, 9263-9267]. 3-Methyl-dUMP (3-MedUMP) is neither a substrate nor an inhibitor of wild type TS but is converted to 3-methyl 2'-deoxythymidine 5'-monophosphate by many TS Asn 229 mutants. Some of the Asn 229 mutants (N229C, -I, -M, -A, and -V) have kcat values for 3-MedUMP methylation which are up to about 20% of that for wild type TS-catalyzed methylation of dUMP, and some mutants (N229C and -A) catalyze methylation of 3-MedUMP more efficiently than that of dUMP. Mutants with hydrophobic side chains tended to be more active in catalysis of methylation of 3-MedUMP than those with hydrophilic side chains. The ability of 3-MedUMP to serve as a substrate for Asn 229 mutants shows that the active form of dUMP involves the neutral pyrimidine base and that ionization of the 3-NH group does not occur in the course of catalysis. In contrast to the negligible binding of 3-MedUMP to wild type TS, both 3-MedUMP and dUMP showed similar Km values with the Asn 229 mutants, suggesting similar binding affinities to the mutants. The X-ray crystal structure of the TS N229C--3-MedUMP complex showed that the side chain of Cys 229 was rotated away from the pyrimidine ring to allow placement of a water molecule and the 3-methyl group of 3-MedUMP in the active site. Our results suggest that the inability of 3-MedUMP to undergo methylation by wild type TS is due to its inability to bind to the enzyme, which in turn is simply a result of steric interference of the 3-methyl group with the side chain of Asn 229.

Entropy in bi-substrate enzymes: proposed role of an alternate site in chaperoning substrate into, and products out of, thymidylate synthase

Three steps along the pathway of binding, orientation of substrates and release of products are revealed by X-ray crystallographic structures of ternary complexes of the wild-type Lactobacillus casei thymidylate synthase enzyme. Each complex was formed by diffusion of either the cofactor 5,10-methylene-5,6,7,8-tetrahydrofolate or the folate analog 10-propargyl-5,8-dideazafolate into binary co-crystals of thymidylate synthase with 2'-deoxyuridine-5'-monophosphate. A two-substrate/enzyme complex is formed where the substrates remain unaltered. The imidazolidine ring is unopened and the pterin of the 5,10-methylene-5,6,7,8-tetrahydrofolate cofactor binds at an unproductive "alternate" site. We propose that the presence of the pterin at this site may represent an initial interaction with the enzyme that precedes all catalytic events. The structure of the 2'-deoxyuridine-5'-monophosphate and 10-propargyl-5,8-dideazafolate folate analog complex identifies both ligands in orientations favorable for the initiation of catalysis and resembles the productive complex. A product complex where the ligands have been converted into products of the thymidylate synthase reaction within the crystal, 2'-deoxythymidine-5'-monophosphate and 7,8-dihydrofolate, shows how ligands are situated within the enzyme after catalysis and on the way to product release.

The complex of the anti-cancer therapeutic, BW1843U89, with thymidylate synthase at 2.0 A resolution: implications for a new mode of inhibition

BACKGROUND

Thymidylate synthase (TS) is critical to DNA synthesis as it catalyzes the rate limiting step in the only biosynthetic pathway for deoxythymidine monophosphate (dTMP) production. TS is therefore an important target for anti-proliferative and anti-cancer drug design. The TS enzymatic mechanism involves the reductive methylation of the substrate, deoxyuridine monophosphate (dUMP), by transfer of a methylene group from the co-factor, methylenetetrahydrofolate (CH2H4folate), resulting in the production of deoxythymidine monophosphate (dTMP) and dihydrofolate (H2folate). Previous drug design efforts based on co-factor analogues have produced good inhibitors of TS, but poor bioavailability and toxicity have limited their usefulness. BW1843U89, a folate analogue, is a recently developed compound which is an exceptionally strong inhibitor (Ki = 0.09 nM), has good bioavailability and in clinical trials thus far has not demonstrated significant toxicity.

RESULTS

We report the crystal structure of E. coli TS in ternary complex with dUMP and BW1843U89 at 2.0 A resolution. Although the benzoquinazoline ring system of the inhibitor binds to TS in much the same manner as previously determined for H2folate and CB3717, the larger size of the ligand is accommodated by the enzyme through a local distortion of the active site, that is not strictly conserved in both monomers in the asymmetric unit. Several conserved waters that had been previously implicated in mechanistic roles have been displaced.

CONCLUSIONS

BW1843U89 forms a ternary complex with dUMP and completes with CH2H4 folate at the active site. Inhibition of TS by BW1843U89 shows four unique aspects in its mechanism of action. BW1843U89 prevents the Michael addition of dUMP to Cys146, in contrast to the mechanisms implicated from crystallography of other quinazoline based inhibitors; displaces a catalytic water from the active site; reorders a peptide loop (Leu72-Trp83) in the active site; and is unique amongst the antifolates in inactivating TS at a stoichiometric ratio of one molecule per TS dimer. Thus, it exploits the principles of negative cooperativity that are increasingly being recognized in the catalytic mechanism of the enzyme per se. The structure suggests that this 'half-the-sites' effect is catalytic and not related to ligand binding. Therefore BW1843U89 is both a competitive inhibitor (at the binding site) and a non-competitive inhibitor at the other site.

Contribution of a salt bridge to binding affinity and dUMP orientation to catalytic rate: mutation of a substrate-binding arginine in thymidylate synthase

Invariant arginine 179, one of four arginines that are conserved in all thymidylate synthases (TS) and that bind the phosphate moiety of the substrate 2'-deoxyuridine-5'-monophosphate (dUMP), can be altered even to a negatively charged glutamic acid with little effect on kcat. In the mutant structures, ordered water or the other phosphate-binding arginines compensate for the hydrogen bonds made by Arg179 in the wild-type enzyme and there is almost no change in the conformation or binding site of dUMP. Correlation of dUMP Kds for TS R179A and TS R179K with the structures of their binary complexes shows, that the positive charge on Arg179 contributes significantly to dUMP binding affinity. kcat/K(m) for dUMP measures the rate of dUMP binding to TS during the ordered bi-substrate reaction, and in the ternary complex dUMP provides a binding surface for the cofactor. kcat/K(m) reflects the ability of the enzyme to accept a properly oriented dUMP for catalysis and is less sensitive than is Kd to the changes in electrostatics at the phosphate binding site.

Crystal structure of human thymidylate synthase: a structural mechanism for guiding substrates into the active site

The crystal structure of human thymidylate synthase, a target for anti-cancer drugs, is determined to 3.0 A resolution and refined to a crystallographic residual of 17.8%. The structure implicates the enzyme in a mechanism for facilitating the docking of substrates into the active site. This mechanism involves a twist of approximately 180 degrees of the active site loop, pivoted around the neighboring residues 184 and 204, and implicates ordering of external, eukaryote specific loops along with the well-characterized closure of the active site upon substrate binding. The highly conserved, but eukaryote-specific insertion of twelve residues 90-101 (h117-128), and of eight residues between 156 and 157 (h146-h153) are known to be alpha-helical in other eukaryotes, and lie close together on the outside of the protein in regions of disordered electron density in this crystal form. Two cysteines [cys 202 (h199) and 213 (h210)] are close enough to form a disulfide bond within each subunit, and a third cysteine [cys 183 (h180)] is positioned to form a disulfide bond with the active site cysteine [cys 198 (h195)] in its unliganded conformation. The amino terminal 27 residues, unique to human TS, contains 8 proline residues, is also in a region of disordered electron density, and is likely to be flexible prior to substrate binding. The drug resistance mutation, Y6H, confers a 4-fold reduction in FdUMP affinity and 8-fold reduction in kcat for the dUMP reaction. Though indirectly connected to the active site, the structure suggests a mechanism of resistance that possibly involves a change in structure. This structure offers a unique opportunity for structure-based drug design aimed at the unliganded form of the human enzyme.

Significance of structural changes in proteins: expected errors in refined protein structures

A quantitative expression key to evaluating significant structural differences or induced shifts between any two protein structures is derived. Because crystallography leads to reports of a single (or sometimes dual) position for each atom, the significance of any structural change based on comparison of two structures depends critically on knowing the expected precision of each median atomic position reported, and on extracting it for each atom, from the information provided in the Protein Data Bank and in the publication. The differences between structures of protein molecules that should be identical, and that are normally distributed, indicating that they are not affected by crystal contacts, were analyzed with respect to many potential indicators of structure precision, so as to extract, essentially by "machine learning" principles, a generally applicable expression involving the highest correlates. Eighteen refined crystal structures from the Protein Data Bank, in which there are multiple molecules in the crystallographic asymmetric unit, were selected and compared. The thermal B factor, the connectivity of the atom, and the ratio of the number of reflections to the number of atoms used in refinement correlate best with the magnitude of the positional differences between regions of the structures that otherwise would be expected to be the same. These results are embodied in a six-parameter equation that can be applied to any crystallographically refined structure to estimate the expected uncertainty in position of each atom. Structure change in a macromolecule can thus be referenced to the expected uncertainty in atomic position as reflected in the variance between otherwise identical structures with the observed values of correlated parameters.