An evaluation of the thermodynamics of binding between various ligands of Vancomycin (Part 2/2)
by Matthew Guberman-Pfeffer*
Vancomycin Molecular Recognition Events (cont’d)
Conversion of the C-terminal D-Ala to D-Lac in the bacterial peptide target results in the loss of one of the important ligand-tethering H-bonds, with significant consequences, as mentioned previously. The change in the magnitude in affinity/efficacy is rather surprising, given that Williams et al. concluded, after extensive investigation, that an amide-amide H-bond in ligated VC is worth 0 to 2 kcal/mol (which agrees with the N-acetylglycine versus acetate comparison earlier). For perspective, a 1000-fold reduction in binding affinity corresponds to a ΔGº that is more positive by 4.1 kcal/mol at 298 K. Some reports in the VC field attribute the reduced binding affinity solely to a lost H-bond, whereas others astutely added a destabilizing lone pair-lone pair (lp-lp) electrostatic repulsion between a carbonyl oxygen of VC and the ester O of remodeled peptidoglycan precursor peptides to explain the drop in affinity.
Consideration of the subtle details implicated in the reduced binding affinity of VC to the remodeled precursor, and thereby the abolished efficacy of the antibiotic against VanA resistant bacteria, has largely been neglected in derivatization efforts to reinstate potent antibacterial activity. Attention has concentrated on strategies for increasing the local concentration of individually weakly binding glycopeptide molecules at the surface of a bacterial membrane (e.g., tethering together two or more antibiotic molecules), as opposed to efforts to directly regain bimolecular binding affinity.[1,3,8] A 2003 paper from Dale Boger’s research group (McComas et al.) is a notable exception. These researchers wondered whether the lost H-bond or the introduced lp-lp repulsion was worse for the binding affinity of VC for D-Ala-D-Lac.
When substituting an ester O for the amide NH of the terminal Ala of cell wall precursor peptides, VanA resistant bacteria skip over an element in the periodic table: carbon. Why do resistant bacteria ‘choose’ not to substitute a methylene group for the amide NH? Presumably, substitution of a methylene CH2 relative to an ester O is disfavored by selection pressures on bacteria to evolve resistance, because this substitution would provide inferior protection against VC. McComas et al. had the innovative idea to test just how inferior methylene substitution would be in reducing the binding affinity of VC for its bacterial peptide target. This research team reasoned that a methylene group could neither donate an H-bond, like an amide NH, nor suffer lp-lp electrostatic repulsion, like an ester O in close proximity to an amide carbonyl O of the antibiotic. Methylene substitution, therefore, offered a chance to partition the effects of a lost H-bond and an introduced electrostatic repulsion on the binding affinity of VC. By synthesizing a peptide used by neither VC-susceptible nor VC-resistant bacteria, knowledge about how to derivatize VC to reduce or remove the most important factor contributing to VanA resistance could be obtained.
After devising a synthetic strategy to prepare ligand 3 (Fig. 4) – containing a CH2 group in place of the NH of the natural ligand 2, McComas et al. determined the binding affinity of VC and VC aglycon to this ligand, as well as for ligands 2 and 4. Binding constants were determined by a titration method employing differential ultraviolet (UV) absorption spectroscopy, according to the procedure used by Perkins in 1968 to establish that VC specifically recognized the consecutive D-Ala sequence of uncross-linked cell wall peptides.
Briefly, VC absorbs at ~280 nm due to the presence of the phenolic groups in its structure (Fig. 1). VC complexed with cell wall peptide analogues also absorbs UV light of ~280 nm, but with a reduced extinction coefficient. The binding constant determination method employed by McComas et al. depends on measuring the difference in the extinction coefficient (Δε) between uncomplexed and complexed VC at a particular wavelength (279 nm) as a function of added ligand concentration.[6,16] By assuming a direct proportionality between VC-ligand complex concentration and Δε, binding isotherms were constructed and used to determine binding constants (Fig. 4).[6,16]
To a first approximation, VC was found to have a binding affinity for the methylene-substituted ligand (3, Fig. 4) 10 times less than for the D-Ala-terminal ligand 2, but 100-fold greater than the D-lactate ligand 4. Ligand 4 had a free energy of binding more positive than ligand 2 by 4.1 kcal/mol. These results suggested that loss of the H-bond upon exchange of the terminal amide NH in the ligand for a CH2 group destabilizes the bimolecular association by 1.5 to 1.8 kcal/mol (Fig. 4). The antibiotic-ligand complex is further destabilized by 2.6 kcal/mol with the replacement of the CH2 group with an ester O (Fig. 4). Thus, the lp-lp repulsive interaction appears to be nearly twice as costly as the removal of an H-bond. This analysis is overly simplified, as will be demonstrated in the next section. Nevertheless, the findings suggest an answer to the question of which destabilizing interaction was more adverse for binding of the antibiotic: an introduced lp-lp repulsion, as opposed to a lost H-bond. By the same logic, a modified VC that does not suffer the electrostatic repulsion with D-lactate-terminating peptides should regain a substantial fraction of the binding affinity that the antibiotic had for D-Ala-terminating ligands. Gratifyingly, this possibility was realized in subsequent research. A synthesized VC aglycon with an amidine (C(=NH)NH) in place of the amide functionality (C(=O)NH) spanning residues 4 and 5 binds D-lactate-terminating bacterial peptide analogues with an affinity 600-fold greater than unmodified VC aglycan.
Down and dirty: physical organic chemistry fundamentals
McComas et al. determined the thermodynamic consequences of systematically varying a single atom from nitrogen to carbon to oxygen (not counting attached hydrogens) in the peptide ligand of VC. This classic structure-activity approach assumes that changes in the thermodynamics of binding are due to the structural modification, and not to any secondary consequences. Though they partitioned the effects from a lost H-bond and introduced lp-lp repulsion to yield a productive synthetic target, it is interesting to consider the binding interactions of each ligand examined by these researchers in more detail. The binding of a ligand by VC is an excellent example of how collectively and cooperatively numerous binding forces give rise to molecular recognition. To motivate the discussion, general comments on cooperativity and enthalpy-entropy compensation are in order.
Formation of a strong (short and stiff) covalent bond is more exothermic than formation of a weaker bond. Formation of a strong (tighter) non-covalent binding interaction is analogously more exothermic than for a weaker interaction. Just as bond formation restricts the motion of the newly bonded group, a binding interaction reduces the translational and rotational freedom of the newly interacting group. The stronger the binding or bonding interaction, the greater the restriction in motion. In principle, there is a limit to motional restriction (complete immobilization), but there is no inherent limit to the exothermicity of an interaction. As an interaction becomes increasingly exothermic, the limiting case of complete immobilization is approached. The entropic cost for an interaction per a given enthalpic investment (increase in exothermicity) decreases with increasing levels of investment (greater exothermicity). In other words, the incremental entropic cost is smaller for every additional increase in exothermicity as the maximum entropic cost for the interaction is approached.
Consider the binding of two parts, the carboxylate terminus (C) and the rest of the peptide ligand (P) to VC. If it is assumed that the enthalpies for the association of C and P are additive, then the more exothermically each binds, the more exothermic will be the binding of the whole ligand. The entropic cost for binding C and P is not the sum of the adverse entropies for binding C and P separately, however. By virtue of C-P binding with greater exothermicity than C and P separately, the entropic price per kcal/mol of enthalpy is less. Alternatively phrased, two parts of the ligand nearly bind for the entropic cost of one part because, by linking C and P, the adverse entropy change for binding P is partially prepaid when C binds (i.e., the second interaction is effectively intramolecular). With a greater exothermicity, but less than a proportionally greater entropic cost, the free energy change for binding C-P is more favorable (more negative) than binding C and P separately.
The entropic advantage of binding C-P relative to C and P individually, a phenomenon classically known as the chelate effect, is arguably accompanied by an advantageous enthalpic effect. In reality, the enthalpy for the association of C-P with VC may not simply be the sum of the enthalpies for the associations of C and P separately. The binding of C of C-P can reduce the freedom of motion of P, and thereby strengthen (cause to be more exothermic) the binding of P. The effect is reciprocal in that the binding of P in C-P also reduces the residual motion of the ligand, and strengthens the binding of C. This coupled enthalpic-entropic chelate phenomenon is a form of cooperativity termed the Gulliver effect, “If you wish to keep a close interaction [reduced residual motion] between Gulliver’s shoulders and the ground, then it is clear that an agitated Gulliver would be better constrained if he were also held at the waist and feet [increased number of attractive binding interactions].” A binding event becomes more negative entropically (unfavorable) and enthalpically (favorable) for one part of a ligand as the binding interaction(s) for a different part of the ligand becomes more negative enthalpically. The Gulliver effect is a cooperatively-orchestrated form of enthalpy-entropy compensation.
The Gulliver effect is operative in the D-Ala-terminating ligand complex with VC (2, Fig. 4). Williams et al. found a strong correlation between the strength of the 1H nuclear magnetic resonance (NMR) chemical shift for the amide proton of residue 2, and the number of additional H-bonds and hydrophobic contacts formed by the ligand with the antibiotic (Fig. 5).[17,18] As systematically added interactions made the binding free energy more favorable for a series of ligands in the order of: acetate < N-acetyl-D-Ala < N-acetyl-D-Ala-D-Ala < di-acetyl-Lys-D-Ala-D-Ala, the chemical shift of the residue 2 amide proton shifted downfield from 8.79 ppm to 11.69 ppm.[17,18] A downfield shift suggests participation in a stronger H-bond, because a stronger interaction would deplete the 1H nucleus of shielding electron density. Thus, the amide proton at residue 2 makes an increasingly stronger H-bond to the carboxylate of the ligand complexed with VC as a function of the other interactions formed at the binding interface.
Admittedly, conformational changes of VC associated with ligand binding, or different ligand binding geometries could also account for the downfield shift of the amide proton resonance. VC, however, is fairly rigid on account of extensive cross-linking of aromatic sidechains (Fig. 1). Further, molecular modeling based on NMR-determined through-space proton distances suggests a conserved geometry for the H-bonding network at the binding interface. Differences in antibiotic conformation and/or ligand binding geometry would be variable and therefore explain scatter in the experimental correlation between additional antibiotic-ligand interactions and an increasingly downfield shift of the particular amide proton resonance, not the correlation itself. Moreover, a correlation that holds over a ~3 ppm range with a linear regression R2 value of 0.99 (Fig. 5) seems not to be the artifact of experimental error, which is an alternative explanation for the observation of enthalpy-entropy compensation offered by Houk. Though there is no fundamental thermodynamic basis for enthalpy-entropy compensation, the findings of Williams et al. suggest that enthalpy-entropy compensation is a real physical phenomenon in the context of ligand recognition by VC.[17,19] The implication of the Gulliver effect is that the strength of the amide-amide H-bond determined by McComas et al. (1.5-1.8 kcal/mol) is necessarily an overestimation, because replacement of the H-bond donating amide with a methylene group not only removes an H-bond, but also weakens all the other interactions formed by the ligand to VC. The difference in the energetics of binding the amide- and methylene-containing ligands is not simply equivalent to the strength of the removed amide-amide H-bond. As will be discussed shortly, methylene substitution introduces advantages and disadvantages to binding that further question the assumption by McComas et al. that methylene substitution is a neutral structural alteration.
The VC:D-Lac-terminal ligand complex (4, Fig. 4) offers a clear case of enthalpy-entropy compensation by way of contrast to the preceding comments for the D-Ala-terminal ligand (2, Fig. 4). Replacement of an amide NH with an ester O changes the ligand C-P (2, Fig. 4) such that P (now P’) has a repulsive, instead of an attractive, interaction with VC (4, Fig. 4). For the following argument, it is assumed that the lp-lp repulsion (4, Fig. 4) overwhelms the remaining favorable interactions formed by P’ with the antibiotic, so as to make the net interaction of P’ with VC endothermic. If the binding of P’ was still exothermic, but to a lesser extent because of the lp-lp repulsion introduced in place of an H-bond, there would still be an advantageous enthalpic and entropic effect caused by tethering P’ to C (i.e., tethering would lower the entropic cost, and enlarge the enthalpic reward for bimolecular association, but the binding would not be as favorable as when the repulsive interaction was not present and P’ = P).
For the ligand C-P’, binding of C would reduce the motional freedom of P’ in the proximity of a repulsive interaction. The exothermic binding of C is now opposed by the endothermic binding of P’, and the opposition should be greater than the difference between the enthalpies for the separate binding of C and P’. Just as the exothermic binding of C enhanced the exothermicity of the binding of P when C and P were tethered together, the exothermic binding of C should enhance the endothermicity of the binding of P’ when C-P’ binds to the same receptor. Since the effect is reciprocal, the repulsive or ‘anti-binding’ interaction of P weakens the binding interaction of C.
Crystal structure data supports the notion that the endothermicity of the repulsive lp-lp interaction decreases the exothermicity of neighboring interactions. The H-bond between the final amide proton of the D-Ala-terminal ligand and the carbonyl oxygen of residue 4 on VC (2, Fig. 4) has an N–H⋯O length of 2.95 Å. The corresponding O⋯O distance between VC and the D-Lac-terminal ligand (4, Fig. 4) is elongated by 0.13 Å to 3.08 Å. The adjacent H-bond from the amide proton of residue 3 on VC to the carboxylate anion of the ligand (4, Fig. 4) is also elongated from 2.79 Å to 2.91 Å. The implication is that the estimate for the magnitude of the lp-lp repulsive interaction obtained by McComas et al. (2.6 kcal/mol) is necessarily an overestimation, as it also reflects the weakening of neighboring H-bonds. The energetic destabilization of the D-Lac-terminal ligand, relative to the ligand with methylene substitution, is not solely the consequence of lp-lp repulsion as assumed by McComas et al.
The ligands terminating in D-Ala and D-Lac illustrate the concepts of positive and negative cooperativity, respectively. For both ligands, the binding free energy is not simply the sum of the free energies for the individual interactions between VC and the ligand, because the presence or absence of one interaction (an H-bond or a lp-lp repulsion) strengthens or weakens other interactions. For the D-Ala-terminal ligand, the binding free energy is greater than the sum of the individual exothermic binding interactions, because an additional H-bond reduces the residual motions of the ligand, and thereby strengthens or tightens all the other interactions formed by the ligand with VC. The D-Lac-terminal ligand has a binding free energy less than the sum of the exo- and endothermic interactions in which this ligand participates, because of the presence of an additional repulsive interaction that pushes the ligand and antibiotic apart, elongates and weakens other interactions, and allows the ligand to be held relatively loosely by VC. Positive cooperativity results in tighter binding, and negative cooperativity, looser binding, than would otherwise be expected. Given this perspective, the 1000-fold reduction in the binding affinity of VC for D-Lac, relative to D-Ala-terminating ligands, is more understandable.
Since a methylene group will neither participate in H-bonding nor lp-lp repulsion, the ligand with a methylene moiety in place of the amide NH or ester O can not partake in the cooperative effects discussed so far, it should have an intermediate binding affinity. This is in fact the case (3, Fig. 4), but there are interesting subtleties. A methylene group, in the place of an amide NH or ester O, increases the hydrophobic nature of the ligand, which potentially changes the solvation of the ligand so as to promote its binding into the hydrophobic pocket of VC. The exclusion of hydrophobic solutes from an aqueous medium – the hydrophobic effect – is a significant contributor to the free energy change for a bimolecular association. To an approximation, the hydrophobic effect scales with the surface area of the nonpolar solute exposed to water that will be buried upon aggregation with other nonpolar solutes. Williams et al. found that the contribution of the hydrophobic effect to the free energy of binding was 50 cal/mol/Å2 of exposed nonpolar surface area in the context of peptide ligands associating with VC.15 Given that a methylene group contributes a hydrophobic surface of 29 Å2, the free energy change for binding of the methylene-substituted ligand to VC should be enhanced by 1.4 kcal/mol relative to the D-Ala- or D-Lac ligands (if differences in solvation between these other ligands are neglected). Once bound, the methylene group increases the hydrophobic character of the VC-ligand interface, and thereby lowers the dielectric constant of the binding region. In a less polar microenvironment, nearby H-bonds, which are primarily electrostatic interactions, would be strengthened.
A contrary conclusion is reached if the conformational flexibility of the ligands is considered. Both the D-Ala- and D-Lac ligands have substantially less conformational flexibility about the C-X bond in Fig. 4 compared to the ligand with methylene substitution. Resonance within the terminal amide group of 2 in Fig. 4 imparts partial double bond character to, and thereby hindered rotation about, the central bond. Resonance within the ester group of 4 in Figure 4 similarly imparts rigidity to the carbonyl-O bond, but the rotational barrier is less relative to the barrier for the peptide bond. The resonance structure that would place a partial positive charge on X in Figure 4 is a lesser contributor when X = O, compared to when X = N, because it is less favorable for a positive charge to be on a more electronegative element. By contrast, no resonance is possible when X = C in Figure 4. Though a CH2 π group orbital will interact with the carbonyl π system, this interaction is worth <5 kcal/mol, whereas resonance within the amide group is worth 15 – 20 kcal/mol. The ester group has an intermediate rotational barrier.
Hindered rotation in the ligand when X = N or O in Figure 4 reduces the adverse entropy of bimolecular association relative to the ligand for which X = C, because there is one less bond that needs to be frozen out upon association with the antibiotic. Furthermore, hindered rotation in ligands 2 and 3 of Figure 4 locks the ligand into a preferred conformation in which the substituent on X is syn to the carbonyl. This orientation is critical for establishing hydrophobic contact of a methyl group with the glycosolated aromatic ring of VC, and for positioning of the terminal carboxylate of the ligand for binding into the receptor pocket (Fig. 3b). Free rotation of the methylene, as opposed to the amide NH or ester O, gives the carboxylate-containing substituent on the methylene greater conformational flexibility, which, in turn, would loosen the binding interactions of the carboxylate into the receptor pocket.
All of the foregoing arguments underscore the genuine complexity of ligand recognition by VC. The ligand with a methylene in place of an amide NH or ester O is not simply a neutral reference point from which to judge the worth in binding free energy of a lost H-bond or an introduced lp-lp repulsive interaction. The methylene group introduces its own effects that advantageously, as well as adversely, influence binding to VC.
Vancomycin (VC) has long served as a reliable vanquisher of pathogenic Gram-positive bacteria that have outmaneuvered other antimicrobial defenses.[1-3] This archetypical glycopeptide antibiotic is indispensable in the fight against MRSA, and Enterococcal infections that prey on the immunocompromised, but the clinical utility of the drug is seriously threatened by the relatively recent emergence of bacterial resistance.[1-3] The simple replacement of an amide NH with an ester O reduces the binding affinity of VC by 1000-fold. The dramatic reduction in binding affinity has frequently been attributed to a lost H-bond and/or the introduction of a repulsive lone pair-lone pair interaction, but not until a 2003 study by McComas et al. was the relative importance of these factors quantified.[6,8]The introduced repulsive interaction was found to account for a 100-fold reduction in binding affinity (equivalently 2.6 kcal/mol), whereas the effect of the lost H-bond was less by an order of magnitude (only 1.5 kcal/mol).
In the structure-activity study of McComas et al., the binding constants of peptide ligands having an amide NH, methylene group, or ester O linking the terminal residue to the rest of the ligand were examined (Fig. 4). The ligand with the amide NH formed an additional H-bond to the antibiotic, relative to the other ligands. The additional attractive interaction increased the exothermicity of binding, and reduced the residual motion of the ligand (enthalpy-entropy compensation), thereby strengthening all the other binding interactions (positive cooperativity). The ligand with an ester O had an additional repulsive interaction, relative to the other ligands. The exothermicity of binding for the ligand was consequently lessened, and greater residual motion was retained, which resulted in the weakening of other binding interactions with the antibiotic (negative cooperativity). Because positive cooperativity enhanced the exergonicity of an additional H-bond, and negative cooperativity accentuated the endergonicity of an introduced lp-lp repulsion, there was a 1000-fold difference in the binding affinity of the amide- and ester-containing ligands to VC (Fig. 4). This analysis is more sophisticated than the partitioning of the dramatically decreased binding affinity into a 10-fold reduction due to the loss of a single H-bond upon exchange of an amide NH for a CH2, and a 100-fold reduction because of the introduction of one lp-lp repulsive interaction upon the replacement of a methylene group with an ester O (Fig. 4).
Subtler effects influenced the binding of the ligand with the methylene group. The CH2 unit promoted binding by enhancing the contribution of the hydrophobic effect to the binding free energy of the ligand, and by strengthening adjacent H-bonds through the lowering of the dielectric constant of the microenvironment. The CH2 substitution was adverse for binding because it increased the conformational flexibility of the ligand, thereby increasing the entropic penalty for binding to the antibiotic and weakening other interactions at the binding interface. With these opposing factors, as well as the absence of the cooperative effects of the additional H-bond or repulsive interaction of the amide- or ester containing ligands, the ligand with methylene substitution had an intermediate binding affinity. However, this analysis shows that methylene substitution does not offer the neutral reference point assumed by McComas et al. for the assessment of the free energy worth of an H-bond and lp-lp repulsive interaction. Rather, the differential binding of ligands varying in a single atom (not counting hydrogens) to VC is an excellent example of how collectively and cooperatively numerous forces govern a molecular recognition event.
(1) Williams, D. H.; Bardsley, B. The Vancomycin Group of Antibiotics and the Fight against Resistant Bacteria. Angew. Chem. Int. Ed. 1999, 38, 1172-1193.
(2) Williams, D.H. The Glycopeptide Story : How to Kill the Deadly ‘Superbugs.’ Nat. Prod. Rep. 1996, 13, 469-477.
(3) Nicolaou, K. C.; Boddy, C. N. C.; Bräse, S.; Winssinger, N. Chemistry, Biology, and Medicine of the Glycopeptide Antibiotics. Angew. Chem. Int. Ed. 1999, 38, 2096-2152.
(4) Xie, J.; Pierce, J. G.; James, R. C.; Okano, A.; Boger, D. L. A Redesigned Vancomycin Engineered for Dual D-Ala-D-Ala and D-Ala-D-Lac Binding Exhibits Potent Antimicrobial Activity Against Vancomycin-Resistant Bacteria. J. Am. Chem. Soc. 2011, 133, 13946-13949.
(5) Williams, D. H.; Waltho, J. Molecular basis of the activity of antibiotics of the vancomycin group. Pure & Appl. Chem. 1989, 61, 585-588.
(6) McComas, C. C.; Crowley, B. M.; Boger, D. L. Partitioning the Loss in Vancomycin Binding Affinity for D-Ala-D-Lac into Lost H-Bond and Repulsive Lone Pair Contributions. J. Am. Chem. Soc. 2003, 125, 9314-9315.
(7) Breukink, E.; de Kruijff, B. Lipid II as a Target for Antibiotics. Nat. Rev. Drug Discov. 2006, 5, 321-323.
(8) Loll, P. J.; Axelsen, P. H. The structural Biology of Molecular Recognition by Vancomycin. Annu. Rev. Biophys. Biomol. Struct. 2000, 29, 265-289.
(9) Jusuf, S.; Axelsen, P. H. Synchronized Conformational Fluctuations and Binding Site Desolvation during Molecular Recognition. Biochemistry 2004, 43, 15446-15452.
(10) Walsh, C. T.; Fisher, S. L.; Park, I-S.; Prahalad, M.; Wu, Z. Bacterial resistance to vancomycin: five genes and one missing hydrogen bond tell the story. Chem. Biol. 1996, 3, 21-28.
(11) Rekharsky, M.; Hesek, D.; Lee, M.; Meroueh, S. O.; Inoue, Y.; Mobashery, S. Thermodynamics of Interactions of Vancomycin and Synthetic Surrogates of Bacterial Cell Wall. J. Am. Chem. Soc. 2006, 128, 7736-7737.
(12) Waltho, J. P.; Williams, D. H.; Stone, D. J. M.; Skelton, N. J. Intramolecular Determinants of Conformation and Mobility within the Antibiotic Vancomycin. J. Am. Chem. Soc. 1988, 110, 5638-5643.
(13) Pearce, C. M.; Gerhard, U.; Williams, D. H. Ligands which Bind Weakly to Vancomycin: Studies by 13C NMR Spectroscopy. J. Chem. Soc., Perkin Trans. 2. 1995, 1, 159-162.
(14) Périchon, B.; Courvalin, P. VanA-Type Vancomycin-Resistant Staphylococcus aureus. Antimicrob. Agents Chemother. 2009, 53, 4580-4587.
(15) Williams, D.; Westwell, M. Aspects of Weak Interactions. Chem. Soc. Rev. 1998, 27, 57-64.
(16) Perkins, H. R. Specificity of Combination between Mucopeptide Precursors and Vancomycin or Ristocetin. Biochem. J. 1969, 111, 195-205.
(17) Searle, M. S.; Sharman, G. J.; Groves, P.; Benhamu, B.; Beauregard, D. A.; Westwell, M. S.; Dancer, R. J.; Maguire, A. J.; Try, A. C.; Williams, D. H. Enthalpic (electrostatic) contribution to the chelate effect: a correlation between ligand binding constant and a specific hydrogen bond strength in complexes of glycopeptide antibiotics with cell wall. J. Chem. Soc., Perkin Trans. 1. 1996, 23, 2781-2786.
(18) Cristofaro, M. F.; Beauregard, D. A.; Yan, H.; Osborn, N. J.; Williams, D. H. Cooperativity between Non-polar and Ionic Forces in the Binding of Bacterial Cell Wall Analogues by Vancomycin in Aqueous Solution. J. Antibiot. 1995, 48, 805-810.
(19) Houk, K. N.; Leach, A. G.; Kim, S. P.; Zhang, X. Binding Affinities of Host–Guest, Protein–Ligand, and Protein–Transition-State Complexes. Angew. Chem. Int. Ed. 2003, 42, 4872-4897.
(20) Nitanai, Y.; Kikuchi, T.; Kakoi, K.; Hanamaki, S.; Fujisawa, I.; Aoki, K. Crystal Structures of the Complexes between Vancomycin and Cell-Wall Precursor Analogs. J. Mol. Biol. 2009, 385, 1422-1432.
(21) Anslyn, E. V.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books: Sausalito, 2006, pp 23, 114, 189.