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Parikh vectors
6AFV_1 7AUD_1 7ZYR_1 Letter Amino acid
36 44 20 K Lycine
47 28 11 T Threonine
31 30 26 D Aspartic acid
6 5 5 W Tryptophan
22 21 23 Y Tyrosine
99 30 15 A Alanine
23 21 15 N Asparagine
10 19 2 C Cysteine
9 24 9 Q Glutamine
79 34 14 G Glycine
6 21 16 H Histidine
64 29 19 I Isoleucine
74 57 30 L Leucine
15 27 24 R Arginine
46 24 13 F Phenylalanine
58 42 15 S Serine
67 35 26 V Valine
20 15 9 M Methionine
25 24 14 P Proline
29 33 22 E Glutamic acid 

6AFV_1|Chains A, B|Pyrophosphate-energized vacuolar membrane proton pump|Vigna radiata var. radiata (3916)
>7AUD_1|Chains A, B, C, D, E, F|Bloom syndrome protein,Bloom syndrome protein|Homo sapiens (9606)
>7ZYR_1|Chain A|Casein kinase II subunit alpha|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 \(w=f(c)\)
6AFV , Knot 285 766 0.82 40 264 669 
MGAAILPDLGTEILIPVCAVIGIAFALFQWLLVSKVKLSAVRDASPNAAAKNGYNDYLIEEEEGINDHNVVVKCAEIQNAISEGATSFLFTEYKYVGIFMVAFAILIFLFLGSVEGFSTSPQACSYDKTKTCKPALATAIFSTVSFLLGGVTSLVSGFLGMKIATYANARTTLEARKGVGKAFITAFRSGAVMGFLLAANGLLVLYIAINLFKIYYGDDWGGLFEAITGYGLGGSSMALFGRVGGGIYTKAADVGADLVGKVERNIPEDDPRNPAVIADNVGDNVGDIAGMGSDLFGSYAESSCAALVVASISSFGLNHELTAMLYPLIVSSVGILVCLLTTLFATDFFEIKAVKEIEPALKKQLVISTVLMTIGVAVVSFVALPTSFTIFNFGVQKDVKSWQLFLCVAVGLWAGLIIGFVTEYYTSNAYSPVQDVADSCRTGAATNVIFGLALGYKSVIIPIFAIAISIFVSFTFAAMYGIAVAALGMLSTIATGLAIDAYGPISDNAGGIAEMAGMSHRIRERTDALDAAGNTTAAIGKGFAIGSAALVSLAKFGAFVSRASITTVDVLTPKVFIGLIVGAMLPYWFSAMTMKSVGSAALKMVEEVRRQFNTIPGLMEGTAKPDYATCVKISTDASIKEMIPPGALVMLTPLVVGILFGVETLSGVLAGSLVSGVQIAISASNTGGAWDNAKKYIEAGASEHARSLGPKGSDCHKAAVIGDTIGDPLKDTSGPSLNILIKLMAVESLVFAPFFATHGGLLFKIF
7AUD , Knot 230 563 0.86 40 280 536 
MGSAWSHPQFEKSSGLEVLFQGGPHMSRNLKHERFQSLSFPHTKEMMKIFHKKFGLHNFRTNQLEAINAALLGEDCFILMPTGGGKSLCYQLPACVSPGVTVVISPLRSLIVDQVQKLTSLDIPATYLTGDKTDSEATNIYLQLSKKDPIIKLLYVTPEKICASNRLISTLENLYERKLLARFVIDEAHCVSQWGHDFRQDYKRMNMLRQKFPSVPVMALTATANPRVQKDILTQLKILRPQVFSMSFNRHNLKYYVLPKKPKKVAFDCLEWIRKHHPYDSGIIYCLSRRECDTMADTLQRDGLAALAYHAGLSDSARDEVQQKWINQDGCQVICATIAFGMGIDKPDVRFVIHASLPKSVEGYYQESGRAGRDGEISHCLLFYTYHDVTRLKRLIMMEKDGNHHTRETHFNNLYSMVHYCENITECRRIQLLAYFGENGFNPDFCKKHPDVSCDNCCKTKGSGGSKALVAKVSQREEMVKKCLGELTEVCKSLGKVFGVHYFNIFNTVTLKKLAESLSSDPEVLLQIDGVTEDKLEKYGAEVISVLQKYSEWTSPAEDSSPG
7ZYR , Knot 147 328 0.86 40 194 315 
SGPVPSRARVYTDVNTHRPSEYWDYESHVVEWGNQDDYQLVRKLGRGKYSEVFEAINITNNEKVVVKILKPVAAAKIKREIKILENLRGGPNIITLADIVKDPVSRTPALVFEHVNNTDFKQLYQTLTDYDIRFYMYEILKALDYCHSMGIMHRDVKPHNVMIDHEHRKLRLIDWGLAEFYHPGQEYNVRVASRYFKGPELLVDYQMYDYSLDMWSLGCMLASMIFRKEPFFHGHDNYDQLVRIAKVLGTEDLYDYIDKYNIELDPRFNDILGRHSRKRWERFVHSENQHLVSPEALDFLDKLLRYDHQSRLTAREAMEHPYFYTVVK

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 \(c\).

\(|P_{f(6AFV_1)}(2) \setminus P_{f(7AUD_1)}(2)|=56\), \(|P_{f(7AUD_1)}(2) \setminus P_{f(6AFV_1)}(2)|=72\). 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 1:1111111011001111101111111111011110010101100101011100100001100001100001110010100110011001110000011111111111111111010110001010000000000111101110010111111001101111101100101000101001110111011001111111111011111011101101001001111101101011110011111011111000110111011101000110001001111100110011011111001110010000111111010011100010111011110011111011001110011010110010111000111001110111111011111001011011100010010111011111111111111000000010011001100000111001111111100011111111110111010111101111111111001101111010111000111110111100010000011011100011110111110111101101111100101001011010111111111111011011010011011101100100010011111010101001001010001010011111111110111111111100101111101101101110100011110010001011100010011101000001111100110110000110101110111100111111110011111011
Pair \(Z_2\) Length of longest common subsequence
6AFV_1,7AUD_1 128 4
6AFV_1,7ZYR_1 174 4
7AUD_1,7ZYR_1 184 4

Newick tree

 
[
	7ZYR_1:96.55,
	[
		6AFV_1:64,7AUD_1:64
	]:32.55
]

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 \((0.85)(0.8)(\frac{1329 }{\log_{20} 1329}-\frac{563}{\log_{20}563})=195.\)
Status Protein1 Protein2 d d1/2
Query variables 6AFV_1 7AUD_1 246 216
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]