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Parikh vectors
6ERH_1 6JXT_1 4KGJ_1 Letter Amino acid
30 16 49 R Arginine
18 8 20 N Asparagine
22 12 29 Q Glutamine
27 25 10 I Isoleucine
39 16 41 S Serine
26 24 56 A Alanine
63 33 75 L Leucine
23 13 33 T Threonine
49 24 23 E Glutamic acid
49 22 13 K Lycine
2 6 16 W Tryptophan
31 23 47 V Valine
19 13 21 Y Tyrosine
37 21 33 D Aspartic acid
4 6 6 C Cysteine
26 22 44 G Glycine
8 8 22 H Histidine
15 13 6 M Methionine
28 8 26 F Phenylalanine
28 18 57 P Proline 

6ERH_1|Chains A, C|X-ray repair cross-complementing protein 6|Homo sapiens (9606)
>6JXT_1|Chain A|Epidermal growth factor receptor|Homo sapiens (9606)
>4KGJ_1|Chains A, B|Alpha-L-iduronidase|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 \(w=f(c)\)
6ERH , Knot 213 544 0.82 40 242 506 
MSGWESYYKTEGDEEAEEEQEENLEASGDYKYSGRDSLIFLVDASKAMFESQSEDELTPFDMSIQCIQSVYISKIISSDRDLLAVVFYGTEKDKNSVNFKNIYVLQELDNPGAKRILELDQFKGQQGQKRFQDMMGHGSDYSLSEVLWVCANLFSDVQFKMSHKRIMLFTNEDNPHGNDSAKASRARTKAGDLRDTGIFLDLMHLKKPGGFDISLFYRDIISIAEDEDLRVHFEESSKLEDLLRKVRAKETRKRALSRLKLKLNKDIVISVGIYNLVQKALKPPPIKLYRETNEPVKTKTRTFNTSTGGLLLPSDTKRSQIYGSRQIILEKEETEELKRFDDPGLMLMGFKPLVLLKKHHYLRPSLFVYPEESLVIGSSTLFSALLIKCLEKEVAALCRYTPRRNIPPYFVALVPQEEELDDQKIQVTPPGFQLVFLPFADDKRKMPFTEKIMATPEQVGKMKAIVEKLRFTYRSDSFENPVLQQHFRNLEALALDLMEPEQAVDLTLPKVEAMNKRLGSLVDEFKELVYPPDYNPEGKVTKRK
6JXT , Knot 147 331 0.86 40 212 324 
GAMGGEAPNQALLRILKETEFKKIKVLGSGAFGTVYKGLWIPEGEKVKIPVAIKELREATSPKANKEILDEAYVMASVDNPHVCRLLGICLTSTVQLITQLMPFGCLLDYVREHKDNIGSQYLLNWCVQIAKGMNYLEDRRLVHRDLAARNVLVKTPQHVKITDFGLAKLLGAAAAEYHAEGGKVPIKWMALESILHRIYTHQSDVWSYGVTVWELMTFGSKPYDGIPASEISSILEKGERLPQPPICTIDVYMIMVKCWMIDADSRPKFRELIIEFSKMARDPQRYLVIQGDERMHLPSPTDSNFYRALMDEEDMDDVVDADEYLIPQQG
4KGJ , Knot 249 627 0.85 40 270 586 
EAPHLVQVDAARALWPLRRFWRSTGFCPPLPHSQADPYVLSWDQQLNLAYVGAVPHRGIKQVRTHWLLELVTTRGSTGQGLSYNFTHLDGYLDLLRENQLLPGFELMGSASGHFTDFEDKQQVFEWKDLVSSLARRYIGRYGLAHVSKWNFETWNEPDHHDFDNVSMTMQGFLNYYDACSEGLRAASPALRLGGPGDSFHTPPRSPLSWGLLRHCHDGTNFFTGEAGVRLDYISLHRKGARSSISILEQEKVVAQQIRQLFPKFADTPIYNDEADPLVGWSLPQPWRADVTYAAMVVKVIAQHQNLLLANTTSAFPYALLSNDNAFLSYHPHPFAQRTLTARFQVNNTRPPHVQLLRKPVLTAMGLLALLDEEQLWAEVSQAGTVLDSNHTVGVLASAHRPQGPADAWRAAVLIYASDDTRAHPNRSVAVTLRLRGVPPGPGLVYVTRYLDNGLCSPDGEWRRLGRPVFPTAEQFRRMRAAEDPVAAAPRPLPAGGRLTLRPALRLPSLLLVHVCARPEKPPGQVTRLRALPLTQGQLVLVWSDEHVGSKCLWTYEIQFSQDGKAYTPVSRKPSTFNLFVFSPDTGAVSGSYRVRALDYWARPGPFSDPVPYLEVPVPRGPPSPGNP

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 \(c\).

\(|P_{f(6ERH_1)}(2) \setminus P_{f(6JXT_1)}(2)|=89\), \(|P_{f(6JXT_1)}(2) \setminus P_{f(6ERH_1)}(2)|=59\). 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 1:1011000000010001000000010101000001000111110100111000000010110101001001010011000001111110100000001010010110010011100110100101001000100111010000100111101011001010100001111000001010001010010001101000111101101001111010110001101100001010100000100110010100000011001010100011101110011001101111010000001100000010000111111000000010100011100000001001001111111101111100000101011101000111100011011110010001111000010001110111111000010000101011110111111100000111000111010011010111001010000001001110001001011110110100110101101011000110110010011011000101010000
Pair \(Z_2\) Length of longest common subsequence
6ERH_1,6JXT_1 148 4
6ERH_1,4KGJ_1 152 4
6JXT_1,4KGJ_1 172 4

Newick tree

 
[
	4KGJ_1:83.40,
	[
		6ERH_1:74,6JXT_1:74
	]:9.40
]

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 \((0.85)(0.8)(\frac{875 }{\log_{20} 875}-\frac{331}{\log_{20}331})=146.\)
Status Protein1 Protein2 d d1/2
Query variables 6ERH_1 6JXT_1 183 149
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]