The distances between the beads and other nucleus components.

<p>The distance between the beads belonging to the same chromosome is shown as <i>d</i>_<i>1</i> and is calculated using parameter <i>ε</i>_<i>1</i>. Two subsequently drawn beads are tangent. The distance between the beads belonging to different chromosomes or between the beads and nucleus or nucleolus boundary is shown as <i>d</i>_<i>2</i> and is calculated using parameter <i>ε</i>_<i>2</i>. <i>Cen[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160303#pone.0160303.ref001" target="_blank">1</a>]</i> and Cen <i>[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160303#pone.0160303.ref002" target="_blank">2</a>]</i> represent centromeric beads (grey circles).</p

Steps of modelling.

<p>The modelling process is divided into six blocks (numbers I–VI). The middle column gives more detailed description of each step, including the conditions (C1-C5 and C1’-C3’) that have to be met for the program to proceed.</p

State of the model after I-IV steps of the modelling process.

<p>The spheres representing nucleus, nucleolus and the centromeres of <i>N</i> chromosomes are drawn. <i>R</i> and <i>r</i> stand for the radius of the nucleus and nucleolus, respectively while (<i>nu</i>) and (<i>no</i>) stand for the coordinates of their centres, also respectively. Checking the conditions <b>C1–C3</b> (see text) ensures that the nucleolus and the centromeres are located inside the nucleus and that the drawn structures do not collide with each other.</p

Types of homologous CT distribution patterns modelled by ChroTeMo and visualised by ChroTeVi.

<p>A–an idiogram showing the colouring of Bd2 chromosome (top arm–green, bottom arm–red). B–the nucleus with complete association of Bd2 chromosome arm territories. Chromosomes other than Bd2 are coloured white. C–the same nucleus as B. Chromosomes other than Bd2 are transparent. D–the nucleus with the association of Bd2 top arm territories. Chromosomes other than Bd2 are coloured white. E–the same nucleus as D. Chromosomes other than Bd2 are transparent. F–the nucleus with the association of Bd2 bottom arm territories. Chromosomes other than Bd2 are coloured white. G–the same nucleus as F. Chromosomes other than Bd2 are transparent. H–the nucleus with complete separation of Bd2 chromosome arm territories. Chromosomes other than Bd2 are coloured white. I–the same nucleus as G. Chromosomes other than Bd2 are transparent. J–the nucleus with association between the top arm of one Bd2 homologue and the bottom arm of another homologue. Chromosomes other than Bd2 are coloured white. K–the same nucleus as J. Chromosomes other than Bd2 are transparent. Nucleolus is visible as a yellow sphere inside the nucleus.</p

Chromosome Territory Modeller and Viewer

<div><p>This paper presents ChroTeMo, a tool for chromosome territory modelling, accompanied by ChroTeVi–a chromosome territory visualisation software that uses the data obtained by ChroTeMo. These tools have been developed in order to complement the molecular cytogenetic research of interphase nucleus structure in a model grass <i>Brachypodium distachyon</i>. Although the modelling tool has been initially created for one particular species, it has universal application. The proposed version of ChroTeMo allows for generating a model of chromosome territory distribution in any given plant or animal species after setting the initial, species-specific parameters. ChroTeMo has been developed as a fully probabilistic modeller. Due to this feature, the comparison between the experimental data on the structure of a nucleus and the results obtained from ChroTeMo can indicate whether the distribution of chromosomes inside a nucleus is also fully probabilistic or is subjected to certain non-random patterns. The presented tools have been written in Python, so they are multiplatform, portable and easy to read. Moreover, if necessary they can be further developed by users writing their portions of code. The source code, documentation, and wiki, as well as the issue tracker and the list of related articles that use ChroTeMo and ChroTeVi, are accessible in a public repository at Github under GPL 3.0 license.</p></div

Step VI of the modelling process: simulating chromatin decondensation.

<p>The condensed state of a chromosome is represented by a chain of beads identified with three numbers (white circles). The chromosome decondensation is simulated by adding new beads (grey circles) along the length of the entire chromosome, not only at the last created bead. The coordinates of the new beads are generated randomly. The candidate beads <i>B4</i>, <i>B5</i>, <i>B6</i> (dotted line circles) will be discarded because they do not pass collision detection procedures: <i>B4</i> and <i>B5</i> are too far from the”own” chromosome (condition <b>C4</b> is not met), <i>B6</i> is too close to the”foreign” beads (condition <b>C5</b> is not met).</p

Association of homologous and heterologous chromosome territories in <i>B</i>. <i>distachyon</i> interphase nuclei of roots.

<p>A–an idiogram showing the labelling of Bd5 chromosome (top arm–green, bottom arm–red; each nucleus contains two sets of chromosomes). B–the nucleus with complete separation of Bd5 chromosome arm territories revealed by FISH. Nucleolus is visible as dark blue spherical gap inside the nucleus. C–an idiogram showing the labelling of two heterologous chromosomes (Bd2 –green, Bd5 –red), without discrimination between chromosome arms. D–the nucleus with association of Bd2 and Bd5 chromosome territories revealed by FISH. Photomicrographs in B and D are supplied with diagrams representing the distribution of CTs. Scale bars: 2 μm.</p

Step V of the modelling process: creating condensed chromosomes.

<p>Already existing beads (solid line circles) are named by assigning them a letter <i>B</i> followed by three numbers: identifier of the chromosome, identifier of the chromosome arm (<i>t</i>–top or <i>b</i>—bottom), and identifier of a bead in each arm. For example, <i>B(4</i>,<i>t</i>,<i>5)</i> should be read as bead number 5, in top arm of chromosome 4. Temporary beads (dotted line circles), which are introduced only for presentation purposes are numbered with the use of only one identifier which is a single number. The temporary beads (”bead candidates”) <i>B1</i>, <i>B2</i>, and <i>B3</i> will be discarded because they do not pass”collision detection” procedure, i.e. <i>B1</i> collides with the nucleolus (condition <b>C2</b> is not met), bead <i>B2</i> collides with the nucleus boundary (condition <b>C1</b> is not met) and <i>B3</i> (which belongs to chromosome 4) is too close to <i>B[1</i>, <i>b</i>, <i>j</i>_<i>c</i><i>]</i> and does not meet the condition <b>C3</b>.</p

Model parameters and their visual presentation.

<p>Nucleus has radius <i>R</i> that varies in range from <i>R</i>_<i>min</i> to <i>R</i>_<i>max</i>. Nucleolus has radius <i>r</i> that varies in range from <i>r</i>_<i>min</i> to <i>r</i>_<i>max</i>. The chromosome in its condensed state is represented by a chain of spherical domains with fixed radius <i>r</i>_<i>b</i>. Each chromosome has one centromere <i>Cen[]</i> and consists of a top and bottom arm with a given length.</p

Exemplary visualisation of nuclei modelled by ChroTeMo and visualised by ChroTeVi.

<p>A–an idiogram showing the colouring of Bd5 chromosome (top arm–green, bottom arm–red; a nucleus contains two sets of chromosomes). B–the nucleus with complete separation of Bd5 chromosome arm territories. Chromosomes other than Bd5 are coloured white. C–the same nucleus as B. Chromosomes other than Bd5 are transparent. Nucleolus is visible as a yellow sphere inside the nucleus. D–an idiogram showing the colouring of two heterologous chromosomes (Bd2 –green, Bd5 –red), without discrimination between chromosome arms. E–the nucleus with association of Bd2 and Bd5 chromosome territories. Chromosomes other than Bd2 and Bd5 are coloured white. F–the same nucleus as E. Chromosomes other than Bd2 and Bd5 are transparent. Nucleolus is visible as a yellow sphere inside the nucleus.</p