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Parikh vectors
2CHL_1 7FZL_1 8FDP_1 Letter Amino acid
17 1 0 P Proline
22 2 0 Y Tyrosine
26 14 0 K Lycine
13 5 0 M Methionine
17 8 0 I Isoleucine
17 6 0 F Phenylalanine
17 2 0 Q Glutamine
26 11 3 G Glycine
4 2 3 C Cysteine
21 9 0 E Glutamic acid
16 10 0 S Serine
15 12 3 T Threonine
2 2 0 W Tryptophan
15 17 0 V Valine
13 4 0 N Asparagine
21 11 0 D Aspartic acid
15 2 0 H Histidine
38 5 0 L Leucine
14 6 3 A Alanine
22 6 0 R Arginine 

2CHL_1|Chain A|CASEIN KINASE I ISOFORM GAMMA-3|HOMO SAPIENS (9606)
>7FZL_1|Chain A|Fatty acid-binding protein, adipocyte|Homo sapiens (9606)
>8FDP_1|Chains A[auth B], B[auth C]|DNA (5'-D(*CP*GP*CP*AP*AP*AP*TP*TP*TP*GP*CP*G)-3')|Homo sapiens (9606)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
2CHL , Knot 148 351 0.82 40 216 334 
MHHHHHHSSGVDLGTENLYFQSMGVLMVGPNFRVGKKIGCGNFGELRLGKNLYTNEYVAIKLEPMKSRAPQLHLEYRFYKQLGSGDGIPQVYYFGPCGKYNAMVLELLGPSLEDLFDLCDRTFSLKTVLMIAIQLISRMEYVHSKNLIYRDVKPENFLIGRPGNKTQQVIHIIDFALAKEYIDPETKKHIPYREHKSLTGTARYMSINTHLGKEQSRRDDLEALGHMFMYFLRGSLPWQGLKADTLKERYQKIGDTKRATPIEVLCENFPEMATYLRYVRRLDFFEKPDYDYLRKLFTDLFDRKGYMFDYEYDWIGKQLPTPVGAVQQDPALSSNREAHQHRDKMQQSKNQ
7FZL , Knot 69 135 0.83 40 104 129 
GSHMCDAFVGTWKLVSSENFDDYMKEVGVGFATRKVAGMAKPNMIISVNGDVITIKSESTFKNTEISFILGQEFDEVTADDRKVKSTITLDGGVLVHVQKWDGKSTTIKRKREDDKLVVECVMKGVTSTRVYERA
8FDP , Knot 6 12 0.41 8 7 10 
CGCAAATTTGCG

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(2CHL_1)}(2) \setminus P_{f(7FZL_1)}(2)|=156\), \(|P_{f(7FZL_1)}(2) \setminus P_{f(2CHL_1)}(2)|=44\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:100000000110110001010011111111010110011010110101100100000111010110001101010001000110101110100111010001111011110100110100001010011111101100100100001100010100111101100000110110111100010100000110000001010100101000110000000010111011101101011101101001000000110000101101100011011001001001011001000010011001100010110000011100110111110001110000010000001000000
Pair \(Z_2\) Length of longest common subsequence
2CHL_1,7FZL_1 200 3
2CHL_1,8FDP_1 215 3
7FZL_1,8FDP_1 107 2

Newick tree

 
[
	2CHL_1:11.83,
	[
		7FZL_1:53.5,8FDP_1:53.5
	]:62.33
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{486 }{\log_{20} 486}-\frac{135}{\log_{20}135})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 2CHL_1 7FZL_1 133 92
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]