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Parikh vectors
6PVE_1 5OUZ_1 8YGK_1 Letter Amino acid
10 10 8 R Arginine
7 7 10 N Asparagine
8 1 0 C Cysteine
19 8 15 G Glycine
10 9 16 I Isoleucine
15 5 8 P Proline
20 2 23 K Lycine
5 5 4 M Methionine
11 9 12 F Phenylalanine
29 15 17 S Serine
18 7 19 V Valine
19 24 24 A Alanine
10 16 8 Q Glutamine
18 11 26 E Glutamic acid
9 3 1 H Histidine
36 18 16 L Leucine
10 12 27 T Threonine
3 2 1 W Tryptophan
12 5 11 Y Tyrosine
14 13 18 D Aspartic acid 

6PVE_1|Chains A, B, C, D|NNMT protein|Homo sapiens (9606)
>5OUZ_1|Chain A|Ferritin|Synechococcus sp. CC9311 (64471)
>8YGK_1|Chains A[auth C], B[auth D]|SPR|Bacillus subtilis A29 (2508883)
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 \(w=f(c)\)
6PVE , Knot 123 283 0.81 40 179 271 
MGSSHHHHHHSSGLVPRGSMESGFTSKDTYLSHFNPRDYLEKYYKFGSRHSAESQILKHLLKNLFKIFCLDGVKGDLLIDIGSGPTIYQLLSACESFKEIVVTDYSDQNLQELEKWLKAAPAAFDWSPVVTYVCDLEGNRVKGPEKEEKLRQAVKQVLKCDVTQSQPLGAVPLPPADCVLSTLCLDAACPDLPTYCRALRNLGSLLKPGGFLVIMDALKSSYYMIGEQKFSSLPLGREAVEAAVKEAGYTIEWFEVISQSYSSTMANNEGLFSLVARKLSRPL
5OUZ , Knot 87 182 0.83 40 134 175 
MATDVAQGPNGRALAESMNPDLLSAIQQHISIERYASVTFLAMSIWCAERELAGFYQFFDGEAKDEQSHAVHFTQYLIARSQSNDLQTLDAPRQNWDSLASLMATAFQMEADTTSSIQSVYALAERNSDTRTTVFLDPLIEAQIQSEDQFAYLLGRVKFANGDPTALLVIDNELRAGQTQRG
8YGK , Knot 117 264 0.82 38 167 260 
MKTVIQDTADVYFKRKSDGKLVFTAEAQTASFSQAISEEKLRGGIGNKPLYILKSEKEINLTVKNAFFDLEWLAMTQGETIQEETKVKVFDREHGLIVDDTNKVTLKGKPVSDVTFYNKKGLTYKIAVSTDGTYTIPTAFAAAKDKLTAVYQIEKVGRRLAIKASKFSERYEVEYRTIAYNPDTEEVYSDIYIQFPNVSPSGEFEMSLENGNALAPEIKFEALADTDTDEMAVVIEASRDENTAAPVEDTTGSTQSSDLGGTTE

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 \(c\).

\(|P_{f(6PVE_1)}(2) \setminus P_{f(5OUZ_1)}(2)|=104\), \(|P_{f(5OUZ_1)}(2) \setminus P_{f(6PVE_1)}(2)|=59\). 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 1:1100000000001111010100110000001001010001000001100001000110011001101101011010111011011010011010001001110000000100100110111111010111001001010010110000010011001100010000111111111100110010101101011000011001101101111111101100000111000100111100110111001100101101100000001100011101110010011
Pair \(Z_2\) Length of longest common subsequence
6PVE_1,5OUZ_1 163 4
6PVE_1,8YGK_1 162 5
5OUZ_1,8YGK_1 155 3

Newick tree

 
[
	6PVE_1:82.46,
	[
		8YGK_1:77.5,5OUZ_1:77.5
	]:4.96
]

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 \((0.85)(0.8)(\frac{465 }{\log_{20} 465}-\frac{182}{\log_{20}182})=82.9\)
Status Protein1 Protein2 d d1/2
Query variables 6PVE_1 5OUZ_1 106 85.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]