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Parikh vectors
1IVQ_1 8CPZ_1 6WRV_1 Letter Amino acid
11 133 41 G Glycine
5 125 44 K Lycine
3 125 24 Y Tyrosine
8 170 36 N Asparagine
4 147 37 D Aspartic acid
6 136 34 E Glutamic acid
0 53 12 H Histidine
1 40 11 W Tryptophan
5 229 50 A Alanine
2 148 21 Q Glutamine
3 91 38 F Phenylalanine
5 93 25 P Proline
7 156 38 T Threonine
0 10 4 C Cysteine
11 142 27 I Isoleucine
10 270 64 L Leucine
2 55 10 M Methionine
4 197 49 S Serine
9 114 48 V Valine
3 101 26 R Arginine 

1IVQ_1|Chains A, B|HIV-2 PROTEASE|Human immunodeficiency virus 2 (11709)
>8CPZ_1|Chains A, B, C, D, E|TcdA1|Photorhabdus luminescens (29488)
>6WRV_1|Chains A, B, C[auth E]|Transferrin receptor protein 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 \(w=f(c)\)
1IVQ , Knot 52 99 0.80 36 81 96 
PQFSLWKRPVVTAYIEGQPVEVLLDTGADDSIVAGIELGNNYSPKIVGGIGGFINTLEYKNVEIEVLNKKVRATIMTGDTPINIFGRNILTALGMSLNL
8CPZ , Knot 826 2535 0.85 40 365 1943 
MAHHHHHHSSGLEVLFQGPMNESVKEIPDVLKSQCGFNCLTDISHSSFNEFRQQVSEHLSWSETHDLYHDAQQAQKDNRLYEARILKRANPQLQNAVHLAILAPNAELIGYNNQFSGRASQYVAPGTVSSMFSPAAYLTELYREARNLHASDSVYYLDTRRPDLKSMALSQQNMDIELSTLSLSNELLLESIKTESKLENYTKVMEMLSTFRPSGATPYHDAYENVREVIQLQDPGLEQLNASPAIAGLMHQASLLGINASISPELFNILTEEITEGNAEELYKKNFGNIEPASLAMPEYLKRYYNLSDEELSQFIGKASNFGQQEYSNNQLITPVVNSSDGTVKVYRITREYTTNAYQMDVELFPFGGENYRLDYKFKNFYNASYLSIKLNDKRELVRTEGAPQVNIEYSANITLNTADISQPFEIGLTRVLPSGSWAYAAAKFTVEEYNQYSFLLKLNKAIRLSRATELSPTILEGIVRSVNLQLDINTDVLGKVFLTKYYMQRYAIHAETALILCNAPISQRSYDNQPSQFDRLFNTPLLNGQYFSTGDEEIDLNSGSTGDWRKTILKRAFNIDDVSLFRLLKITDHDNKDGKIKNNLKNLSNLYIGKLLADIHQLTIDELDLLLIAVGEGKTNLSAISDKQLATLIRKLNTITSWLHTQKWSVFQLFIMTSTSYNKTLTPEIKNLLDTVYHGLQGFDKDKADLLHVMAPYIAATLQLSSENVAHSVLLWADKLQPGDGAMTAEKFWDWLNTKYTPGSSEAVETQEHIVQYCQALAQLEMVYHSTGINENAFRLFVTKPEMFGAATGAAPAHDALSLIMLTRFADWVNALGEKASSVLAAFEANSLTAEQLADAMNLDANLLLQASIQAQNHQHLPPVTPENAFSCWTSINTILQWVNVAQQLNVAPQGVSALVGLDYIQSMKETPTYAQWENAAGVLTAGLNSQQANTLHAFLDESRSAALSTYYIRQVAKAAAAIKSRDDLYQYLLIDNQVSAAIKTTRIAEAIASIQLYVNRALENVEENANSGVISRQFFIDWDKYNKRYSTWAGVSQLVYYPENYIDPTMRIGQTKMMDALLQSVSQSQLNADTVEDAFMSYLTSFEQVANLKVISAYHDNINNDQGLTYFIGLSETDAGEYYWRSVDHSKFNDGKFAANAWSEWHKIDCPINPYKSTIRPVIYKSRLYLLWLEQKEITWQTGNSKDGYQTETDYRYELKLAHIRYDGTWNTPITFDVNKKISELKLEKNRAPGLYCAGYQGEDTLLVMFYNQQDTLDSYKNASMQGLYIFADMASKDMTPEQSNVYRDNSYQQFDTNNVRRVNNRYAEDYEIPSSVSSRKDYGWGDYYLSMVYNGDIPTINYKAASSDLKIYISPKLRIIHNGYEGQKRNQCNLMNKYGKLGDKFIVYTSLGVNPNNSSNKLMFYPVYQYSGNTSGLNQGRLLFHRDTTYPSKVEAWIPGAKRSLTNQNAAIGDDYATDSLNKPDDLKQYIFMTDSKGTATDVSGPVEINTAISPAKVQIIVKAGGKEQTFTADKDVSIQPSPSFDEMNYQFNALEIDGSGLNFINNSASIDVTFTAFAEDGRKLGYESFSIPVTLKVSTDNALTLHHNENGAQYMQWQSYRTRLNTLFARQLVARATTGIDTILSMETQNIQEPQLGKGFYATFVIPPYNLSTHGDERWFKLYIKHVVDNNSHIIYSGQLTDTNINITLFIPLDDVPLNQDYHAKVYMTFKKSPSDGTWWGPHFVRDDKGIVTINPKSILTHFESVNVLNNISSEPMDFSGANSLYFWELFYYTPMLVAQRLLHEQNFDEANRWLKYVWSPSGYIVHGQIQNYQWNVRPLLEDTSWNSDPLDSVDPDAVAQHDPMHYKVSTFMRTLDLLIARGDHAYRQLERDTLNEAKMWYMQALHLLGDKPYLPLSTTWSDPRLDRAADITTQNAHDSAIVALRQNIPTPAPLSLRSANTLTDLFLPQINEVMMNYWQTLAQRVYNLRHNLSIDGQPLYLPIYATPADPKALLSAAVATSQGGGKLPESFMSLWRFPHMLENARGMVSQLTQFGSTLQNIIERQDAEALNALLQNQAAELILTNLSIQDKTIEELDAEKTVLEKSKAGAQSRFDSYGKLYDENINAGENQAMTLRASAAGLTTAVQASRLAGAAADLVPNIFGFAGGGSRWGAIAEATGYVMEFSANVMNTEADKISQSETYRRRRQEWEIQRNNAEAELKQIDAQLKSLAVRREAAVLQKTSLKTQQEQTQSQLAFLQRKFSNQALYNWLRGRLAAIYFQFYDLAVARCLMAEQAYRWELNDDSARFIKPGAWQGTYAGLLAGETLMLSLAQMEDAHLKRDKRALEVERTVSLAEVYAGLPKDNGPFSLAQEIDKLVSQGSGSAGSGNNNLAFGAGTDTKTSLQASVSFADLKIREDYPASLGKIRRIKQISVTLPALLGPYQDVQAILSYGDKAGLANGCEALAVSHGMNDSGQFQLDFNDGKFLPFEGIAIDQGTLTLSFPNASMPEKGKQATMLKTLNDIILHIRYTIK
6WRV , Knot 255 639 0.86 40 285 591 
RLYWDDLKRKLSEKLDSTDFTSTIKLLNENSYVPREAGSQKDENLALYVENQFREFKLSKVWRDQHFVKIQVKDSAQNSVIIVDKNGRLVYLVENPGGYVAYSKAATVTGKLVHANFGTKKDFEDLYTPVNGSIVIVRAGKITFAEKVANAESLNAIGVLIYMDQTKFPIVNAELSFFGHAHLGTGDPYTPGFPSFNHTQFPPSRSSGLPNIPVQTISRAAAEKLFGNMEGDCPSDWKTDSTCRMVTSESKNVKLTVSNVLKEIKILNIFGVIKGFVEPDHYVVVGAQRDAWGPGAAKSGVGTALLLKLAQMFSDMVLKDGFQPSRSIIFASWSAGDFGSVGATEWLEGYLSSLHLKAFTYINLDKAVLGTSNFKVSASPLLYTLIEKTMQNVKHPVTGQFLYQDSNWASKVEKLTLDNAAFPFLAYSGIPAVSFCFCEDTDYPYLGTTMDTYKELIERIPELNKVARAAAEVAGQFVIKLTHDVELNLDYERYNSQLLSFVRDLNQYRADIKEMGLSLQWLYSARGDFFRATSRLTTDFGNAEKTDRFVMKKLNDRVMRVEYHFLSPYVSPKESPFRHVFWGSGSHTLPALLENLKLRKQNNGAFNETLFRNQLALATWTIQGAANALSGDVWDIDNE

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 \(c\).

\(|P_{f(1IVQ_1)}(2) \setminus P_{f(8CPZ_1)}(2)|=1\), \(|P_{f(8CPZ_1)}(2) \setminus P_{f(1IVQ_1)}(2)|=285\). 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 1:101011001110101010110111001100011111011000010111111111001000010101100010101101001101110011011110101
Pair \(Z_2\) Length of longest common subsequence
1IVQ_1,8CPZ_1 286 4
1IVQ_1,6WRV_1 224 4
8CPZ_1,6WRV_1 98 6

Newick tree

 
[
	1IVQ_1:14.58,
	[
		6WRV_1:49,8CPZ_1:49
	]:96.58
]

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 \((0.85)(0.8)(\frac{2634 }{\log_{20} 2634}-\frac{99}{\log_{20}99})=637.\)
Status Protein1 Protein2 d d1/2
Query variables 1IVQ_1 8CPZ_1 805 417
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]