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Parikh vectors
6UZY_1 9JMD_1 7LUF_1 Letter Amino acid
23 18 29 N Asparagine
20 28 66 D Aspartic acid
12 16 89 G Glycine
6 4 33 H Histidine
29 24 50 K Lycine
24 18 56 F Phenylalanine
5 4 9 W Tryptophan
17 18 31 Q Glutamine
19 8 70 P Proline
24 18 56 T Threonine
34 23 80 V Valine
25 29 123 A Alanine
23 22 77 E Glutamic acid
29 26 54 I Isoleucine
37 20 49 S Serine
21 15 48 Y Tyrosine
12 29 86 R Arginine
10 7 20 C Cysteine
63 27 117 L Leucine
4 7 20 M Methionine 

6UZY_1|Chains A, B, C, D, E, F, G|Pannexin|Xenopus tropicalis (8364)
>9JMD_1|Chain A|Guanine nucleotide-binding protein G(q) subunit alpha|Homo sapiens (9606)
>7LUF_1|Chains A, D[auth B]|DNA polymerase|Human herpesvirus 1 (10298)
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 \(w=f(c)\)
6UZY , Knot 178 437 0.82 40 221 412 
MAIAHIATEYVFSDFLLKDPPESKYKGLRLELAVDKLVSCIAVGLPLLLISLAFAQEITLGSQISCFAPTSFSWRQAAYVDSFCWAAVQQKHLSQSDSGNVPLWLHKFFPYILLLVAVLLYLPNLFWRFTAAPHLSSDLKFVMEELDKCYNRDIKDIKAANNLNSSDKRDGLNSPVVSENLQQSLWEIPLSHYKYPIVEQYLKTKNNSYGLIIKYLICRVVTLIIVFTACIYLGYYISLFSLTDEFTCNIRTGILRNDTALPPLVQCKLIAVGVFRLLSYINLIIYVLIMPFIIYAMLVPFRKTANVLKVYEVLPTFSVQQAPSKTYDDHSLFLLFLEENVSELKSYKFLKVLENIKNTGENFDTIQYLTSLGTVKTDTVDGKLAFKCTSEVPNNTEQNEVELTVQPSSDNAKTEEKKVRQRLLDSSCSNSLEVLFQ
9JMD , Knot 158 361 0.86 40 216 345 
MGCTLSAEDKAAVERSKMIEKQLQKDKQVYRRTLRLLLLGADNSGKSTIVKQMRIYHVNGYSEEECKQYKAVVYSNTIQSIIAIIRAMGRLKIDFGDSARADDARQLFVLAGAAEEGFMTAELAGVIKRLWKDSGVQACFNRSREYQLNDSAAYYLNDLDRIAQPNYIPTQQDVLRTRVKTSGIFETKFQVDKVNFHMFDVGAQRDERRKWIQCFNDVTAIIFVVDSSDYNRLQEALNDFKSIWNNRWLRTISVILFLNKQDLLAEKVLAGKSKIEDYFPEFARYTTPEDATPEPGEDPRVTRAKYFIRKEFVDISTASGDGRHICYPHFTCSVDTENARRIFNDCKDIILQMNLREYNLV
7LUF , Knot 417 1163 0.84 40 328 1011 
LEVLFQGPNFYNPYLAPVGTQQKPTGPTQRHTYYSECDEFRFIAPRVLDEDAPPEKRAGVHDGHLKRAPKVYCGGDERDVLRVGSGGFWPRRSRLWGGVDHAPAGFNPTVTVFHVYDILENVEHAYGMRAAQFHARFMDAITPTGTVITLLGLTPEGHRVAVHVYGTRQYFYMNKEEVDRHLQCRAPRDLCERMAAALRESPGASFRGISADHFEAEVVERTDVYYYETRPALFYRVYVRSGRVLSYLCDNFCPAIKKYEGGVDATTRFILDNPGFVTFGWYRLKPGRNNTLAQPRAPMAFGTSSDVEFNCTADNLAIEGGMSDLPAYKLMCFDIACKAGGEDELAFPVAGHPEDLVIQISCLLYDLSTTALEHVLLFSLGSCDLPESHLNELAARGLPTPVVLEFDSEFEMLLAFMTLVKQYGPEFVTGYNIINFDWPFLLAKLTDIYKVPLDGYGRMNGRGVFRVWDIGQSHFQKRSKIKVNGMVNIDMYGIITDKIKLSSYKLNAVAEAVLKDKKKDLSYRDIPAYYAAGPAQRGVIGEYCIQDSLLVGQLFFKFLPHLELSAVARLAGINITRTIYDGQQIRVFTCLLRLADQKGFILPDTQGRFRGAGGEAPKRPAAAREDEERPEEEGEDEDEREEGGGEREPEGARETAGRHVGYQGARVHDPTSGFHVNPVVGFDFASLYPSIIQAHNLCFSTLSLRADAVAHLEAGKDYLEIEVGGRRLFFVKAHVRESLLSILLRDWLAMRKQIRSRIPQSSPEEAVLLDKQQAAIKVVCNSVYGFTGVQHGLLPCLHVAATVTTIGREMLLATREYVHARWAAFEQLLADFPEAADMRAPGPYSMRIIYGDTDSIFVLCRGLTAAGLTAMGDKMASHISRALFLPPIKLECEKTFTKLLLIAKKKYIGVIYGGKMLIKGVDLVRKNNCAFINRTSRALVDLLFYDDTVSGAAAALAERPAEEWLARPLPEGLQAFGAVLVDAHRRITDPERDIQDFVLTAELSRHPRAYTNKRLAHLTVYYKLMARRAQVPSIKDRIPYVIVAQTREVEETVARLAALRELDAAAPGDEPAPPAALPSPAKRPRETPSHADPPGGASKPRKLLVSELAEDPAYAIAHGVALNTDYYFSHLLGAACVTFKALFGNNAKITESLLKRFIPEVWH

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 \(c\).

\(|P_{f(6UZY_1)}(2) \setminus P_{f(9JMD_1)}(2)|=86\), \(|P_{f(9JMD_1)}(2) \setminus P_{f(6UZY_1)}(2)|=81\). 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 1:11110110001100111001100000110101110011001111111111011110010110010011100101001101001011110000100000101111100111011111111101101110101110100010111001000000010010110010000000110011100010001101110000011100010000000111100110011011111010101100101101000100010011100001111110001111111011001011101111111101111110001011010011101010011000000001111110001001000011011001000100100100100110100001010111000001100000001010101000010000001000110000000101110
Pair \(Z_2\) Length of longest common subsequence
6UZY_1,9JMD_1 167 3
6UZY_1,7LUF_1 153 6
9JMD_1,7LUF_1 154 4

Newick tree

 
[
	9JMD_1:81.54,
	[
		6UZY_1:76.5,7LUF_1:76.5
	]:5.04
]

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 \((0.85)(0.8)(\frac{798 }{\log_{20} 798}-\frac{361}{\log_{20}361})=118.\)
Status Protein1 Protein2 d d1/2
Query variables 6UZY_1 9JMD_1 152 138.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]