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

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