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Parikh vectors
8FJA_1 1HCU_1 6SCQ_1 Letter Amino acid
2 10 1 H Histidine
1 4 3 M Methionine
12 49 8 A Alanine
12 26 6 D Aspartic acid
13 13 2 K Lycine
15 25 9 V Valine
15 43 5 L Leucine
10 29 6 F Phenylalanine
30 59 6 S Serine
6 17 5 R Arginine
13 50 5 G Glycine
15 19 3 Q Glutamine
10 19 5 E Glutamic acid
9 20 4 I Isoleucine
10 23 2 P Proline
18 35 2 T Threonine
2 11 0 W Tryptophan
8 25 0 N Asparagine
5 1 1 C Cysteine
8 25 1 Y Tyrosine 

8FJA_1|Chain A[auth D]|REGN6972 Fab light chain|Homo sapiens (9606)
>1HCU_1|Chains A, B, C, D|ALPHA-1,2-MANNOSIDASE|TRICHODERMA REESEI (51453)
>6SCQ_1|Chains A, B|Cell division protein SepF|Corynebacterium glutamicum ATCC 13032 (196627)
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 \(w=f(c)\)
8FJA , Knot 99 214 0.82 40 152 205 
DIQMTQSPSSLSASVGDRVTITCQASQDISNYLNWYQQKRGKAPKLLIYDASILETGVPSRFSGSGSGTDFTFTISSLQPEDIATYFCQQFDNVPLTFGGGTKVEIKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC
1HCU , Knot 204 503 0.84 40 233 465 
YVEFATKRGSPNPTRAAAVKAAFQTSWNAYHHFAFPHDDLHPVSNSFDDERNGWGSSAIDGLDTAILMGDADIVNTILQYVPQINFTTTAVANQGSSVFETNIRYLGGLLSAYDLLRGPFSSLATNQTLVNSLLRQAQTLANGLKVAFTTPSGVPDPTVFFNPTVRRSGASSNNVAEIGSLVLEWTRLSDLTGNPQYAQLAQKGESYLLNPKGSPEAWPGLIGTFVSTSNGTFQDSSGSWSGLMDSFYEYLIKMYLYDPVAFAHYKDRWVLGADSTIGHLGSHPSTRKDLTFLSSYNGQSTSPNSGHLASFGGGNFILGGILLNEQKYIDFGIKLASSYFGTYTQTASGIGPEGFAWVDSVTGAGGSPPSSQSGFYSSAGFWVTAPYYILRPETLESLYYAYRVTGDSKWQDLAWEALSAIEDACRAGSAYSSINDVTQANGGGASDDMESFWFAEALKYAYLIFAEESDVQVQATGGNKFVFNTEAHPFSIRSSSRRGGHLA
6SCQ , Knot 40 74 0.77 36 65 71 
MSYQSTIVPVELHSFEDAQVIGGAFRDGDAVVFDMSLLSREEARRIVDFAAGLCFALRGKMQKIDSVTFAVVPE

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 \(c\).

\(|P_{f(8FJA_1)}(2) \setminus P_{f(1HCU_1)}(2)|=46\), \(|P_{f(1HCU_1)}(2) \setminus P_{f(8FJA_1)}(2)|=127\). 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 1:0101000100101011001010001000100010100000101101110010110011100101010100101010010100110010001001110111100101000111101111110000100101011011001010010101010011001000001000000000001000101001000000101001000110011000100100
Pair \(Z_2\) Length of longest common subsequence
8FJA_1,1HCU_1 173 4
8FJA_1,6SCQ_1 149 3
1HCU_1,6SCQ_1 200 4

Newick tree

 
[
	1HCU_1:99.01,
	[
		8FJA_1:74.5,6SCQ_1:74.5
	]:24.51
]

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 \((0.85)(0.8)(\frac{717 }{\log_{20} 717}-\frac{214}{\log_{20}214})=140.\)
Status Protein1 Protein2 d d1/2
Query variables 8FJA_1 1HCU_1 176 124.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]