The binding potencies from carbohydrates to lectins are usually rather weak (typically in the mM to µM range[4]) unless multivalent effects are involved. Multivalency is the ability of a molecule (ligand) to bind to another molecule (receptor) via multiple simultaneous non-covalent interactions.[56] Since the blocking of carbohydrate-protein interactions is desired for the treatment of many diseases, in the last decade a huge variety of multivalent inhibitors have been synthesized.[57-58] Higher binding affinity is thereby achieved through either high valency (e.g. dendrimers[59]), a spherical geometry (e.g. fullerenes[60]) or bridging binding systems[9,
61-62] of carbohydrate moieties or a combination thereof. A central concept for understanding molecular recognition is cooperativity. Cooperativity arises from the interplay of two or more interactions leading to a system that behaves differently than expected from the properties of the individual isolated interactions. The interactions can thereby lead to positive or negative cooperativity, depending on whether one interaction favors or disfavors another. In the essays from Whitty[63], Hunter and Anderson[64], and Ercolani and Schiaffino[65] two types of cooperativity are theoretically described: allosteric and chelate cooperativity. The best understood example for positive allosteric cooperativity is oxygen binding to hemoglobin.[66] Here oxygen binding to each of the four bindig sites increaseas the affinity to the remaining binding sites. With strong positive cooperativity, only the extreme states are significantly populated leading to an “all-or-nothing”
behavior which occurs widely in nature switching between “on” and “off” states. To explore the different scenarios of allosteric and chelate cooperativity Hunter and Anderson[64] start by considering simple equilibria involving receptors with only one or two binding sites and only monovalent ligands (Figure 7). As reference point serves the system in Figure 7 A, since no cooperativity is possible because there is only one interaction.
This simple two state equilibrium is characterized by the association constant K, the concentrations of bound AB and free receptor A and the concentration of free ligand B:
𝐾 = [𝐴𝐵]
[𝐴][𝐵]
Figure 7: Complexation equilibria from a mono- and a divalent receptor with monovalent ligands. A: The reference system.
B: Discrete allosteric systems. Figure adapted from Hunter and Anderson.[64]
Allosteric ligand binding: The simplest case of allosteric cooperativity is shown in Figure 7 B. Two ligands, each with one binding site interact with a divalent ligand. In this system three states are possible: free AA, partially bound AA∙B and fully bound AA∙B2. The equilibria are characterized by two microscopic association constants K1
and K2:
2𝐾1= [𝐴𝐴 ∙ 𝐵]
[𝐴𝐴][𝐵]
1
2𝐾2= [𝐴𝐴 ∙ 𝐵2] [𝐴𝐴 ∙ 𝐵][𝐵]
Whether an allosteric cooperativity is positive or negative depends on the interaction parameter :
∝= 𝐾1
𝐾2
In the absence of cooperativity the microscopic association constants are identical, K1 = K2 = K and = 1. In case of positive cooperativity is greater than 1, in case of negative cooperativity is less than 1. Another important parameter is the binding-site occupancy of the receptor A:
𝜃𝐴=
1
2[𝐴𝐴 ∙ 𝐵] + [𝐴𝐴 ∙ 𝐵2] [𝐴𝐴0]
with [AA0] given as:
[𝐴𝐴0] = [𝐴𝐴] + [𝐴𝐴 ∙ 𝐵] + [𝐴𝐴 ∙ 𝐵2] = [𝐴𝐴](1 + 2𝐾1+ 𝐾1𝐾2[𝐵]2)
Figure 8 shows the speciation profile for negative and positive allosteric cooperativity, which show how [AA∙B], [AA∙B2], and A vary with the ligand concentration B0. In case of negative cooperativity (Figure 8 left) the state of the partially occupied receptor AA∙B is the predominant species over a broad concentration range. Only with high ligand concentration the state of the fully occupied receptor AA∙B2 becomes occupied. In contrast we observe for positive cooperativity (Figure 8 right) an all-or-nothing-, two-state-behavior between the state of the unoccupied receptor and the fully occupied receptor. Assembly and disassembly of the complex take place over a narrower range of ligand concentration than for the single-site reference system (Figure 7 a).
Figure 8: Speciation profiles for negative allosteric cooperativity with = 0.01 (left) and positive allosteric cooperativity with = 100 (right). Fully bound AA∙B2 is depicted in blue, partially bound AA∙B in red, and the total binding site occupancy
in black. The y-axis shows the population of the state. The speciation profile for the reference system (Figure 7 a) is shown as gray dots. Figure taken with permission from Hunter and Anderson.[64] Copyright (2009) WILEY-VCH.
Chelate ligand binding: For the discussion of chelate cooperativity Ercolani and Schiaffino consider the simplest possible system: binding of a divalent ligand BB to a divalent receptor AA with the prerequisite = 1 to exclude allosteric cooperativity. The ligand is presented in excess relative to the receptor to neglect complexes involving more than one receptor (Figure 9).
Figure 9: Binding scheme of divalent ligand BB to divalent receptor AA assuming [BB]0 ≫[AA]0 and = 1. Figure adapted from Ercolani and Schiaffino.[65]
In this model system four states are possible for the receptor: free receptor AA, partially bound 1:1 open complex o-AA∙BB, the fully bound 1:1 cyclic complex c-AA∙BB, and the 1:2 complex AA∙(BB)2. The population of the different receptor states are determined through the intramolecular binding interaction Kintra = ½ K∙EM and the intermolecular binding constant K. The microscopic effective molarity EM (in units of molL-1) quantifies the amount of cyclic complex c-AA∙BB and K determines the strength of the intermolecular binding interaction between receptor and ligand. Figure 10 shows the speciation profile for the equilibria depicted in Figure 9 in the absence (K EM = 0.01) and in the presence (K EM = 100) of chelate cooperativity. Comparison of the two speciation profiles show that postitive chelate cooperativity leads to a sharp decrease of the partially bound open complex o-AA∙BB to favor the fully bound 1:1 cyclic complex c-AA∙BB. Similar to the case of allosteric cooperativity we observe at the macroscopic level an all-or-nothing behavior, characteristic for cooperativity.
At high ligand concentrations, however, the cyclic complex c-AA∙BB is replaced by the 1:2 complex AA∙(BB)2
since the concentration of the 1:2 complex depends on the square of the ligand concentration:
[𝑐 − 𝐴𝐴 ∙ 𝐵𝐵] = 2𝐾2𝐸𝑀[𝐴𝐴][𝐵𝐵]
[𝐴𝐴(𝐵𝐵)2] = 4𝐾2[𝐴𝐴][𝐵𝐵]2
The speciation profile of the cyclic complex c-AA∙BB is bell-shaped, suggesting that the intramolecular process can be regarded as “none-all-none” behavior. At the ligand concentration at which the population of the cyclic complex c-AA∙BB and the 1:2 complex AA∙(BB)2 become equal we can define:
[𝐵𝐵𝑠𝑤𝑖𝑡𝑐ℎ] =𝐸𝑀 2
According to this equation EM/2 can also be seen as the ligand concentration BBswitch above which the intramolecular process (formation of the cyclic complex c-AA∙BB from the open complex o-AA∙BB) loses the competition with the intermolecular one (binding of a second divalent ligand to the open complex o-AA∙BB).
From the comparison of the speciation profiles of allosteric (Figure 8) and chelate (Figure 10) cooperativity we see, that both can lead to the same macroscopic behavior. However, only chelate cooperativity is dependent on the ligand concentration. Only in exceptional cases with a suitable reference system it is possible to determine the parameter EM to characterize chelate dependend cooperativity.[67-69]
In chapter 3.2 we present a new experimental method to determine the parameter EM via cw-EPR spectroscopy of spin-labeled WGA ligands.
Figure 10: Speciation profiles for the equilibria shown in Figure 9. Left for missing chelate cooperativity (K∙EM = 0.01) and right for chelate cooperativity (K∙EM = 100). Population of the cyclic complex c-AA∙BB in green, open complex o-AA∙B in red, 1:2 complex AA∙(B2) in blue, and total binding-site occupancy A in black. The y-axis shows the population of the state. As reference the speciation profile for the reference system (Figure 7 a) is shown as gray dots. Figure taken with permission from Hunter and Anderson.[64] Copyright (2009) WILEY-VCH.