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Parikh vectors
9MYP_1 5WSH_1 5CKY_1 Letter Amino acid
12 23 16 A Alanine
9 2 26 N Asparagine
13 22 23 E Glutamic acid
7 11 10 P Proline
8 20 10 G Glycine
16 17 45 L Leucine
4 5 6 M Methionine
5 8 16 F Phenylalanine
11 23 20 R Arginine
6 17 7 Q Glutamine
6 14 30 S Serine
6 23 14 T Threonine
10 17 15 V Valine
6 18 15 D Aspartic acid
10 4 6 C Cysteine
10 13 2 H Histidine
8 4 27 I Isoleucine
14 10 27 K Lycine
2 10 3 W Tryptophan
4 14 6 Y Tyrosine 

9MYP_1|Chains A, B, C|HORMA domain-containing protein|Patiria miniata (46514)
>5WSH_1|Chain A|HLA class I histocompatibility antigen, A-2 alpha chain|Homo sapiens (9606)
>5CKY_1|Chain A[auth O]|Transcription termination factor 1, mitochondrial|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 \(w=f(c)\)
9MYP , Knot 82 167 0.83 40 131 160 
MKSSHHHHHHENLYFQSNANIVRCPCGCNEDDGLMIRCEECKLWQHAVCFAIISEDDAPEQHVCNQCAKIVPRHMKPTDPYLTTLAPVVLQATCLWRRALLAATEMDRILVPNFSRRLGVEITVAHGLINRLEKEGYCQNAKGKRLGRLVNKEKLKSEGFKKYFEKK
5WSH , Knot 122 275 0.83 40 183 263 
GSHSMRYFFTSVSRPGRGEPRFIAVGYVDDTQFVRFDSDAASQRMEPRAPWIEQEGPEYWDGETRKVKAHSQTHRVDLGTLRGYYNQSEAGSHTVQRMYGCDVGSDWRFLRGYHQYAYDGKDYIALKEDLRSWTAADMAAQTTKHKWEAAHVAEQLRAYLEGTCVEWLRRYLENGKETLQRTDAPKTHMTHHAVSDHEATLRCWALSFYPAEITLTWQRDGEDQTQDTELVETRPAGDGTFQKWVAVVVPSGQEQRYTCHVQHEGLPKPLTLRWE
5CKY , Knot 139 324 0.82 40 178 308 
EDLLKNLLTMGVDIDMARKRQPGVFHRMITNEQDLKMFLLSKGASKEVIASIISRYPRAITRTPENLSKRWDLWRKIVTSDLEIVNILEASPESFFRSNNNLNLENNIKFLYSVGLTRKCLCRLLTNAPRTFSNSLDLNKQMVEFLQAAGLSLGHNDPADFVRKIIFKNPFILIQSTKRVKANIEFLRSTFNLNSEELLVLICGPGAEILDLSNDYARRSYANIKEKLFSLGCTEEEVQKFVLSYPDVIFLAEKKFNDKIDCLMEENISISQIIENPRVLDSSISTLKSRIKELVNAGCNLSTLNITLLSWSKKRYEAKLKKLS

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 \(c\).

\(|P_{f(9MYP_1)}(2) \setminus P_{f(5WSH_1)}(2)|=71\), \(|P_{f(5WSH_1)}(2) \setminus P_{f(9MYP_1)}(2)|=123\). 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 1:10000000000010100010110010100000111100000011001101111000011000100001011100101001010011111101001100111110010011110100011101011011100100010000101001101100001000110001000
Pair \(Z_2\) Length of longest common subsequence
9MYP_1,5WSH_1 194 3
9MYP_1,5CKY_1 171 4
5WSH_1,5CKY_1 203 3

Newick tree

 
[
	5WSH_1:10.46,
	[
		9MYP_1:85.5,5CKY_1:85.5
	]:17.96
]

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 \((0.85)(0.8)(\frac{442 }{\log_{20} 442}-\frac{167}{\log_{20}167})=81.3\)
Status Protein1 Protein2 d d1/2
Query variables 9MYP_1 5WSH_1 107 85
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]