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Parikh vectors
6JVJ_1 2MIZ_1 3ZHF_1 Letter Amino acid
11 2 9 Q Glutamine
12 12 7 E Glutamic acid
5 2 8 I Isoleucine
4 9 1 Y Tyrosine
2 4 1 C Cysteine
1 18 8 N Asparagine
16 9 7 G Glycine
5 8 0 M Methionine
13 15 8 V Valine
8 12 6 R Arginine
3 3 3 H Histidine
16 16 17 L Leucine
11 5 7 F Phenylalanine
12 11 3 D Aspartic acid
9 15 4 K Lycine
7 15 12 P Proline
5 19 7 S Serine
8 16 7 T Threonine
4 3 1 W Tryptophan
4 6 8 A Alanine 

6JVJ_1|Chains A, B|7,8-dihydro-8-oxoguanine triphosphatase|Homo sapiens (9606)
>2MIZ_1|Chain A|m04 immunoevasin|Murine cytomegalovirus (69156)
>3ZHF_1|Chain A|AP-1 COMPLEX SUBUNIT GAMMA-LIKE 2|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 \(w=f(c)\)
6JVJ , Knot 74 156 0.79 40 119 151 
MGASRLYTLVLVLQPQRVLLGMKKRGFGAGRWNGFGGKVQEGETIEDGARRELQEESGLTVDALHKVGQIVFEFVGEPELMDVHVFCTDSIQGTPVESDEMRPCWFQLDQIPFKDMWPDDSYWFPLLLQKKKFHGYFKFQGQDTILDYTLREVDTV
2MIZ , Knot 93 200 0.82 40 142 194 
MASSRNDNESEKMQKEYKEKMKYRHSLGCYFKGINPTKVPSSDPRTVLKCTLPDVKVNASWTLEWVVVNLHTSVDVTSYYESSPNSEPRFLRAILNFTPMHGLRTKNLLKVKDGFQVDNSTDNGNGGNLYVYPNATTGSADSVRCRLRMCPWTSNSKMTAPDEEMLRKMSEVLNLPNYGVPDLTPPRRDEFYTKNESPNT
3ZHF , Knot 62 124 0.80 38 96 119 
GGSAPIPDLKVFEREGVQLNLSFIRPPENPALLLITITATNFSEGDVTHFICQAAVPKSLQLQLQAPSGNTVPARGGLPITQLFRILNPNKAPLRLKLRLTYDHFHQSVQEIFEVNNLPVESWQ

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 \(c\).

\(|P_{f(6JVJ_1)}(2) \setminus P_{f(2MIZ_1)}(2)|=75\), \(|P_{f(2MIZ_1)}(2) \setminus P_{f(6JVJ_1)}(2)|=98\). 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 1:111001001111101001111100011111010111101001001001100010000110101100110111011101011010110000101011000010101101001110011100001111110000101010101000110001001001
Pair \(Z_2\) Length of longest common subsequence
6JVJ_1,2MIZ_1 173 3
6JVJ_1,3ZHF_1 149 4
2MIZ_1,3ZHF_1 162 3

Newick tree

 
[
	2MIZ_1:86.67,
	[
		6JVJ_1:74.5,3ZHF_1:74.5
	]:12.17
]

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 \((0.85)(0.8)(\frac{356 }{\log_{20} 356}-\frac{156}{\log_{20}156})=60.5\)
Status Protein1 Protein2 d d1/2
Query variables 6JVJ_1 2MIZ_1 77 69
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]