How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?

摘要

Single molecule fluorescence microscopy is a relatively novel technique that is used, for example, to study thebehavior of individual biomolecules in cells. Since a single molecule can move in all three dimensions in acellular environment, the three dimensional tracking of single molecules can provide valuable insights into cellularprocesses. It is therefore of importance to know the accuracy with which the location of a single molecule canbe determined with a fluorescence microscope. We study this performance limit of a fluorescence microscopefrom a statistical point of view by deriving the Fisher information matrix for the estimation problem of thelocation of the single molecule. In this way we obtain a lower bound on the standard deviation of any reasonable(unbiased) estimation method of the location parameters. This lower bound provides a fundamental limit on theaccuracy with which a single molecule can be localized using a fluorescence microscope and is given in terms ofsuch quantities as the photon detection rate of the single molecule, the acquisition time, the numerical apertureof the objective lens etc. We also present results that show how factors such as noise sources, detector sizeand pixelation deteriorate the fundamental limit of the localization accuracy. The present results can be usedto evaluate and optimize experimental setups in order to carry out three dimensional single molecule trackingexperiments and provide guidelines for experimental design.