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Automatic tracking of single molecules in fluorescence microscopy

par Pierre-Louis Porté - 27 février 2007

A collaboration is underway between our team and Laurent Cohen, senior scientist in the applied mathematics and image processing group of CEREMADE laboratory (University Paris-Dauphine). It takes the form of a PhD which is currently pursued by Stéphane Bonneau.

The aim of this collaboration is to develop computational methods, both automatic and robust, to extract relevant information from the different kinds of images that biophysicists have to deal with.

Context

Among the variety of experimental techniques aiming at measuring molecular dynamics in live cells, single particle tracking (SPT) is one of the most sensitive. In this approach, a marker is specifically attached to a protein of interest whose lateral motion is then recorded with high spatial (about 10 nanometers) and temporal resolution (in the millisecond range). Such trajectories contain a wealth of information and they can inform on the local organization of the membrane. In particular, they may potentially reveal transient interactions or temporary confinement that remain hidden with conventional imaging.

SPT was initially developped using large labels such as micron-sized latex beads or 40 nm gold nanoparticles. Progress in single molecule biophysics have recently allowed their replacement by smaller fluorescent probes (green fluorescent proteins, fluorophores or quantum dots) that enable investigations at a truly molecular scale. For single molecule tracking (SMT), semiconductor quantum dots (QDs) are probably the most favorable probes since they combine a relatively small size (5-15 nm) with a remarkable brightness and a superior photostability, allowing long-term acquisition with a good signal to noise ratio.

While very promising for the study of cell dynamics, the development of SMT raises however new challenges in terms of image processing. In these experiments, the motion of several tagged molecules is simultaneously recorded and needs to be quantitatively analyzed. The image sequences can be composed of up to thousands of frames and contain a number of molecules which varies from a couple to hundreds, depending on experimental conditions and protocols. This number may also fluctuate in consecutives frames since molecules can entry and exit in the field of view. Using QDs as fluorescent probes raises additional difficulties. Due to complex physical processes, the QD fluorescence is intermittent, i.e. its emission intensity randomly alternates between bright and dark periods. It means that tagged-molecules might temporarily disappear from the field of view. A robust processing tool is therefore required to account for all the specificities of SMT measurements and automatically extract the trajectories of single molecules.

Contribution

To track single molecules, we develop a novel method which does not use the traditionnal frame by frame approach but considers the fluorescence image stack as a single 3D spatio-temporal volume. In this representation, molecular trajectories are viewed as 3D curves which we consider as minimal paths in an image-dependent metric and seek to retrieve using an energy minimization technique.

First, fluorescent spots are detected in each frame of the sequence, using a model of the diffraction-limited pattern. This step gives rise to a set of points in the spatio-temporal volume. These points are not randomly scattered but exhibit significant amount of organization. The problem of motion correspondence is then mapped into a perceptual grouping one, given a set of unstructured points and the image sequence. The underlying idea is to use the fluorescence image to guide the grouping process, taking into account the fluorescence signal which exists but is too low to have been detected. We sequentially find pairs of points (among the set of detected spots) that have to be linked and the paths that join them, such that these paths are geodesics in a Riemannian metric computed from the three-dimensional image stack. Therefore, our approach naturally allows the inference of the fluorescent probe trajectory even when the fluorescence signal is below the detection threshold. Finally, an additional stage is applied to process the set of minimal paths, in order to get true molecular trajectories with a localization accuracy of a few nanometers.

Results

To illustrate the capability of our approach, we present here some results issued from the tracking of glycine receptors tagged with QDs in the membrane of live neurons. For each analyzed film a movie is provided. This movie presents both the fluorescence image sequence (on the left side) and a synthetic reconstruction of molecular trajectories (on the right side). For a better visualization, these trajectories are also represented in a 3D spatio-temporal volume. Experimental data are provided by Marie-Virginie Ehrensperger.

The presented fluorescence image sequences have in common the following parameters :
Pixel width : 216.7 nm,
Temporal sampling period : 75 ms,
Approximative standard deviation of the PSF : 85 nm.