Abstract
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 was 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, during an exposure time interval. 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 Fisher information matrix for this parameter estimation problem. The analytical results are complicated through the fact that the observation process in a microscope prohibits the use of standard Kalman filter type approaches. The analytical framework presented here is illustrated with examples of low photon count scenarios for which we rely on Monte Carlo methods to compute the associated probability distributions.
Highlights
T HE STUDY of intercellular and intracellular trafficking processes of objects of interest has been the subject of many research projects during the past few decades
In [16], we focused on the fundamental microscopy data model, in which the image of a molecule is acquired by an unpixelated detector
We introduced the Fisher information matrix conditioned on the number of detected photons, which will be further used to derive an expression for the the Fisher information matrix of the practical data model
Summary
T HE STUDY of intercellular and intracellular trafficking processes of objects of interest has been the subject of many research projects during the past few decades. There are several methods available concerning the problem of the parameter estimation of single molecule trajectories in cellular contexts The majority of these methods model the effect of pixelation by using an additive noise in the fundamental data model. For a similar observation model, Relich et al [11] have proposed a method for the maximum likelihood estimation of the diffusion coefficient, with an information-based confidence interval, from Gaussian measurements Using these approximate observation models makes all corresponding computations simpler, it does not model the effect of the pixelated camera accurately. We propose a general framework to investigate the effect of pixelation of the detector on the parameter estimation of single molecule trajectories accurately.
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