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Parikh vectors
7AHH_1 1ZFC_1 2KVX_1 Letter Amino acid
55 0 2 L Leucine
23 0 1 P Proline
16 0 0 W Tryptophan
52 2 0 A Alanine
49 3 3 G Glycine
38 2 1 T Threonine
8 0 1 Y Tyrosine
52 0 2 V Valine
18 0 0 E Glutamic acid
45 0 1 K Lycine
20 0 0 Q Glutamine
24 0 1 F Phenylalanine
26 0 2 N Asparagine
27 0 3 D Aspartic acid
11 0 0 H Histidine
48 0 1 I Isoleucine
23 0 0 M Methionine
42 0 4 S Serine
8 0 0 R Arginine
0 3 6 C Cysteine 

7AHH_1|Chains A, B|ABC transporter permease subunit|Lactococcus lactis subsp. lactis (1360)
>1ZFC_1|Chains A, B|5'-D(*CP*CP*GP*AP*TP*AP*TP*CP*GP*G)-3'|null
>2KVX_1|Chain A|Kalata-B12|Oldenlandia affinis (60225)
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 \(w=f(c)\)
7AHH , Knot 222 585 0.80 38 233 539 
MIDLAIGQVPIANWVSSATDWITSTFSSGFDVIQKSGTVLMNGITGALTAVPFWLMIAVVTILAILVSGKKIAFPLFTFIGLSLIANQGLWSDLMSTITLVLLSSLLSIIIGVPLGIWMAKSDLVAKIVQPILDFMQTMPGFVYLIPAVAFFGIGVVPGVFASVIFALPPTVRMTNLGIRQVSTELVEAADSFGSTARQKLFKLEFPLAKGTIMAGVNQTIMLALSMVVIASMIGAPGLGRGVLAAVQSADIGKGFVSGISLVILAIIIDRFTQKLNVSPLEKQGNPTVKKWKRGIALVSLLALIIGAFSGMSFGKTASDKKVDLVYMNWDSEVASINVLTQAMKEHGFDVKTTALDNAVAWQTVANGQADGMVSAWLPNTHKTQWQKYGKSVDLLGPNLKGAKVGFVVPSYMNVNSIEDLTNQANKTITGIEPGAGVMAASEKTLNSYDNLKDWKLVPSSSGAMTVALGEAIKQHKDIVITGWSPHWMFNKYDLKYLADPKGTMGTSENINTIVRKGLKKENPEAYKVLDKFNWTTKDMEAVMLDIQNGKTPEEAAKNWIKDHQKEVDKWFKGSIEGRHHHHHH
1ZFC , Knot 6 10 0.46 8 7 8 
CCGATATCGG
2KVX , Knot 19 28 0.75 26 25 26 
GSLCGDTCFVLGCNDSSCSCNYPICVKD

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 \(c\).

\(|P_{f(7AHH_1)}(2) \setminus P_{f(1ZFC_1)}(2)|=230\), \(|P_{f(1ZFC_1)}(2) \setminus P_{f(7AHH_1)}(2)|=4\). 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 1:110111101111011001001100010011011000101110110111011111111111011111101001111110111101110011100110010111100110111111111111000111011011101100111110111111111111111111011111110101001110010001101100110010001101011110101111100011111011111011111111011111100101101110110111111110010001010110001010100100111110111111111011011001000010110101000110101100110001101000110011110011010101110111100000010001001011110101101111110010100100100010001011011111111000010000010010111000111011110110000011101101011100001001101010110000100110011000010100110010100001011110100100100110011000000100110101010000000
Pair \(Z_2\) Length of longest common subsequence
7AHH_1,1ZFC_1 234 2
7AHH_1,2KVX_1 238 2
1ZFC_1,2KVX_1 28 2

Newick tree

 
[
	7AHH_1:13.01,
	[
		1ZFC_1:14,2KVX_1:14
	]:12.01
]

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 \((0.85)(0.8)(\frac{595 }{\log_{20} 595}-\frac{10}{\log_{20}10})=180.\)
Status Protein1 Protein2 d d1/2
Query variables 7AHH_1 1ZFC_1 220 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]