An Analysis of the Origins of a Cooperative Binding Energy of Dimerization

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Science  01 May 1998:
Vol. 280, Issue 5364, pp. 711-714
DOI: 10.1126/science.280.5364.711


The cooperativity between binding of cell wall precursor analogs (ligands) to and antibiotic dimerization of the clinically important vancomycin group antibiotics was investigated by nuclear magnetic resonance. When dimerization was weak in the absence of a ligand, the increase in the dimerization constant in the presence of a ligand derived largely from changes associated with tightening of the dimer interface. When dimerization was strong in the absence of a ligand, the increase in the dimerization constant in the presence of a ligand derived largely from changes associated with tightening of the ligand-antibiotic interface. These results illustrate how, when a protein has a loose structure, the binding energy of another molecule to the protein can derive in part from changes occurring within the protein.

Cooperativity lies at the heart of molecular recognition, which leads to biological function (1). It is typically exercised when numerous weak interactions operate simultaneously. We may define an interaction between two molecules of A to give A·A (dimerization) as being cooperative with the binding of B to A if the equilibrium constant for the association of two molecules of B·A (to give B·A·A·B) is greater than that for A + A → A·A. Here, we investigate the molecular origins of such cooperativity and define a method for locating the origins of cooperative binding energy. We define the interfacial bindings in B·A and A·A as “loose” or “tight.” In tight binding, the bonds that identify the individual interactions at the interface give a relatively large (perhaps near maximal) binding energy; that is, the average bond lengths are relatively short. In contrast, loose binding means that the corresponding interactions are associated with longer average bond lengths, which give an appreciably lower binding energy than that available in a tight structure. Loose interactions occur when the sum of the favorable bonding interactions (enthalpy) is sufficiently small to be counteracted by the adverse entropy of binding and when there is a relatively large amount of residual motion in the bound state (2).

We provide experimental evidence for the validity of the above considerations in the following sequence of steps:

1) The occurrence of loose and tight interactions, but otherwise involving a common set of weak bonds, was shown through the use of proton chemical shift changes upon association. Using the chemical shift criterion, we showed that associated structures involving one interface (B + A → B·A or A + A → A·A) tighten at that interface as the equilibrium constant for their formation increases.

2) In cases in which structural tightening could occur at two different interfaces, we used the chemical shift criterion to show the extent to which it occurs at one of these interfaces. Thus, when B·A·A·B is formed from two molecules of B·A, structural tightening could occur at both the B-A (or A-B) and A-A interfaces. A chemical shift change at the A-A interface was used to determine the extent of structural tightening at this interface.

The cell wall precursor analogs (ligands) 1 to 4(Scheme 1) bind progressively more strongly to glycopeptide antibiotics of the vancomycin group. A common feature of all these ligand-antibiotic interactions is the binding of a carboxylate anion of the ligand into a pocket of three amide NH groups of the antibiotics (Scheme 2). The binding constants (K lig) of 1, 2,3, and 4 are about 10, 3 × 102, 105, and 106 M−1, respectively (3). We recently concluded that one of the carboxylate oxygen molecules of the carboxyl group (which is common to 1to 4) binds more intimately to the NH w2(labeled in Scheme 2) of the antibiotics as K ligincreases (4, 5). This conclusion was shown from the increasing downfield chemical shifts of w2 in the fully bound states.

Figure 1

(A) Plot of −ΔG dim versus Δδx4 limfor the free antibiotics 5 to 10. [Modified from (5) and reproduced with permission of Current Biology Limited.] (B) Plot of −ΔG dim versus Δδx4 limfor the antibiotic–di-N-acetyl-Lys-d-Ala-d-Ala complexes for 5 to 10.

Figure 2

(A) Plot of −ΔG dim versus Δδx4 limfor hypothetical data points for free antibiotics W, X, Y, and Z (open circles) and the same set of four antibiotics when dimerizing as antibiotic-ligand complexes (filled circles). The arrows connect the hypothetical points for a given antibiotic, and the series of antibiotics W, X, Y, and Z have increasing dimerization constants. (B) Because the free energy of dimerization associated with changes at the dimer interface is defined by the curve connecting the points (open circles) for the dimerization of antibiotic alone, the extent to which the filled circle lies vertically above this curve gives the free energy of dimerization associated with changes in the ligand-antibiotic interfaces.

Figure 3

Combined plot of −ΔG dimversus Δδx4 lim for free (open circles) and ligand-bound (filled circles) antibiotics 5 to10. For any one antibiotic, arrows represent changes occurring upon ligand binding.

Scheme 1

Cell wall precursor analogs, which bind progressively more strongly (in the order 1, 2,3, 4) to vancomycin group antibiotics.

Scheme 2

The binding interface between di-N-acetyl-Lys-d-Ala-d-Ala (Ac2KdAdA) (4) and vancomycin (6), with the interfacial hydrogen bonds represented by broken lines and with the monitored proton w2 indicated.

Such phenomena should be general, and therefore we next sought analogous data in the dimerization of the glycopeptide antibiotics, a property that promotes their antibiotic action (6,7). The antibiotics dechlorovancomycin (5) (R3 = Cl, R4 = H), vancomycin (6) (R3 = R4 = Cl), chloroeremomycin (7) (R3 = R4 = Cl), phenylbenzylchloroeremomycin (8) (R3 = R4 = Cl), and eremomycin (9) (R3 = H, R4 = Cl) (Scheme 3) exhibit dimerization constants in the range of 102 to 105.7 M−1. Ristocetin-pseudoaglycone (ristocetin-Ψ; 10) (Scheme 3), which has some different peptide side chains than 5 to9, has a dimerization constant of 50 M−1.

Scheme 3

Structures of the glycopeptide antibiotics (with the nature of the R3 and R4groups indicated in the text), which have dimerization constants over the range of about 102 to 106M−1.

Despite the large variation in the dimerization constants, the dimer interfaces for the six glycopeptide antibiotic dimers discussed here all contain the common arrangement of four interfacial amide-amide hydrogen bonds (Scheme 4) (6,8-10). In particular, the proton x4(Scheme 4) at the dimer interface suffers a relatively large downfield shift upon dimerization. The extent of this downfield shift (Δδx4 lim) was used to reach conclusions with regard to the looseness or tightness of the dimer interfacial structure as a function of the dimerization constant (5). The change in chemical shift of x4 (Δδx4 lim) in passing from monomer to dimer structure is much larger in the case of the formation of a strongly bound dimer than for that of a weakly bound dimer (Table 1 and Fig.1A). We emphasize that the nuclear magnetic resonance (NMR) experiments gave Δδx4 limvalues that corresponded to the difference in chemical shift between fully monomeric and fully dimeric species (Δδx4 lim) (5) and that the smaller Δδx4 lim values observed for the more weakly dimerizing antibiotics therefore did not correspond to only partially dimerized antibiotics. In summary, the two sets of data indicate that, in the binding of a ligand to an antibiotic or in the dimerization of the antibiotics, the entities come into more intimate contact as the equilibrium constants for the respective associations increase.

Scheme 4

Structure of the antibiotic dimer with its peptide backbone indicated in bold, shown here with acetyl-d-Ala-d-Ala (ligand) bound in each binding site. Hydrogen bonds at the dimer interface are indicated by open arrows, and those at the ligand-antibiotic interface are indicated by dashed lines. N-terminus, NH2-terminus.

Table 1

Chemical shifts of the proton x4 in monomeric and dimeric forms of the glycopeptide antibiotics5 to 10 [both in the presence and absence of di-N-acetyl-Lys-d-Ala-d-Ala (Ac2KdAdA)]. δx4mon lim is the chemical shift of the proton x4 in the antibiotic monomer, δx4dim limis the chemical shift of x4 in the fully bound dimer, and Δδx4 lim is the difference between these chemical shifts. ΔG dim is the free energy change for the formation of a dimer from a monomer.

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The free energy ΔG values for the conversions of the ligand-bound monomers of 5 to 10 to ligand-bound dimers show that, in all cases, the dimerization is cooperative with ligand binding (Table 1). The corresponding changes in the chemical shift of x4 for 5 to 10 for the conversion of ligand-bound monomers to ligand-bound dimers suggest that when dimerization is strong even in the absence of a ligand (8 and 9), the cooperative binding expressed in the presence of a ligand causes little tightening at the dimer interface (Table 1); that is, there is little increase in Δδx4 lim caused by the presence of a ligand (compare Fig. 1, A and B) (11-13).

If the dimer interface is loose in the absence of a ligand [small value of the dimer binding constant K dim (and of −ΔG dim)], an important contribution to the increase in K dim (and of −ΔG dim) in the presence of a ligand will come from changes associated with the tightening of the dimer interface (increase in limiting chemical shift of x4). Conversely, if the dimer interface is tight even in the absence of a ligand (large values of K dim and −ΔG dim), then the major portion of the favorable free energy change that causes an increase inK dim in the presence of a ligand should actually come from changes associated with the tightening of the ligand-antibiotic interface, and there should be little accompanying change in the limiting chemical shift of x4. The way in which the cooperative free energy of dimerization can be partitioned into changes associated with the dimer interface or with the ligand-antibiotic interface is indicated by sets of hypothetical points in Fig. 2A. The expectation is that a weakly dimerizing compound will largely exercise cooperativity by tightening the dimer interface (arrows joining open and filled circles for the same antibiotic at a shallow angle to the horizontal; for example, W in Fig. 2A). In contrast, a strongly dimerizing compound will largely exercise cooperativity by tightening the interface with the ligand (arrows joining open and closed circles for the same antibiotic at a very steep angle to the horizontal; for example, Z in Fig. 2A).

The experimental data (Fig. 3) follow the postulated expectation from Fig. 2 remarkably closely. The weakly dimerizing antibiotics ristocetin-Ψ (10) and dechlorovancomycin (5) dimerized more strongly in the presence of di-N-acetyl-Lys-d-Ala-d-Ala than in its absence essentially because the free energy of binding associated with changes at the dimerization interface is more favorable. The more strongly dimerizing antibiotics chloroeremomycin (7), phenylbenzylchloroeremomycin (8), and eremomycin (9) dimerized more strongly in the presence of di-N-acetyl-Lys-d-Ala-d-Ala than in its absence largely because the free energy of binding associated with changes at the antibiotic-ligand interface is more favorable in B·A·A·B than in B·A. There was little change in the free energy of binding associated with changes at the dimer interface. The behavior of vancomycin (6) was between these two extremes.

Our findings have implications for the study of protein-protein interactions and for drug design. In both areas, it is common practice to seek the origins of binding affinity at the interface formed between the associating entities (14, 15). Our data (Fig. 3) show that when the antibiotics 8 and9 dimerize more strongly in the presence of a ligand (relative to its absence), the increase in the equilibrium constant for dimerization arises largely from changes associated with the tightening of the interaction between the ligand and the antibiotic. By analogy, when proteins (or, more specifically, receptors) have loose structures before binding another protein (or in the specific case of a receptor, its natural ligand or a drug), then a portion of the binding affinity can be derived by tightening of the internal structures of the proteins in the resulting bound state. Given this possibility, the thermodynamic parameters for protein-protein associations, which are perplexing when analyzed in terms of interfacial interactions (14), can be seen to have much more complex origins. The findings may also be relevant to transmembrane signal transduction, most obviously when signal activation is coincident with receptor dimerization (16). Suppose a ligand binds strongly to the monomeric form of a receptor (which itself dimerizes weakly in the absence of a ligand) and binds cooperatively to the dimeric form of the receptor. Such a system is well constituted to produce a tightening of the structure of the receptor at its dimer interface and hence to assist in ligand-induced changes in geometry (even without obvious allosteric changes) at points remote from ligand binding.

  • * To whom correspondence should be addressed. E-mail: dhw1{at}


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