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Parikh vectors
6DDH_1 7BDV_1 3RGI_1 Letter Amino acid
31 19 22 R Arginine
38 19 15 D Aspartic acid
34 13 27 G Glycine
33 15 16 F Phenylalanine
33 19 8 T Threonine
24 25 38 A Alanine
18 26 5 N Asparagine
36 21 10 K Lycine
23 17 15 P Proline
46 18 15 S Serine
31 16 8 Y Tyrosine
7 5 4 C Cysteine
28 17 18 E Glutamic acid
22 12 3 H Histidine
16 4 8 M Methionine
5 5 1 W Tryptophan
30 19 22 V Valine
16 29 13 Q Glutamine
23 31 12 I Isoleucine
60 36 26 L Leucine 

6DDH_1|Chain A|Cytosolic purine 5'-nucleotidase|Homo sapiens (9606)
>7BDV_1|Chains A, B, C, D|Can2|Sulfobacillus thermosulfidooxidans (28034)
>3RGI_1|Chain A|DisD protein|Sorangium cellulosum (56)
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 \(w=f(c)\)
6DDH , Knot 223 554 0.84 40 275 516 
GSSHHHHHHSSGLVPRGSMSTSWSDRLQNAADMPANMDKHALKKYRREAYHRVFVNRSLAMEKIKCFGFNMDYTLAVYKSPEYESLGFELTVERLVSIGYPQELLSFAYDSTFPTRGLVFDTLYGNLLKVDAYGNLLVCAHGFNFIRGPETREQYPNKFIQRDDTERFYILNTLFNLPETYLLACLVDFFTNCPRYTSCETGFKDGDLFMSYRSMFQDVRDAVDWVHYKGSLKEKTVENLEKYVVKDGKLPLLLSRMKEVGKVFLATNSDYKYTDKIMTYLFDFPHGPKPGSSHRPWQSYFDLILVDARKPLFFGEGTVLRQVDTKTGKLKIGTYTGPLQHGIVYSGGSSDTICDLLGAKGKDILYIGDHIFGDILKSKKRQGWQTFLVIPELAQELHVWTDKSSLFEELQSLDIFLAELYKHLDSSSNERPDISSIQRRIKKVTHDMDMCYGMMGSLFRSGSRQTLFASQVMRYADLYAASFINLLYYPFSYLFRAAHVLMPHESTVEHTHVDINEMESPLATRNRTSVDFKDTDYKRHQLTRSISEIKPPNL
7BDV , Knot 162 366 0.87 40 221 356 
MARLDDLFIIHDTYVCLLSDHLLPNVIPVIQAPPQRVILLYTPNNKERVQRFRQATESVPTEIIEKQVHPYQYAQTQRICDEILEQFPNAILNVTGGTKIMALAAFDRFRHNHRPIIYVDSDSQRILYLHNGESERLGDPLTVKQYLACYGFKADNINRQDNLPKTWREVEDLFAQNSTKWQNQLGRLNWIAAQQQPIFTLQTGELQDLLLKANLIKPAEAKNAGFQFTSDQARQFINGGWFEHYVYSLLRQISAQYPIKNLTKNIEISNDSVSNELDVVFLYHNKLHVIECKTRHFTADGKINPMETIYKIDSVTNRVAGIKGKSMFASYYPLTQAAKKRCLNNSIYVSDQPSQLHHQLIKWINA
3RGI , Knot 122 286 0.80 40 169 269 
MKAYMFPGQGSQAKGMGRALFDAFPALTARADGVLGYSIRALCQDDPDQRLSQTQFTQPALYVVNALSYLKRREEEAPPDFLAGHSLGEFSALFAAGVFDFETGLALVKKRGELMGDARGGGMAAVIGLDEERVRELLDQNGATAVDIANLNSPSQVVISGAKDEIARLQVPFEAAGAKKYTVLRVSAAFHSRFMRPAMVEFGRFLEGYDFAPPKIPVISNVTARPCKADGIRAALSEQIASPVRWCESIRYLMGRGVEEFVECGHGIVLTGLYAQIRRDAQPLVV

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 \(c\).

\(|P_{f(6DDH_1)}(2) \setminus P_{f(7BDV_1)}(2)|=111\), \(|P_{f(7BDV_1)}(2) \setminus P_{f(6DDH_1)}(2)|=57\). 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 1:10000000000111101010001000100110111010001100000010001110001110010011101000111000100001110101001101101001101100001100111100101011010101011101011011011000000100110000000101100110110001110110110001000000011001011100001100100110110001010000100100011001011111001001101111000000000011001101101101100001100010111101001111101011001000010101100011100111001100001001111010011011001110110000001100111110110010110000011001001011110100010000000101001000100100010100111101100100001110011001010110110110011001101101111000010000101001001110000001010000000001000100101101
Pair \(Z_2\) Length of longest common subsequence
6DDH_1,7BDV_1 168 3
6DDH_1,3RGI_1 178 4
7BDV_1,3RGI_1 170 4

Newick tree

 
[
	3RGI_1:88.00,
	[
		6DDH_1:84,7BDV_1:84
	]:4.00
]

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 \((0.85)(0.8)(\frac{920 }{\log_{20} 920}-\frac{366}{\log_{20}366})=148.\)
Status Protein1 Protein2 d d1/2
Query variables 6DDH_1 7BDV_1 188 156
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]