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Parikh vectors
5SOV_1 5LXB_1 6IUB_1 Letter Amino acid
19 20 34 L Leucine
5 12 13 P Proline
11 22 23 S Serine
6 17 13 T Threonine
22 23 13 V Valine
15 13 19 A Alanine
16 9 11 N Asparagine
6 9 24 I Isoleucine
7 11 9 Y Tyrosine
13 11 19 G Glycine
6 9 10 H Histidine
6 9 12 E Glutamic acid
3 5 1 C Cysteine
3 11 12 Q Glutamine
13 8 21 K Lycine
2 6 8 M Methionine
5 11 13 F Phenylalanine
0 5 0 W Tryptophan
2 12 8 R Arginine
9 19 13 D Aspartic acid 

5SOV_1|Chains A, B|Non-structural protein 3|Severe acute respiratory syndrome coronavirus 2 (2697049)
>5LXB_1|Chains A, B, C, D, E, F, G, H, I, J|Soluble acetylcholine receptor|Aplysia californica (6500)
>6IUB_1|Chains A, B|SpoOJ regulator (Soj)|Helicobacter pylori (strain ATCC 700392 / 26695) (85962)
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 \(w=f(c)\)
5SOV , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL
5LXB , Knot 111 242 0.84 40 173 233 
MLVSVYLALLVACVGQAHSQANLMRLKSDLFNRSPMYPGPTKDDPLTVTLGFTLQDIVKVDSSTNEVDLVYWERQRWKLNSLMWDPNEYGNITDFRTSAADIWTPDITAYSSTRPVQVLSPQIAVVTHDGSVMFIPAQRLSFMCDPTGVDSEEGVTCAVKFGSWVYSGFEIDLKTDTDQVDLSSYYASSKYEILSATQTRQVQHYSCCPEPYIDVNLVVKFRERRAGNGFFRNLFDHHHHHH
6IUB , Knot 123 276 0.83 38 168 264 
MRGSHHHHHHGSMMSEIIAVANQKGGVGKTTTAVNLAASLAVHEKKILLIDFDPQANATSSLGFRRDKIDYDIYHVLIGRKQISQVILKTQMPFLDLVPSNLGLAGFEKTFYDSQDENKRGELMLKNALESVVGLYDYIIIDSPPALGPLTINSLSAAHSVIIPIQCEFFALEGTKLLLNTIRMLQKSTNPKLKIRGFLPTMHVPQLNLTKGVLAELFKYFDSEFFRDSATGEYIMIPKSVKLAESPSFGKPILLYDIKSNGSIAYQKLAQSILQG

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 \(c\).

\(|P_{f(5SOV_1)}(2) \setminus P_{f(5LXB_1)}(2)|=54\), \(|P_{f(5LXB_1)}(2) \setminus P_{f(5SOV_1)}(2)|=108\). 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 1:0110010101010001010010110010010101110110101001111111100100011010000011001110111001101001100010111101001001011001000100001111111011111101100101010010001011110001000110011
Pair \(Z_2\) Length of longest common subsequence
5SOV_1,5LXB_1 162 4
5SOV_1,6IUB_1 153 3
5LXB_1,6IUB_1 173 6

Newick tree

 
[
	5LXB_1:86.08,
	[
		5SOV_1:76.5,6IUB_1:76.5
	]:9.58
]

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 \((0.85)(0.8)(\frac{411 }{\log_{20} 411}-\frac{169}{\log_{20}169})=71.9\)
Status Protein1 Protein2 d d1/2
Query variables 5SOV_1 5LXB_1 91 75.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]