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Parikh vectors
8YLT_1 6OFT_1 7LZT_1 Letter Amino acid
64 13 11 Y Tyrosine
67 25 17 D Aspartic acid
86 35 9 E Glutamic acid
49 17 27 G Glycine
87 25 11 K Lycine
10 0 12 C Cysteine
19 17 13 P Proline
70 25 17 S Serine
83 20 12 I Isoleucine
73 18 17 F Phenylalanine
34 27 24 T Threonine
9 12 3 W Tryptophan
33 46 17 A Alanine
40 28 11 R Arginine
64 32 22 N Asparagine
21 8 7 H Histidine
26 36 13 Q Glutamine
96 47 29 L Leucine
23 13 10 M Methionine
51 27 27 V Valine 

8YLT_1|Chains A, B, C, D|SIR2-like domain-containing protein|Bacillus subtilis subsp. natto (strain BEST195) (645657)
>6OFT_1|Chains A, B|Probable zinc protease PqqL|Escherichia coli (strain K12) (83333)
>7LZT_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
8YLT , Knot 372 1005 0.85 40 300 887 
MVKVDLESKRYGEKLKEVFLMLDNNVVECIKEITESSRNGKLVFFVGAGVSTLSDYPQWWRLVDKYHEELYGSPKKGNYSSDEYLRIPQIFYNVKGEMAFDGILKDFFQVDKPTNPIHDKILAMNPAHVITTNYDNLIDTACWKRGKYFSVISAEEDVANATSSRYLLKVHGDFRKGFKGENVVLKEDDYLNYDQNYPLISNLMKTIIATHTIVFIGYGLGDYNINMLLNWVRKLQKDSFHKPFFIRTDPSPIENETLIYYENKGLRIIDAASLIDSNEYDYLERYSAVMDLLIESQENKFITKDDEVIDYIYGKISPLFALQYIRKIDLKHVFEYDYHFEVNGTVVRHKNKGFGYMERFFELKESCDERSKLSKKQYERFNALFNFFEKNGVICMAKDAGTLNTSIEINSLAYHGKYDVMKKFIEEQSVSIEDDYKKAFFLACLGRWEESYDLYSNIILNSIDESNGCVYYLSQINRYRIYQSITQAVTQFNGLGLLTFGRHYKPFTDEFLARIEREMTNFNIDDLFNGMPFEFQKKYKILEFLSDNQFLYDDTVKLFELTNKVRSEMSEGSYSFGMSSDIVVLLRLYDNLRFLYENCLWSVSFHEFHQYIRNSMSLLIEKAEYERTRDIDELGFSFFGKKSGFFMEYYDFVNISRHFKIDDIKNLERSCSIDKIRFGEQEKIEEYLVGIAEEITKQFSANGMNVVFYTQFISEAKAALYFAKYVKLSEEGLGKIVKALLFYFPERDLDIGKRYVWLERLTKCNELPKSIISIIDDFLVLQAEKHIDQNYSEVSSNGLYSRDYGALIKHFEKNFISKRLSEITLCLTQDKQKQIDFLFKLLPLLSTNAKSHLLSFKSVENINDLMNGIRIGLIDEFTPEHEELIIEYLETRKVNYIVEKEKGIQTFSSNDYMSTFGIWYFLEEINNSKMEEFIGMDDQYDFFVDPENFDYKKFIPSWLKNYNDKLLGKIAGNKHMKHHVIEVLKERVKNSNDKRYLEILMNYFI
6OFT , Knot 198 471 0.86 38 249 445 
AALPQDEKLITGQLDNGLRYMIYPHAHPKDQVNLWLQIHTGSLQEEDNELGVAHFVEHMMFNGTKTWPGNKVIETFESMGLRFGRDVNAYTSYDETVYQVSLPTTQKQNLQQVMAIFSEWSNAATFEKLEVDAERGVITEEWRAHQDAKWRTSQARRPFLLANTRNLDREPIGLMDTVATVTPAQLRQFYQRWYQPNNMTFIVVGDIDSKEALALIKDNLSKLPANKAAENRVWPTKAENHLRFNIINDKENRVNGIALYYRLPMVQVNDEQSFIEQAEWSMLVQLFNQRLQERIQSGELKTISGGTARSVKIAPDYQSLFFRVNARDDNMQDAANALMAELATIDQHGFSAEELDDVKSTRLTWLKNAVDQQAERDLRMLTSRLASSSLNNTPFLSPEETYQLSKRLWQQITVQSLAEKWQQLRKNQDAFWEQMVNNEVAAKKALSPAAILALEKEYANKKLAAYVFPGR
7LZT , Knot 136 309 0.84 40 195 293 
SNIGSGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTF

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 \(c\).

\(|P_{f(8YLT_1)}(2) \setminus P_{f(6OFT_1)}(2)|=92\), \(|P_{f(6OFT_1)}(2) \setminus P_{f(8YLT_1)}(2)|=41\). 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 1:110101000001001001111100011001001000000101111111110010001011011000000101010010000000101101100101011101110011010010011000111101101100000011001010010010110100011010000011010101001101001110000010000001110011001110001111101110001011101100100001001111000101100001100000110110110110000000100001110111000000110000011001010101111100100101001100000101010110000011101001101000000000100000001011101100011101100110100010100110010001100110000101000000111110110100000100011100100001010010010000100010011001011111011000011000111010001001010011011110100000110110000110000101101000100010010001110001111101000101100001101010010001000101110010000000100111011100011110000110100010100100100000100101100001000111110010001010110111000110010111011001010001110110111101100010110001110010000011001101100111101000100000010001100000111100100011000100101010000000101110111110001000110100100100110110111100101000011100100001001100001100100000100111101100100001001111000001110100100001110110000001110111000100011011000100000000101110011
Pair \(Z_2\) Length of longest common subsequence
8YLT_1,6OFT_1 133 4
8YLT_1,7LZT_1 181 5
6OFT_1,7LZT_1 186 4

Newick tree

 
[
	7LZT_1:98.75,
	[
		8YLT_1:66.5,6OFT_1:66.5
	]:32.25
]

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 \((0.85)(0.8)(\frac{1476 }{\log_{20} 1476}-\frac{471}{\log_{20}471})=256.\)
Status Protein1 Protein2 d d1/2
Query variables 8YLT_1 6OFT_1 321 235.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]