Supporting Online Materials
Generation of interaction frequency (IF) heatmap
We extracted the 1 Mb binned heatmap data (1) from GEO database http://www.ncbi.nlm.nih.gov/geo/ , accession no. GSE18199). The observed, expected, and observed/expected datasets were normalized by dividing the selected value by the average value of each dataset. Since IFs are positive values, the Pearson correlation values of intra chromosomal interactions (-1.0 to +1.0) were brought to positive values by adding a value of +1.0. Similarly, the correlation values of inter-chromosomal interactions (-0.25 to +0.25) were brought to positive values by adding a value of +0.25. To draw multiple chromosomes in the nucleus, inter- and intra-interaction IF heatmaps were pooled to generate one combined IF heatmap that contained full IF data across the heatmap table.
Generation of 3D platforms
We have developed a 3D platform that is capable of constructing 3D models from IF heatmap tables. The algorithm utilizes a combination of the gradient search method and Bremmerman random search scheme that serves as a mechanism to overcome once the solution enters local minimums. When we employ variable step sizes, the platform is capable of arriving at the “best fit” final solution for a large heatmap up to 512x512 without noticeable performance degradation. The 3D Platform features 3D photos capturing and replaying post data processing and analysis.
Preparing computers to view 3D photos
Written in Java for portability, the software platform has been designed to take advantage of the graphic hardware resided in most PCs today. In order to view the captured 3D photos and live 3D rendering of heatmaps on a PC laptop or desktop, the user must download and install the Java 3D package "j3d-1_5_2-windows-i586.exe" available free at https://java3d.dev.java.net/binary-builds.html .
Viewing 3D Photos
Fig. 1. Three dimensional modeling of functional intra- and inter-chromosomal interactions reveals an active-versus -silent dipolar structure and the putative spatial distribution of multi chromosomes in nucleus.
(A ) Chr14x20a Dipolar interactive structure of chromosomes # 14 and # 20. Active (green) and silent (red) chromosomal sections (1 Mb each) are represented as color balls. Regions of intermediate gene expression are marked in yellow. White and grey balls denote the telomere section of the short and long arms, respectively.
(B ) Chr11x17a Location of the H19 ICR (purple ball on chromosomes #11) and NF1 (purple ball on chromosome #17) may allow a putative interchromosomal interaction
(C ) Chr18x19x20x21x22 Graphic representation of the co-localization active (green) regions of chromosomes 19, 20, 21, and 22. Gene-poor chromosome 18 is localized at a distance.
(D ) Chr1-22 and chrX Three dimensional models of 23 chromosomes. Five representative active (green) and five silent (red) segments on each chromosome depict the chromosomal dipolar structure.
Fig. S1 Three dimensional interactive model of human chromosomes at 1Mb resolution (GM06690 cell) showing “lattice folding” and dipolar structure. Transcriptionally-active and -silent chromosome segments (1Mb each) are marked as green (active), red (inactive), and yellow (neutral) according to the eigenvector and the DNAseI hypersensitivity data (1 ).
(A ) The raw dataset of experimental values (chromosome 11, Observed value ) produced an untangled, 3D coil of active (green) and silent (red) chromosome segments in separate domains. This is in contrast to an evenly-coiled structure from expected value in the absence of chromosomal interactions (1 ).
(B ) The ratio of observed/expected values formed a coarse 3D structure that transformed to a smoothly folding structure with the use of the Pearson correlation dataset.
(C, D ) Sections of the 3D model of chromosome 11 interactions that are generated from Pearson correlation data set, by step-wise increasing chromosome length from 1Mb to 120 Mb.