Probe-Dependent Cooperativity Patterns in Hill-Plots
Larry D. Byers Tulane University New Orleans, Louisiana 701 18
Protein-protein interactions are common biological phenomena. These interactions serve structural and functional roles. Multisubunit enzymes provide convenient systems for studying protein-protein interactions. There are over 500 known enzymes which consist of a t least two suhunits (I); the suhunits of most of these consist of identical polypeptide chains. The earliest evidence for subunit interactions in multisub~mitproteins was obtained from ligand binding data. The bindinn of substrates to most single subunit enzymes is quite s i m p l e y ~plot of bound substrate versus free substrate concentration yields a rectangular hyperbola. The binding of oxygen to hemoglobin (a four subunit protein), however, has a sigmoidal dependence on free oxygen concentration. In 1910, A. V. Hill (2) analyzed this data in terms of the cooperativity between the subunits in ability to bind oxygen. Cooperativity in ligand binding is the effect of the presence of a molecule of ligand bound to one subunit on the ability of a neighboring nonliganded subunit to bind another molecule of the ligand. Thus, cooperativity depends not on the absolute binding constant but on differences in the binding constant. There are now many cases known where a ligand can induce a conformation change in a protein (3)and cooperativity can readily be described by the ability of the ligand induced conformation change to alter suhunit interactions (4). Detection of these conformation changes, however, is dependent on the nature of the probe (5). Cooperativity in substrate binding measures tbat component of the conformational change transmitted across subunit domains which alters substrate binding a t the nonliganded subunit. Cooperativity in initial velocities measures tbat component of the conformational change transmitted across subunit domains which alters the catalytic reactivity of the subunit. Since one of the sources of the catalytic power of enzymes may be the transduction of potential binding energy into catalytic energy via an induced conformation change, a comparison of both catalytic and binding cooperativity can provide insight into the mechanism of action of enzvmes. For most enzymes studied, however, the cat;dytic coope;afivity parallels the hlnding cooperafivity (6). A differrncc in cooperati\,its patrerns is expected if u l V is ~ not proportional toethe fraction of enzyme present as an enzyme-bound substrate complex (Y.). As pointed out by # CY,occur when (1) Koshland (6), two cases in which u l V ~ the rate-limiting step is a conformation change after substrate binds and (2) the rate-limiting step in the decomposition of ES complexes is not the same for all molecular species. This latter situation can result from facilitation of a chemical reaction (or slow product release) a t one subunit by the binding of substrate to another suhunit. Analysis of various cooperativity patterns can provide insight into the role of suhunit interactions in the catalytic mechanism. These are described in detail below for the simplest case; namely, a dimer. n u Ds~endsncson K . / K ,
Relationship
Relsfionrhip between
K. and K. K
2 suhstrate inhibition will occur. Figure 1illustrates the effect of a on a u versus (S) plot. The dimer is assumed to show negative cooperativity in hinding of S (K1 = 10, Kz = 1).Teipel and Koshland (12) have analyzed a similar situation for tetramers. For an enzyme which has more than two subunits an appropriate relationship between the intrinsic catalytic constants can result in intermediary plateau regions in a u versus S plot. The concentration of S required for the maximal velocity can he obtained by differention of eqn. (12) with respect to S and setting d(u/E,)ldS = 0. The results are summarized a ( S ) for maximum
(9)
where a and b are inherent suhunit reactivity coefficients. Thus, substitution of eqns. (7) and (8)into eqn. (9) yields .
In general, a hiphasic loss of activity is expected. If b = 0 or k l
