Céline Reyes, Yannick Gachet, Sylvie Tournier, Guillaume Gay
In eucaryotic cells, during mitosis, the two daughter cells must inherit the full set of duplicated chromosomes, containing the genetic information. An error in the spatial segregation of the chromosome pairs prior to division might lead to an uneven distribution of the genetic material (or aneuploidy), with dire consequences for the cell or even the organism.
The segregation of the genetic material is achieved by a specialized structure called the mitotic spindle, composed of microtubules  and molecular motors such as kinesin. During the S phase of the cell cycle, the genetic material is duplicated. Prior to entering mitosis, the chromosomes condense, each copy of the cell's DNA forming a sister chromatid (the two chromatids form the branches of the X-shaped chromosomes as seen in karyotypes pictures). Those chromatids are bound together by cohesin. During prophase, while the spindle assembles, the sister chromatids are captured by microtubules targeted to a protein complex in their centromeric region called the kinetochore. From pro-metaphase to metaphase, chromosomes oscillate between the spindle poles until they organize into the metaphase plate. At anaphase execution, cohesin is degradated and both sister chromatid is transported towards one pole of the spindle, and the cell can be physically divided.
In a recent article  we demonstrated that a simple model could describe chromosome segregation, with a focus on the correction of the errors in the attachment of the microtubules to the kinetochore. A particular effort was made on reducing the number of parameter and having them based on actual in vivo data. Mathematically, the various elements of the model are described by a set of coupled first order differential equations reflecting the force balance between the various elements.
The Numpy, Scipy, Cython and Pylab tool suite was instrumental in the design of a simple, object oriented and fast simulation engine. The source code of the simulation is now available on github (https://github.com/glyg/Kinetochore-segregation).
In the future, our framework will be extended to encompass more aspects of the cell division, until a full cell division can be simulated.
Another possibility opened by the model is its coupling with machine learning strategies for video-microscopy sequence analysis.
The most obvious use of the model is as a source of synthetic images that can be used as ground truth for the evaluation of detection algorithms. But a more ambitious objective is to extract directly from the video-microscopy data a trajectory in the model state space, at least in a maximum likelihood sense. We will present here the first steps toward this goal, with the use of the skimage and scikits-learn python kits.
|||Microtubules are filamentous protein assembly that dynamically grow and shrink and can span several micrometers across the cell.|
|||G. Gay, T. Courthéoux, C. Reyes, S. Tournier, Y. Gachet. A stochastic model of kinetochore–microtubule attachment accurately describes fission yeast chromosome segregation J. Cell Biol 2012 http://dx.doi.org/10.1083/jcb.201107124|