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Parikh vectors
8VVK_1 5OHZ_1 1EOH_1 Letter Amino acid
8 51 16 A Alanine
13 44 8 R Arginine
13 9 8 N Asparagine
29 45 32 L Leucine
12 18 7 F Phenylalanine
23 12 7 I Isoleucine
18 23 10 S Serine
8 5 4 C Cysteine
8 14 13 Q Glutamine
20 31 18 G Glycine
7 10 2 H Histidine
10 15 12 Y Tyrosine
12 29 12 D Aspartic acid
17 27 10 E Glutamic acid
22 7 12 K Lycine
1 9 2 M Methionine
9 30 11 P Proline
22 23 9 T Threonine
1 19 2 W Tryptophan
15 27 14 V Valine 

8VVK_1|Chains A, B|GP38|Crimean-Congo hemorrhagic fever virus (652961)
>5OHZ_1|Chains A, B, C, D|Hydrolase|Mycobacterium hassiacum DSM 44199 (1122247)
>1EOH_1|Chains A, B, C, D, E, F, G, H|GLUTATHIONE S-TRANSFERASE|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 \(w=f(c)\)
8VVK , Knot 117 268 0.81 40 170 256 
NLKMEIILTLSQGLKKYYGKILRLLQLTLEEDTEGLLEWCKRNLGLDCDDTFFQKRIEEFFITGEGHFNEVLQFRTPGTLSTTESTPAGLPTAEPFKSYFAKGFLSIDSGYYSAKCYSGTSNSGLQLINITRHSTRIVDTPGPKITNLKTINCINLKASIFKEHREVEINVLLPQVAVNLSNCHVVIKSHVCDYSLDIDGAVRLPHIYHEGVFIPGTYKIVIDKKNKLNDRCTLFTDCVIKGREVRKGQSVLRQYKTEIRIGKASTGS
5OHZ , Knot 185 448 0.84 40 232 421 
GAMPHDPSFTPTQLAARAAYLLRGNDLGTMTTAAPLLYPHMWSWDAAFVAIGLAPLSVERAVVELDTLLSAQWRNGMIPHIVFANGVDGYFPGPARWATATLADNAPRNRLTSGITQPPVHAIAVQRILEHARTRGRSTRAVAEAFLDRRWGDLMRWHRWLAECRDRNERGRITLYHGWESGMDNSPRWDSAYANVVPGKLPEYQRADNVIITDPSQRPSDGEYDRYLWLLEEMKAVRYDDERLPSVMSFQVEDVFFSAIFSVACQVLAEIGEDYKRPHADVKDLYLWAERFRAGVVETTDQRTGAARDFDVLAEKWLVTETAAQFAPLLCGGLPHDRERALLKLLEGPRFCGHPDLKYGLIPSTSPVSRDFRPREYWRGPVWPVLTWLFSWCFARRGWAERARLLRQEGLRQASDGSFAEYYEPFTGEPLGSMQQSWTAAAVLDWLG
1EOH , Knot 97 209 0.82 40 137 200 
PPYTVVYFPVRGRCAALRMLLADQGQSWKEEVVTVETWQEGSLKASCLYGQLPKFQDGDLTLYQSNTILRHLGRTLGLYGKDQQEAALVDMVNDGVEDLRCKYISLIYTNYEAGKDDYVKALPGQLKPFETLLSQNQGGKTFIVGDQISFAAYNLLDLLLIHEVLAPGCLDAFPLLSAYVGRLSARPKLKAFLASPEYVNLPINGNGKQ

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 \(c\).

\(|P_{f(8VVK_1)}(2) \setminus P_{f(5OHZ_1)}(2)|=65\), \(|P_{f(5OHZ_1)}(2) \setminus P_{f(8VVK_1)}(2)|=127\). 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 1:0101011101001100001011011010100000111010000111000001100010011101010100110100110100000011111010110001101110100100010000100001101101000000110011101001001001010101100000101011110111010000111000100001010111011010001111110001110000010000011000110100100100110000001011010010
Pair \(Z_2\) Length of longest common subsequence
8VVK_1,5OHZ_1 192 3
8VVK_1,1EOH_1 173 4
5OHZ_1,1EOH_1 199 4

Newick tree

 
[
	5OHZ_1:10.24,
	[
		8VVK_1:86.5,1EOH_1:86.5
	]:14.74
]

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 \((0.85)(0.8)(\frac{716 }{\log_{20} 716}-\frac{268}{\log_{20}268})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 8VVK_1 5OHZ_1 159 126.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]