3-D reconstruction of microtubules from multi-angle total internal reflection fluorescence microscopy using Bayesian framework.

Total internal reflection fluorescence (TIRF) microscopy excites a thin evanescent field which theoretically decays exponentially. Each TIRF image is actually the projection of a 3-D volume and hence cannot alone produce an accurate localization of structures in the z-dimension, however, it provides greatly improved axial resolution for biological samples. Multiple angle-TIRF microscopy allows controlled variation of the incident angle of the illuminating laser beam, thus generating a set of images of different penetration depths with the potential to reconstruct the 3-D volume of the sample. With the ultimate goal to quantify important biological parameters of microtubules, we present a method to reconstruct 3-D position and orientation of microtubules based on multi-angle TIRF data, as well as experimental calibration of the actual decay function of the evanescent field at each angle. We validate our method using computer simulations, by creating a phantom simulating the curvilinear characteristics of microtubules and project the artificially constructed volume into a set of TIRF image for different penetration depth. The reconstructed depth information for the phantom data is shown to be accurate and robust to noise. We apply our method to microtubule TIRF images of PtK(2) cells in vivo. By comparing microtubule curvatures of the reconstruction results and several electron microscopy (EM) images of vertically sliced sample of microtubules, we find that the curvature statistics of our reconstruction agree well with the ground truth (EM data). Quantifying the distribution of microtubule curvature reveals an interesting discovery that microtubules can buckle and form local bendings of considerably small radius of curvature which is also visually spotted on the EM images, while microtubule bendings on a larger scale generally have a much larger radius and cannot bear the stress of a large curvature. The presented method has the potential to provide a reliable tool for 3-D reconstruction and tracking of microtubules.