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Parikh vectors
5AXL_1 3ZXG_1 7WXP_1 Letter Amino acid
21 14 27 R Arginine
1 2 2 C Cysteine
8 13 15 H Histidine
24 13 31 L Leucine
17 8 9 F Phenylalanine
7 17 15 Y Tyrosine
9 26 14 V Valine
10 9 13 N Asparagine
26 23 12 E Glutamic acid
14 26 26 G Glycine
5 6 17 M Methionine
11 9 21 P Proline
18 15 59 A Alanine
8 15 23 D Aspartic acid
5 10 18 Q Glutamine
17 24 10 I Isoleucine
21 20 9 K Lycine
16 26 19 S Serine
9 27 18 T Threonine
4 6 9 W Tryptophan 

5AXL_1|Chains A, B|tRNA(His)-5'-guanylyltransferase (Thg1) like protein|Methanosarcina acetivorans (2214)
>3ZXG_1|Chains A, B|LYSENIN|EISENIA FETIDA (6396)
>7WXP_1|Chain A|poly(beta-D-mannuronate) lyase|Pandoraea apista (93218)
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 \(w=f(c)\)
5AXL , Knot 110 251 0.80 40 159 236 
MKTREIYAEMRCIPPVVLRADGRNFKNTLSGLGFEKPYDKTFARAMADTAELFIKKSGLSPLFAYTFSDEISFLFTDLPFDGRVEKIDSVVASFLGSALTIKLRLEEPIAFDSRLVALQKEEIPEYFHRRQLEAWRNFVASWGYYALRNEGMGRNEAAKYLKRKKESEIHEMLFERGINLATLPSWQRRGVIISKEAREIQGFNPVSGKEEKSLRRKITQNWEIPKFKSEKGIPFLEKLINRNLEHHHHHH
3ZXG , Knot 135 309 0.83 40 195 291 
SAKAAEGYEQIEVDVVAVWKEGYVYENRGSTSVDQKITITKGMKNVNSETRTVTATHSIGSTISTGDAFEIGSVEVSYSHSHEESQVSMTETEVYESKVIEHTITIPPTSKFTRWQLNADVGGADIEYMYLIDEVTPIGGTQSIPQVITSRAKIIVGRQIILGKTEIRIKHAERKEYMTVVSRKSWPAATLGHSKLFKFVLYEDWGGFRIKTLNTMYSGYEYAYSSDQGGIYFDQGTDNPKQRWAINKSLPLRHGDVVTFMNKYFTRSGLCYDDGPATNVYCLDKREDKWILEVVGLVPRGSGHHHHHH
7WXP , Knot 150 367 0.80 40 190 339 
MGSSHHHHHHSSGLVPRGSHMLEVLFQGPMRFQSLSLAGSVAMLLHINAFAAQNDCPAPPPGSPDIRAIGYYTDAARSVIDPRLKTQNDAAVKPLNAFAAHVAKFADAYAKGADEAAGRCALTWLDAWARSGAMLGRMAHVNNDQSDYMRQWTHGAAAMAYLRTQALASEQQRTDIETWLKRLSAANLAYWDNPKHKRNNAYYWTGVGIMATAVATRDDTLLNTAQGIYRAGIDAIEPDGRLPMEMARKRLALHYHDYATAPLVLMAEMARLQGEDWYTYRQGALERLAARVADGYRDPSWFNTQSGAVQETATPKASSGWVEFYRLRSPDPMRFDAMHAAGPFQDPRMGGNLTLMAQEGIVPLPQQ

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 \(c\).

\(|P_{f(5AXL_1)}(2) \setminus P_{f(3ZXG_1)}(2)|=57\), \(|P_{f(3ZXG_1)}(2) \setminus P_{f(5AXL_1)}(2)|=93\). 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 1:10000101010011111101010010001011110010000110111001011100011011110010001011100111010100100111011101101010100111100011110000110010000101100111011001100011100011001000000010011100110110110100011110001001011011010000010001000101101000011111001100010000000
Pair \(Z_2\) Length of longest common subsequence
5AXL_1,3ZXG_1 150 6
5AXL_1,7WXP_1 163 6
3ZXG_1,7WXP_1 179 7

Newick tree

 
[
	7WXP_1:88.84,
	[
		5AXL_1:75,3ZXG_1:75
	]:13.84
]

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 \((0.85)(0.8)(\frac{560 }{\log_{20} 560}-\frac{251}{\log_{20}251})=87.7\)
Status Protein1 Protein2 d d1/2
Query variables 5AXL_1 3ZXG_1 109 98
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]