Binding Revisited-Avidity in Cellular Function and Signaling

Abstract

When characterizing biomolecular interactions, avidity, is an umbrella term used to describe the accumulated strength of multiple specific and unspecific interactions between two or more interaction partners. In contrast to the affinity, which is often sufficient to describe monovalent interactions in solution and where the binding strength can be accurately determined by considering only the relationship between the microscopic association and dissociation rates, the avidity is a phenomenological macroscopic parameter linked to several microscopic events. Avidity also covers potential effects of reduced dimensionality and/or hindered diffusion observed at or near surfaces e.g., at the cell membrane. Avidity is often used to describe the discrepancy or the "extra on top" when cellular interactions display binding that are several orders of magnitude stronger than those estimated in vitro. Here we review the principles and theoretical frameworks governing avidity in biological systems and the methods for predicting and simulating avidity. While the avidity and effects thereof are well-understood for extracellular biomolecular interactions, we present here examples of, and discuss how, avidity and the underlying kinetics influences intracellular signaling processes.

Keywords: avidity; cellular avidity; functional affinity; modeling avidity; retention time.

Figure 1

Schematic figure showing monovalent, cooperative and homo- and heterobivalent reactions. In cooperative binding either one or both the association and dissociation rates of the second binding step may be modulated by cooperativity factors c₁ and c₋₁. Only cases where only one of the interacting species are multitopic and where the reaction is not diffusion limited allows for accurate determination of the cooperativity. In multivalent binding, both of the interacting species are multitopic. For simplicity we have presented reaction schemes for both a homo- and heterobivalent interactions. In these cases the association rate of the second binding step is modulated by the local concentration, [L], and an empirical penalty factor, f. Multivalent interactions can also be cooperative but the direct effect is difficult to determine accurately.

Figure 2

Simulations of binding curves. (A) Equilibrium binding curve for a monovalent ligand binding to a monovalent receptor. (B) Equilibrium binding curves for a monovalent ligand binding to a dimeric (or divalent) receptor in case of negative cooperativity, K_d1 = 0.01K_d2 (red), no cooperativity (blue) and positivity cooperativity, K_d1 = 100K_d2 (green). In the case of cooperativity, the scale on the x-axis is calculated with K = √K_d1K_d2. For the non-cooperative case K = K_d. (C) Model for binding of a homo-divalent ligand to a homo-divalent receptor. All steps are assumed to have the same microscopic rate constants, k₁ and k₋₁. The intra-molecular binding reaction AAaa to aAAa is also controlled by the effective ligand concentration [L] and the empiric proximity factor f that accounts for steric restrictions on the intramolecular process compared with the intermolecular process. (D) For the intramolecular binding to a receptor on a surface, the local concentration is calculated as the concentration of the ligand in half-sphere with a radius equal to the distance between two binding sites on the ligand when it is fully extended. (E) Binding curves for the model in c with [AA] = 0.1 nM k₁ = 1.85 × 10⁵ M⁻¹min⁻¹ and k₋₁ = 8.5 × 10⁻³ min⁻¹ at three different values of f and [L] = 136 μM simulated after 1,200 min equilibration. (F) Same as in (E) except that the curves were extracted after 120 min. (G) Time traces of binding and dissociation for the model in (C) at three different ligand concentrations, with f = 1,000 and other parameters as in (E). For comparison the time trace for at 1 to 1 binding reactions with k_on = 1.85 × 10⁵ M⁻¹min⁻¹ and k_off = 8.5 × 10⁻³ min⁻¹. (H) Same as in (G), except f = 35. ll simulations were performed with COPASI (Hoops et al., 2006).