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Parikh vectors
5JTL_1 4YDA_1 7LON_1 Letter Amino acid
3 0 8 H Histidine
8 7 17 S Serine
14 6 32 A Alanine
4 4 19 R Arginine
7 7 18 N Asparagine
8 5 24 D Aspartic acid
4 3 6 C Cysteine
14 5 7 Q Glutamine
13 17 27 E Glutamic acid
8 7 27 I Isoleucine
12 10 43 L Leucine
7 3 23 P Proline
3 14 25 K Lycine
9 6 14 F Phenylalanine
10 15 30 V Valine
9 8 35 G Glycine
5 3 6 M Methionine
11 12 19 T Threonine
1 3 6 W Tryptophan
5 2 18 Y Tyrosine 

5JTL_1|Chains A, B, C, D|Protein-export protein SecB|Escherichia coli O157:H7 (83334)
>4YDA_1|Chain A|Cellular retinoic acid-binding protein 2|Homo sapiens (9606)
>7LON_1|Chains A, B, C|Ornithine aminotransferase, mitochondrial|Homo sapiens (9606)
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 \(w=f(c)\)
5JTL , Knot 76 155 0.82 40 125 151 
MSEQNNTEMTFQIQRIYTKDISFEAPNAPHVFQKDWQPEVKLDLDTASSQLADDVYEVVLRVTVTASLGEETAFLCEVQQGGIFSIAGIEGTQMAHCLGAYCPNILFPYARECITSMVSRGTFPQLNLAPVNFDALFMNYLQQQAGEGTEEHQDA
4YDA , Knot 66 137 0.79 38 108 132 
PNFSGNWKIIRSENFEELLKVLGVNVMLRKIAVAAASKQAVEIKQEGDTFYIKVSTTVYTTEINFKVGEEFEEQTVDGRPCKSLVKWESENKMVCEQKLLKGEGPKTSWTKELTNDGELILTMTADDVVCTQVFVRE
7LON , Knot 170 404 0.84 40 225 384 
GPPTSDDIFEREYKYGAHNYHPLPVALERGKGIYLWDVEGRKYFDFLSSYSAVNQGHCHPKIVNALKSQVDKLTLTSRAFYNNVLGEYEEYITKLFNYHKVLPMNTGVEAGETACKLARKWGYTVKGIQKYKAKIVFAAGNFWGRTLSAISSSTDPTSYDGFGPFMPGFDIIPYNDLPALERALQDPNVAAFMVEPIQGEAGVVVPDPGYLMGVRELCTRHQVLFIADEIQTGLARTGRWLAVDYENVRPDIVLLGKALSGGLYPVSAVLCDDDIMLTIKPGEHGSTYGGNPLGCRVAIAALEVLEEENLAENADKLGIILRNELMKLPSDVVTAVRGKGLLNAIVIKETKDWDAWKVCLRLRDNGLLAKPTHGDIIRFAPPLVIKEDELRESIEIINKTILSF

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 \(c\).

\(|P_{f(5JTL_1)}(2) \setminus P_{f(4YDA_1)}(2)|=84\), \(|P_{f(4YDA_1)}(2) \setminus P_{f(5JTL_1)}(2)|=67\). 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 1:10000000101010010000101011011011000101010101001000110010011101010101100011100100111101111010011001110010111101000100110010110101111010111100100011010000001
Pair \(Z_2\) Length of longest common subsequence
5JTL_1,4YDA_1 151 4
5JTL_1,7LON_1 184 3
4YDA_1,7LON_1 181 3

Newick tree

 
[
	7LON_1:95.93,
	[
		5JTL_1:75.5,4YDA_1:75.5
	]:20.43
]

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 \((0.85)(0.8)(\frac{292 }{\log_{20} 292}-\frac{137}{\log_{20}137})=48.0\)
Status Protein1 Protein2 d d1/2
Query variables 5JTL_1 4YDA_1 63 59
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]