Improved kymography tools and its applications to mitosis
Introduction
Analysis of biological processes generally involves the study of correlations among a large set of variables with the ultimate aim of extracting causal relations between them. Graphical representation of the dependencies between variables represents a crucial step towards true understanding of these problems. However, one often faces the problem of presenting multi-variable data in the two-dimensional (2D) manuscript or computer monitor, a ‘data compression’ procedure which inevitably implies information loss. In fact, dynamic 2D representations in a computer and holography are not science fiction, but static 2D still is and will likely remain a compression procedure important for both visualization and comprehension of even the most complex data. We focus this article on a specific type of 2D graphical representation which is called a kymograph, useful in the study of dynamic 1D or quasi-1D processes. Mitosis, meiosis, neuron and filament-based protein traffic are among the range of quasi-1D processes amenable for kymograph analysis.
As a working frame, we will focus on the use of kymography to study mitotic spindle and chromosome dynamics. The ultimate goal of mitosis is to form two cells which are genetically identical to the precursor cell. To accomplish this, a microtubule-based spindle assembles around the chromatin after the nuclear envelope breaks down and attaches to all chromosomes through dedicated chromosome structures termed kinetochores [1]. With the involvement of a large number of motor and non-motor proteins, the mitotic spindle is capable of driving chromosome alignment at the metaphase plate [2] and their subsequent segregation towards opposite sides of the cell. During mitotic progression, chromosome distribution evolves from a 3D distribution inside the nucleus (at prophase) to a 2D distribution (at metaphase), thereby its name – metaphase plate. This remarkable conformational change is essential because it liberates one of the three spatial dimensions to define an axis for cell division. In fact, most chromosome and spindle internal dynamics occur preferentially along this axis. As an example, chromosomes typically display oscillations about the spindle equator during metaphase [3] and finally move processively towards opposite sides of the cell. Both movements are essentially parallel to the spindle axis, which in fact is the division axis. Also, microtubules are not static but undergo a permanent renewal process which involves their permanent poleward translocation, even while attached chromosomes remain still (or oscillating) at the metaphase plate [4], [5]. Indeed, such poleward motion is also approximately parallel to the spindle axis and was termed microtubule poleward flux [4], a prominent process that occurs in most metazoans and plant spindles.
The above examples of quasi-linear motion are among the variety of mitotic processes amenable for kymograph analysis, of which we show some examples in this article. We will present an overview of conventional kymography and propose some improved variations and generalized procedures which help minimizing information loss. We conclude with a brief discussion on the use of those variations applied to time-projections. Admittedly, with one exception (the guided-kymograph, which we discuss as the first variation on kymography), the analysis tools presented here do not aim to (and do not) provide new quantification potential, but essentially assist visualization of multi-dimensional microscopy data in the 2D manuscript. All algorithms were implemented in Matlab programming environment (Matlab, MA; release 2007b).
Section snippets
Conventional kymography
The kymograph, popular among live cell microscopists, is a straightforward example of a compressed 2D representation. Kymography is useful when the configuration of the object of study evolves more slowly along one of the spatial dimensions than along the orthogonal dimension, allowing the ‘slow’ component to be considered frozen and disregarded. This liberates that spatial dimension to represent non-spatial variables, such as time. Originally, spatial assignment of time in this fashion was
Guided-kymography
In conventional kymographs, a single ROI is used to extract information from all sequential images, which leads to the abovementioned problems of (i) guaranteeing the permanence of the object inside the ROI, especially if this is too thin and (ii) allowing the correct estimation of velocity, which may become more critical when trying to solve the first problem. An easy way to circumvent these issues involves the use of a dynamic ROI, i.e., a ROI which is translated and rotated every frame to
Chromo-kymography
Conventional kymographs use three of the variables we are sensitive to – intensity, x-position and y-position. In the kymograph, these reflect three variables of the experiment – intensity, x-position and time. Information on y-axis has been lost in the process, but it may be partially rescued if we make use of yet another variable which the retina is sensitive to – color, therefore the name chromo-kymograph. This information rescue is particularly relevant when performing thick-ROI kymography,
Chromo-projections
The principle applied to chromo-kymograph generation may be also applied to projections along dimensions other than y. For example, instead of sacrificing y-axis information, we may want to keep it while sacrificing (again, as little as possible) time information. Geometrically, what we do is stack up all 2D images (time frames) to construct a 3D pixel matrix and perform a projection along the z-axis (time axis) of the 3D matrix. Conventional projection may be again based on some weighted
Conclusion
We presented some visualization procedures which may be useful for correct velocity quantification in kymograph analysis and for retrieval of information discarded in image projection procedures, of which the kymograph is one example. For correct velocity determination we focused on the generation of guided-kymographs, which rely on tracking of two reference objects that are used to define the ROI movement from frame to frame, thus compensating for rotation and translation of the structures of
Acknowledgments
We thank Irina Matos for providing experimental data for kymograph generation. A.J.P. was supported by Crioestaminal/Viver a Ciência and Fundação para a Ciência e a Tecnologia (FCT). Work in the lab. of H.M. is supported by Grants PTDC/BIA-BCM/66106/2006 and PTDC/SAU-OBD/66113/2006 from FCT, and the Gulbenkian Programmes for Research Stimulation and Frontiers in the Life Sciences.
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