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Parikh vectors
9ISK_1 6NDI_1 7VBD_1 Letter Amino acid
18 24 8 R Arginine
28 20 7 D Aspartic acid
14 11 5 Q Glutamine
22 19 7 I Isoleucine
29 38 9 L Leucine
13 7 4 F Phenylalanine
0 2 3 W Tryptophan
37 26 3 V Valine
42 21 16 G Glycine
15 24 10 P Proline
25 18 11 T Threonine
3 9 7 Y Tyrosine
16 7 1 M Methionine
13 22 4 S Serine
46 33 11 A Alanine
16 10 8 N Asparagine
0 5 0 C Cysteine
26 16 4 E Glutamic acid
3 13 2 H Histidine
17 9 7 K Lycine 

9ISK_1|Chains A, B, C, D, E, F|Cell division protein FtsZ|Klebsiella pneumoniae subsp. pneumoniae MGH 78578 (272620)
>6NDI_1|Chains A, B|Transcriptional regulator|Klebsiella pneumoniae subsp. pneumoniae (72407)
>7VBD_1|Chains A, B, C, D|Nucleoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
9ISK , Knot 157 383 0.81 36 188 364 
MFEPMELTNDAVIKVIGVGGGGGNAVEHMVRERIEGVEFFAVNTDAQALRKTAVGQTIQIGSGITKGLGAGANPEVGRNAADEDREALRAALDGADMVFIAAGMGGGTGTGAAPVVAEVAKDLGILTVAVVTKPFNFEGKKRMAFAEQGITELSKHVDSLITIPNDKLLKVLGRGISLLDAFGAANDVLKGAVQGIAELITRPGLMNVDFADVRTVMSEMGYAMMGSGVASGEDRAEEAAEMAISSPLLEDIDLSGARGVLVNITAGFDLRLDEFETVGNTIRAFASDNATVVIGTSLDPDMNDELRVTVVATGIGMDKRPEITLVTNKQVQQPVMDRYQQHGMSPLTQEQKPAAKVVNDNTPQTAKEPDYLDIPAFLRKQAD
6NDI , Knot 142 334 0.82 40 191 318 
SNAMASLKDVAKLANVSLMTVSRALNTPERLKPETLARVQAAIAETNYVPDLSAKKIRGARATPSTIGVLALDTVTTPFSVEITLSIEETARAHGWNSFVVNMFSDDRPEAVVDLLLSHRPDGIIFTTMGLRQVPLPEKLLTLPCVLANCESLSQPVASYIPDDEQGQYDAVKALLAAGYRRPLCLHLPASQPATIRRRRGLERACREAGIEPDHLSHSYMGQGDEHYHDIPAVVLAHIREGKPGFDSVICGNDRIAFMVYQTLLGQGLRIPQDVAVVGYDNMVGIGDLFLPPLSTVQLPHYDIGRLSALHIIHGDNHRETRKVASPWLPRASH
7VBD , Knot 64 127 0.81 38 100 125 
NTASWFTALTQHGKEDLKFPRGQGVPINTNSSPDDQIGYYRRATRRIRGGDGKMKDLSPRWYFYYLGTGPEAGLPYGANKDGIIWVATEGALNTPKDHIGTRNPANNAAIVLQLPQGTTLPKGFYAE

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 \(c\).

\(|P_{f(9ISK_1)}(2) \setminus P_{f(6NDI_1)}(2)|=74\), \(|P_{f(6NDI_1)}(2) \setminus P_{f(9ISK_1)}(2)|=77\). 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 1:11011010001110111111111011001100010110111100010110001110010110110011111101011001100000110111011011111111111010111111101100111101111001101010001111001100100010011011000110111011011011111001101110111011001111010110100110011011110111010001001101110011100101011011110101110101001001100101110001011110010101000101011101111000101011000010011100000011011000001110110000100100100101111100010
Pair \(Z_2\) Length of longest common subsequence
9ISK_1,6NDI_1 151 4
9ISK_1,7VBD_1 164 3
6NDI_1,7VBD_1 169 5

Newick tree

 
[
	7VBD_1:85.68,
	[
		9ISK_1:75.5,6NDI_1:75.5
	]:10.18
]

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 \((0.85)(0.8)(\frac{717 }{\log_{20} 717}-\frac{334}{\log_{20}334})=105.\)
Status Protein1 Protein2 d d1/2
Query variables 9ISK_1 6NDI_1 131 123
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]