Example

Sequence#

Consider the 500 nucleotides of sequences below. It’s enough to wrap at least two eukaryotic nucleosomes.

CCAACATTTTGACTTTTTGGGAGGGCACTAGCACCTATCTACCCTGAATC
TAAGTGCTAACAGGAAAGGATGCCAGATTGCATGCCTGCTGATAAAGCCA
CAGTTTGGACTGTCACTCAATCACCATCGTTCCTCCTGTGACTCAGTATA
ACAAGATTGGGAGAATACTCTACAGTTCCTGATTCCCCCACAGAAGTGAA
AGAGAATACTGCAACACACATTCAGTGTTCAGACTTCAGGGGAGTTGCCA
AGTGATTGTTTTCTGTCTTGCCTGAATTTAAGCGTTAACAGGAAAGCTTT
CCAGGTTGGGGATATTAAGAATAAATGAGTTGAGGAAGTTTGGGTTAGCA
TACATTCACTTATCATATCATCCTTCCCTGGATCAATATGCAATGAGTGG
GACAAAACCCTCAACTCCTGGCTTCCCCTTGGAGAAGGAAAAAGCTGGAG
TGTGCATCCAGAATTTCAACTTTTCCCAGTCAGCCTGATGGACTGTTTTC

This sequence will be \(S\) with \(n=500\). Now let’s consider \(W\), with \(w_1 = \text{CCA}\), \(w_2 = \text{CAA}\), and so on until \(w_{498} = \text{TTC}\).

Parameters#

For this example, we’ll use a typical set of parameters:

• \(a = 5\)
• \(b = 15\)
• \(c = 51\)
• \(\lambda = 0.33335\)
• \(\rho = \rho^\beta\)

3-mer step values and coordinates#

Below is a table of the sequence values, 3-mers, matrix values, and finally the calculated coordinates. Note that because multiple bases may be used in some of the calculations, some of the values at the edges are missing.

Rolling mean, curvature, and symmetry#