excluded volume ͉ analytical ultracentrifugation ͉ sedimentation equilibrium I t has been predicted that in ''crowded'' solutions-solutions containing a total volume fraction of inert proteins or other macromolecules comparable to that found in physiological fluid media-volume exclusion will significantly enhance the tendency of dilute as well as concentrated proteins to self-associate (1-6). Indirect evidence for crowding-induced changes in the equilibrium average state of association of several proteins has been provided by measurement of crowding-linked changes in enzyme activity (7), rotational relaxation times (8), and rates of protein aggregation (9). However, direct evidence for such an effect has been difficult to obtain, because conventional methods for direct measurement of equilibrium average molar masses of proteins, such as light scattering, osmotic pressure, and analytical ultracentrifugation, are poorly suited for the study of the properties of a dilute protein in a solution containing high concentrations of other proteins.A newly developed analytical method, referred to as nonideal tracer sedimentation equilibrium (NITSE), permits the simultaneous measurement of the concentration gradients at sedimentation equilibrium of a labeled dilute tracer macrosolute and an unlabeled, arbitrarily concentrated ''background'' macrosolute together in solution (10). From these gradients one can calculate apparent equilibrium weight-average molar masses of both tracer and background species as functions of the concentration of background. To determine the true weight-average molar masses of tracer and background from the experimentally measured apparent weight-average molar masses at high background concentration, it is necessary to take into account repulsive as well as attractive interactions between macrosolute molecules, which requires a description of the approximate size and shape of each macrosolute species present in significant abundance. Lacking such information, the initial study of protein self-association carried out by using NITSE (10) used an empirical approximation that, whereas reasonable, adds uncertainty to the final interpretation of experimental results.In the present work, we present a NITSE study of the selfassociation in crowded solution of a bacterial protein, FtsZ, whose self-association has recently been well-characterized in dilute solution by using conventional measurements of sedimentation equilibrium and sedimentation velocity (11). FtsZ is a prokaryotic homolog of tubulin (M r ϭ 40,000) that has been shown to constitute a major protein component of the septation ring in Escherichia coli and is essential for cell division (12). It has been shown that FtsZ self-associates in a manner and to an extent determined by environmental concentrations of guanine nucleotide(s) and Mg 2ϩ (13)(14)(15). By means of sedimentation equilibrium and sedimentation velocity experiments, it was established that, in the presence of saturating concentrations of GDP, FtsZ reversibly forms linear oligomers ...

The technique of tracer sedimentation equilibrium [Rivas, G., et al. (1994) Biochemistry, 2341-2348 (1); Rivas, G., et al. (1996) J. Mol. Recognit. 9, 31-38 (2)] is utilized, together with an extension of the theory of sedimentation equilibrium of highly nonideal solutions [Chatelier and Minton, (1987) Biopolymers 26, 1097-1113 (3)], to characterize the thermodynamic activity and/or the state of association of a dilute, labeled macromolecular solute in the presence of an arbitary concentration of a second, unlabeled macromolecular solute. Experiments are performed on solutions of labeled fibrinogen (0.25-1 g/L) in bovine serum albumin (0-100 g/L) in the presence and absence of divalent cations (Ca(2+), Mg(2+)), and on solutions of labeled tubulin (0.2-0.6 g/L) in dextran (0-100 g/L). It is found that in the absence of the divalent cations, the large dependence of the thermodynamic activity of fibrinogen on BSA concentration is well accounted for by a simple model for steric repulsion. In the presence of the cations and sufficiently large concentrations of BSA (>30 g/L), fibrinogen appears to self-associate to a weight-average molar mass approximately twice that of monomeric fibrinogen. Tubulin appears to self-associate to an extent that increases monotonically with increasing dextran concentration, reaching a weight-average molar mass almost 3 times that of the alphabeta dimer in the presence of 100 g/L dextran. Possible biological ramifications are discussed.