Mechanistic Aspects of Multivalent Interactions

Multivalent interactions are characterized by the simultaneous binding of several ligands on one biological entity (surface, macromolecule) with several receptors on another entity (Figure 2.7.1) [8]. This type of interaction has unique collective properties that are qualitatively different from those of the corresponding monovalent systems. Not only it is possible to regulate the strength of an interaction by the number of receptor-ligand contacts, multivalent interactions also have different kinetic properties. As Whitesides et al. have demonstrated, it is possible to increase monovalent monovalent receptor ligand monovalent complex

AGmono = -RTlnKm monovalent monovalent receptor ligand

monovalent complex

-RTl nKm multivalent multivalent multivalent receptor ligand complex

Fig. 2.7.1. Comparison of monovalent and multivalent interactions.

the rate of dissociation (koff) of a multivalent complex by addition of a monovalent ligand [9]. A complete mechanistic description of multivalent binding is, however, difficult because of the complexity of such systems. The formation of a multivalent interaction involves many possible intermediates. Beside intramolecular binding of a multivalent receptor and a multivalent ligand, intermolecular binding may occur, leading to cross-linking and precipitation. The next section therefore focuses on the basic thermodynamics of the simplest multivalent system, the interaction of a bivalent ligand with a bivalent receptor, according to an analysis by Whitesides etal. [8].

The parameter AGmulti is made up of enthalpic (AHmulti) and entropic (ASmulti) components (Eq. 1) which have to be considered separately.

AGmuti = ahmulti - TASmulti (1)

The enthalpy of binding (AHmulti) is, to a first approximation, the sum of the enthalpies of the individual monovalent interactions, i.e. for a bivalent system AHbi = 2AHmono (Figure 2.7.2A, Case 1). This, however, only applies if the bivalent complex is unstrained and the binding events do not interfere with each other. If the binding of the first ligand interferes with binding of the second, the enthalpy of binding is less favorable (less negative) and AHbi > 2AHmono (Figure 2.7.2A, Case 2). Such binding is enthalpically diminished and might occur if the bivalent complex is strained or if the first binding event exerts a negative allosteric effect on the second. Enthalpically enhanced binding is observed if the second binding event is more favorable than the first, because of a positive allosteric effect or because of favorable secondary interactions between the tether and the receptor and AHbi < 2AHmono (Figure 2.7.2A, Case 3). A possible example of enthalpically enhanced binding is the interaction of the pentameric cholera toxin with five GM1 molecules on cell surfaces [10].

Case 1

AHb > 2 AHmono enthalpically diminished

Case 3

AHb < 2 AHmono enthalpically enhanced

Case 1

« ASmono maximally entropically enhanced

Case 2

ASconf > A S trans + ASrot entropically enhanced Case 3

ASconf < A Strans + ASrot Fig. 2.7.2. Enthalpy and entropy of different binding modes of bivalent interactions.

The entropy of binding (ASmulti) of a multivalent interaction can be divided into contributions from changes in translational (ASmU^), rotational (ASrmtulti), conformational (ASCf and hydrational (ASH^U?) entropy. The latter is assumed to be similar in each situation and is therefore ignored in this discussion. Also the weak logarithmic dependence of translational and rotational entropy on the mass and size of different molecules is ignored. For a bivalent interaction several cases can again be distinguished. If the two ligands and the two receptors are connected by rigid, perfectly fitting spacers, A scof = 0 and the interaction occurs with an entropy equivalent to a single monovalent interaction (Figure 2.7.2B, Case 1). This case of maximum entropic enhancement is, in general, unrealistic, because all tethers are somewhat flexible and ASmf is almost always unfavorable (less than zero). If this conformational cost is less than the total translational and rotational cost (AScmnf > ASms + ASm^), the bivalent association is still entropically enhanced and favored over an intermolecular interaction (Figure 2.7.2B, Case 2). If AScmf < ASmi^ + ASrmtulti, bivalent binding is entropically diminished and a (1+2) association is favored (Figure 2.7.2B, Case 3).

According to this discussion, AGmulti for a (theoretical) bivalent system with rigid perfectly fitting spacers is given by Eqs (2) and (3).

0 0

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