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Parikh vectors
1JCO_1 3EVV_1 1JOJ_1 Letter Amino acid
0 32 12 K Lycine
0 2 4 W Tryptophan
1 25 17 V Valine
1 47 16 G Glycine
0 16 6 H Histidine
2 22 15 I Isoleucine
2 16 7 Y Tyrosine
0 41 18 D Aspartic acid
2 16 5 Q Glutamine
0 20 2 M Methionine
2 19 31 S Serine
1 35 19 T Threonine
0 22 18 A Alanine
0 20 11 F Phenylalanine
0 12 11 P Proline
2 38 7 E Glutamic acid
2 34 18 L Leucine
0 19 6 R Arginine
2 19 14 N Asparagine
4 2 0 C Cysteine

1JCO_1|Chain A|Insulin A chain|Homo sapiens (9606)
>3EVV_1|Chain A|Myosin light chain kinase, Green fluorescent protein, Calmodulin chimera|Aequorea victoria (6100)
>1JOJ_1|Chains A, B, C, D|Concanavalin-Br|Canavalia ensiformis (3823)
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 \(w=f(c)\)
1JCO , Knot 15 21 0.72 22 20 19
GIVEQCCTSICSLYQLENYCN
3EVV , Knot 186 457 0.83 40 229 412
MRGSHHHHHHGMASMTGGQQMGRDLYDDDDKDLATMVDSSRRKWNKTGHAVRAIGRLSSLENVYIMADKQKNGIKANFKIRHNIEDGGVQLAYHYQQNTPIGDGPVLLPDNHYLSTQSKLSKDPNEKRDHMVLLEFVTAAGITLGMDELYKGGTGGSMVSKGEELFTGVVPILVELDGDVNGHKFSVSGEGEGDATYGKLTLKFICTTGKLPVPWPTLVTTLTYGTYGTYGVQCFSRYPDHMKQHDFFKSAMPEGYIQERTIFFKDDGNYKTRAEVKFEGDTLVNRIELKGIDFKEDGNILGHKLEYNTRDQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGNGTIDFPEFLTMMARKMKDTDSEEEIREAFRVFDKDGNGYISAAELRHVMTNLGEKLTDEEVDEMIREADIDGDGQVNYEEFVQMMTAK
1JOJ , Knot 104 237 0.80 38 151 226
ADTIVAVELDTYPNTDIGDPSYPHIGIDIKSVRSKKTAKWNMQNGKVGTAHIIYNSVDKRLSAVVSYPNADSATVSYDVDLDNVLPEWVRVGLSASTGLYKETNTILSWSFTSKLKSNSTHETNALHFMFNQFSKDQKDLILQGDATTGTDGNLELTRVSSNGSPQGSSVGRALFYAPVHIWESSAVVASFEATFTFLIKSPDSHPADGIAFFISNIDSSIPSGSTGRLLGLFPDAN

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 \(c\).

\(|P_{f(1JCO_1)}(2) \setminus P_{f(3EVV_1)}(2)|=7\), \(|P_{f(3EVV_1)}(2) \setminus P_{f(1JCO_1)}(2)|=216\). 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 1:111000000100100100000
Pair \(Z_2\) Length of longest common subsequence
1JCO_1,3EVV_1 223 3
1JCO_1,1JOJ_1 157 2
3EVV_1,1JOJ_1 180 4

Newick tree

 
[
	3EVV_1:10.86,
	[
		1JCO_1:78.5,1JOJ_1:78.5
	]:29.36
]

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 \((0.85)(0.8)(\frac{478 }{\log_{20} 478}-\frac{21}{\log_{20}21})=143.\)
Status Protein1 Protein2 d d1/2
Query variables 1JCO_1 3EVV_1 176 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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