Measuring the length distribution of a fibril system: A flow birefringence technique applied to amyloid fibrils

Relaxation of flow birefringence can give a direct measure of the rotational diffusion of rodlike objects in solution. With a suitable model of the rotational diffusivity, a length distribution can be sought by fitting the decay curve. We have measured the flow birefringence decay from solutions of amyloid fibrils composed of beta-lactoglobulin and extracted a length distribution using the Doi-Edwards-Marrucci-Grizzuti theory of semidilute rotational diffusion. The concentration scaling of the results shows that the fibrils diffuse as free rods: they cannot be significantly branched, sticky, or break up under dilution. The length distribution obtained shows a single broad peak, consistent with measurements of the fibrils by electron microscopy. This comparison, and combination of the experiment with an assay to find the total concentration of fibrils, allows calibration of the length scale and concentration scale of the length distribution. It is our hope that this method can be used for following the growth kinetics of amyloid fibrils in vitro and for studying the length distribution of rodlike systems in general.