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Parikh vectors
4PGT_1 5JKB_1 4RTZ_1 Letter Amino acid
8 11 2 R Arginine
18 14 5 G Glycine
32 18 5 L Leucine
3 3 1 M Methionine
11 18 2 P Proline
8 12 3 N Asparagine
13 9 2 Q Glutamine
10 17 4 E Glutamic acid
2 6 2 H Histidine
6 5 2 I Isoleucine
9 6 7 T Threonine
13 8 4 D Aspartic acid
12 11 2 K Lycine
12 5 4 Y Tyrosine
15 10 3 V Valine
15 12 3 A Alanine
4 16 0 C Cysteine
7 11 2 F Phenylalanine
10 17 6 S Serine
2 12 2 W Tryptophan 

4PGT_1|Chains A, B|PROTEIN (GLUTATHIONE S-TRANSFERASE)|Homo sapiens (9606)
>5JKB_1|Chains A, B, C, D|Sperm-egg fusion protein Juno|Homo sapiens (9606)
>4RTZ_1|Chain A|Proto-oncogene tyrosine-protein kinase Src|Gallus gallus (9031)
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 \(w=f(c)\)
4PGT , Knot 97 210 0.82 40 138 201 
MPPYTVVYFPVRGRCAALRMLLADQGQSWKEEVVTVETWQEGSLKASCLYGQLPKFQDGDLTLYQSNTILRHLGRTLGLYGKDQQEAALVDMVNDGVEDLRCKYVSLIYTNYEAGKDDYVKALPGQLKPFETLLSQNQGGKTFIVGDQISFADYNLLDLLLIHEVLAPGCLDAFPLLSAYVGRLSARPKLKAFLASPEYVNLPINGNGKQ
5JKB , Knot 106 221 0.86 40 169 217 
RSPWGDELLNICMNAKHHKRVPSPEDKLYEECIPWKDNACCTLTTSWEAHLDVSPLYNFSLFHCGLLMPGCRKHFIQAICFYECSPNLGPWIQPVGSLGWEVAPSGQGERVVNVPLCQEDCEEWWEDCRMSYTCKSNWRGGWDWSQGKNRCPKGAQCLPFSHYFPTPADLCEKTWSNSFKASPERRNSGRCLQKWFEPAQGNPNVAVARLFASEFLEVLFQ
4RTZ , Knot 36 61 0.80 38 56 59 
GSHMTFVALYDYESRTETDLSFKKGERLQIVNNTEGDWWLAHSLTTGQTGYIPSNYVAPSD

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 \(c\).

\(|P_{f(4PGT_1)}(2) \setminus P_{f(5JKB_1)}(2)|=69\), \(|P_{f(5JKB_1)}(2) \setminus P_{f(4PGT_1)}(2)|=100\). 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 1:111001101110100111011110010010001101001001010100101011010010101000001100110011101000001111011001100100001011000001100001011110101100110000110011110010110001101111001111101011111010110101010101111010010111010100
Pair \(Z_2\) Length of longest common subsequence
4PGT_1,5JKB_1 169 4
4PGT_1,4RTZ_1 142 2
5JKB_1,4RTZ_1 173 4

Newick tree

 
[
	5JKB_1:89.82,
	[
		4PGT_1:71,4RTZ_1:71
	]:18.82
]

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 \((0.85)(0.8)(\frac{431 }{\log_{20} 431}-\frac{210}{\log_{20}210})=64.7\)
Status Protein1 Protein2 d d1/2
Query variables 4PGT_1 5JKB_1 85 80
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]