Birefringence of single and bundled microtubules

We have measured the birefringence of microtubules (MTs) and of MT-based macromolecular assemblies in vitro and in living cells by using the new Pol-Scope. A single microtubule in aqueous suspension and imaged with a numerical aperture of 1.4 had a peak retardance of 0.07 nm. The peak retardance of a small bundle increased linearly with the number of MTs in the bundle. Axonemes (prepared from sea urchin sperm) had a peak retardance 20 times higher than that of single MTs, in accordance with the nine doublets and two singlets arrangement of parallel MTs in the axoneme. Measured filament retardance decreased when the filament was defocused or the numerical aperture of the imaging system was decreased. However, the retardance "area," which we defined as the image retardance integrated along a line perpendicular to the filament axis, proved to be independent of focus and of numerical aperture. These results are in good agreement with a theory that we developed for measuring retardances with imaging optics. Our theoretical concept is based on Wiener's theory of mixed dielectrics, which is well established for nonimaging applications. We extend its use to imaging systems by considering the coherence region defined by the optical set-up. Light scattered from within that region interferes coherently in the image point. The presence of a filament in the coherence region leads to a polarization dependent scattering cross section and to a finite retardance measured in the image point. Similar to resolution measurements, the linear dimension of the coherence region for retardance measurements is on the order lambda/(2 NA), where lambda is the wavelength of light and NA is the numerical aperture of the illumination and imaging lenses.