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Parikh vectors
6FUT_1 2FJL_1 8EDC_1 Letter Amino acid
6 6 11 K Lycine
4 3 2 W Tryptophan
22 10 18 V Valine
22 7 11 G Glycine
6 8 13 I Isoleucine
27 15 10 L Leucine
9 19 7 E Glutamic acid
14 10 9 P Proline
16 16 19 S Serine
5 7 6 N Asparagine
16 9 21 D Aspartic acid
8 7 11 Q Glutamine
0 4 2 F Phenylalanine
8 4 14 T Threonine
4 5 8 Y Tyrosine
27 9 18 A Alanine
18 5 11 R Arginine
8 1 6 C Cysteine
10 4 10 H Histidine
2 1 3 M Methionine 

6FUT_1|Chain A|Complement factor D|Homo sapiens (9606)
>2FJL_1|Chain A|1-phosphatidylinositol-4,5-bisphosphate phosphodiesterase gamma 1|Rattus norvegicus (10116)
>8EDC_1|Chain A|Netrin receptor unc-5|Caenorhabditis elegans (6239)
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 \(w=f(c)\)
6FUT , Knot 103 232 0.80 38 145 218 
ILGGREAEAHARPYMASVQLNGAHLCGGVLVAEQWVLSAAHCLEDAADGKVQVLLGAHSLSQPEPSKRLYDVLRAVPHPDSQPDTIDHDLLLLQLSEKATLGPAVRPLPWQRVDRDVAPGTLCDVAGWGIVNHAGRRPDSLQHVLLPVLDRATCNRRTHHDGAITERLMCAESNRRDSCKGDSGGPLVCGGVLEGVVTSGSRVCGNRKKPGIYTRVASYAAWIDSVLASAAA
2FJL , Knot 74 150 0.82 40 115 145 
SIKNGILYLEDPVNHEWYPHYFVLTSSKIYYSEETSSDQGNEDEEEPKEASGSTELHSSLEVLFQGPNPAILEPEREHLDENSPLGDLLRGVLDVPACQIAIRPEGKNNRLFVFSISMPSVAQWSLDVAADSQEELQDWVKKIREVAQTA
8EDC , Knot 95 210 0.80 40 142 201 
ADPGMDEITITTQPKSGYVIRNKPLRLQCRANHATKIRYKCSSKWIDDSRIEKLIGTDSTSGVGYIDASVDISRIDVDTSGHVDAFQCQCYASGDDDQDVVASDVATVHLAYMRKHFLKSPVAQRVQEGTTLQLPCQAPESDPKAELTWYKDGVVVQPDANVIRASDGSLIMSAARLSDSGNYTCEATNVANSRKTDPVEVQIYHHHHHH

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 \(c\).

\(|P_{f(6FUT_1)}(2) \setminus P_{f(2FJL_1)}(2)|=88\), \(|P_{f(2FJL_1)}(2) \setminus P_{f(6FUT_1)}(2)|=58\). 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 1:1111001010101011010101101011111100111011001001101010111110010010100010011011101000100100011110100010111110111100100011110100111111100110010010011111100100000000011100011010000000001001111101111011100100101000011100011001111001110111
Pair \(Z_2\) Length of longest common subsequence
6FUT_1,2FJL_1 146 3
6FUT_1,8EDC_1 155 3
2FJL_1,8EDC_1 161 3

Newick tree

 
[
	8EDC_1:80.91,
	[
		6FUT_1:73,2FJL_1:73
	]:7.91
]

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 \((0.85)(0.8)(\frac{382 }{\log_{20} 382}-\frac{150}{\log_{20}150})=69.9\)
Status Protein1 Protein2 d d1/2
Query variables 6FUT_1 2FJL_1 84 71
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]