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Parikh vectors
8JSB_1 2ZEC_1 8ABG_1 Letter Amino acid
9 22 22 P Proline
13 10 18 Y Tyrosine
12 25 26 V Valine
4 5 18 N Asparagine
17 13 6 Q Glutamine
6 12 12 H Histidine
18 20 55 L Leucine
12 12 10 R Arginine
4 8 5 C Cysteine
6 9 5 E Glutamic acid
4 9 7 W Tryptophan
8 15 10 D Aspartic acid
13 8 10 K Lycine
8 4 36 F Phenylalanine
19 11 15 T Threonine
37 10 26 S Serine
18 14 28 A Alanine
33 21 24 G Glycine
8 11 39 I Isoleucine
4 4 13 M Methionine 

8JSB_1|Chains A, B, C, D|single chain variable fragment|Homo sapiens (9606)
>2ZEC_1|Chains A, B, C, D|Tryptase beta 2|Homo sapiens (9606)
>8ABG_1|Chains A[auth C], K[auth N]|Cytochrome b|Yarrowia lipolytica (4952)
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 \(w=f(c)\)
8JSB , Knot 102 253 0.74 40 140 220 
MAKVQLLESGGGLVQPGGSLRLSCAASGFTFSSYAMSWVRQAPGKGLEWVSTISSQGQATKYADSVKGRFTISRDNSKNTLYLQMNSLRAEDTAVYYCAKKRYPFDYWGQGTLVTVSSGGGGSGGGGSGGGGSTDIQMTQSPSSLSASVGDRVTITCRASQSISSYLNWYQQKPGKAPKLLIYSASRLQSGVPSRFSGSGSGTDFTLTISSLQPEDFATYYCQQRYKTPGTFGQGTKVEIKRAAALEHHHHHH
2ZEC , Knot 115 243 0.86 40 178 237 
IVGGQEAPRSKWPWQVSLRVHGPYWMHFCGGSLIHPQWVLTAAHCVGPDVKDLAALRVQLREQHLYYQDQLLPVSRIIVHPQFYTAQIGADIALLELEEPVKVSSHVHTVTLPPASETFPPGMPCWVTGWGDVDNDERLPPPFPLKQVKVPIMENHICDAKYHLGAYTGDDVRIVRDDMLCAGNTRRDSCQGDSGGPLVCKVNGTWLQAGVVSWGEGCAQPNRPGIYTRVTYYLDWIHHYVPK
8ABG , Knot 160 385 0.82 40 193 351 
MALRKKNSLLNMANSYVLDSPQPSNLNYFWNFGSLLALCLVIQLATGITLAMHYTSHASLAFDSVEHIMRDVNFGWFIRYAHANTASFFFICIYAHMGRNIYYGSYKTPRVLPWSIGVIIFLLLIITAFMGYVLVFGQMSLWGATVICNLVSAIPWLGEDIVHFLWGGFSVGNPTLQRFFALHYLMPFVLAVFALLHLIALHTAGSSNPLGITSNVDKLSMHPYYSFKDLITVFAFLLMFTLFVFFSPDKLGHPDNYIPANPMVTPASIVPEWYLLPFYAILRAIPDKLGGVIAMVAAILILLILPIVDRSIIRGNAFKPISKLLFGFFICNFLLLGVLGQVHIEPPFIVLGQICTIFYFSYFLILLPMVSTIENIFFYIGSLRK

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 \(c\).

\(|P_{f(8JSB_1)}(2) \setminus P_{f(2ZEC_1)}(2)|=75\), \(|P_{f(2ZEC_1)}(2) \setminus P_{f(8JSB_1)}(2)|=113\). 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 1:1101011001111101110101001101101000110110011101101100100010100010010101010000000010101001010001100010000110011010110100111101111011110001010001001010110010100010001000101000011011011100100100111001010101001010100101001100000000001101101001010011110000000
Pair \(Z_2\) Length of longest common subsequence
8JSB_1,2ZEC_1 188 4
8JSB_1,8ABG_1 169 4
2ZEC_1,8ABG_1 195 3

Newick tree

 
[
	2ZEC_1:99.23,
	[
		8JSB_1:84.5,8ABG_1:84.5
	]:14.73
]

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 \((0.85)(0.8)(\frac{496 }{\log_{20} 496}-\frac{243}{\log_{20}243})=72.6\)
Status Protein1 Protein2 d d1/2
Query variables 8JSB_1 2ZEC_1 93 90
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]