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Parikh vectors
5WJJ_1 9QYS_1 6MZV_1 Letter Amino acid
13 9 7 F Phenylalanine
23 27 9 S Serine
19 21 11 T Threonine
26 28 33 A Alanine
14 18 6 N Asparagine
12 4 4 M Methionine
27 11 6 D Aspartic acid
22 20 18 V Valine
17 18 9 P Proline
17 19 15 G Glycine
22 9 15 I Isoleucine
43 21 20 L Leucine
23 4 17 E Glutamic acid
12 12 4 H Histidine
19 5 6 K Lycine
5 4 1 W Tryptophan
15 11 6 Y Tyrosine
19 16 12 R Arginine
2 4 0 C Cysteine
15 6 13 Q Glutamine 

5WJJ_1|Chain A|Mitogen-activated protein kinase 14|Homo sapiens (9606)
>9QYS_1|Chain A|Leaf-branch compost cutinase|uncultured bacterium (77133)
>6MZV_1|Chains A, B, C, D, E, F|Microcompartments protein|Haliangium ochraceum (strain DSM 14365 / JCM 11303 / SMP-2) (502025)
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 \(w=f(c)\)
5WJJ , Knot 158 365 0.85 40 222 351 
GAMGSMSQERPTFYRQELNKTIWEVPERYQNLSPVGSGAYGSVCAAFDTKTGLRVAVKKLSRPFQSIIHAKRTYRELRLLKHMKHENVIGLLDVFTPARSLEEFNDVYLVTHLMGADLNNIVKSQKLTDDHVQFLIYQILRGLKYIHSADIIHRDLKPSNLAVNEDSELKILDFGLARHTDDEMTGYVATRWYRAPEIMLNWMHYNQTVDIWSVGCIMAELLTGRTLFPGTDHIDQLKLILRLVGTPGAELLKKISSESARNYIQSLTQMPKMNFANVFIGANPLAVDLLEKMLVLDSDKRITAAQALAHAYFAQYHDPDDEPVADPYDQSFESRDLLIDEWKSLTYDEVISFVPPPLDQEEMES
9QYS , Knot 118 267 0.82 40 169 254 
MSNPYQRGPNPTRSALTADGPFSVATYTVSRLSVSGFGGGVIYYPTGTSYTFGGIAMSPGYTADASSLAWLGRRLASHGFVVLVINTNSRFDGPDSRASQLSAALNYLRTSSPSAVRARLDANRLAVAGHSMGGGGTLRIAEQNPSLKAAVPLTPWHTDKTFNTSVPVLIVGAEADTVAPVSQHAIPFYQNLPSTTPKVYVELCNASHIAPNSNNAAISVYTISWMKLWVDNDTRYRKFLCNVNDPALCDFRTNNRHCQLEHHHHHH
6MZV , Knot 97 212 0.81 38 140 196 
MSITLRTYIFLDALQPQLATFIGKTARGFLPVPGQASLWVEIAPGIAINRVTDAALKATKVQPAVQVVERAYGLLEVHHFDQGEVLAAGSTILDKLEVREEGRLKPQVMTHQIIRAVEAYQTQIINRNSQGMMILPGESLFILETQPAGYAVLAANEAEKAANVHLVNVTPYGAFGRLYLAGSEAEIDAAAEAAEAAIRSVSGVAQESFRDR

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 \(c\).

\(|P_{f(5WJJ_1)}(2) \setminus P_{f(9QYS_1)}(2)|=115\), \(|P_{f(9QYS_1)}(2) \setminus P_{f(5WJJ_1)}(2)|=62\). 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 1:11110100001010000100011011000001011101101010111000011011100100110011010000001011001000011111011011001001001011001111010011000010000101110011011001001011000101001110000010110111100000010101100100110111011000001011011011101101001111000100101110111011101100100001000100100110101101111101111011001111000001011011101011000010001110100001000011100100100001101111110000100
Pair \(Z_2\) Length of longest common subsequence
5WJJ_1,9QYS_1 177 4
5WJJ_1,6MZV_1 174 3
9QYS_1,6MZV_1 157 4

Newick tree

 
[
	5WJJ_1:90.62,
	[
		6MZV_1:78.5,9QYS_1:78.5
	]:12.12
]

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 \((0.85)(0.8)(\frac{632 }{\log_{20} 632}-\frac{267}{\log_{20}267})=102.\)
Status Protein1 Protein2 d d1/2
Query variables 5WJJ_1 9QYS_1 133 112.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]