Protein self-association induced by macromolecular crowding: a quantitative analysis by magnetic relaxation dispersion

Abstract

In the presence of high concentrations of inert macromolecules, the self-association of proteins is strongly enhanced through an entropic, excluded-volume effect variously called macromolecular crowding or depletion attraction. Despite the predicted large magnitude of this universal effect and its far-reaching biological implications, few experimental studies of macromolecular crowding have been reported. Here, we introduce a powerful new technique, fast field-cycling magnetic relaxation dispersion, for investigating crowding effects on protein self-association equilibria. By recording the solvent proton spin relaxation rate over a wide range of magnetic field strengths, we determine the populations of coexisting monomers and decamers of bovine pancreatic trypsin inhibitor in the presence of dextran up to a macromolecular volume fraction of 27%. Already at a dextran volume fraction of 14%, we find a 30-fold increase of the decamer population and 510(5)-fold increase of the association constant. The analysis of these results, in terms of a statistical-mechanical model that incorporates polymer flexibility as well as the excluded volume of the protein, shows that the dramatic enhancement of bovine pancreatic trypsin inhibitor self-association can be quantitatively rationalized in terms of hard repulsive interactions.

FIGURE 1

¹H relaxation dispersion profiles from aqueous solutions of dextran at pH 4.5 and 27°C. The dextran concentrations for samples D1–D5 are given in Table 1. The curves were obtained by three-Lorentzian fits as described in the text.

FIGURE 2

Dependence of the zero-frequency excess ¹H relaxation rate, in dextran solutions D1–D5 on the dextran hydroxyl proton fraction, The bulk water relaxation rate at 27°C is

FIGURE 3

¹H difference relaxation dispersion profiles from aqueous solutions of BPTI and dextran at pH 4.5 and 27°C. BPTI and dextran concentrations for samples P0–P5 are given in Table 1. The curves were obtained by two-Lorentzian (samples P0–P3) or three-Lorentzian (samples p4 and p5) fits as described in the text. The data have been normalized to a water/BPTI mol ratio of

FIGURE 4

The fraction, p_B, of decamer-forming BPTI molecules as a function of dextran volume fraction, φ_M. The points were derived from the MRD data (samples P0–P3) and the curve resulted from a fit to the model described in the text (with δ = 3.0 Å). The dashed curve was calculated with the same model parameters, but without the nonideality contribution from BPTI.

FIGURE 5

Variation of (A) the Kuhn length, λ_M, and (B) the natural logarithm of the ideal association constant, K₀, with the thickness, δ, of the undisplacable water layer. The shaded regions correspond to one standard deviation in the fitted parameters.

FIGURE 6

Dependence of the natural logarithm of the nonideality factor, Γ, on the dextran volume fraction, φ_M. The solid curve was calculated from the model with the parameter values resulting from the fit in Fig. 4. The dashed curve was calculated with the same parameter values, but without the nonideality contribution from BPTI.