Scaling Behavior and Cluster Fractal Dimension Determined by Light Scattering from Aggregating Proteins

Abstract

The size distribution ${n}_{i}(t)$ for systems with Smoluchowski aggregation kinetics is shown to have the dynamic scaling form ${n}_{i}(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\theta}}g(\frac{1}{{t}^{z}})$, with $\ensuremath{\theta}=2$ and $z=1$. This gives a light-scattering intensity $〈I〉\ensuremath{\sim}{t}^{z}$, and an effective hydrodynamic cluster radius $〈R〉\ensuremath{\sim}{t}^{\frac{z}{D}}$, where $D$ is the cluster fractal dimension. We find that human immunoglobulin (IgG) monomers exhibit Smoluchowski aggregation kinetics with $z=1$, and $D=2.56\ifmmode\pm\else\textpm\fi{}0.3$, upon heating to 47-62\ifmmode^\circ\else\textdegree\fi{}C.