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Parikh vectors
7MIM_1 1OWL_1 2ODV_1 Letter Amino acid
56 23 26 E Glutamic acid
105 53 33 L Leucine
12 17 4 W Tryptophan
15 11 7 H Histidine
45 25 7 I Isoleucine
25 7 6 M Methionine
51 25 9 S Serine
54 62 22 A Alanine
43 27 9 D Aspartic acid
13 4 0 C Cysteine
26 44 18 Q Glutamine
51 17 5 T Threonine
43 14 14 V Valine
39 14 5 N Asparagine
47 18 7 F Phenylalanine
35 35 8 P Proline
25 14 6 Y Tyrosine
41 31 22 R Arginine
33 29 12 G Glycine
49 14 15 K Lycine 

7MIM_1|Chains A, B, C, D|Transient receptor potential cation channel subfamily V member 3|Mus musculus (10090)
>1OWL_1|Chain A|Deoxyribodipyrimidine photolyase|Synechococcus elongatus (269084)
>2ODV_1|Chain A|Plectin 1|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 \(w=f(c)\)
7MIM , Knot 307 808 0.84 40 311 733 
MNAHSKEMAPLMGKRTTAPGGNPVVLTEKRPADLTPTKKSAHFFLEIEGFEPNPTVTKTSPPIFSKPMDSNIRQCLSGNCDDMDSPQSPQDDVTETPSNPNSPSANLAKEEQRQKKKRLKKRIFAAVSEGCVEELRELLQDLQDLCRRRRGLDVPDFLMHKLTASDTGKTCLMKALLNINPNTKEIVRILLAFAEENDILDRFINAEYTEEAYEGQTALNIAIERRQGDITAVLIAAGADVNAHAKGVFFNPKYQHEGFYFGETPLALAACTNQPEIVQLLMENEQTDITSQDSRGNNILHALVTVAEDFKTQNDFVKRMYDMILLRSGNWELETMRNNDGLTPLQLAAKMGKAEILKYILSREIKEKPLRSLSRKFTDWAYGPVSSSLYDLTNVDTTTDNSVLEIIVYNTNIDNRHEMLTLEPLHTLLHTKWKKFAKYMFFLSFCFYFFYNITLTLVSYYRPREDEDLPHPLALTHKMSWLQLLGRMFVLIWATCISVKEGIAIFLLRPSDLQSILSDAWFHFVFFVQAVLVILSVFLYLFAYKEYLACLVLAMALGWANMLYYTRGFQSMGMYSVMIQKVILHDVLKFLFVYILFLLGFGVALASLIEKCSKDKKDCSSYGSFSDAVLELFKLTIGLGDLNIQQNSTYPILFLFLLITYVILTFVLLLNMLIALMGETVENVSKESERIWRLQRARTILEFEKMLPEWLRSRFRMGELCKVADEDFRLCLRINEVKWTEWKTHVSFLNEDPGPIRRTADLNKIQDSSRSNSKTTLYAFDELDEFPETSVLVPRGSAAAWSHPQFEK
1OWL , Knot 193 484 0.82 40 232 446 
MAAPILFWHRRDLRLSDNIGLAAARAQSAQLIGLFCLDPQILQSADMAPARVAYLQGCLQELQQRYQQAGSRLLLLQGDPQHLIPQLAQQLQAEAVYWNQDIEPYGRDRDGQVAAALKTAGIRAVQLWDQLLHSPDQILSGSGNPYSVYGPFWKNWQAQPKPTPVATPTELVDLSPEQLTAIAPLLLSELPTLKQLGFDWDGGFPVEPGETAAIARLQEFCDRAIADYDPQRNFPAEAGTSGLSPALKFGAIGIRQAWQAASAAHALSRSDEARNSIRVWQQELAWREFYQHALYHFPSLADGPYRSLWQQFPWENREALFTAWTQAQTGYPIVDAAMRQLTETGWMHNRCRMIVASFLTKDLIIDWRRGEQFFMQHLVDGDLAANNGGWQWSASSGMDPKPLRIFNPASQAKKFDATATYIKRWLPELRHVHPKDLISGEITPIERRGYPAPIVNHNLRQKQFKALYNQLKAAIAEPEAEPDS
2ODV , Knot 105 235 0.81 38 148 226 
GSHMRANELQLRWQEYRELVLLLLQWMRHHTAAFEERRFPSSFEEIEILWSQFLKFKEMELPAKEADKNRSKGIYQSLEGAVQAGQLKVPPGYHPLDVEKEWGKLHVAILEREKQLRSEFERLEALQRIVTKLQMEAGLAEEQLNQADALLQSDVRLLAAGKVPQRAGEVERDLDKADSMIRLLFNDVQTLKDGRHPQGEQMYRRVYRLHKRLVAIRTEYNLRLKAGVAAPATQV

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 \(c\).

\(|P_{f(7MIM_1)}(2) \setminus P_{f(1OWL_1)}(2)|=118\), \(|P_{f(1OWL_1)}(2) \setminus P_{f(7MIM_1)}(2)|=39\). 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 1:1010000111111000011110111100001101010000101110101101010100001111001100010001010000100100100010001001001010110000000000100011111001010010011001001000001101101110010100010001101110101000011011111100001100110100000100100110111000010101111111101010101111010000011011001111110000101101110000001000000100110111011001000001100100111100101010010000110110111011010110011000100011001000100110111000100100100000001101110000100000110101100110001001100111101010110010101100001000001101111000101101110111111100101001111111010010011001110111110111111011101110000110111111111101100001100111001110011100110111101111111111110110000000000000101001110110101111010100000011111111100111011111011111110010010000001101001001101001110110001011010011000101010100101001000101100011110001010010000000000010110010011000111101011110010100
Pair \(Z_2\) Length of longest common subsequence
7MIM_1,1OWL_1 157 4
7MIM_1,2ODV_1 199 4
1OWL_1,2ODV_1 164 5

Newick tree

 
[
	2ODV_1:95.01,
	[
		7MIM_1:78.5,1OWL_1:78.5
	]:16.51
]

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 \((0.85)(0.8)(\frac{1292 }{\log_{20} 1292}-\frac{484}{\log_{20}484})=207.\)
Status Protein1 Protein2 d d1/2
Query variables 7MIM_1 1OWL_1 268 210.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]