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Parikh vectors
2XTO_1 6DVZ_1 6MJF_1 Letter Amino acid
18 48 18 K Lycine
4 33 29 P Proline
13 51 22 T Threonine
11 40 16 R Arginine
10 38 13 N Asparagine
15 43 24 D Aspartic acid
20 33 22 G Glycine
6 14 10 H Histidine
24 104 33 L Leucine
7 25 12 M Methionine
6 46 15 F Phenylalanine
16 52 37 A Alanine
7 13 7 C Cysteine
14 25 17 Q Glutamine
16 55 24 E Glutamic acid
11 42 26 V Valine
12 45 22 I Isoleucine
20 49 21 S Serine
2 11 2 W Tryptophan
8 24 16 Y Tyrosine 

2XTO_1|Chains A, B|GTPASE IMAP FAMILY MEMBER 2|HOMO SAPIENS (9606)
>6DVZ_1|Chains A, B, C, D|Transient receptor potential cation channel subfamily V member 3|Mus musculus (10090)
>6MJF_1|Chains A, B, C, D, E, F|dbOphM|Dendrothele bispora CBS 962.96 (1314807)
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 \(w=f(c)\)
2XTO , Knot 111 240 0.84 40 160 230 
SELRIILVGKTGTGKSAAGNSILRKQAFESKLGSQTLTKTCSKSQGSWGNREIVIIDTPDMFSWKDHCEALYKEVQRCYLLSAPGPHVLLLVTQLGRYTSQDQQAAQRVKEIFGEDAMGHTIVLFTHKEDLNGGSLMDYMHDSDNKALSKLVAACGGRICAFNNRAEGSNQDDQVKELMDCIEDLLMEKNGDHYTNGLYSLIQRSKCGPVGSDERVKEFKQSLIKYMETQRSYTALAEAN
6DVZ , Knot 302 791 0.85 40 307 720 
MGAHSKEMAPLMGKRTTAPGGNPVVLTEKRPADLTPTKKSAHFFLEIEGFEPNPTVTKTSPPIFSKPMDSNIRQCLSGNCDDMDSPQSPQDDVTETPSNPNSPSANLAKEEQRQKKKRLKKRIFAAVSEGCVEELRELLQDLQDLCRRRRGLDVPDFLMHKLTASDTGKTCLMKALLNINPNTKEIVRILLAFAEENDILDRFINAEYTEEAYEGQTALNIAIERRQGDITAVLIAAGADVNAHAKGVFFNPKYQHEGFYFGETPLALAACTNQPEIVQLLMENEQTDITSQDSRGNNILHALVTVAEDFKTQNDFVKRMYDMILLRSGNWELETMRNNDGLTPLQLAAKMGKAEILKYILSREIKEKPLRSLSRKFTDWAYGPVSSSLYDLTNVDTTTDNSVLEIIVYNTNIDNRHEMLTLEPLHTLLHTKWKKFAKYMFFLSFCFYFFYNITLTLVSYYRPREDEDLPHPLALTHKMSWLQLLGRMFVLIWATCISVKEGIAIFLLRPSDLQSILSDAWFHFVFFVQAVLVILSVFLYLFAYKEYLACLVLAMALGWANMLAYTRGFQSMGMYSVMIQKVILHDVLKFLFVYILFLLGFGVALASLIEKCSKDKKDCSSYGSFSDAVLELFKLTIGLGDLNIQQNSTYPILFLFLLITYVILTFVLLLNMLIALMGETVENVSKESERIWRLQRARTILEFEKMLPEWLRSRFRMGELCKVADEDFRLCLRINEVKWTEWKTHVSFLNEDPGPIRRTADLNKIQDSSRSNSKTTLYAFDELDEFPETSV
6MJF , Knot 167 386 0.86 40 224 367 
MESSTQTKPGSLIVVGTGIESIGQMTLQALSYIEAASKVFYCVIDPATEAFILTKNKNCVDLYQYYDNGKSRMDTYTQMAELMLKEVRNGLDVVGVFYGHPGVFVNPSHRALAIARSEGYQARMLPGVSAEDCLFADLCIDPSNPGCLTYEASDFLIRERPVNVHSHLILFQVGCVGIADFNFSGFDNSKFTILVDRLEQEYGPDHTVVHYIAAMMPHQDPVTDKFTIGQLREPEIAKRVGGVSTFYIPPKARKDINTDIIRLLEFLPAGKVPDKHTQIYPPNQWEPDVPTLPPYGQNEQAAITRLEAHAPPEEYQPLATSKAMTDVMTKLALDPKALAEYKADHRAFAQSVPDLTPQERAALELGDSWAIRCAMKNMPSSLLEAA

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 \(c\).

\(|P_{f(2XTO_1)}(2) \setminus P_{f(6DVZ_1)}(2)|=22\), \(|P_{f(6DVZ_1)}(2) \setminus P_{f(2XTO_1)}(2)|=169\). 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 1:001011111001010011100110001100011000100000000101100011110010110100000110001000011011110111110011000000001100100111001110011110000010110110010000001100111101101011000101000000100110010011100010000011001100000111100001001000110010000000111010
Pair \(Z_2\) Length of longest common subsequence
2XTO_1,6DVZ_1 191 4
2XTO_1,6MJF_1 178 4
6DVZ_1,6MJF_1 147 4

Newick tree

 
[
	2XTO_1:97.77,
	[
		6MJF_1:73.5,6DVZ_1:73.5
	]:24.27
]

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 \((0.85)(0.8)(\frac{1031 }{\log_{20} 1031}-\frac{240}{\log_{20}240})=213.\)
Status Protein1 Protein2 d d1/2
Query variables 2XTO_1 6DVZ_1 272 173
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]