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Parikh vectors
5OVY_1 7GDJ_1 8IHT_1 Letter Amino acid
7 11 7 I Isoleucine
7 10 2 M Methionine
6 13 6 P Proline
4 3 0 W Tryptophan
30 17 20 A Alanine
20 26 6 G Glycine
9 17 4 F Phenylalanine
8 16 6 S Serine
15 27 6 V Valine
22 11 18 R Arginine
1 12 0 C Cysteine
6 14 8 Q Glutamine
8 7 2 H Histidine
20 29 12 L Leucine
4 11 3 Y Tyrosine
6 21 1 N Asparagine
12 17 4 D Aspartic acid
23 9 7 E Glutamic acid
5 11 13 K Lycine
9 24 10 T Threonine 

5OVY_1|Chains A, B|Putative transcriptional regulator, TetR family|Mycobacterium abscessus (strain ATCC 19977 / DSM 44196 / CIP 104536 / JCM 13569 / NCTC 13031 / TMC 1543) (561007)
>7GDJ_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>8IHT_1|Chains A, E|Histone H3|Xenopus laevis (8355)
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 \(w=f(c)\)
5OVY , Knot 104 222 0.84 40 153 218 
GMNGREVAHRPLRKDAERNRKRVIAAARELFAVHGLESTLNEVAHHAGLGVGTVYRRFPTKEALFEAIYVDGMDQLSGLAEAALRHENSWEGFEWFVHQMCEITATNRGLREIAFSKAHGGDHVEAGRARLLPLLSKVVERAQEDGYLRPEASATDMPFFGVLTGAVSEFAGEVNADLWRRYMAILIEGMRRRDDQERLEVDALDEAQIDAAMTTWQPAGSG
7GDJ , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
8IHT , Knot 65 135 0.78 36 100 126 
ARTKQTARKSTGGKAPRKQLATKAARKSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEASEAYLVALFEDTNLAAIHAKRVTIMPKDIQLARRIRGERA

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 \(c\).

\(|P_{f(5OVY_1)}(2) \setminus P_{f(7GDJ_1)}(2)|=66\), \(|P_{f(7GDJ_1)}(2) \setminus P_{f(5OVY_1)}(2)|=109\). 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 1:110100110011000100000011111001111011000100110011111101000110001110110101100101110111000001011011100100101000110011100101100101101011111001100100010101010100111111101110011101010110001111101100000000101011001010111001011101
Pair \(Z_2\) Length of longest common subsequence
5OVY_1,7GDJ_1 175 5
5OVY_1,8IHT_1 135 4
7GDJ_1,8IHT_1 186 5

Newick tree

 
[
	7GDJ_1:96.70,
	[
		5OVY_1:67.5,8IHT_1:67.5
	]:29.20
]

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 \((0.85)(0.8)(\frac{528 }{\log_{20} 528}-\frac{222}{\log_{20}222})=87.8\)
Status Protein1 Protein2 d d1/2
Query variables 5OVY_1 7GDJ_1 112 96
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]