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Parikh vectors
8SVC_1 7CCM_1 7XPG_1 Letter Amino acid
13 9 39 T Threonine
7 2 29 Y Tyrosine
43 15 48 A Alanine
18 7 29 D Aspartic acid
12 11 20 Q Glutamine
14 15 12 E Glutamic acid
27 15 34 G Glycine
7 7 12 M Methionine
7 6 40 R Arginine
19 8 6 H Histidine
9 11 26 I Isoleucine
35 16 46 L Leucine
15 5 44 P Proline
24 18 50 S Serine
8 7 30 N Asparagine
0 5 8 C Cysteine
21 5 19 K Lycine
8 6 27 F Phenylalanine
4 2 9 W Tryptophan
25 13 37 V Valine 

8SVC_1|Chain A|Metal ABC transporter substrate-binding protein|Klebsiella pneumoniae (573)
>7CCM_1|Chains A, B, C|Bcl-2-like protein 15|Homo sapiens (9606)
>7XPG_1|Chains A, B, C|Capsid protein alpha|Lake Sinai virus 1 (1041806)
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 \(w=f(c)\)
8SVC , Knot 134 316 0.81 38 168 285 
MKYLLPTAAAGLLLLAAQPAMAMAKTLNVVSSFSVLGDIAQQVGGEHVHVDTLVGPDGDPHTFEPSPKDSALLSKADVVVVNGLGLEGWLDRLIKASGFKGELVVASKGVKTHALDEEGKTVTDPHAWNSAANGALYAQNILDGLVKADPEDKAALTSSGKRYIDQLTSLDGWAKAQFSAIPLAKRKVLTSHDAFGYFGRAYHVTFLAPQGLSSESEASAAQVAALIKQIKADGVHTWFMENQLDPRLVKQIASATGAQPGGELYPEALSKPGGVADSYVKMMRHNVELIANSMKELALVPRGSSAHHHHHHHHHH
7CCM , Knot 89 183 0.84 40 140 176 
MGSSHHHHHHSSGLVPRGSHMKSSQTFEEQTECIVNTLLMDFLSPTLQVASRNLCCVDEVDSGEPCSFDVAIIAGRLRMLGDQFNGELEASAKNVIAETIKGQTGAILQDTVESLSKTWCAQDSSLAYERAFLAVSVKLLEYMAHIAPEVVGQVAIPMTGMINGNQAIREFIQGQGGWENLES
7XPG , Knot 227 565 0.84 40 262 535 
MNSICSLYCLFRRVMPYSSEILSSTVYRPPFLATSGLFFTRDHYKFIIMNQQQINPAQRSLRPRAQSAPSRSARRRRNRRRRNPSTPAGTVALQPSRITRRVVSNLARRPLTITTAGLAWLRQYLNPMGPSTSSVSGFPDGSAVTTCIADYTNTFNISFPPREAIYCTGSNSDEKPVMLDAATYAKIDAWTKSDITLCILALPMLRNVVMIRLYASTPTAFTLSEGVPNFVQRFPNWSAFTTEGKVLNNGDSPGYIQSFVYLPNVDKHLSAARGFRLLSRGLTGIYTAPSLETQGFVTACQYLAEGALQTQTVGNDFVQSVEVNADKTVKNVNGKRLHYSGPPKFVFPLEGDNCAPSSLVETYHQAYQARAVDGFYMPILSSSRDNPFISPKPQPIAVFNRWYYRGCLDPVPASKVADGPSQYYYDLNVADDVAPLYNTGVVWMEGISSKFSLKLKTRTVIQYIPTSGSVLANFTRHEPTYDQVALDAADRIRNMMPHAYPAAYNDWGWLGDLLDSTLSMLPGIGTAYRFAKPLIKPAWNWLGGKVSDFFGNPVSRDGDIYFDAK

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 \(c\).

\(|P_{f(8SVC_1)}(2) \setminus P_{f(7CCM_1)}(2)|=88\), \(|P_{f(7CCM_1)}(2) \setminus P_{f(8SVC_1)}(2)|=60\). 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 1:1001110111111111101111110010110010111011001110010100111101010010101000111001011110111101110011010110101111001100011000100100101100110111010011011101010001110001000100100101110101011111000110000111011010010111101100000101101111100101011001110001010110011010110111010101100111110001011000101110010011111010010000000000
Pair \(Z_2\) Length of longest common subsequence
8SVC_1,7CCM_1 148 6
8SVC_1,7XPG_1 182 3
7CCM_1,7XPG_1 200 3

Newick tree

 
[
	7XPG_1:10.79,
	[
		8SVC_1:74,7CCM_1:74
	]:27.79
]

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 \((0.85)(0.8)(\frac{499 }{\log_{20} 499}-\frac{183}{\log_{20}183})=92.0\)
Status Protein1 Protein2 d d1/2
Query variables 8SVC_1 7CCM_1 110 87.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]