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Parikh vectors
6GTJ_1 2FBL_1 1DIH_1 Letter Amino acid
23 10 3 P Proline
12 9 15 R Arginine
1 0 2 C Cysteine
12 6 16 I Isoleucine
9 4 9 M Methionine
34 11 32 G Glycine
24 18 24 L Leucine
13 9 11 F Phenylalanine
6 7 13 S Serine
15 3 10 H Histidine
28 11 14 T Threonine
4 2 1 W Tryptophan
13 5 2 Y Tyrosine
33 9 40 A Alanine
20 7 21 D Aspartic acid
7 8 6 Q Glutamine
21 18 16 E Glutamic acid
14 1 7 N Asparagine
17 7 12 K Lycine
34 8 19 V Valine 

6GTJ_1|Chain A|Copper-containing nitrite reductase|Achromobacter cycloclastes (223)
>2FBL_1|Chains A, B|hypothetical protein NE1496|Nitrosomonas europaea (915)
>1DIH_1|Chain A|DIHYDRODIPICOLINATE REDUCTASE|Escherichia coli (562)
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 \(w=f(c)\)
6GTJ , Knot 140 340 0.80 40 195 317 
AAGAAPVDISTLPRVKVDLVKPPFVHAHDQVAKTGPRVVEFTMTIEEKKLVIDREGTEIHAMTFNGSVPGPLMVVHENDYVELRLINPDTNTLLHNIDFHAATGALGGGALTQVNPGEETTLRFKATKPGVFVYHCAPEGMVPWHVTSGMNGAIMVLPRDGLKDEKGQPLTYDKIYYVGEQDFYVPKDEAGNYKKYETPGEAYEDAVKAMRTLTPTHIVFNGAVGALTGDHALTAAVGERVLVVHSQANRDTRPHLIGGHGDYVWATGKFRNPPDLDQETWLIPGGTAGAAFYTFRQPGVYAYVNHNLIEAFELGAAGHFKVTGEWNDDLMTSVVKPASM
2FBL , Knot 78 153 0.85 38 112 149 
GHMTEIERKFLVATFPDGELHAVPLRQGYLTTPTDSIELRLRQQGTEYFMTLKSEGGLSRQEYEIQIDVTQFEMLWPATEGRRVEKTRYSGKLPDGQLFELDVFAGHLSPLMLVEVEFLSEDAAQAFIPPPWFGEEVTEDKRYKNKALALSIP
1DIH , Knot 114 273 0.78 40 155 260 
MHDANIRVAIAGAGGRMGRQLIQAALALEGVQLGAALEREGSSLLGSDAGELAGAGKTGVTVQSSLDAVKDDFDVFIDFTRPEGTLNHLAFCRQHGKGMVIGTTGFDEAGKQAIRDAAADIAIVFAANFSVGVNVMLKLLEKAAKVMGDYTDIEIIEAHHRHKVDAPSGTALAMGEAIAHALDKDLKDCAVYSREGHTGERVPGTIGFATVRAGDIVGEHTAMFADIGERLEITHKASSRMTFANGAVRSALWLSGKESGLFDMRDVLDLNNL

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 \(c\).

\(|P_{f(6GTJ_1)}(2) \setminus P_{f(2FBL_1)}(2)|=126\), \(|P_{f(2FBL_1)}(2) \setminus P_{f(6GTJ_1)}(2)|=43\). 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 1:1111111010011010101101111010001100110110101010000111000100101101010111111110000010101101000011001010110111111110010110000101010011111000110111110100110111111100110000101100001001100010110001100000001101000110110010100111011111101001101111001111000100000101111010011101010011010000111111011111001001110101000110110111110101010100011001101101
Pair \(Z_2\) Length of longest common subsequence
6GTJ_1,2FBL_1 169 4
6GTJ_1,1DIH_1 154 4
2FBL_1,1DIH_1 155 4

Newick tree

 
[
	2FBL_1:82.38,
	[
		6GTJ_1:77,1DIH_1:77
	]:5.38
]

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 \((0.85)(0.8)(\frac{493 }{\log_{20} 493}-\frac{153}{\log_{20}153})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 6GTJ_1 2FBL_1 123 89
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]