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Parikh vectors
2EVD_1 1GJO_1 1FKZ_1 Letter Amino acid
3 6 6 C Cysteine
4 5 0 H Histidine
24 31 0 L Leucine
10 9 0 F Phenylalanine
6 11 0 S Serine
10 13 0 N Asparagine
8 8 0 Q Glutamine
14 13 0 I Isoleucine
18 23 0 K Lycine
10 13 0 Y Tyrosine
9 20 2 G Glycine
6 18 0 M Methionine
11 18 0 P Proline
11 17 1 T Threonine
3 5 0 W Tryptophan
20 20 2 A Alanine
6 16 0 R Arginine
8 22 0 D Aspartic acid
16 26 0 E Glutamic acid
12 22 0 V Valine 

2EVD_1|Chain A|Glycolipid transfer protein|Homo sapiens (9606)
>1GJO_1|Chain A|FIBROBLAST GROWTH FACTOR RECEPTOR 2|HOMO SAPIENS (9606)
>1FKZ_1|Chain A|DNA (5'-D(*GP*CP*CP*AP*CP*CP*AP*GP*CP*TP*C)-3')|
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 \(w=f(c)\)
2EVD , Knot 97 209 0.82 40 155 203 
MALLAEHLLKPLPADKQIETGPFLEAVSHLPPFFDCLGSPVFTPIKADISGNITKIKAVYDTNPAKFRTLQNILEVEKEMYGAEWPKVGATLALMWLKRGLRFIQVFLQSICDGERDENHPNLIRVNATKAYEMALKKYHGWIVQKIFQAALYAAPYKSDFLKALSKGQNVTEEECLEKIRLFLVNYTATIDVIYEMYTQMNAELNYKV
1GJO , Knot 139 316 0.84 40 198 298 
GAMDTPMLAGVSEYELPEDPKWEFPRDKLTLGKPLGEGCFGQVVMAEAVGIDKDKPKEAVTVAVKMLKDDATEKDLSDLVSEMEMMKMIGKHKNIINLLGACTQDGPLYVIVEYASKGNLREYLRARRPPGMEYSYDINRVPEEQMTFKDLVSCTYQLARGMEYLASQKCIHRDLAARNVLVTENNVMKIADFGLARDINNIDYYKKTTNGRLPVKWMAPEALFDRVYTHQSDVWSFGVLMWEIFTLGGSPYPGIPVEELFKLLKEGHRMDKPANCTNELYMMMRDCWHAVPSQRPTFKQLVEDLDRILTLTTNEE
1FKZ , Knot 6 11 0.43 8 7 8 
GCCACCAGCTC

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 \(c\).

\(|P_{f(2EVD_1)}(2) \setminus P_{f(1GJO_1)}(2)|=67\), \(|P_{f(1GJO_1)}(2) \setminus P_{f(2EVD_1)}(2)|=110\). 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 1:11111001101111000100111101100111110011011101101010101001011000011010010011010001011011011101111110011011011100100100000010110101001001110000111100110111011100001101100100100000100101111000101011001000101010001
Pair \(Z_2\) Length of longest common subsequence
2EVD_1,1GJO_1 177 3
2EVD_1,1FKZ_1 162 1
1GJO_1,1FKZ_1 197 2

Newick tree

 
[
	1GJO_1:97.48,
	[
		2EVD_1:81,1FKZ_1:81
	]:16.48
]

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 \((0.85)(0.8)(\frac{525 }{\log_{20} 525}-\frac{209}{\log_{20}209})=91.0\)
Status Protein1 Protein2 d d1/2
Query variables 2EVD_1 1GJO_1 113 95
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]