Biomedical subjects

R W Harrison

Publications and source records attributed to R W Harrison.

At least 37 records · Page 2Linked to original sources

PubMed1999

Structural model of human glucokinase in complex with glucose and ATP: implications for the mutants that cause hypo- and hyperglycemia.

Mutations in human glucokinase are implicated in the development of diabetes and hypoglycemia. Human glucokinase shares 54% identical amino acid residues with human brain hexokinase I. This similarity was used to model the structure of glucokinase by analogy to the crystal structure of brain hexokinase. Glucokinase was modeled with both its substrates, glucose and MgATP, to understand the effect of mutations. The glucose is predicted to form hydrogen bond interactions with the side chains of glucokinase residues Thr 168, Lys 169, Asn 204, Asp 205, Asn 231, and Glu 290, similar to those observed for brain hexokinase I. The magnesium ion is coordinated by the carboxylates of Asp 78 and Asp 205 and the gamma-phosphate of ATP. ATP is predicted to form hydrogen bond interactions with residues Gly 81, Thr 82, Asn 83, Arg 85, Lys 169, Thr 228, Lys 296, Thr 332, and Ser 336. Mutations of residues close to the predicted ATP binding site produced dramatic changes in the Km for ATP, the catalytic rate, and a loss of cooperativity, which confirmed our model. Mutations of residues in the glucose binding site dramatically reduced the catalytic activity, as did a mutation that was predicted to disrupt an alpha-helix. Other mutations located far from the active site gave smaller changes in kinetic parameters. In the absence of a crystal structure for glucokinase, our models help rationalize the potential effects of mutations in diabetes and hypoglycemia, and the models may also facilitate the discovery of pharmacological glucokinase activators and inhibitors.

Adenosine Triphosphate↗

PubMed1998

Drug-resistant HIV-1 proteases identify enzyme residues important for substrate selection and catalytic rate.

A series of mutations, first identified in protease inhibitor-resistant HIV-1 viral isolates, were introduced into HIV-1 PR as individual substitutions. Mutants containing R8K, V32I, V82T, I84V, G48V/L90M, or V82T/I84V substitutions were analyzed for differences in substrate preference and catalytic efficiency using a set of single amino acid substituted HIV-1 CA-NCa cleavage site peptides. All mutants exhibited wild-type preference for large hydrophobic residues, especially Phe, in the P1' substrate position. Only the R8K and V32I mutants showed significant differences in subsite selection compared to wild-type enzyme. In a parallel study, the individual mutations R10K, L12V, I44V, A60M, I71V, and I108V were introduced into RSV PR. These amino acid positions are structurally equivalent to Arg8, Leu10, Val32, Met46, Ile54, and Ile84 in HIV-1 PR, respectively, which mutate in drug-resistance. The RSV R10K substitution significantly altered substrate specificity and catalytic rate, compared to wild-type, in a manner similar to that of the HIV-1 R8K mutant. Crystal structures of the RSV PR R10K, I44V, I71V, and Il08V mutant enzymes presented here indicate that each of these substitutions has little effect on the overall structure of the respective enzymes. Taken together, these data provide an explanation for the reported in vivo predilection for selection of large hydrophobic residues in the P1' substrate position of second locus mutations in the Gag polyprotein PR cleavage sites. The data also suggest that the selection of resistant enzymes is not simply limited to loss of binding to inhibitor but affects other steps in proteolysis.

Amino Acid Substitution↗

PubMed1998

Structural basis for specificity of retroviral proteases.

The Rous sarcoma virus (RSV) protease S9 variant has been engineered to exhibit high affinity for HIV-1 protease substrates and inhibitors in order to verify the residues deduced to be critical for the specificity differences. The variant has 9 substitutions (S38T, I42D, I44V, M73V, A100L, V104T, R105P, G106V, and S107N) of structurally equivalent residues from HIV-1 protease. Unlike the wild-type enzyme, RSV S9 protease hydrolyzes peptides representing the HIV-1 protease polyprotein cleavage sites. The crystal structure of RSV S9 protease with the inhibitor, Arg-Val-Leu-r-Phe-Glu-Ala-Nle-NH2, a reduced peptide analogue of the HIV-1 CA-p2 cleavage site, has been refined to an R factor of 0.175 at 2.4-A resolution. The structure shows flap residues that were not visible in the previous crystal structure of unliganded wild-type enzyme. Flap residues 64-76 are structurally similar to residues 47-59 of HIV-1 protease. However, residues 61-63 form unique loops at the base of the flaps. Mutational analysis indicates that these loop residues are essential for catalytic activity. Side chains of flap residues His 65 and Gln 63' make hydrogen bond interactions with the inhibitor P3 amide and P4' carbonyl oxygen, respectively. Other interactions of RSV S9 protease with the CA-p2 analogue are very similar to those observed in the crystal structure of HIV-1 protease with the same inhibitor. This is the first crystal structure of an avian retroviral protease in complex with an inhibitor, and it verifies our knowledge of the molecular basis for specificity differences between RSV and HIV-1 proteases.

Aspartic Acid Endopeptidases↗

PubMed1998

Crystal structure of MTCP-1: implications for role of TCL-1 and MTCP-1 in T cell malignancies.

Two related oncogenes, TCL-1 and MTCP-1, are overexpressed in T cell prolymphocytic leukemias as a result of chromosomal rearrangements that involve the translocation of one T cell receptor gene to either chromosome 14q32 or Xq28. The crystal structure of human recombinant MTCP-1 protein has been determined at 2.0 A resolution by using multiwavelength anomalous dispersion data from selenomethionine-enriched protein and refined to an R factor of 0.21. MTCP-1 folds into a compact eight-stranded beta barrel structure with a short helix between the fourth and fifth strands. The topology is unique. The structure of TCL-1 has been predicted by molecular modeling based on 40% amino acid sequence identity with MTCP-1. The identical residues are clustered inside the barrel and on the surface at one side of the barrel. The overall structure of MTCP-1 superficially resembles the structures of proteins in the lipocalin family and calycin superfamily. These proteins have diverse functions, including transport of retinol, fatty acids, chromophores, pheromones, synthesis of prostaglandin, immune modulation, and cell regulation. However, MTCP-1 differs in the topology of the beta strands. The structural similarity suggests that MTCP-1 and TCL-1 form a unique family of beta barrel proteins that is predicted to bind small hydrophobic ligands and function in cell regulation.

Amino Acid Sequence↗

PubMed1997

Crystallographic analysis of human immunodeficiency virus 1 protease with an analog of the conserved CA-p2 substrate -- interactions with frequently occurring glutamic acid residue at P2' position of substrates.

Human immunodeficiency virus type 1 (HIV-1) protease hydrolysis of the Gag CA-p2 cleavage site is crucial for virion maturation and is optimal at acidic pH. To understand the processing of the CA-p2 site, we have determined the structure of HIV-1 protease complexed with an analog of the CA-p2 site, the reduced peptide inhibitor Arg-Val-Leu-r-Phe-Glu-Ala-Ahx-NH2 [r denotes the reduced peptide bond and Ahx 2-aminohexanoic acid (norleucine), respectively]. The crystal structure was refined to an R-factor of 0.17 at 0.21-nm resolution. The crystals have nearly the same lattice as related complexes in P2(1)2(1)2(1) which have twofold disordered inhibitor, but are in space group P2(1). and the asymmetric unit contains two dimers of HIV-1 protease related by 180 degrees rotation. An approximate non-crystallographic symmetry has replaced the exact crystal symmetry resulting in well-ordered inhibitor structure. Each protease dimer binds one ordered inhibitor molecule, but in opposite orientations. The interactions of the inhibitor with the two dimers are very similar for the central P2 Val to P2' Glu residues, but show more variation for the distal P3 Arg and P4' Ahx residues. Importantly, the carboxylate oxygens of Glu at P2' in the inhibitor are within hydrogen-bonding distance of a carboxylate oxygen of Asp30 of the protease suggesting that the two side chains share a proton. This interaction suggests that the enzyme-substrate complex is additionally stabilized at lower pH. The importance of this interaction is emphasized by the absence of polymorphisms of Asp30 in the protease and variants of P2' Glu in the critical CA-p2 cleavage site.

Amino Acid Sequence↗

PubMed1997

Activity of tethered human immunodeficiency virus 1 protease containing mutations in the flap region of one subunit.

The tethered-dimer protease of human immunodeficiency virus 1 (HIV-1) [Cheng Y.-S. E., Yin, F.H., Foundling, S., Blomstrom, D. & Kettner, C. A. (1990) Proc. Natl Acad. Sci. USA 87, 9660-9664] and its mutants containing amino acid substitutions or deletions or both in only one flap region were expressed in Escherichia coli. These mutant enzymes showed various degrees of self-processing and significantly reduced catalytic activity toward oligopeptide substrates compared with the wild type. Kinetic parameters determined for one of the oligopeptide substrates showed a dramatic increase in K(m) and decrease in Kcat values. Unexpectedly, the substrate cleavage was more efficient in low salt concentration for a mutant containing a shortened hydrophilic flap. Assays with oligopeptides representing naturally occurring cleavage sites or oligopeptides containing single amino acid substitutions at the P2 and P2' substrate positions showed only moderate changes in the substrate specificity of the mutant proteases. Predicted structures for the mutants were constructed by molecular modeling and used to interpret the results of kinetic measurements. In general, the data suggest that the mutated part of the flaps does not have a major role in determining substrate specificity; rather, it provides the hydrophobic environment and hydrogen-bond interactions with the conserved water that are necessary for efficient substrate binding and catalysis.

Amino Acid Sequence↗

PubMed1997

Clinical use of asymmetric collimators.

PURPOSE: To illustrate some of the radiation treatment techniques with asymmetric collimators in one field dimension. METHODS AND MATERIALS: Treatment planning for various sites is done with an in-house developed treatment planning system. Dose distributions in the central plane are illustrated. RESULTS: The use of asymmetric collimation, in addition to being a replacement for cerrobend and lead blocks, can facilitate treatment setup with boost fields and with half-beam asymmetric fields as in matching two adjacent fields, in avoiding nearby critical organ or tissue, and in tangential breast treatment. The use of asymmetric collimators would alter the dose distribution across the radiation field and should be accounted for during treatment planning. In conjunction with arc rotation or multiple asymmetric fields, two-dimensional conformal radiotherapy is possible. CONCLUSION: The full potential of asymmetric collimation requires the use of a proper treatment planning algorithm. Some of the treatment techniques with asymmetric collimation in one field dimension are shown here.

Breast Neoplasms↗

PubMed1997

Analysis of comparative modeling predictions for CASP2 targets 1, 3, 9, and 17.

Comparative modeling targets 1, 3, 9 and 17 were predicted by alignment of multiple sequences and structures, when available, followed by minimization using the program AMMP. The minimization used improved potentials, and distance restraints for regions of common structure. New prediction procedures were evaluated. Three tested solvent corrections did not significantly improve the predictions. Target 17 had 85.3% sequence identity with the parent and no insertions or deletions. The prediction had a root-mean-square deviation from target 17 of 0.56 A on C alpha atoms, and 0.59 A for the ligand atoms, which verified the accuracy of the minimization. Targets 1, 3, and 9 had 36.4%, 46.7%, and 33.3% identity with the parent sequences, and predictions resulted in root-mean-square deviations for 79-85% of C alpha atoms of 1.49, 1.11, and 1.24 A, respectively. Conformational differences between parent and target crystal structures were difficult to predict. The use of distance restraints and multiple structures improved the positioning of gaps in sequence alignment. Distance restraints did not overcome errors in sequence alignment or ambiguities due to conformational variation in proteins. Predictions for targets 3 and 9 successfully reduced large deviations between parent and target structures.

Animals↗

PubMed1997

Molecular mechanics calculations on Rous sarcoma virus protease with peptide substrates.

Molecular models of Rous sarcoma virus (RSV) protease and 20 peptide substrates with single amino acid substitutions at positions from P4 to P3', where the scissile bond is between P1 and P1'. were built and compared with kinetic measurements. The unsubstituted peptide substrate. Pro-Ala-Val-Ser-Leu-Ala-Met-Thr, represents the NC-PR cleavage site of RSV protease. Models were built of two intermediates in the catalytic reaction, RSV protease with peptide substrate and with the tetrahedral intermediate. The energy minimization used an algorithm that increased the speed and eliminated a cutoff for nonbonded interactions. The calculated protease-substrate interaction energies showed correlation with the relative catalytic efficiency of peptide hydrolysis. The calculated interaction energies for the 8 RSV protease-substrate models with changes in P1 to P1' next to the scissile bond gave the highest correlation coefficient of 0.79 with the kinetic measurements, whereas all 20 substrates showed the lower, but still significant correlation of 0.46. Models of the tetrahedral reaction intermediates gave a correlation of 0.72 for the 8 substrates with changes next to the scissile bond, whereas a correlation coefficient of only 0.34 was observed for all 20 substrates. The differences between the energies calculated for the tetrahedral intermediate and the bound peptide gave the most significant correlation coefficients of 0.90 for models with changes in P1 and P1', and 0.56 for all substrates. These results are compared to those from similar calculations on HIV-1 protease and discussed in relation to the rate-limiting steps in the catalytic mechanism and the entropic contributions.

Aspartic Acid Endopeptidases↗

PubMed1997

Crystal structure of TNF-alpha mutant R31D with greater affinity for receptor R1 compared with R2.

Crystal structures have been determined of recombinant human tumor necrosis factor-alpha (TNF-alpha) and its R31D mutant that preferentially binds to TNF receptor R1 with more than seven times the relative affinity of binding to receptor R2. Crystals of the wild-type TNF were of space group P4(1)2(1)2 and had unit cell dimensions of a = b = 94.7 and c = 117.4 A. Refinement of the structure gave an R-factor of 22.3% at 2.5 A resolution. The crystals of TNF R31D mutant diffracted to 2.3 A resolution, and were of identical space group to the wild type with unit cell dimensions of a = b = 95.4 and c = 116.2 A, and the structure was refined to an R-factor of 21.8%. The trimer structures of the wild-type and mutant TNF were similar with a root mean square (r.m.s.) deviation of 0.56 A for Calpha atoms; however, the subunits within each trimer were more variable with an average r.m.s. deviation of 1.00 A on Calpha atoms for pairwise comparison of subunits. Model complexes of TNF with receptors R1 and R2 have been used to predict TNF-receptor interactions. Arg31 in all three subunits of wild-type TNF is predicted to form an ionic interaction with the equivalent glutamic acid in both receptors R1 and R2. Asp31 of the TNF R31D mutant is predicted to interact differently with the two receptors. The side chain of Asp31 in two subunits of the TNF mutant is predicted to form hydrogen bond interactions with Ser59 or Cys70 of R1, while it has no predicted interactions with R2. The loss of three strong ionic interactions of Arg31 and the electrostatic repulsion of Asp31 with Glu in the receptors is consistent with the reduced binding of the R31D mutant to both receptors relative to wild-type TNF. The replacement of these ionic interactions by two weaker hydrogen bond interactions between Asp31 of the R31D mutant and R1, compared with no interactions with R2, is in agreement with the observed preferential binding of the R31D mutant to R1 over R2. Analysis of the structure and function of receptor-discriminating mutants of TNF will help understand the biological role of TNF and facilitate its use as an antitumor agent.

Binding Sites↗

PubMed1997

Easy gene walking.

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Chromosome Walking↗

PubMed1996

Model structure of decorin and implications for collagen fibrillogenesis.

The three-dimensional structure of human decorin, a secreted proteoglycan involved in the regulation of collagen fibrillogenesis and cellular growth, has been modeled based on the crystal structure of the porcine ribonuclease inhibitor. Both proteins contain leucine-rich repeats and share 18% identical residues. This model structure of decorin has an arch shape with the single glycosaminoglycan chain and the three N-linked oligosaccharides located on the same side of the molecule. Decorin was modeled as binding to a polar sequence of collagen type I found in the d band. The inner concave surface is the appropriate size and shape to accommodate only one collagen triple helix of approximately 3 nm in length. The binding of one collagen triple helix to decorin is proposed to play a major role in the formation of the staggered arrangement of collagen molecules within the microfibrils by preventing lateral fusion of collagen molecules.

Amino Acid Sequence↗

PubMed1996

ATP-binding site of human brain hexokinase as studied by molecular modeling and site-directed mutagenesis.

The interaction of ATP with the active site of hexokinase is unknown since the crystal structure of the hexokinase-ATP complex is unavailable. It was found that the ATP binding site of brain hexokinase is homologous to that of actin, heat shock protein hsc70, and glycerol kinase. On the basis of these similarities, the ATP molecule was positioned in the catalytic domain of human brain hexokinase, which was modeled from the X-ray structure of yeast hexokinase. Site-directed mutagenesis was performed to test the function of residues presumably involved in interaction with the tripolyphosphoryl moiety of ATP. Asp532, which is though to be involved in binding the Mg2+ ion of the MgATP2- complex, was mutated to Lys and Glu. The kcat values decreased 1000- and 200-fold, respectively, for the two mutants. Another residue, Thr680 was proposed to interact with the gamma-phosphoryl group of ATP through hydrogen bonds and was mutated to Val and Ser. The kcat value of the Thr680Val mutant decreased 2000-fold, whereas the kcat value of the Thr680Ser decreased only 2.5-fold, implying the importance of the hydroxyl group. The Km and dissociation constant values for either ATP or glucose of all the above mutants showed little or no change relative to the wild-type enzyme. The Ki values for the glucose 6-phosphate analogue 1,5-anhydroglucitol 6-phosphate, were the same as that of the wild-type enzyme, and the inhibition was reversed by inorganic phosphate (Pi) for all four mutants. The circular dichroism spectra of the mutants were the same as that of the wild-type enzyme. The results from the site-directed mutagenesis demonstrate that the presumed interactions of investigated residues with ATP are important for the stabilization of the transition state.

Adenosine Triphosphate↗

PubMed1996

Effects of Pax3 modifier genes on craniofacial morphology, pigmentation, and viability: a murine model of Waardenburg syndrome variation.

Waardenburg syndrome type 1 is caused by mutations in PAX3. Over 50 human PAX3 mutations that lead to hearing, craniofacial, limb, and pigmentation anomalies have been identified. A PAX3 mutant allele, segregating in a family, can show reduced penetrance and variable expressivity that cannot be explained by the nature of the mutation alone. The Mus musculus Pax3 mutation Spd (Splotch-delayed, Pax3Spd), coisogenic on the C57BL/6J (B6) genetic background, produces in heterozygotes a white belly spot with 100% penetrance and very few other anomalies. By contrast, many Spd/+ BC1 progeny [F1 female Spd/+ (female Spd/+ B6 x male +/+ Mus spretus) x male +/+ B6] exhibit highly variable craniofacial and pigmentary anomalies. Of the BC1 Spd/+ progeny, 23.9% are estimated to be nonviable, and 32.1% are nonpenetrant for the white belly spot. The penetrance and expressivity of the Spd/+ genotype are controlled in part by the genetic background and the sex of the individual. A minimum of two genes interact with Spd to influence the craniofacial features of these mice. One of these genes may be either X-linked or sex-influenced, while the other is autosomal. The A-locus (Agouti) or a gene closely linked to A also plays a role in determining craniofacial features. At least one additional gene, possibly the A-locus or a gene linked to A, interacts with Spd and determines the presence and size of the white belly spot. The viability of BC1 mice is influenced by at least three factors: Spd, A-locus alleles or a gene closely linked to the A-locus, and the sex of the mouse. These BC1 mice provide an opportunity to identify genes that interact with and modify the expression of Pax3 and serve as a model to identify the genes that modify the expression of human PAX3 mutations.

Alleles↗

PubMed1996

Human immunodeficiency virus, type 1 protease substrate specificity is limited by interactions between substrate amino acids bound in adjacent enzyme subsites.

The specificity of the retroviral protease is determined by the ability of substrate amino acid side chains to bind into eight individual subsites within the enzyme. Although the subsites are able to act somewhat independently in selection of amino acid side chains that fit into each pocket, significant interactions exist between individual subsites that substantially limit the number of cleavable amino acid sequences. The substrate peptide binds within the enzyme in an extended anti-parallel beta sheet conformation with substrate amino acid side chains adjacent in the linear sequence extending in opposite directions in the enzyme-substrate complex. From this geometry, we have defined both cis and trans steric interactions, which have been characterized by a steady state kinetic analysis of human immunodeficiency virus, type-1 protease using a series of peptide substrates that are derivatives of the avian leukosis/sarcoma virus nucleocapsid-protease cleavage site. These peptides contain both single and double amino acid substitutions in seven positions of the minimum length substrate required by the retroviral protease for specific and efficient cleavage. Steady state kinetic data from the single amino acid substituted peptides were used to predict effects on protease-catalyzed cleavage of corresponding double substituted peptide substrates. The calculated Gibbs' free energy changes were compared with actual experimental values in order to determine how the fit of a substrate amino acid in one subsite influences the fit of amino acids in adjacent subsites. Analysis of these data shows that substrate specificity is limited by steric interactions between pairs of enzyme subsites. Moreover, certain enzyme subsites are relatively tolerant of substitutions in the substrate and exert little effect on adjacent subsites, whereas others are more restrictive and have marked influence on adjacent cis and trans subsites.

Amino Acid Sequence↗

PubMed1996

Two crystal structures of the leupeptin-trypsin complex.

Three-dimensional structures of trypsin with the reversible inhibitor leupeptin have been determined in two different crystal forms. The first structure was determined at 1.7 A resolution with R-factor = 17.7% in the trigonal crystal space group P3(1)21, with unit cell dimensions of a = b = 55.62 A, c = 110.51 A. The second structure was determined at a resolution of 1.8 A with R-factor = 17.5% in the orthorhombic space group P2(1)2(1)2(1), with unit cell dimensions of a = 63.69 A, b = 69.37 A, c = 63.01 A. The overall protein structure is very similar in both crystal forms, with RMS difference for main-chain atoms of 0.27 A. The leupeptin backbone forms four hydrogen bonds with trypsin and a fifth hydrogen bond interaction is mediated by a water molecule. The aldehyde carbonyl of leupeptin forms a covalent bond of 1.42 A length with side-chain oxygen of Ser-195 in the active site. The reaction of trypsin with leupeptin proceeds through the formation of stable tetrahedral complex in which the hemiacetal oxygen atom is pointing out of the oxyanion hole and forming a hydrogen bond with His-57.

Binding Sites↗

PubMed1996

Predicted ligand interactions of 3'5'-cyclic nucleotide-gated channel binding sites: comparison of retina and olfactory binding site models.

Cyclic nucleotide-gated channels (CNGC) open in response to the binding of 3'5'-cyclic nucleotides. Members of the CNGC family vary as much as 100-fold in their ability to respond to cAMP and cGMP. Molecular models of the nucleotide binding domains of the bovine retina and catfish and rat olfactory CNGCs were built from the crystal structure of cAMP bound to catabolite gene activator protein (CAP) with AMMP, a program for molecular mechanics and dynamics. The nucleotide conformation can be predicted from the number of strong and weak interactions between the purine ring and the binding site. The amino acids predicted to be important for determining the nucleotide affinity and specificity are residues 61, 83 (mediated through a water molecule), 119 and 127 (CAP sequence numbers) which interact with the purine ring. These residues also dictate the conformation of the ligand in the binding pocket. cGMP is preferentially bound in the syn conformation in bovine retina, bovine olfactory and rat olfactory CNGCs due to Thr83, while either conformation can bind in catfish olfactory CNGC. cAMP is predicted to bind either in syn or anti conformation, depending on the interaction with residue 119: the anti conformation is preferentially bound in olfactory CNGCs.

Animals↗

PubMed1996

Molecular mechanics calculations on HIV-1 protease with peptide substrates correlate with experimental data.

Molecular models of HIV-1 protease and 21 peptide substrates with single amino acid substitutions at positions from P4 to P3' were built and compared with kinetic measurements. The crystal structure of HIV-1 protease with a peptidic inhibitor was modified to model the peptide substrate Pro-Ala-Val-Ser-Leu-Ala-Met-Thr for the starting geometry. Models were built of two reaction intermediates, HIV protease with peptide substrate and with its tetrahedral intermediate. The energy minimization used a new algorithm that increased the speed and eliminated a cut-off for non-bonded interactions. After minimization the models for substrate and tetrahedral intermediate both had root mean square deviations of 0.48 A for all atoms of the HIV protease compared to the starting crystal structure. Differences in the model structures and interaction energies for HIV protease with different substrates were analyzed. The calculated interaction energies for the 21 HIV protease-tetrahedral intermediate models gave a correlation coefficient of 0.64 with the kinetic measurements. The eight substrates with changes in the P1 and P1' residues next to the scissile bond gave the highest correlation of 0.93, while the 14 substrates with changes in P2-P2' gave a correlation coefficient of 0.86. The catalytic mechanism and factors influencing the catalytic efficiency of the different substrates are discussed in relation to the models. The predictive ability of molecular mechanics calculations is discussed in the context of the statistical mechanics analysis of the differences in free energy.

Crystallography, X-Ray↗