Studies of Ligand Binding by Sedimentation Equilibrium

For a reversible interacting between an acceptor A and a ligand B, there are only two independent sedimentation equilibrium distributions - one for the acceptor constituent which includes the acceptor contribution to AB complex(es) as well as free reactant; and the corresponding distribution for the ligand constituent. Thus:

Figure 6 presents sedimentation equilibrium distributions for the individual species in centrifugation of a 1:1 interacting system with MA(1—vAps) = 12 kDa, Mb(1 — vBps) = 3 kDa and KAB = 50000 mol L^1 at 15 000rpm. Also shown are the constituent distributions.

Substituting the condition of sedimentation equilibrium (eqn [7]) for the individual reactants into the above expressions allows them to be rewritten in the form:

Radial distance r(cm)

Figure 6 Simulated sedimentation equilibrium distributions for the individual species (—) resulting from centrifugation at 15000 rpm of a mixture of acceptor with MA(1 — V/s) = 12 kDa and ligand with MB(1 — vB/s) = 3 kDa undergoing reversible 1 : 1 interaction governed by a binding constant of 50 000 mol L~1. The solid curves describe distributions in terms of the total concentrations of the separate constituents (CA, CB).

Radial distance r(cm)

Figure 6 Simulated sedimentation equilibrium distributions for the individual species (—) resulting from centrifugation at 15000 rpm of a mixture of acceptor with MA(1 — V/s) = 12 kDa and ligand with MB(1 — vB/s) = 3 kDa undergoing reversible 1 : 1 interaction governed by a binding constant of 50 000 mol L~1. The solid curves describe distributions in terms of the total concentrations of the separate constituents (CA, CB).

Furthermore, because pA(r) = [^B(r)]u where u = [Ma(1 — z/Aps)]/[MB(1 — WBps)], these expressions become discrete polynomials in terms of pB(r) and the constant parameters CA(rF), CB(rF) and KAB. The problem of evaluating KAB thus amounts to nonlinear regression analysis of the [Ci, ^B(r)] distributions to obtain the three constants as curve-fitting parameters.

The extent to which advantage may be taken of this approach clearly depends upon the nature and number of sedimentation equilibrium distributions available for analysis. In that regard, the maximum potential for quantitative analysis pertains to the situation in which the optical system provides information on the separate concentrations of acceptor and ligand constituents. However, the optical system may well only monitor one constituent, or it may yield a single distribution related to the combined constituent concentrations, CA(r) + CB(r). The latter situations are clearly less than optimal from the viewpoint of characterizing the interactions, but procedures (admittedly less accurate) have been devised to illustrate the feasibility of a quantitative analysis, even under these adverse circumstances.

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