Stepwise binding constants

The corresponding stepwise binding constants (also called formation constant Kf, association constant Kay or stability constant Ks) are given by the equations... 

In these circumstances, an overall binding constant, fin may be defined for the overall process, the individual if values are then known as the stepwise binding constants ... 

The subscript numbers in stepwise binding constant notation refer to the ratio of one complexing partner to another, thus in a multi-step process the association of the host with the first guest might be denoted Ku, while the association of the resulting 1 1 complex with a further guest to produce a 1 2... 

Besides the stepwise binding constants, Kj, it is also usefirl to consider the cumulative binding constants, (d with i ranging from 1 to n, defined by ... 

Each stepwise binding constant Kj can be factored into the product of a statistical factor and the corresponding microscopic equilibrium constant K. The statistical factor is easily obtained considering that in the forward reaction there are n—j+1 empty sites available for the ligand, whereas in the reverse reaction there are j Hgands that may dissociate from the receptor. Accordingly, Eq. [39] holds ... 

Here = Ki in (1) but the former notion is chosen to distinguish the 1 1 binding constant from the stepwise binding constant A" in the 1 2 and more complex equilibria discussed below. 

In some circumstances, it is easier to use the overall binding constant than the stepwise one however, it must be remembered that it is extremely unlikely that a teimolecular complex HG2 can be formed by simultaneous collision of one host and two guest molecules. Hence, the stepwise binding constants are a much better physical description... 

If the binding sites A and B are identical, then it follows immediately that Aia = Aib and A2A = A2b- We define this quantity as the first microscopic binding constant = Aim with Aim - Aia = Aib- Likewise, it follows that the second microscopic binding constant can be defined as = A2m with A2m = KiA = A2B- It is not possible to measure these microscopic binding constants directly but it is easy to link them to the macroscopic stepwise binding constants Ai and A2 using (52) and (53) to obtain (54) and (55). 

In principle, one could also apply the simplification yAHG2 = 2yAHG in (50) and (51) that explicitly use the stepwise binding constants K and K2 using (67) with Y... 

As is true for other spectroscopic methods, the stepwise binding constants in higher order complexation eventually are quite hard to extract by ITC due to statistical parameter correlation and, once determined, they may not correspond to the microscopic binding events. The situation is substantially alleviated when different hosts (or guests) are... 

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