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Parikh vectors
1UEN_1 5CHO_1 6PZQ_1 Letter Amino acid
3 22 8 A Alanine
3 13 11 D Aspartic acid
4 3 16 I Isoleucine
2 4 1 W Tryptophan
8 20 11 R Arginine
3 6 3 Q Glutamine
16 21 6 G Glycine
8 18 20 L Leucine
7 0 18 K Lycine
11 16 9 V Valine
6 6 7 H Histidine
2 3 4 M Methionine
3 8 4 F Phenylalanine
10 12 6 P Proline
6 10 13 T Threonine
7 4 20 N Asparagine
0 3 4 C Cysteine
6 8 12 E Glutamic acid
16 16 16 S Serine
4 3 5 Y Tyrosine 

1UEN_1|Chain A|KIAA0343 protein|Homo sapiens (9606)
>5CHO_1|Chains A, B, C, D, E, F, G, H|Flavin reductase|uncultured bacterium (77133)
>6PZQ_1|Chains A, B, C, D|Matrix M2-1|Human respiratory syncytial virus A (strain A2) (11259)
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 \(w=f(c)\)
1UEN , Knot 63 125 0.81 38 95 117 
GSSGSSGHSGEDLPMVAPGNVRVNVVNSTLAEVHWDPVPLKSIRGHLQGYRIYYWKTQSSSKRNRRHIEKKILTFQGSKTHGMLPGLEPFSHYTLNVRVVNGKGEGPASPDRVFNTPEGSGPSSG
5CHO , Knot 93 196 0.83 38 129 188 
MEGSVNGSQRGNGSQRERVPEPGAGPTTDLLRDSRSLRGIFSSFATGVTVVTVGGDSPHAMTANSFTSVSLDPPLILVCVECDAAMHGSLLEVGSFGVSVLAADQQHVALLYANRWRPRDPTQFDRPGWARGARTGAPLARGALAWFECALWRAYDAGDHSIFVGRLLTAERHDRRDALVYHSGQFRGLPDRAPVE
6PZQ , Knot 91 194 0.82 40 136 186 
MSRRNPCKFEIRGHCLNGKRCHFSHNYFEWPPHALLVRQNFMLNRILKSMDKSIDTLSEISGAAELDRTEEYALGVVGVLESYIGSINNITKQSACVAMSKLLTELNSDDIKKLRDNEELNSPKIRVYNTVISYIESNRKNNKQTIHLLKRLPADVLKKTIKNTLDIHKSITINNPKELTVSDTNDHAKNNDTT

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 \(c\).

\(|P_{f(1UEN_1)}(2) \setminus P_{f(5CHO_1)}(2)|=54\), \(|P_{f(5CHO_1)}(2) \setminus P_{f(1UEN_1)}(2)|=88\). 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 1:10010010010011111110101011000110101011110010101010010010000000000001000110101000011111101100001010110101011101001100101011001
Pair \(Z_2\) Length of longest common subsequence
1UEN_1,5CHO_1 142 3
1UEN_1,6PZQ_1 149 4
5CHO_1,6PZQ_1 173 3

Newick tree

 
[
	6PZQ_1:83.71,
	[
		1UEN_1:71,5CHO_1:71
	]:12.71
]

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 \((0.85)(0.8)(\frac{321 }{\log_{20} 321}-\frac{125}{\log_{20}125})=60.5\)
Status Protein1 Protein2 d d1/2
Query variables 1UEN_1 5CHO_1 80 64
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]