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Parikh vectors
7ZJP_1 3BFU_1 2EGO_1 Letter Amino acid
9 19 5 A Alanine
10 13 3 D Aspartic acid
17 20 9 E Glutamic acid
9 2 4 H Histidine
6 10 1 M Methionine
11 17 8 T Threonine
1 4 0 W Tryptophan
17 18 9 V Valine
10 16 6 I Isoleucine
18 20 9 L Leucine
15 7 3 F Phenylalanine
10 13 2 Y Tyrosine
6 4 0 C Cysteine
12 25 10 G Glycine
15 28 3 K Lycine
7 7 2 P Proline
10 10 7 R Arginine
13 10 4 N Asparagine
9 3 6 Q Glutamine
15 17 5 S Serine 

7ZJP_1|Chains A, B|Transcriptional enhancer factor TEF-1|Homo sapiens (9606)
>3BFU_1|Chains A, B, C, D|Glutamate receptor 2|Rattus norvegicus (10116)
>2EGO_1|Chains A, B|General receptor for phosphoinositides 1-associated scaffold protein|Rattus norvegicus (10116)
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 \(w=f(c)\)
7ZJP , Knot 103 220 0.84 40 162 213 
GPRSIGTTKLRLVEFSAFLEQQRDPDSYNKHLFVHIGHANHSYSDPLLESVDIRQIYDKFPEKKGGLKELFGKGPQNAFFLVKFWADLNCNIQDDAGAFYGVTSQYESSENMTVTCSTKVCSFGKQVVEKVETEYARFENGRFVYRINRSPMCEYMINFIHKLKHLPEKYMMNSVLENFTILLVVTNRDTQETLLCMACVFEVSNSEHGAQHHIYRLVKD
3BFU , Knot 122 263 0.86 40 173 253 
GANKTVVVTTILESPYVMMKKNHEMLEGNERYEGYCVDLAAEIAKHCGFKYKLTIVGDGKYGARDADTKIWNGMVGELVYGKADIAIAPLTITLVREEVIDFSKPFMSLGISIMIKKGTPIESAEDLSKQTEIAYGTLDSGSTKEFFRRSKIAVFDKMWTYMRSAEPSVFVRTTAEGVARVRKSKGKYAYLLESTMNEYIEQRKPCDTMKVGGNLDSKGYGIATPKGSSLGNAVNLAVLKLNEQGLLDKLKNKWWYDKGECGS
2EGO , Knot 50 96 0.79 36 77 93 
GSQQRKVLTLEKGDNQTFGFEIQTYGLHHREEQRVEMVTFVARVHESSPAQLAGLTPGDTIASVNGLNVEGIRHREIVDIIKASGNVLRLETLYGT

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 \(c\).

\(|P_{f(7ZJP_1)}(2) \setminus P_{f(3BFU_1)}(2)|=89\), \(|P_{f(3BFU_1)}(2) \setminus P_{f(7ZJP_1)}(2)|=100\). 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 1:1100110001011010111000001000000111011010000001110010100100011000111001110110011111011101000100011110110000000001010000010011001100100001010010110010001100011011001001100011001100101111100000000110110110100000110001001100
Pair \(Z_2\) Length of longest common subsequence
7ZJP_1,3BFU_1 189 4
7ZJP_1,2EGO_1 163 3
3BFU_1,2EGO_1 152 4

Newick tree

 
[
	7ZJP_1:91.95,
	[
		2EGO_1:76,3BFU_1:76
	]:15.95
]

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 \((0.85)(0.8)(\frac{483 }{\log_{20} 483}-\frac{220}{\log_{20}220})=76.1\)
Status Protein1 Protein2 d d1/2
Query variables 7ZJP_1 3BFU_1 99 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]