Requirements for reliable determination of binding affinity constants by saturation analysis approach.

Accurate calculation of the equilibrium association constant (K) and binding site concentration (N) related to a receptor (R)/ligand (L) interaction, via R saturation analysis, requires exact determination of the specifically bound L concentration (B(S)) and the unbound L concentration (U) at equilibrium. However, most binding determinations involve a procedure for separation of bound and unbound L. In such situations, it was previously shown that correct calculation of B(S) and U from binding data requires prior determination of alpha, i.e. the procedure parameter representing the proportion of equilibrium B(S) recovered after running the separation process, and of kn, i.e. the equilibrium nonspecific binding coefficient. For the simplest model of R/L interaction, the consequences of alpha neglect and/or kn neglect on determination of K and N, via R saturation analysis, are investigated. When alpha but not kn has been determined, B(S) can be accurately calculated, whereas U is overestimated by factor (kn + 1). Consequently the type (linear or hyperbolic) of theoretic curves obtained by usual representations (such as the Scatchard, the Lineweaver-Burk or the Michaelis-Menten plot) of the R/L binding is unchanged; these curves afford correct N and underestimation of K by factor (kn + 1). When alpha (alpha < 1) has not been determined B(S) and U are underestimated and overestimated, respectively. Then erroneous representations of the R/L binding result (e.g. instead of regular straight line segments, Scatchard plot and Lineweaver-Burk plot involve convex-upward and convex-downward hyperbola portions, respectively, suggestive of positive cooperativity of L binding), which leads to incorrect N and K. Errors in N and K would depend on (i) the binding (K, N and kn) and method (alpha) parameters and (ii) the expressions used to calculate approximate B(S) and U values. Simulations involving variable alpha, KN and kn values indicate that: (1) the magnitude of error in N determination (mainly involving moderate underestimation) directly depends on the alpha value; (2) the magnitude of K underestimation mainly depends on the KN value; it is moderate (usually < two-fold) with KN values < 1, but could become very high (e.g. > 100-fold), when KN > 10(2). In this case, the K underestimation is modulated by the alpha and kn values. Practical situations which afford high KN and thus might result in very marked underestimation of K are discussed. A single R dilution method is proposed to assess the validity of K determinations using the R saturation analysis approach.