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Parikh vectors
7ULN_1 7CTV_1 7XPK_1 Letter Amino acid
17 23 9 D Aspartic acid
6 2 2 W Tryptophan
5 11 10 F Phenylalanine
12 8 7 Y Tyrosine
12 23 7 A Alanine
9 14 5 R Arginine
3 5 4 C Cysteine
16 28 13 I Isoleucine
4 19 1 H Histidine
14 23 14 K Lycine
10 13 3 M Methionine
11 17 7 P Proline
16 11 8 N Asparagine
11 11 6 Q Glutamine
14 21 13 E Glutamic acid
17 21 12 G Glycine
18 22 10 S Serine
15 16 9 V Valine
11 35 15 L Leucine
17 13 4 T Threonine

7ULN_1|Chains A, B|Minor capsid protein P3-RTD|Turnip yellows virus (131083)
>7CTV_1|Chains A, B|Leucine-rich repeat receptor-like serine/threonine/tyrosine-protein kinase SOBIR1|Arabidopsis thaliana (3702)
>7XPK_1|Chains A, C|BAH domain-containing protein|Oryza sativa Japonica Group (39947)
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 \(w=f(c)\)
7ULN , Knot 112 238 0.85 40 173 233
KKYRFIVYTGVPVTRIMAQSTDDAISLYDMPSQRFRYIEDENMNWTNLDSRWYSQNSLKAIPMIIVPVPQGEWTVEISMEGYQPTSSTTDPNKDKQDGLIAYNDDLSEGWNVGIYNNVEITNNKADNTLKYGHPDMELNGCHFNQGQCLERDGDLTCHIKTTGDNASFFVVGPAVQKQSKYNYAVSYGAWTDRMMEIGMIAIALDEQGSSGSVKTERPKRVGHSMAVSTWETIKLPEK
7CTV , Knot 147 336 0.84 40 210 322
MGSSHHHHHHSSGLVPRGSHMSIFSPLIKKAEDLAFLENEEALASLEIIGRGGCGEVFKAELPGSNGKIIAVKKVIQPPKDADELTDEDSKFLNKKMRQIRSEINTVGHIRHRNLLPLLAHVSRPECHYLVYEYMEKGSLQDILTDVQAGNQELMWPARHKIALGIAAGLEYLHMDHNPRIIHRALKPANVLLDDDMEARISDFGLAKAMPDAVTHITTSHVAGTVGYIAPEFYQTHKFTDKCDIYSFGVILGILVIGKLPSDEFFQHTDEMSLIKWMRNIITSENPSLAIDPKLMDQGFDEQMLLVLKIACYCTLDDPKQRPNSKDVRTMLSQIK
7XPK , Knot 78 159 0.83 40 122 156
GGIKMDTQFYDSFTFDNVKYSLYDNVYLFKSGESEPYIGKIIKIWQQNQAKKVKILWFFLPDEIRKHLSGPVMEKEIFLACGEGVGLADINPLEAIGGKCTVLCISKDERNRQPSPRELAMADYIFYRFFDVNSCTLSEQLPEKIAGVEGNLLLNSKVE

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 \(c\).

\(|P_{f(7ULN_1)}(2) \setminus P_{f(7CTV_1)}(2)|=78\), \(|P_{f(7CTV_1)}(2) \setminus P_{f(7ULN_1)}(2)|=115\). 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 1:0000111001111001110000011010011000100100001010010001000001011111111110101010101010010000001000000111100001001101110001010000100010010101010100100100100010100010001001011111111000000001100111000110111111110001001010000100110011100100101100
Pair \(Z_2\) Length of longest common subsequence
7ULN_1,7CTV_1 193 3
7ULN_1,7XPK_1 179 4
7CTV_1,7XPK_1 168 4

Newick tree

 
[
	7ULN_1:95.89,
	[
		7XPK_1:84,7CTV_1:84
	]:11.89
]

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 \((0.85)(0.8)(\frac{574 }{\log_{20} 574}-\frac{238}{\log_{20}238})=95.4\)
Status Protein1 Protein2 d d1/2
Query variables 7ULN_1 7CTV_1 124 105.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]