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Parikh vectors
4FKA_1 3OXL_1 7CLV_1 Letter Amino acid
0 29 5 R Arginine
2 14 12 N Asparagine
2 35 8 E Glutamic acid
2 50 29 L Leucine
1 13 12 T Threonine
2 20 7 Q Glutamine
1 21 31 G Glycine
0 24 11 D Aspartic acid
4 23 3 C Cysteine
0 9 4 H Histidine
2 19 12 I Isoleucine
0 16 6 M Methionine
0 19 11 P Proline
2 24 18 S Serine
0 25 18 A Alanine
0 29 14 K Lycine
0 18 5 F Phenylalanine
0 4 3 W Tryptophan
2 11 5 Y Tyrosine
1 25 8 V Valine 

4FKA_1|Chains A, C|Insulin A chain|Homo sapiens (9606)
>3OXL_1|Chain A|SET and MYND domain-containing protein 3|Homo sapiens (9606)
>7CLV_1|Chains A, B|TIM23 isoform 1|Saccharomyces cerevisiae (4932)
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 \(w=f(c)\)
4FKA , Knot 15 21 0.72 22 20 19 
GIVEQCCTSICSLYQLENYCN
3OXL , Knot 184 428 0.86 40 239 406 
MEPLKVEKFATANRGNGLRAVTPLRPGELLFRSDPLAYTVCKGSRGVVCDRCLLGKEKLMRCSQCRVAKYCSAKCQKKAWPDHKRECKCLKSCKPRYPPDSVRLLGRVVFKLMDGAPSESEKLYSFYDLESNINKLTEDRKEGLRQLVMTFQHFMREEIQDASQLPPAFDLFEAFAKVICNSFTICNAEMQEVGVGLYPSISLLNHSCDPNCSIVFNGPHLLLRAVRDIEVGEELTICYLDMLMTSEERRKQLRDQYCFECDCFRCQTQDKDADMLTGDEQVWKEVQESLKKIEELKAHWKWEQVLAMCQAIISSNSERLPDINIYQLKVLDCAMDACINLGLLEEALFYGTRTMEPYRIFFPGSHPVRGVQVMKVGKLQLHQGMFPQAMKNLRLAFDIMRVTHGREHSLIEDLILLLEECDANIRAS
7CLV , Knot 104 222 0.84 40 145 214 
MSWLFGDKTPTDDANAAVGGQDTTKPKELSLKQSLGFEPNINNIISGPGGMHVDTARLHPLAGLDKGVEYLDLEEEQLSSLEGSQGLIPSRGWTDDLCYGTGAVYLLGLGIGGFSGMMQGLQNIPPNSPGKLQLNTVLNHITKRGPFLGNNAGILALSYNIINSTIDALRGKHDTAGSIGAGALTGALFKSSKGLKPMGYSSAMVAAACAVWCSVKKRLLEK

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 \(c\).

\(|P_{f(4FKA_1)}(2) \setminus P_{f(3OXL_1)}(2)|=5\), \(|P_{f(3OXL_1)}(2) \setminus P_{f(4FKA_1)}(2)|=224\). 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 1:111000000100100100000
Pair \(Z_2\) Length of longest common subsequence
4FKA_1,3OXL_1 229 3
4FKA_1,7CLV_1 149 2
3OXL_1,7CLV_1 204 5

Newick tree

 
[
	3OXL_1:11.58,
	[
		4FKA_1:74.5,7CLV_1:74.5
	]:43.08
]

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 \((0.85)(0.8)(\frac{449 }{\log_{20} 449}-\frac{21}{\log_{20}21})=135.\)
Status Protein1 Protein2 d d1/2
Query variables 4FKA_1 3OXL_1 174 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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