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Parikh vectors
6HSO_1 8XQD_1 8SIK_1 Letter Amino acid
16 15 6 Q Glutamine
24 21 21 E Glutamic acid
37 18 11 G Glycine
23 18 6 R Arginine
29 14 17 D Aspartic acid
32 14 2 P Proline
26 20 12 T Threonine
2 4 0 W Tryptophan
39 23 7 V Valine
14 20 6 N Asparagine
16 23 8 K Lycine
29 24 8 I Isoleucine
16 7 10 M Methionine
10 9 8 F Phenylalanine
19 18 4 S Serine
7 16 2 Y Tyrosine
26 15 11 A Alanine
9 12 1 H Histidine
5 4 0 C Cysteine
40 18 9 L Leucine 

6HSO_1|Chain A|Gephyrin|Rattus norvegicus (10116)
>8XQD_1|Chains A, B|Receptor-type tyrosine-protein phosphatase gamma|Homo sapiens (9606)
>8SIK_1|Chains A[auth B], C[auth D], D[auth F], E[auth H]|Calmodulin-1|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 \(w=f(c)\)
6HSO , Knot 171 419 0.82 40 225 395 
MSPFPLTSMDKAFITVLEMTPVLGTEIINYRDGMGRVLAQDVYAKDNLPPFPASVKDGYAVRAADGPGDRFIIGESQAGEQPTQTVMPGQVMRVTTGAPIPCGADAVVQVEDTELIRESDDGTEELEVRILVQARPGQDIRPIGHDIKRGECVLAKGTHMGPSEIGLLATVGVTEVEVNKFPVVAVMSTGNELLNPEDDLLPGKIRDSNRSTLLATIQEHGYPTINLGIVGDNPDDLLNALNEGISRADVIITSGGVSMGEKDYLKQVLDIDLHAQIHFGRVFMKPGLPTTFATLDIDGVRKIIFALPGNPVSAVVTCNLFVVPALRKMQGILDPRPTIIKARLSCDVKLDPRPEYHRCILTWHHQEPLPWAQSTGNQMSSRLMSMRSANGLLMLPPKTEQYVELHKGEVVDVMVIGRL
8XQD , Knot 139 313 0.85 40 204 300 
SLPIPDDMEAIPVKQFVKHIGELYSNNQHGFSEDFEEVQRCTADMNITAEHSNHPENKHKNRYINILAYDHSRVKLRPLPGKDSKHSDYINANYVDGYNKAKAYIATQGPLKSTFEDFWRMIWEQNTGIIVMITNLVEKGRRKCDQYWPTENSEEYGNIIVTLKSTKIHACYTVRRFSIRNTKVKKGQKGNPKGRQNERVVIQYHYTQWPDMGVPEYALPVLTFVRRSSAARMPETGPVLVHCSAGVGRTGTYIVIDSMLQQIKDKSTVNVLGFLKHIRTQRNYLVQTEEQYIFIHDALLEAILGKETEVSSN
8SIK , Knot 67 149 0.75 36 97 134 
MADQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGNGTIDFPEFLTMMARKMKDTDSEEEIREAFRVFDKDGNGYISAAELRHVMTNLGEKLTDEEVDEMIREADIDGDGQVNYEEFVQMMTAK

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 \(c\).

\(|P_{f(6HSO_1)}(2) \setminus P_{f(8XQD_1)}(2)|=97\), \(|P_{f(8XQD_1)}(2) \setminus P_{f(6HSO_1)}(2)|=76\). 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 1:10111100100111011010111100110000111011100101000111111010010110110111001111000110010001111011010011111011011101000011000001000101011101011001011100100100111010011100111110111001010011111110010011010001111010000000111010001010101111100100110110011001011100111011000010011010101010110111011110011010101100111111101101110001111111001011101010110101000101010100000110100001111100010010001101001011111110000010100101101111101
Pair \(Z_2\) Length of longest common subsequence
6HSO_1,8XQD_1 173 4
6HSO_1,8SIK_1 188 4
8XQD_1,8SIK_1 175 4

Newick tree

 
[
	8SIK_1:92.19,
	[
		6HSO_1:86.5,8XQD_1:86.5
	]:5.69
]

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 \((0.85)(0.8)(\frac{732 }{\log_{20} 732}-\frac{313}{\log_{20}313})=115.\)
Status Protein1 Protein2 d d1/2
Query variables 6HSO_1 8XQD_1 144 126
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]