A kinetic scheme for a bivalent linker: the reduced system consists of a flexible bivalent receptor binding a ligand at either one of the binding sites. States 1-3 may also describe the three-state model of a system with a receptor and ligand in absence of the linker, as depicted outside the graph, with a dotted red line. The assignments of diffusion-limited rates are according to SSS theory (see XX), and it is assumed that the intrinsic molecular rates (q, ) are independent of whether the species are bound to other species or not. The even-numbered states (2, 4, 6 & 8) describe encounter complexes, where the reactants are proximal in space but have not reacted to form a stable complex. The ligand B is free in state 1, singly-bound in states 3 and 7, and doubly-bound in state 5. The values marked kD are diffusion on- and off-rates, and they depend on the diffusion coefficient, the reaction radii and the Jacobson-Stockmayer factor (equation XX). Once bound to the linker, the ligand cannot freely diffuse and is constrained by the flexible linker. States 3-5 (blue background), are considered productive states, in which the two ligands A and B interact directly. In the corresponding, the system without the linker, state 3 alone is considered to be the productive state.