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Parikh vectors
7QQX_1 8SRE_1 1UDD_1 Letter Amino acid
0 88 13 R Arginine
0 61 7 N Asparagine
0 72 15 I Isoleucine
0 54 6 M Methionine
0 63 6 P Proline
0 20 5 W Tryptophan
0 98 14 V Valine
0 85 20 E Glutamic acid
0 87 10 T Threonine
0 93 12 D Aspartic acid
0 53 3 Q Glutamine
19 87 11 G Glycine
0 146 29 L Leucine
0 76 16 K Lycine
29 131 14 A Alanine
15 15 1 C Cysteine
0 43 9 H Histidine
0 83 11 F Phenylalanine
0 100 11 S Serine
0 39 13 Y Tyrosine 

7QQX_1|Chain A|FANCF sgRNA|synthetic construct (32630)
>8SRE_1|Chains A, B, C, D|TRPM2 chanzyme|Salpingoeca rosetta (946362)
>1UDD_1|Chains A, B, C, D|transcriptional regulator|Pyrococcus horikoshii (70601)
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 \(w=f(c)\)
7QQX , Knot 27 84 0.47 8 16 44 
GGGGAAUCCCUUCUGCAGCACCGUUUUAGAGCUAGAAAUAGCAAGUUAAAAUAAGGCUAGUCCGUUAUCAACUUGAAAAAGUGA
8SRE , Knot 524 1494 0.85 40 351 1298 
MQRARPGELVEVIMFRPTGKARVSNLDESMAMEFTDLRTRAMSSAAMIRQSVAAKTLLIENEDGKGSTRMEVQDFMKRFHMHASEDDKTGSPSTAWGTLRFPTKEATAPYLRLSVNDDPEDALLFVKAMLAQKYGETYDRPSLILSVTGGARNFTLPPRLETAIAKGLRLAAQRTNAWVVTGGTNTGVMKLTGQIMEALSKTQSHFIPPTIGIATYGVIIGGDDMTRGEPPKIGLEYEMHKKDPPKTTPLDDNHNLFLLVDDGSTNKFGKEIKFRAAFENAAGQAFAAPVVTIVVQGGPGTLGTALQAVRQGTPIVVVDGSGLAADVLAYAYNFMHNPLTRFKSYTIDDLRQKVAQTFNPKSSQQLTNLLDSALECVQDPNLVVVYSLQESGIDEFDDCILKAIFSSQGKLGNKLKQAMYFDQLDVAKRALSEASKNGQHNEIAACINDNLMAAMMHNKPHFVELYLGFDAKIYELKPSEEVAKTNITALDELPSFALAIEELYKREAKKPHSHVQRLVSLSNTDVLGRHYRVSTQRGDGTTRRIGRDLANTRAYNVLRMDQIFARLVSKDFSVNRDFTIYDSKYDKVPGIQFRRTAQASHMLFLWAICLDRFRMARHFWLIGDQSIINALVASRILERLSTHRALQGPHLAEERAKMQHNAKKFEELAVGVLGECHGSDSHMASEMLHSKNDMFNKKNAINIAYDAKSLAFLSHPATQSVINADWYGHLKSVTSFWAVLFAFFFPFFVLPFINFSEDHAEQQVEAPRDFFTDAPRSSHSANSTTSGAHRLRRKFAKFYSAPYTRFISDLLSHFVLCVVTSYFVLDKLEDTISAIEWILLVWFVALLLEELRQMIFCDGIAEYISDTWNRLDLIMITLFFVGFFTHASDPSNQDSKVVSKGIHAFLVVVLWLRFMRYYALSKNLGPKLIMMMEMMKDVSTFVFLLLIFLIGYGVAAQSLLSPDEDFSSRTFIGVLFRPYFQIYGELFLDDLNSEANCLGDTPFTECSRETVRMVPFFLAVYILGSNVLLVNLLIAMFNDTYMKVQEAAEDLWRKQNYELCAEYKDRPFLPAPFILLAHVHMLFMRLLRLCGVHTQEHEKIQDDETKRKITTFEELNTDKFLRRWERERQEMLEARVKMTNDNVVQAMGMMDQLLEHMISFRFSLDQQATKIKQEIRDDGLPSTEPTGLVSRTPSQPINRLNSAVAVHGHTAEAAEWYVPPEEYPKSGGVKRYLIDASMVPLSIMCPSYDPVEYTHPSVAAQPVWADPADPRKIKFNVKDEVNGKVVDRTSCHPSGISIDSNTGRPINPWGRTGMTGRGLLGKWGVNQAADTVVTRWKRSPDGSILERDGKKVLEFVAIQRQDNKMWAIPGGFVDNGEDVALTSGREFMEEALGMGTSADLMSAESKDSLAALFSSGTIVARIYCEDPRNTDNAWVETTCVNFHDESGRHAARLKLQGGDDAEHARWMMVHGGLNLFASHRTLLQHVTSALNAYF
1UDD , Knot 102 226 0.81 40 159 213 
MRVMITDKLRRDSEQIWKKIFEHPFVVQLYSGTLPLEKFKFYVLQDFNYLVGLTRALAVISSKAEYPLMAELIELARDEVTVEVENYVKLLKELDLTLEDAIKTEPTLVNSAYMDFMLATAYKGNIIEGLTALLPCFWSYAEIAEYHKDKLRDNPIKIYREWGKVYLSNEYLNLVGRLRKIIDSSGHSGYDRLRRIFITGSKFELAFWEMAWRGGDVFLEHHHHHH

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 \(c\).

\(|P_{f(7QQX_1)}(2) \setminus P_{f(8SRE_1)}(2)|=9\), \(|P_{f(8SRE_1)}(2) \setminus P_{f(7QQX_1)}(2)|=344\). 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 1:111111000000001011010010000111100111110110111001111011110011000100100110001111111011
Pair \(Z_2\) Length of longest common subsequence
7QQX_1,8SRE_1 353 3
7QQX_1,1UDD_1 173 2
8SRE_1,1UDD_1 206 4

Newick tree

 
[
	8SRE_1:15.20,
	[
		7QQX_1:86.5,1UDD_1:86.5
	]:72.70
]

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 \((0.85)(0.8)(\frac{1578 }{\log_{20} 1578}-\frac{84}{\log_{20}84})=397.\)
Status Protein1 Protein2 d d1/2
Query variables 7QQX_1 8SRE_1 520 273
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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