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Parikh vectors
4UVK_1 7SFE_1 7EON_1 Letter Amino acid
34 60 0 R Arginine
81 54 0 E Glutamic acid
25 58 0 P Proline
26 36 0 Y Tyrosine
57 49 0 D Aspartic acid
10 25 18 C Cysteine
28 20 0 H Histidine
70 56 0 K Lycine
8 19 0 M Methionine
46 37 0 T Threonine
9 13 0 W Tryptophan
36 57 4 A Alanine
50 36 0 N Asparagine
39 30 0 Q Glutamine
37 64 18 G Glycine
57 38 0 F Phenylalanine
61 33 0 I Isoleucine
138 73 0 L Leucine
81 61 0 S Serine
61 55 0 V Valine 

4UVK_1|Chain A|ZYRO0D15994P|ZYGOSACCHAROMYCES ROUXII (4956)
>7SFE_1|Chain A|DNA (cytosine-5)-methyltransferase 1|Homo sapiens (9606)
>7EON_1|Chain A|Pepper (49-MER)|synthetic construct (32630)
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 \(w=f(c)\)
4UVK , Knot 341 954 0.81 40 290 801 
SKQDQETYLETIKDFQPTELFQVLATSEDLSIDELLRDSLESYSQDRDRFLQEFINLLLCCCGAIARLEVHDVHSNESSNETVGELQLLFQRQKVHEFHLLISKDSKKKSKYPPLYANFVEFMFRLMDVANDLQLLYVESDEDESEIGTGPLIIDLLTWLSPLSVCKIRSLRYIATLTLYLFQDFLTDHVVDLDKNYLSKLSKQLSVENKKKRPNGKTVEKLESTIAEIQSSKMVTQGIIDNIIKLCFVHRFKDVDETIRCESMVHLASWTKSFPEYFLKVTFLKYFGWLLSDSSVTVRLQVLKILPQLISQHHNRAVDNSAVRQFFERFKERILEIALKDSNLEVRLSAVQVLVEVASLGYLEDTEILSISSLIFEDNEIKVSSLGKNSRYLASVAKFFACITEEKFQEFTNNRVLPKELFDVKGSSAVRIGIFMNLLNESLTEYLQKVPQIGSEKRIHILFQAAEFLYPYFGSLIKDICKVLTFEGEFTHESLETPTYTGDNNNEENNDENNRSNLLLPTDSNNIILYVTTLHGLAYGGTHMRGQPKFKVAEAVLPHLDQLIKRLPIESSNVLASILGVFNLFAFEDWIHTGYEKDIRKILEKIIKAFNESTLTSGAQDLKYKSFSETVSQVRKLGFNELDELWLNHISQLKIHLGKFLEEKLHPDVQDTENDENMNTLYGVFLNKLALLGKVYPIEFQENLLSLFLNRFVQRLPQIGVHCQLETIQEIHLKLLALLTTWQLQKWVDILEKSSENDSPSPVSEFSLRTVSSIVKSFKVIFDALSSDTNDNDGTLGDFLLKWSTSNSFIDIIISLKVFELGVAESEKSWRHALRENFVPYVTDSANQVLLKVFLYLESLFANESSEHLDRNPQEDVNLNDIKYDGFGDGCEKELLLFTIKLKGLMKLGLLDEALFSRIALNKEKLGPLYAKVIEDTIFDQDKKGRVPHHHHHH
7SFE , Knot 338 874 0.87 40 331 797 
HMNRISWVGEAVKTDGKKSYYKKVCIDAETLEVGDCVSVIPDDSSKPLYLARVTALWEDSSNGQMFHAHWFCAGTDTVLGATSDPLELFLVDECEDMQLSYIHSKVKVIYKAPSENWAMEGGMDPESLLEGDDGKTYFYQLWYDQDYARFESPPKTQPTEDNKFKFCVSCARLAEMRQKEIPRVLEQLEDLDSRVLYYSATKNGILYRVGDGVYLPPEAFTFNIKLSSPVKRPRKEPVDEDLYPEHYRKYSDYIKGSNLDAPEPYRIGRIKEIFCPKKSNGRPNETDIKIRVNKFYRPENTHKSTPASYHADINLLYWSDEEAVVDFKAVQGRCTVEYGEDLPECVQVYSMGGPNRFYFLEAYNAKSKSFEDPPNHARSPGNKGKGKGKGKGKPKSQACEPSEPEIEIKLPKLRTLDVFSGCGGLSEGFHQAGISDTLWAIEMWDPAAQAFRLNNPGSTVFTEDCNILLKLVMAGETTNSRGQRLPQKGDVEMLCGGPPCQGFSGMNRFNSRTYSKFKNSLVVSFLSYCDYYRPRFFLLENVRNFVSFKRSMVLKLTLRCLVRMGYQCTFGVLQAGQYGVAQTRRRAIILAAAPGEKLPLFPEPLHVFAPRACQLSVVVDDKKFVSNITRLSSGPFRTITVRDTMSDLPEVRNGASALEISYNGEPQSWFQRQLRGAQYQPILRDHICKDMSALVAARMRHIPLAPGSDWRDLPNIEVRLSDGTMARKLRYTHHDRKNGRSSSGALRGVCSCVEAGKACDPAARQFNTLIPWCLPHTGNRHNHWAGLYGRLEWDGFFSTTVTNPEPMGKQGRVLHPEQHRVVSVRECARSQGFPDTYRLFGNILDKHRQVGNAVPPPLAKAIGLEIKLCMLAKA
7EON , Knot 16 48 0.43 8 15 28 
GCGCACUGGCGCUGCGCCUUCGGGCGCCAAUCGUAGCGUGUCGGCGCC

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 \(c\).

\(|P_{f(4UVK_1)}(2) \setminus P_{f(7SFE_1)}(2)|=35\), \(|P_{f(7SFE_1)}(2) \setminus P_{f(4UVK_1)}(2)|=76\). 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 1:000000001001001010011011100001010011000100000000011001101110001111010100100000000011010111000010010111000000000011101011011101101100101101000000001101111101101101101001001001101010110011000110100001001000101000000101001001000110100001100111001101011001001000100001101101000110011010110011111000010101011011101100000011000110011001000110111000010101011011101101101000011010011100001010011000001101101110100001001000011100110101001101111101100010001001101100001011101101101011011001001101010100001001000100000000000000011110000011101001011101100101010101101111010011001110000111011111011110011001000010011001101100001001100100001000100100111001001110010010101101100010101000000001001011110011111010110100011011100110011011100010010010101111100101001101100000000101100101001001100101110110000000010110111010000011011101011011110000010011000111010001001110111010011100000010001000101001000111010000111101010111011110011100111000011110101100011000001011000000
Pair \(Z_2\) Length of longest common subsequence
4UVK_1,7SFE_1 111 5
4UVK_1,7EON_1 293 2
7SFE_1,7EON_1 332 3

Newick tree

 
[
	7EON_1:17.91,
	[
		4UVK_1:55.5,7SFE_1:55.5
	]:12.41
]

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 \((0.85)(0.8)(\frac{1828 }{\log_{20} 1828}-\frac{874}{\log_{20}874})=232.\)
Status Protein1 Protein2 d d1/2
Query variables 4UVK_1 7SFE_1 288 282
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]