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Parikh vectors
5JLG_1 5QGU_1 6YIZ_1 Letter Amino acid
4 3 2 M Methionine
4 14 11 P Proline
10 11 10 T Threonine
4 10 19 R Arginine
5 13 14 D Aspartic acid
8 4 4 C Cysteine
3 9 13 I Isoleucine
12 14 18 A Alanine
10 6 10 N Asparagine
3 9 10 F Phenylalanine
15 4 21 S Serine
10 12 5 K Lycine
7 7 9 Q Glutamine
5 11 14 E Glutamic acid
3 11 12 G Glycine
2 23 27 L Leucine
4 9 5 H Histidine
0 0 2 W Tryptophan
6 8 7 Y Tyrosine
9 18 16 V Valine 

5JLG_1|Chains A, B|Ribonuclease pancreatic|Bos taurus (9913)
>5QGU_1|Chain A|Peroxisomal coenzyme A diphosphatase NUDT7|Homo sapiens (9606)
>6YIZ_1|Chains A, B|Transcriptional regulator MvfR|Pseudomonas aeruginosa (strain ATCC 15692 / DSM 22644 / CIP 104116 / JCM 14847 / LMG 12228 / 1C / PRS 101 / PAO1) (208964)
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 \(w=f(c)\)
5JLG , Knot 64 124 0.83 38 107 121 
KETAAAKFERQHMDSSTSAASSSNYCNQMMKSRNLTKDRCKPVNTFVHESLADVQAVCSQKNVACKNGQTNCYQSYSTMSITDCRETGSSKYPNCAYKTTQANKHIIVACEGNPYVPVHFDASV
5QGU , Knot 92 196 0.82 38 147 187 
SMLDDAKARLRKYDIGGKYSHLPYNKYSVLLPLVAKEGKLHLLFTVRSEKLRRAPGEVCFPGGKRDPTDMDDAATALREAQEEVGLRPHQVEVVCCLVPCLIDTDTLITPFVGLIDHNFQAQPNPAEVKDVFLVPLAYFLHPQVHDQHYVTRLGHRFINHIFEYTNPEDGVTYQIKGMTANLAVLVAFIILEKKPT
6YIZ , Knot 106 229 0.83 40 151 217 
GPRNLRVLLDTAIPPSFCDTVSSVLLDDFNMVSLIRTSPADSLATIKQDNAEIDIAITIDEELKISRFNQCVLGYTKAFVVAHPQHPLCNASLHSIASLANYRQISLGSRSGQHSNLLRPVSDKVLFVENFDDMLRLVEAGVGWGIAPHYFVEERLRNGTLAVLSELYEPGGIDTKVYCYYNTALESERSFLRFLESARQRLRELGRQRFDDAPAWQPSIVETAQRRSG

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 \(c\).

\(|P_{f(5JLG_1)}(2) \setminus P_{f(5QGU_1)}(2)|=69\), \(|P_{f(5QGU_1)}(2) \setminus P_{f(5JLG_1)}(2)|=109\). 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 1:0001110100001000001100000000110000100000011001100011010110000011000100000000001010000001000010010000010001111001010111010101
Pair \(Z_2\) Length of longest common subsequence
5JLG_1,5QGU_1 178 2
5JLG_1,6YIZ_1 178 3
5QGU_1,6YIZ_1 166 4

Newick tree

 
[
	5JLG_1:90.91,
	[
		5QGU_1:83,6YIZ_1:83
	]:7.91
]

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 \((0.85)(0.8)(\frac{320 }{\log_{20} 320}-\frac{124}{\log_{20}124})=60.6\)
Status Protein1 Protein2 d d1/2
Query variables 5JLG_1 5QGU_1 78 64.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]