Figure 1.
Loop Entropy Factor Estimation
The exact loop entropy factor for σ = 3.5 · 10−5, α = 1.75, and d = 0 is plotted (red) as a function of loop size, together with two Fixman–Freire approximations: a 10-exponentials approximation (blue), which is valid up to loop size about 104, and a 21-exponentials approximation (green), which is valid up to loop size about 108.
Table 1.
Overall Satistics of the Human Genomic Melting Map
Figure 2.
Correlations of Melting Temperature (Tm) with G + C Content
The correlation coefficients between GC content and Tm are plotted as a function of window sizes. For each chromosome, excluding the segments which contain unknown bases (N's), the correlation coefficient was calculated from all pairs of GC content and average Tm over all nonoverlapping segments of a given window size. Across the chromosomes, the average correlation coefficients and SDs were calculated for each window size. The figure shows the average correlations with SDs (error bars) for window sizes from 10 bp to 1 Mbp for the human chromosomes (red) and the randomized chromosomes (blue).
Table 2.
Correlations between Melting Temperature and SNP Frequency, Recombination Rate
Figure 3.
EpiGRAPH-Generated Diagrams Comparing Genomic Regions with Distinct Melting Profiles
Displays boxplots comparing two genomic features between regions of high and low melting temperature (A) and flat and nonflat melting segments (B). Standard boxplots are drawn for the region itself and for ten windows surrounding the region, from −20 Kbp to +20 Kbp (x-axis), in order to capture neighborhood effects. The y-axis shows averages and distribution of the analyzed genomic feature. For each window, two boxplots are drawn, one for each class of melting profiles.
(A) Regions are characterized by the extreme melting temperatures observed throughout the human genome. “Class 0” comprises 20 regions having low melting temperatures (below 50 °C in all cases), while “class 1” comprises 20 cases having high melting temperature (above 90 °C in all cases). Comparison with the average solvent-accessible surface area of the DNA (as predicted for each base pair using sequence trimers for which solvent accessibility has been established experimentally by the hydroxyl radical method [64]) shows that regions of high melting temperature exhibit substantially higher values than regions of low melting temperature. This is true not only for the region itself (center boxplot), but to a lesser extent also for its sequence neighborhood.
(B) Regions are characterized by a flat/nonflat segmentation algorithm of the melting profile. “Class 0” contains 50 flat segments having an end-to-end step height of ±0.11 °C or less, while “class 1” contains 50 nonflat segments defined as having an end-to-end step height of ±6 °C or more. All segments were taken from Chromosome 21, exhibit an equal melting temperature of 68 °C and a segment length of 19 or 20 bps. Comparison with the average length of Alu repeat overlap per 1,000 base pairs (as identified by RepeatMasker) shows that flat regions are typically free of Alu repeats, while nonflat regions frequently exhibit substantial overlap with Alu repeats.
Figure 4.
Scatter Plot of Melting Temperature versus GC Content of Flat Melting Segments
Using Chromosome 21, the relationship between local GC content and melting temperature was examined for all flat segments of 50 bps. Figure 4 shows the scatter plot of melting temperature versus GC content. Each data point in this figure represents a 50-bp flat segment. The red dots represent those segments that have higher melting temperatures (Tm) in its neighboring regions at both sides (denoted as category I). The blue dots represent those that have lower Tm in its neighbors (denoted as category III). And, the green dots represent those that have lower Tm in one side neighbor and higher Tm in another (denoted as category II).
Figure 5.
Local spectral analysis was performed on several randomly chosen 2-bp segments from various chromosomes. The segments were further divided into subsegments of 20 Kbp for which spectral analysis was performed individually. Wavelengths in the range of 2 bp to 1,024 bp, in steps of 2 bp, were assessed for each segment. This figure shows a representative segment (chr21: 39,620,001–39,640,000). The main part of the figure shows a heat map representation of the results from the spectral analysis. Below the main part, the power spectrum along the bases of the segment is displayed, followed by annotations of repeat structures and exons residing in the given segment. Below this again, the GC content profile (based on 10-p nonoverlapping windows), and then the melting map (as extracted from the corresponding region of the genomic melting map), are shown. The black dots in the melting curve represent the locations where known SNPs occur. On the right hand side, the power spectrum over the wavelengths is displayed; normalized to a value of 1 for the maximum.