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Parikh vectors
7JUJ_1 8JIM_1 5JQA_1 Letter Amino acid
10 17 6 N Asparagine
23 30 11 G Glycine
11 32 9 L Leucine
4 8 10 M Methionine
9 8 0 W Tryptophan
25 30 11 A Alanine
13 10 21 E Glutamic acid
4 12 1 H Histidine
5 10 8 K Lycine
8 6 2 P Proline
7 8 2 Y Tyrosine
3 22 6 R Arginine
9 18 8 I Isoleucine
14 28 12 T Threonine
9 30 17 D Aspartic acid
8 14 0 C Cysteine
10 13 6 Q Glutamine
3 12 8 F Phenylalanine
19 30 4 S Serine
21 18 7 V Valine 

7JUJ_1|Chains A, B, C, D, E, F|Cruzipain|Trypanosoma cruzi (5693)
>8JIM_1|Chain A[auth B]|Guanine nucleotide-binding protein G(I)/G(S)/G(T) subunit beta-1|Homo sapiens (9606)
>5JQA_1|Chain A|Calmodulin|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 \(w=f(c)\)
7JUJ , Knot 99 215 0.82 40 154 207 
APAAVDWRARGAVTAVKDQGQCGSCWAFSAIGNVECQWFLAGHPLTNLSEQMLVSCDKTDSGCSGGLMNNAFEWIVQENNGAVYTEDSYPYASGEGISPPCTTSGHTVGATITGHVELPQDEAQIAAWLAVNGPVAVAVDASSWMTYTGGVMTSCVSEQLDHGVLLVGYNDSAAVPYWIIKNSWTTQWGEEGYIRIAKGSNQCLVKEEASSAVVG
8JIM , Knot 151 356 0.83 40 199 331 
MHHHHLEVLFQGPGSSGSELDQLRQEAEQLKNQIRDARKACADATLSQITNNIDPVGRIQMRTRRTLRGHLAKIYAMHWGTDSRLLVSASQDGKLIIWDSYTTNKVHAIPLRSSWVMTCAYAPSGNYVACGGLDNICSIYNLKTREGNVRVSRELAGHTGYLSCCRFLDDNQIVTSSGDTTCALWDIETGQQTTTFTGHTGDVMSLSLAPDTRLFVSGACDASAKLWDVREGMCRQTFTGHESDINAICFFPNGNAFATGSDDATCRLFDLRADQELMTYSHDNIICGITSVSFSKSGRLLLAGYDDFNCNVWDALKADRAGVLAGHDNRVSCLGVTDDGMAVATGSWDSFLKIWN
5JQA , 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 \(c\).

\(|P_{f(7JUJ_1)}(2) \setminus P_{f(8JIM_1)}(2)|=67\), \(|P_{f(8JIM_1)}(2) \setminus P_{f(7JUJ_1)}(2)|=112\). 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 1:11111010101110110001001001110111010001111101100100011100000001001111001101110000111000000101010110110000100111010101011000101111111011111110100110001111000100010011111100001111011100010001100101011010000110001001111
Pair \(Z_2\) Length of longest common subsequence
7JUJ_1,8JIM_1 179 4
7JUJ_1,5JQA_1 155 3
8JIM_1,5JQA_1 186 3

Newick tree

 
[
	8JIM_1:95.41,
	[
		7JUJ_1:77.5,5JQA_1:77.5
	]:17.91
]

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 \((0.85)(0.8)(\frac{571 }{\log_{20} 571}-\frac{215}{\log_{20}215})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 7JUJ_1 8JIM_1 128 103.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]