The full description of the system, even with a discrete kinetic scheme, is quite complex (Figure 4a). This is actually a narrowed-down view of a larger system involving many copies of each reactant (Figure 4b). Such a system may form polycondensates - potentially lengthy chains or rings of linkers (see
(Jacobson 1950)), glued together by the binding partners A and B. However, we are only interested in the population of the AB bound state, so it is enough to look at the system of a single copy. As mentioned, we further narrow down the scope of our system to that of a reduced system, with one of the ligands (A) being constitutively bound to a linker (L) (Figure 4d). The description we ultimately chose is depicted in Figure 5. It includes additional assumptions that were made to our model, as follows. First, the middle state in Figure 4d, where two encounter complexes are formed having B proximal both to A and X, is excluded from the model. Such a state is expected to be occupied only negligibly, as the expression for its occupation involves the concentration of the receptor, of the ligand, and the effective concentration (see equation (10)) between the termini of the linker. Second, the transition rates between states 1-3 are taken to be identical for the system with the linker, and that without. The diffusive transitions between states in the cycle are described using rates from SSS theory. The chemical details of short-range interactions that characterize the subsequent reactive steps are not considered, and the intrinsic reaction rates will be regarded as a 'black box' for the purposes of this work. These are thought to be independent of context (specifically, whether the linker exists or not). This assumption of equal transition rates results in a slight shift in the probabilities to occupy the active states, as we show later (5.2.2. Model of multivalent flexible polymer receptor).