Effective Long-Range Attraction between Protein Molecules in Solutions Studied by Small Angle Neutron Scattering

Small angle neutron scattering intensity distributions taken from cytochrome C and lysozyme protein solutions show a rising intensity at a very small wave vector $Q$, which can be interpreted in terms of the presence of a weak long-range attraction between protein molecules. This interaction has a range several times that of the diameter of the protein molecule, much greater than the range of the screened electrostatic repulsion. We show evidence that this long-range attraction is closely related to the type of anion present and ion concentration in the solution.

Figure 1

Theoretical calculations of $I(Q)$ resulting from one Yukawa attraction at 1% volume fraction. (a) The effect due to the variation of the attraction strength, $K$, at $Z=10$. (b) The effect due to the variation of the attraction range, $1/Z$, at $K=0.5$. The inset shows $I(Q)$ from a cytochrome C sample at 1% volume fraction in 1 M NaCl at $pD=11$.

Figure 2

SANS intensity distribution of cytochrome C solutions at $pD=11$ and at 1% volume fraction with different salts added. The solid lines are the theoretical analyses.

Figure 3

SANS intensity distributions of cytochrome C samples at 5% volume fraction. The solid lines are theoretical analyses using two-Yukawa potential.

Figure 4

SANS intensity distributions of lysozyme samples at $pD=5.1$ with 20 mM HEPES buffer. Dotted lines (a) and (b) are fitted by considering only a short-range attraction and electrostatic repulsion. Solid lines (a) and (b) are the fitted results by using three Yukawa form potential. Lower panel shows the calculated structure factor, $S(Q)$.