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Parikh vectors
6VQZ_1 9FZT_1 7GPE_1 Letter Amino acid
16 17 7 P Proline
22 41 17 T Threonine
13 34 16 V Valine
5 0 3 C Cysteine
18 40 18 G Glycine
10 17 6 H Histidine
6 36 10 F Phenylalanine
12 35 4 S Serine
4 32 10 N Asparagine
20 30 12 D Aspartic acid
26 36 6 E Glutamic acid
9 10 0 W Tryptophan
13 14 7 Y Tyrosine
2 10 6 M Methionine
23 52 12 A Alanine
25 13 10 R Arginine
16 17 5 Q Glutamine
7 30 13 I Isoleucine
21 48 13 L Leucine
8 43 7 K Lycine 

6VQZ_1|Chains A, C|MHC class I antigen|Homo sapiens (9606)
>9FZT_1|Chain A|Glucose-6-phosphate isomerase|Candida albicans (5476)
>7GPE_1|Chains A, B|Protease 3C|Human Enterovirus D68 (42789)
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 \(w=f(c)\)
6VQZ , Knot 123 276 0.83 40 180 265 
GSHSMRYFHTSVSRPGRGEPRFITVGYVDDTLFVRFDSDAASPREEPRAPWIEQEGPEYWDRETQICKAKAQTDREDLRTLLRYYNQSEAGSHTLQNMYGCDVGPDGRLLRGYHQDAYDGKDYIALNEDLSSWTAADTAAQITQRKWEAARVAEQLRAYLEGECVEWLRRYLENGKETLQRADPPKTHVTHHPISDHEATLRCWALGFYPAEITLTWQRDGEDQTQDTELVETRPAGDRTFQKWAAVVVPSGEEQRYTCHVQHEGLPKPLTLRWEP
9FZT , Knot 222 555 0.84 38 252 514 
GPLGSMASFKLATDLPEWKKLEETYKSVGEKFSVRDAFAKDPKRFEEFSWIYKNYDDSKILFDFSKNLVNKEILDQLVTLAKEAGVEKLRDAMFAGDHINTTEDRAVYHVALRNRALRKMPVDGKDTAQEVDDVLKHMKEFSDSIRDGSWTGYTGKSITDVVNIGIGGSDLGPVMVTEALKAYSKPGLNVHFISNIDGTHTAETLKNLNPETTLFLIASKTFTTAETITNATSAKNWFLATAKDSKHIAKHFAALSTNEKEVVAFGIDAKNMFGFESWVGGRYSVWSAIGLSVAIYIGFENFNDFLKGAEAMDQHFLTTPLENNIPVIGGLLSVWYNNFFGAQTHLVVPFDQYLHRFPAYLQQLSMESNGKSVTRANVFTNYQTGTILFGEPATNAQHSFFQLVHQGTKLIPADFILAAQSHNPIEKNLHQRMLASNFFAQSEALMVGKDEAKVKAEGATGGLVPHKEFSGNRPTTSILAQKITPATLGSLIAYYEHLTFTEGAIWNINSFDQWGVELGKVLAKVIGKELDDKKAVATHDASTNGLINQFKEWEE
7GPE , Knot 86 182 0.82 38 139 179 
MGPGFDFAQAIMKKNTVIARTEKGEFTMLGVYDRVAVIPTHASVGEIIYINDVETRVLDACALRDLTDTNLEITIVKLDRNQKFRDIRHFLPRCEDDYNDAVLSVHTSKFPNMYIPVGQVTNYGFLNLGGTPTHRILMYNFPTRAGQCGGVVTTTGKVIGIHVGGNGAQGFAAMLLHSYFTD

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 \(c\).

\(|P_{f(6VQZ_1)}(2) \setminus P_{f(9FZT_1)}(2)|=56\), \(|P_{f(9FZT_1)}(2) \setminus P_{f(6VQZ_1)}(2)|=128\). 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 1:100010010001001101010110110100011101000110100010111100011001000001001010000001001100000001100010010100111010110100001001000111000100101100110100001011011001010101001011000100100010010110001000110000101001111101101010100010000000011000111000100111111101000000001000111011010101
Pair \(Z_2\) Length of longest common subsequence
6VQZ_1,9FZT_1 184 4
6VQZ_1,7GPE_1 191 4
9FZT_1,7GPE_1 175 4

Newick tree

 
[
	6VQZ_1:95.76,
	[
		9FZT_1:87.5,7GPE_1:87.5
	]:8.26
]

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 \((0.85)(0.8)(\frac{831 }{\log_{20} 831}-\frac{276}{\log_{20}276})=151.\)
Status Protein1 Protein2 d d1/2
Query variables 6VQZ_1 9FZT_1 193 144
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]