Effect of Pixelation on the Parameter Estimation of Single Molecule Trajectories.

The advent of single molecule microscopy has revolutionized biological investigations by providing a powerful tool for the study of intercellular and intracellular trafficking processes of protein molecules which were not available before through conventional microscopy. In practice, pixelated detectors are used to acquire the images of fluorescently labeled objects moving in cellular environments. Then, the acquired fluorescence microscopy images contain the numbers of the photons detected in each pixel. Therefore, the precise temporal information of detection of the photons is not available. Moreover, instead of having the exact locations of detection of the photons, we only know the pixel areas in which the photons impact the detector. These challenges make the analysis of single molecule trajectories from pixelated images a complex problem. Here, we investigate the effect of pixelation on the parameter estimation of single molecule trajectories. In particular, we develop a stochastic framework to calculate the maximum likelihood estimates of the parameters of a stochastic differential equation that describes the motion of the molecule in living cells. We also calculate the Cramer-Rao lower bound (CRLB), given by the inverse of the Fisher information matrix, on the variance of the parameter estimates. Even in cases that we have a small number of photons, the obtained results show that we are able to estimate the parameters of the molecule trajectory from simulated fluorescence microscopy images using our proposed method.