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Parikh vectors
8PRW_1 8XBH_1 5IVV_1 Letter Amino acid
74 15 15 N Asparagine
10 10 7 C Cysteine
143 30 11 K Lycine
182 31 19 A Alanine
66 18 16 R Arginine
19 3 9 W Tryptophan
139 18 21 G Glycine
114 26 13 I Isoleucine
107 21 11 T Threonine
56 13 12 Y Tyrosine
157 27 21 L Leucine
44 9 11 M Methionine
163 28 35 E Glutamic acid
30 6 10 H Histidine
68 19 23 F Phenylalanine
80 4 27 P Proline
139 18 20 S Serine
128 19 28 V Valine
95 26 11 D Aspartic acid
73 13 10 Q Glutamine

8PRW_1|Chains A, C[auth B], D[auth C], E[auth D], F[auth E], G[auth F]|Fatty acid synthase subunit alpha|Saccharomyces cerevisiae (4932)
>8XBH_1|Chain A|Guanine nucleotide-binding protein G(i) subunit alpha-1|Homo sapiens (9606)
>5IVV_1|Chain A|Lysine-specific demethylase 5A|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 \(w=f(c)\)
8PRW , Knot 636 1887 0.84 40 343 1508
MKPEVEQELAHILLTELLAYQFASPVRWIETQDVFLKDFNTERVVEIGPSPTLAGMAQRTLKNKYESYDAALSLHREILCYSKDAKEIYYTPDPSELAAKEEPAKEEAPAPTPAASAPAPAAAAPAPVAAAAPAAAAAEIADEPVKASLLLHVLVAHKLKKSLDSIPMSKTIKDLVGGKSTVQNEILGDLGKEFGTTPEKPEETPLEELAETFQDTFSGALGKQSSSLLSRLISSKMPGGFTITVARKYLQTRWGLPSGRQDGVLLVALSNEPAARLGSEADAKAFLDSMAQKYASIVGVDLSSAASASGAAGAGAAAGAAMIDAGALEEITKDHKVLARQQLQVLARYLKMDLDNGERKFLKEKDTVAELQAQLDYLNAELGEFFVNGVATSFSRKKARTFDSSWNWAKQSLLSLYFEIIHGVLKNVDREVVSEAINIMNRSNDALIKFMEYHISNTDETKGENYQLVKTLGEQLIENCKQVLDVDPVYKDVAKPTGPKTAIDKNGNITYSEEPREKVRKLSQYVQEMALGGPITKESQPTIEEDLTRVYKAISAQADKQDISSSTRVEFEKLYSDLMKFLESSKEIDPSQTTQLAGMDVEDALDKDSTKEVASLPNKSTISKTVSSTIPRETIPFLHLRKKTPAGDWKYDRQLSSLFLDGLEKAAFNGVTFKDKYVLITGAGKGSIGAEVLQGLLQGGAKVVVTTSRFSKQVTDYYQSIYAKYGAKGSTLIVVPFNQGSKQDVEALIEFIYDTEKNGGLGWDLDAIIPFAAIPEQGIELEHIDSKSEFAHRIMLTNILRMMGCVKKQKSARGIETRPAQVILPMSPNHGTFGGDGMYSESKLSLETLFNRWHSESWANQLTVCGAIIGWTRGTGLMSANNIIAEGIEKMGVRTFSQKEMAFNLLGLLTPEVVELCQKSPVMADLNGGLQFVPELKEFTAKLRKELVETSEVRKAVSIETALEHKVVNGNSADAAYAQVEIQPRANIQLDFPELKPYKQVKQIAPAELEGLLDLERVIVVTGFAEVGPWGSARTRWEMEAFGEFSLEGCVEMAWIMGFISYHNGNLKGRPYTGWVDSKTKEPVDDKDVKAKYETSILEHSGIRLIEPELFNGYNPEKKEMIQEVIVEEDLEPFEASKETAEQFKHQHGDKVDIFEIPETGEYSVKLLKGATLYIPKALRFDRLVAGQIPTGWNAKTYGISDDIISQVDPITLFVLVSVVEAFIASGITDPYEMYKYVHVSEVGNCSGSGMGGVSALRGMFKDRFKDEPVQNDILQESFINTMSAWVNMLLISSSGPIKTPVGACATSVESVDIGVETILSGKARICIVGGYDDFQEEGSFEFGNMKATSNTLEEFEHGRTPAEMSRPATTTRNGFMEAQGAGIQIIMQADLALKMGVPIYGIVAMAATATDKIGRSVPAPGKGILTTAREHHSSVKYASPNLNMKYRKRQLVTREAQIKDWVENELEALKLEAEEIPSEDQNEFLLERTREIHNEAESQLRAAQQQWGNDFYKRDPRIAPLRGALATYGLTIDDLGVASFHGTSTKANDKNESATINEMMKHLGRSEGNPVIGVFQKFLTGHPKGAAGAWMMNGALQILNSGIIPGNRNADNVDKILEQFEYVLYPSKTLKTDGVRAVSITSFGFGQKGGQAIVVHPDYLYGAITEDRYNEYVAKVSAREKSAYKFFHNGMIYNKLFVSKEHAPYTDELEEDVYLDPLARVSKDKKSGSLTFNSKNIQSKDSYINANTIETAKMIENMTKEKVSNGGVGVDVELITSINVENDTFIERNFTPQEIEYCSAQPSVQSSFAGTWSAKEAVFKSLGVKSLGGGAALKDIEIVRVNKNAPAVELHGNAKKAAEEAGVTDVKVSISHDDLQAVAVAVSTKK
8XBH , Knot 153 354 0.84 40 206 335
MGCTLSAEDKAAVERSKMIDRNLREDGEKAAREVKLLLLGAGESGKSTIVKQMKIIHEAGYSEEECKQYKAVVYSNTIQSIIAIIRAMGRLKIDFGDSARADDARQLFVLAGAAEEGFMTAELAGVIKRLWKDSGVQACFNRSREYQLNDSAAYYLNDLDRIAQPNYIPTQQDVLRTRVKTTGIVETHFTFKDLHFKMFDVGGQRSERKKWIHCFEGVTAIIFCVALSDYDLVLAEDEEMNRMHESMKLFDSICNNKWFTDTSIILFLNKKDLFEEKIKKSPLTICYPEYAGSNTYEEAAAYIQCQFEDLNKRKDTKEIYTHFTCATDTKNVQFVFDAVTDVIIKNNLKDCGLF
5IVV , Knot 144 330 0.84 40 208 319
HNMAGVGPGGYAAEFVPPPECPVFEPSWEEFTDPLSFIGRIRPLAEKTGICKIRPPKDWQPPFACEVKSFRFTPRVQRLNELEAMTRVRPREAFGFEQAVREYTLQSFGEMADNFKSDYFNMPVHMVPTELVEKEFWRLVSSIEEDVIVEYGADISSKDFGSGFPVKDGRRKILPEEEEYALSGWNLNNMPVLEQSVLAHINVDISGMKVPWLYVGMCFSSFCWHIEDHWSYSINYLHWGEPKTWYGVPSHAAEQLEEVMRELAPELFESQPDLLHQLVTIMNPNVLMEHGVPVYRTNQCAGEFVVTFPRAYHSGFNQGYNFAEAVNFCT

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 \(c\).

\(|P_{f(8PRW_1)}(2) \setminus P_{f(8XBH_1)}(2)|=154\), \(|P_{f(8XBH_1)}(2) \setminus P_{f(8PRW_1)}(2)|=17\). 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 1:101010001101110011100110110110000111001000011011101011111000100000000111010001100000100100010100111000110001111011101111111111111111111111011001101011101111001000100111000100111100010001110110011001001000110011001000101111000001100110001111101011000100011110100011111110001110110010101110011000101111010011010111111111111110111100100000111000101110010101001000110000011010101001010110111011100100001001000101100011010101101110010001100110110000011101100010000000100001100110011000001101011000110101100110001010000010001001000100111111100000101000100100110101000010000010100100011011000001010000011110100110000000110110000100010001100011110100001110100000100111011001110110100001110111010111011011101110111000010001000000101001101001111110010000101110110000001111101011111111100110100100000110011100110111010000010110001101111101001011101100000101001100100001100101011111100101110100111011001110010000111011111010110100001111010111011101001010100011000010011010011000110100101101010101010101011010100010011110101110100111101110111110100010101110101010101111111100001010101001110000001100001010000011000110110101101001000011001110001011010000100100001001011011001000101101101011011010011110110110100011000110010110111110110111101100100100010100110001011111011011100010001100011000110010111011110001110011110100100101110011010101011110001000101011010100001001001001101001100000111010111101110101110111110111111101000110011111011100100000010010101010000001100010100110001011010100110000001110000010001000101100011001000010111101111001101001111010100001000000101001100110001011111100110101011111111011101100111110001001001100100110100010001101101001111001101111010010111000000001101010000100110011100011100001100001000101011101000000101010000100000010100100101100100001001111101011001010000110001010010000101010001110101001110011100111111100101101000111101010100110011100101010000101111110000
Pair \(Z_2\) Length of longest common subsequence
8PRW_1,8XBH_1 171 4
8PRW_1,5IVV_1 177 5
8XBH_1,5IVV_1 198 3

Newick tree

 
[
	5IVV_1:96.53,
	[
		8PRW_1:85.5,8XBH_1:85.5
	]:11.03
]

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 \((0.85)(0.8)(\frac{2241 }{\log_{20} 2241}-\frac{354}{\log_{20}354})=468.\)
Status Protein1 Protein2 d d1/2
Query variables 8PRW_1 8XBH_1 596 350.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]