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Parikh vectors
1TJT_1 6IXJ_1 6LLN_1 Letter Amino acid
6 5 5 Y Tyrosine
13 12 16 R Arginine
18 19 10 D Aspartic acid
4 1 2 C Cysteine
20 7 18 E Glutamic acid
12 18 39 G Glycine
18 16 16 I Isoleucine
10 16 22 S Serine
23 33 34 A Alanine
20 8 11 K Lycine
12 19 14 T Threonine
12 11 10 N Asparagine
8 11 7 Q Glutamine
26 23 20 L Leucine
7 5 8 M Methionine
9 12 11 P Proline
6 4 4 W Tryptophan
11 21 24 V Valine
6 5 9 H Histidine
9 10 12 F Phenylalanine 

1TJT_1|Chain A|Alpha-actinin 3|Homo sapiens (9606)
>6IXJ_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Sulfoacetaldehyde reductase|Klebsiella oxytoca (571)
>6LLN_1|Chain A|Putative dehydrogenase involved in catabolism of citronellol|Pseudomonas aeruginosa (strain ATCC 15692 / DSM 22644 / CIP 104116 / JCM 14847 / LMG 12228 / 1C / PRS 101 / PAO1) (208964)
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 \(w=f(c)\)
1TJT , Knot 114 250 0.84 40 165 238 
SSYMEQEEDWDRDLLLDPAWEKQQRKTFTAWCNSHLRKAGTQIENIEEDFRNGLKLMLLLEVISGERLPRPDKGKMRFHKIANVNKALDFIASKGVKLVSIGAEEIVDGNLKMTLGMIWTIILRFAIQDISVEETSAKEGLLLWCQRKTAPYRNVNVQNFHTSWKDGLALCALIHRHRPDLIDYAKLRKDDPIGNLNTAFEVAEKYLDIPKMLDAEDIVNTPKPDEKAIMTYVSCFYHAFAGAEQAETAA
6IXJ , Knot 114 256 0.82 40 171 245 
SNMATSKVVFITGATSGFGEAAAQVFADAGWSLVLSGRRFERLKTLQDKLASQVPVHIIELDVRDSDSVAAAVAALPADFADITTLINNAGLALSPQPAQKVDLDDWKTMIDTNVTGLVNVTHALLPTLINHGAGASIINIGSIAGQWPYPGSHVYGASKAFVKQFSYNLRCDLLGTGVRVTDLAPGIAETEFTLVRTKGDQAASDNLYRGTTPLSARDIAEQMFYIATLPDHMNINRVEVMPVRQAWQPFAIDRD
6LLN , Knot 131 292 0.85 40 177 280 
MSYDSIFRPGLFDGQTIIVTGGGSGIGRCTAHELAALGAHVVLVGRKAEKLEKTAGEIVEDGGSVSWHACDIREEEAVKTLVANILAERGTIHHLVNNAGGQYPSPLASISQKGFETVLRTNLVGGFLVAREVFNQSMSKTGGSIVNMLADMWGGMPGMGHSGAARSGMENFTRTAAVEWGHAGVRVNAVAPGWIASSGMDTYEGAFKAVIPTLREHVPLKRIGSESEVAAAIVFLLSPGAAFVSGNTIRIDGAASQGSRAFPLFKGKPGQSRAYNGFHRAYLPDVLKDQED

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 \(c\).

\(|P_{f(1TJT_1)}(2) \setminus P_{f(6IXJ_1)}(2)|=85\), \(|P_{f(6IXJ_1)}(2) \setminus P_{f(1TJT_1)}(2)|=91\). 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 1:0001000001000111011100000001011000010011001001000100110111110110100110100101010011010011011100110110111001101010101111101110111001010000100111110000011000101001000100111101110000101100101000011101001101100010110110100110010100011100100100111110010011
Pair \(Z_2\) Length of longest common subsequence
1TJT_1,6IXJ_1 176 4
1TJT_1,6LLN_1 168 3
6IXJ_1,6LLN_1 166 4

Newick tree

 
[
	1TJT_1:87.00,
	[
		6LLN_1:83,6IXJ_1:83
	]: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 \((0.85)(0.8)(\frac{506 }{\log_{20} 506}-\frac{250}{\log_{20}250})=73.3\)
Status Protein1 Protein2 d d1/2
Query variables 1TJT_1 6IXJ_1 92 91
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]