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Parikh vectors
5MKE_1 5UAN_1 8EJI_1 Letter Amino acid
18 11 10 H Histidine
34 25 7 K Lycine
39 15 20 T Threonine
29 9 13 Y Tyrosine
62 21 14 V Valine
77 24 9 R Arginine
70 21 19 G Glycine
39 11 10 Q Glutamine
42 19 5 P Proline
55 19 8 D Aspartic acid
13 13 10 C Cysteine
53 16 18 I Isoleucine
84 24 21 S Serine
14 2 3 W Tryptophan
33 16 19 N Asparagine
78 28 10 E Glutamic acid
24 12 11 M Methionine
54 13 10 F Phenylalanine
61 27 12 A Alanine
89 39 30 L Leucine 

5MKE_1|Chains A, B, C, D|Polycystin-2|Homo sapiens (9606)
>5UAN_1|Chain A|Retinoic acid receptor RXR-alpha|Homo sapiens (9606)
>8EJI_1|Chains A, C[auth B], G[auth C]|Glycoprotein G1|Lassa mammarenavirus (3052310)
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 \(w=f(c)\)
5MKE , Knot 355 968 0.84 40 311 850 
MVNSSRVQPQQPGDAKRPPAPRAPDPGRLMAGCAAVGASLAAPGGLCEQRGLEIEMQRIRQAAARDPPAGAAASPSPPLSSCSRQAWSRDNPGFEAEEEEEEVEGEEGGMVVEMDVEWRPGSRRSAASSAVSSVGARSRGLGGYHGAGHPSGRRRRREDQGPPCPSPVGGGDPLHRHLPLEGQPPRVAWAERLVRGLRGLWGTRLMEESSTNREKYLKSVLRELVTYLLFLIVLCILTYGMMSSNVYYYTRMMSQLFLDTPVSKTEKTNFKTLSSMEDFWKFTEGSLLDGLYWKMQPSNQTEADNRSFIFYENLLLGVPRIRQLRVRNGSCSIPQDLRDEIKECYDVYSVSSEDRAPFGPRNGTAWIYTSEKDLNGSSHWGIIATYSGAGYYLDLSRTREETAAQVASLKKNVWLDRGTRATFIDFSVYNANINLFCVVRLLVEFPATGGVIPSWQFQPLKLIRYVTTFDFFLAACEIIFCFFIFYYVVEEILEIRIHKLHYFRSFWNCLDVVIVVLSVVAIGINIYRTSNVEVLLQFLEDQNTFPNFEHLAYWQIQFNNIAAVTVFFVWIKLFKFINFNRTMSQLSTTMSRCAKDLFGFAIMFFIIFLAYAQLAYLVFGTQVDDFSTFQECIFTQFRIILGDINFAEIEEANRVLGPIYFTTFVFFMFFILLNMFLAIINDTYSEVKSDLAQQKAEMELSDLIRKGYHKALVKLKLKKNTVDDISESLRQGGGKLNFDELRQDLKGKGHTDAEIEAIFTKYDQDGDQELTEHEHQQMRDDLEKEREDLDLDHSSLPRPMSSRSFPRSLDDSEEDDDEDSGHSSRRRGSISSGVSYEEFQVLVRRVDRMEHSIGSIVSKIDAVIVKLEIMERAKLKRREVLGRLLDGVAEDERLGRDSEIHREQMERLVREELERWESDDAASQISHGLGTPVGLNGQPRPRSSRPSSSQSTEGMEGAGGNGSSNVHV
5UAN , Knot 158 365 0.85 40 220 347 
MNPVSSSEDIKPPLGLNGVLKVPAHPSGNMASFTKHICAICGDRSSGKHYGVYSCEGCKGFFKRTVRKDLTYTCRDNKDCLIDKRQRNRCQYCRYQKCLAMGMKREAVQEERQRGKDRNENEVESTSSANEDMPVERILEAELAVEPKTETYVEANMGLNPSSPNDPVTNICQAADKQLFTLVEWAKRIPHFSELPLDDQVILLRAGWNELLIASFSHRSIAVKDGILLATGLHVHRNSAHSAGVGAIFDRVLTELVSKMRDMQMDKTELGCLRAIVLFNPDSKGLSNPAEVEALREKVYASLEAYCKHKYPEQPGRFAKLLLRLPALRSIGLKCLEHLFFFKLIGDTPIDTFLMEMLEAPHQMT
8EJI , Knot 116 259 0.83 40 170 247 
MGQIVTFFQEVPHVIEEVMNIVLIALSVLAVLKGLYNFATCGLVGLVTFLLLCGRSCTTSLYKGVYELQTLELNMETLNMTMPLSCTKNNSHHYIMVGNETGLELTLTNTSIINHKFCNLSDAHKKNLYDHALMSIISTFHLSIPNFNQYEAMSCDFNGGKISVQYNLSHSYAGDAANHCGTVANGVLQTFMRMAWGGSYIALDSGCGNWDCIMTSYQYLIIQNTTWEDHCQFSRPSPIGYLGLLSQRTRDIYISRRRR

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 \(c\).

\(|P_{f(5MKE_1)}(2) \setminus P_{f(5UAN_1)}(2)|=127\), \(|P_{f(5UAN_1)}(2) \setminus P_{f(5MKE_1)}(2)|=36\). 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 1:11000010100110100111101101101111011111011111110000110101001001110011111110101110000001100001110100000010100111110101010110000110011001110001111001110101000000001110101111101100011101011011110011011011110011000000000010011001100111111101100111000100000110011100110000000100100100110100101101101010100000100001110001111110100101001000110010001000001001000001111100101110000001010001111100011100101000000011011010001110010010110101001010110110111011101111101010110110010010111110011101111001100110101001001001100101111110111111010000010111011000001101001101010100111101111110110110100010010001000100111111111111110101101111001001001000110010111101011010010011111010011111111110111111000000100011000101010011001000111010100001001000100111010100100010101000101011100000010001000000010001000000101000011011000011001000000000001000000101001100001011100100100011011001011110101100101000011101101110000110000100001001100010010000110010011101111010101000010000000110111101000101
Pair \(Z_2\) Length of longest common subsequence
5MKE_1,5UAN_1 163 4
5MKE_1,8EJI_1 197 4
5UAN_1,8EJI_1 190 4

Newick tree

 
[
	8EJI_1:10.34,
	[
		5MKE_1:81.5,5UAN_1:81.5
	]:19.84
]

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 \((0.85)(0.8)(\frac{1333 }{\log_{20} 1333}-\frac{365}{\log_{20}365})=251.\)
Status Protein1 Protein2 d d1/2
Query variables 5MKE_1 5UAN_1 313 215
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]