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Parikh vectors
7LFO_1 2LLO_1 1SGH_1 Letter Amino acid
11 3 13 N Asparagine
14 6 15 G Glycine
17 0 5 H Histidine
30 6 32 L Leucine
24 2 11 S Serine
13 6 14 A Alanine
18 10 18 D Aspartic acid
14 4 16 Q Glutamine
31 9 22 E Glutamic acid
18 4 18 I Isoleucine
14 5 17 F Phenylalanine
22 2 13 P Proline
16 2 19 V Valine
19 2 17 R Arginine
6 0 2 C Cysteine
23 5 29 K Lycine
11 5 6 M Methionine
13 9 12 T Threonine
6 0 6 W Tryptophan
9 0 12 Y Tyrosine 

7LFO_1|Chain A|Tyrosine-protein phosphatase non-receptor type 1|Homo sapiens (9606)
>2LLO_1|Chain A|Calmodulin|Xenopus laevis (8355)
>1SGH_1|Chain A|Moesin|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 \(w=f(c)\)
7LFO , Knot 143 329 0.84 40 208 314 
MEMEKEFEQIDKSGSWAAIYQDIRHEASDFPCRVAKLPKNKNRNRYRDVSPFDHSRIKLHQEDNDYINASLIKMEEAQRSYILTQGPLPNTCGHFWEMVWEQKSRGVVMLNRVMEKGSLKCAQYWPQKEEKEMIFEDTNLKLTLISEDIKSYYTVRQLELENLTTQETREILHFHYTTWPDFGVPESPASFLNFLFKVRESGSLSPEHGPVVVHCSAGIGRSGTFCLADTCLLLMDKRKDPSSVDIKKVLLEMRKFRMGLIQTADQLRFSYLAVIEGAKFIMGDSSVQDQWKELSHEDLEPPPEHIPPPPRPPKRILEPHNLEHHHHHH
2LLO , Knot 42 80 0.76 32 63 77 
ADQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGNGTIDFPEFLTMMARKMKDTD
1SGH , Knot 133 297 0.85 40 188 286 
MPKTISVRVTTMDAELEFAIQPNTTGKQLFDQVVKTIGLREVWFFGLQYQDTKGFSTWLKLNKKVTAQDVRKESPLLFKFRAKFYPEDVSEELIQDITQRLFFLQVKEGILNDDIYCPPETAVLLASYAVQSKYGDFNKEVHKSGYLAGDKLLPQRVLEQHKLNKDQWEERIQVWHEEHRGMLREDAVLEYLKIAQDLEMYGVNYFSIKNKKGSELWLGVDALGLNIYEQNDRLTPKIGFPWSEIRNISFNDKKFVIKPIDKKAPDFVFYAPRLRINKRILALCMGNHELYMRRRKP

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 \(c\).

\(|P_{f(7LFO_1)}(2) \setminus P_{f(2LLO_1)}(2)|=171\), \(|P_{f(2LLO_1)}(2) \setminus P_{f(7LFO_1)}(2)|=26\). 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 1:10100010010001011110001000100110011011000000000010110000101000000010101101001000011001111000101101110000011111001100101001001100000011100001010110001000001001010010000000110100001101111001101101110100010101001111100011110010101100011110000010010100111010010111100100101001111011011110001000100100001011100111110110011010010000000
Pair \(Z_2\) Length of longest common subsequence
7LFO_1,2LLO_1 197 4
7LFO_1,1SGH_1 168 4
2LLO_1,1SGH_1 173 3

Newick tree

 
[
	2LLO_1:95.41,
	[
		7LFO_1:84,1SGH_1:84
	]:11.41
]

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 \((0.85)(0.8)(\frac{409 }{\log_{20} 409}-\frac{80}{\log_{20}80})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 7LFO_1 2LLO_1 127 77.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]