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Parikh vectors
9GFX_1 6SWH_1 8IYZ_1 Letter Amino acid
7 2 2 W Tryptophan
10 15 12 N Asparagine
13 11 16 E Glutamic acid
24 13 21 K Lycine
2 6 5 M Methionine
12 18 17 T Threonine
17 14 10 P Proline
18 11 8 S Serine
13 18 9 A Alanine
19 9 19 D Aspartic acid
11 8 8 Q Glutamine
26 23 21 L Leucine
12 4 13 F Phenylalanine
1 0 2 C Cysteine
12 0 14 H Histidine
8 8 10 Y Tyrosine
7 11 6 R Arginine
22 11 23 G Glycine
9 11 12 I Isoleucine
17 12 17 V Valine 

9GFX_1|Chain A|Carbonic anhydrase 2|Homo sapiens (9606)
>6SWH_1|Chains A, D|Chaperone protein FimC|Escherichia coli (strain K12) (83333)
>8IYZ_1|Chain A|Green fluorescent protein|Aequorea victoria (6100)
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 \(w=f(c)\)
9GFX , Knot 112 260 0.79 40 176 249 
MSHHWGYGKHNGPEHWHKDFPIAKGERQSPVDIDTHTAKYDPSLKPLSVSYDQATSLRILNNGHAFNVEFDDSQDKAVLKGGPLDGTYRLIQFHFHWGSLDGQGSEHTVDKKKYAAELHLVHWNTKYGDFGKAVQQPDGLAVLGIFLKVGSAKPGLQKVVDVLDSIKTKGKSADFTNFDPRGLLPESLDYWTYPGSLTTPPLLECVTWIVLKEPISVSSEQVLKFRKLNFNGEGEPEELMVDNWRPAQPLKNRQIKASFK
6SWH , Knot 95 205 0.82 36 139 197 
GVALGATRVIYPAGQKQEQLAVTNNDENSTYLIQSWVENADGVKDGRFIVTPPLFAMKGKKENTLRILDATNNQLPQDRESLFWMNVKAIPSMDKSKLTENTLQLAIISRIKLYYRPAKLALPPDQAAEKLRFRRSANSLTLINPTPYYLTVTELNAGTRVLENALVPPMGESTVKLPSDAGSNITYRTINDYGALTPKMTGVME
8IYZ , Knot 110 245 0.82 40 160 229 
MVSKGEELFTGVVPILVELDGDVNGHKFSVSGEGEGDATYGKLTLKFICTTGKLPVPWPTLVTTLTWGVQCFARYPDHMKQHDFFKSAMPEGYVQERTIFFKDDGNYKTRAEVKFEGDTLVNRIELKGIDFKEDGNILGHKLEYNYFSDNVYITADKQKNGIKANFKIRHNIEDGGVQLADHYQQNTPIGDGPVLLPDNHYLSTQSKLSKDPNEKRDHMVLLEFVTAAGITLGMDELYKHHHHHH

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 \(c\).

\(|P_{f(9GFX_1)}(2) \setminus P_{f(6SWH_1)}(2)|=108\), \(|P_{f(6SWH_1)}(2) \setminus P_{f(9GFX_1)}(2)|=71\). 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 1:10001101000110010001111010000110100001000101011010000100101100101101010000001110111101000110101011010101000010000011010110100001011011001011111111101101011100110110010001001010010101111001001001101001111001011110011010000110100101010101001110010110110000101010
Pair \(Z_2\) Length of longest common subsequence
9GFX_1,6SWH_1 179 4
9GFX_1,8IYZ_1 168 4
6SWH_1,8IYZ_1 163 3

Newick tree

 
[
	9GFX_1:88.48,
	[
		8IYZ_1:81.5,6SWH_1:81.5
	]:6.98
]

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 \((0.85)(0.8)(\frac{465 }{\log_{20} 465}-\frac{205}{\log_{20}205})=75.7\)
Status Protein1 Protein2 d d1/2
Query variables 9GFX_1 6SWH_1 96 86
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]