Final Report Summary - CVM-EM-PALM (Computing the structure and dynamics of protein assemblies in living cells by coupling sub-diffraction fluorescence microscopy with single-particle reconstruction: application to viral capsids)
Our objective is to develop computational procedures to enhance image sharpness in super-resolution fluorescence microscopy by adequate modeling of the spatial and spatio-temporal dynamics of the marker molecule. Context. Image sharpness is a central issue when medical or biochemical questions are studied by fluorescence microscopy. In the last ten years, modern fluorescence microscopes have been invented that feature a resolution that is not anymore limited by the diffraction of light. Hereby, the image sharpness could be increased by roughly one order of magnitude allowing researchers to investigate many biological objects of high importance that were hidden to the observer before. Specifically, methods like Stimulated Emission Depletion Microscopy (STED) or Stochastic Reconstruction Microscopy (STORM) arrive routinely at resolving objects of the size of ≈ 20nm with visible light and far-field optical equipment. This has opened up a completely new field of research at the crossing of physics, engineering, biochemistry and informatics modeling: super-resolution fluorescence microscopy. A particulary important subclass of the mentioned super-resolution methods relies on switching randomly the fluorescence capability of the marker molecules, classical optical camera detection of the activated molecule and subsequent single-molecule localization. With random fluorescence switching, only a sparse aleatoric subset of otherwise very densely packed molecules is observed. For an isolated molecule the camera image is typically an Airy disc of ≈ 200nm diameter. The aforementioned aleatoric subset of activated molecules is likely to be sufficiently sparse in order to contain few overlapping single-molecule images. From these latter the true molecule position can be estimated to sub-diffraction accuracy depending only on the photons-to-noise ratio of the image, i.e. the strength of the light stream emitted by the isolated molecule compared to the background. These high-resolution position estimates can be used to form a super-resolved image just by tabulating the number of position estimates falling into a certain spatial volume. Doing this, the approach reaches a resolution of a few tens of nm.
Objectives and Results.
Our main scientific question is : Can the resolution be pushed even more, to the single-digit nanometer range? In the project, we propose a step towards achieving this by exploiting the fact that every marker molecule is usually detected and localized in many fluorescence switching cycles. If the information of the different detections is combined, a composite position estimate should be obtainable that is much more precise than the constituent single-cycle detections. This implies that resolution in localization-based superresolution microscopy depends not only on the photon number of the individual molecule detection event, but also on its detection multiplicity. This effect is illustrated in Figure 1. In order to combine the multiple position estimates originating from the same molecule, the researcher has developed algorithms for a computational procedure called Resolution Enhancement by Estimate Pooling (REEP) that allows to cluster position estimates in space and time based on the statistical signature of the individually detected molecules. To this aim, methods from technical computing, data mining, stochastic modeling and unsupervised learning have been combined. Particularly, we have found mathematical formulae that describe the spatial and spatio-temporal clustering of molecular position detections. In our image model, the spatial distribution of position estimates of a collection of K molecules at original positions µk is represented by a Gaussian mixture model, that can ’learn’ its clustering distribution via the expectation-maximization algorithm. In turn, to describe the temporal distribution of position estimates we have calculated the probability that a molecule with mean on and off times τ¯on, τ¯of f and the mean number of fluorescence switching cycles M¯ is detected in an image frame at time t.
Objectives and Results.
Our main scientific question is : Can the resolution be pushed even more, to the single-digit nanometer range? In the project, we propose a step towards achieving this by exploiting the fact that every marker molecule is usually detected and localized in many fluorescence switching cycles. If the information of the different detections is combined, a composite position estimate should be obtainable that is much more precise than the constituent single-cycle detections. This implies that resolution in localization-based superresolution microscopy depends not only on the photon number of the individual molecule detection event, but also on its detection multiplicity. This effect is illustrated in Figure 1. In order to combine the multiple position estimates originating from the same molecule, the researcher has developed algorithms for a computational procedure called Resolution Enhancement by Estimate Pooling (REEP) that allows to cluster position estimates in space and time based on the statistical signature of the individually detected molecules. To this aim, methods from technical computing, data mining, stochastic modeling and unsupervised learning have been combined. Particularly, we have found mathematical formulae that describe the spatial and spatio-temporal clustering of molecular position detections. In our image model, the spatial distribution of position estimates of a collection of K molecules at original positions µk is represented by a Gaussian mixture model, that can ’learn’ its clustering distribution via the expectation-maximization algorithm. In turn, to describe the temporal distribution of position estimates we have calculated the probability that a molecule with mean on and off times τ¯on, τ¯of f and the mean number of fluorescence switching cycles M¯ is detected in an image frame at time t.
