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Parikh vectors
8JTA_1 1SBO_1 7AVK_1 Letter Amino acid
11 3 0 R Arginine
12 13 8 K Lycine
4 0 2 W Tryptophan
33 8 10 V Valine
54 14 4 L Leucine
37 12 8 S Serine
15 2 1 Y Tyrosine
43 5 4 A Alanine
15 10 5 D Aspartic acid
9 0 0 C Cysteine
45 12 1 I Isoleucine
14 5 1 N Asparagine
12 3 5 Q Glutamine
27 3 4 F Phenylalanine
26 0 7 P Proline
23 6 13 T Threonine
10 7 7 E Glutamic acid
39 4 6 G Glycine
6 1 2 H Histidine
22 2 0 M Methionine 

8JTA_1|Chain A|Synaptic vesicular amine transporter|Homo sapiens (9606)
>1SBO_1|Chain A|Putative anti-sigma factor antagonist TM1442|Thermotoga maritima (2336)
>7AVK_1|Chains A, B|LPXTG cell wall surface protein|Streptococcus gordonii (strain Challis / ATCC 35105 / BCRC 15272 / CH1 / DL1 / V288) (467705)
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 \(w=f(c)\)
8JTA , Knot 185 457 0.82 40 217 425 
SRKLILFIVFLALLLDNMLLTVVVPIIPSYLYSIKHEKNATEIQTARPVHTASISDSFQSIFSYYDNSTMVTGNATRDLTLHQTATQHMVTNASAVPSDCPSEDKDLLNENVQVGLLFASKATVQLITNPFIGLLTNRIGYPIPIFAGFCIMFVSTIMFAFSSSYAFLLIARSLQGIGSSCSSVAGMGMLASVYTDDEERGNVMGIALGGLAMGVLVGPPFGSVLYEFVGKTAPFLVLAALVLLDGAIQLFVLQPSRVQPESQKGTPLTTLLKDPYILIAAGSICFANMGIAMLEPALPIWMMETMCSRKWQLGVAFLPASISYLIGTNIFGILAHKMGRWLCALLGMIIVGVSILCIPFAKNIYGLIAPNFGVGFAIGMVDSSMMPIMGYLVDLRHVSVYGSVYAIADVAFCMGYAIGPSAGGAIAKAIGFPWLMTIIGIIDILFAPLCFFLRSPP
1SBO , Knot 54 110 0.77 34 82 104 
MNNLKLDIVEQDDKAIVRVQGDIDAYNSSELKEQLRNFISTTSKKKIVLDLSSVSYMDSAGLGTLVVILKDAKINGKEFILSSLKESISRILKLTHLDKIFKITDTVEEA
7AVK , Knot 45 88 0.76 34 70 82 
VTHKAVHEFVSGTPGKELPQEVKALLPVDQTDLKDGIQVTPTQPSQTEVKTSEGTWSFKSYDKTSETVNGSDVKFVGTWEFTASPAPT

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 \(c\).

\(|P_{f(8JTA_1)}(2) \setminus P_{f(1SBO_1)}(2)|=163\), \(|P_{f(1SBO_1)}(2) \setminus P_{f(8JTA_1)}(2)|=28\). 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 1:0001111111111110011101111111001001000001001001011001010001001100000001101010001010001000110010111000100000110001011111100101011001111110001101111111101111001111100001111110010111000001111111101000000010111111111111111111110110011100111111111111011101111010010100001011001100101111110101101111110111111110010000101111111101001110011111100110110111111111101101111001011111011111111110001111110110100101010101110111011011110111111011111111011111011111101110011
Pair \(Z_2\) Length of longest common subsequence
8JTA_1,1SBO_1 191 3
8JTA_1,7AVK_1 191 3
1SBO_1,7AVK_1 114 3

Newick tree

 
[
	8JTA_1:10.24,
	[
		1SBO_1:57,7AVK_1:57
	]:48.24
]

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 \((0.85)(0.8)(\frac{567 }{\log_{20} 567}-\frac{110}{\log_{20}110})=134.\)
Status Protein1 Protein2 d d1/2
Query variables 8JTA_1 1SBO_1 172 105.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]