Interactions Between Dissimilar Reactants

Although interactions between dissimilar reactants far outnumber those entailing solute self-association in biology, the study of ligand binding by analytical ultracentrifugation has received far less attention - a situation being remedied to some extent now.

Studies of Ligand Binding by Sedimentation Velocity

In considering the quantification of acceptor-ligand interactions by sedimentation velocity, there are two situations to examine: one in which a macromolecule (acceptor, A) reacts with a small molecule (ligand, B); and the situation in which both acceptor and ligand are macromolecular. In the former, provided that the ligand is sufficiently small for the acceptor-ligand complex AB (or complexes ABi for ligand binding to multiple acceptor sites) to co-migrate with acceptor (sAB = sA > sB), the free ligand concentration is readily determined by sedimentation velocity. As depicted schematically in Figure 5A, the subjection of an equilibrium mixture to a high centrifugal field under those circumstances generates a biphasic boundary pattern

^-B ___/

(C/+ CB") Cb

^^ P phase

a phase

r" o/sBt 0)2SAt

r" o/sBt 0)2SAt

CO rf

¡3 phase ra CoVf

Figure 5 Schematic representations of boundary patterns encountered in sedimentation velocity studies of ligand binding. (A) Direct evaluation of the free ligand concentration (CbB) for a system where acceptor and acceptor-ligand complex(es) co-migrate. (B) The corresponding situation when acceptor and ligand are both macromelecular (sAB > sA> sB).

in which the concentration in the slower-migrating phase reflects free ligand at its equilibrium concentration in the mixture (a phase) with total molar concentrations CCA and CB of acceptor and ligand, respectively. Results obtained are thus akin to conventional ligand-binding data obtained by (say) equilibrium dialysis; and may therefore be treated in an analogous fashion.

In the second case in which the ligand is also macromolecular, the sedimentation coefficient of the AB complex is likely to be greater than that of either reactant (sAB > sA > sB). Under those circumstances, a biphasic boundary pattern is again generated, but the slower-migrating phase corresponds to the reactant in molar excess: the situation represented in Figure 5B reflects a molar excess of ligand. Although the concentration of pure ligand in the slower-migrating phase (CB) can be measured, it does not equal the free ligand concentration (CB) in the equilibrium mixture. However for a 1 : 1 interaction, the free concentration of the other reactant may be

determined from the expression:

where Ci again denotes a molar concentration, and where sxl is the sedimentation coefficient of the reaction boundary between the pure solute phase and that corresponding to the original mixture. Combination of the consequent value of CA with the composition of the mixture (CA, CB) then yields the binding constant KAB on the grounds that:

KAB = CAb/(CaCb) = (CA — CA)/[CA(CB — CA + CA)]

For purposes of simplification, the above quantitative treatments assume migration in a rectangular cell under the influence of a homogeneous field. Sedimentation in a sector-shaped cell leads to radial dilution that slightly decreases the magnitudes of the various concentrations. However, the uncertainties inherent in the measurements of CB and the various differences in sedimentation coefficients are usually sufficient to justify the approximations involved in such interpretation of sedimentation velocity patterns.

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