Advantage of Using Spherical over Cartesian Coordinates in the Chromosome Territories 3D Modeling

This paper shows results of chromosome territory modeling in two cases: when the implementation of the algorithm was based on Cartesian coordinates and when implementation was made with Spherical coordinates. In the article, the summary of measurements of computational times of simulation of chromatin decondensation process (which led to constitute the chromosome territory) was presented. Initially, when implementation was made with the use of Cartesian Coordinates, simulation takes a lot of time to create a model (mean 746.7[sec] with the median 569.1[sec]) and additionally requires restarts of the algorithm, also often exceeds acceptable (given a priori) time for the computational experiment. Because of that, authors attempted changing the coordinate system to Spherical Coordinates (in a few previous projects it leads to improving the efficiency of implementation). After changing the way that 3D point is represented in 3D space the time required to make a successful model reduced to the mean 25.3[sec] with a median 18.5[s] (alongside with lowering the number of necessary algorithm restarts) which gives a significant difference in the efficiency of model’s creation. Therefore we showed, that a more efficient way for implementation was the usage of spherical coordinates.