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Parikh vectors
6QPW_1 3GQL_1 6BYH_1 Letter Amino acid
10 22 11 V Valine
13 9 7 Q Glutamine
18 37 12 L Leucine
2 5 3 W Tryptophan
11 14 1 Y Tyrosine
17 20 8 A Alanine
18 17 3 R Arginine
14 22 17 K Lycine
4 19 10 P Proline
15 12 8 N Asparagine
22 24 19 E Glutamic acid
17 20 7 G Glycine
4 14 2 H Histidine
15 13 12 I Isoleucine
5 15 4 M Methionine
7 7 5 F Phenylalanine
20 17 4 S Serine
16 22 19 D Aspartic acid
0 6 3 C Cysteine
14 11 10 T Threonine 

6QPW_1|Chain A|Structural maintenance of chromosomes protein,Structural maintenance of chromosomes protein|Chaetomium thermophilum var. thermophilum DSM 1495 (759272)
>3GQL_1|Chains A, B, C|Basic fibroblast growth factor receptor 1|Homo sapiens (9606)
>6BYH_1|Chains A, B, E[auth G]|S-phase kinase-associated protein 1|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 \(w=f(c)\)
6QPW , Knot 109 242 0.82 38 161 236 
MGKLIRLELFNFKSYKGHHTLLFGDSYFTSIIGPNGSGKSNSMDAISFVLGIKSSHLRSSNLRDLIYRGRVMKTSKIQDDGTTAPATNGDVNGYENGDAGDDEDTSQRTSRNDPKTAWVMAVYEDDAGELHRWKRTITANGTSEYRINDRVVNAQQYNEALEKENILIKARNFLVFQGDVEAIASQSPQDLTRLIEQISGSLEYKEEYERLEEEVRQATEEQAYKLQRRRAANSEIKQYMEQ
3GQL , Knot 141 326 0.83 40 202 313 
MGHHHHHHMAGVSEYELPEDPRWELPRDRLVLGKPLGEGAFGQVVLAEAIGLDKDKPNRVTKVAVKMLKSDATEKDLSDLISEMEMMKMIGKHKNIINLLGACTQDGPLYVIVEYASKGNLREYLQARRPPGLEYCYNPSHNPEEQLSSKDLVSCAYQVARGMEYLASKKCIHRDLAARNVLVTEDNVMKIADFGLARDIHHIDYYKKTTNGRLPVKWMAPEALFDRIYTHQSDVWSFGVLLWEIFTLGGSPYPGVPVEELFKLLKEGHRMDKPSNCTNELYMMMRDCWHAVPSQRPTFKQLVEDLDRIVALTSNQEYLDLSMPLD
6BYH , Knot 78 165 0.80 40 119 157 
GAMPSIKLQSSDGEIFEVDVEIAKQSVTIKTMLEDLGMDDEGDDDPVPLPNVNAAILKKVIQWCTHHKDDPPPPEDDENKEKRTDDIPVWDQEFLKVDQGTLFELILAANYLDIKGLLDVTCKTVANMIKGKTPEEIRKTFNIKNDFTEEEEAQVRKENQWCEEK

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 \(c\).

\(|P_{f(6QPW_1)}(2) \setminus P_{f(3GQL_1)}(2)|=60\), \(|P_{f(3GQL_1)}(2) \setminus P_{f(6QPW_1)}(2)|=101\). 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 1:11011010110100001000111100010011110101000010110111110000100001001100101100001000100111001010100010110000000000000100111111000011010010001010100000100011010000011000011101001111010101110001001001100101010000000010001001000010010000110001000100
Pair \(Z_2\) Length of longest common subsequence
6QPW_1,3GQL_1 161 3
6QPW_1,6BYH_1 162 3
3GQL_1,6BYH_1 173 3

Newick tree

 
[
	6BYH_1:84.86,
	[
		6QPW_1:80.5,3GQL_1:80.5
	]:4.36
]

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 \((0.85)(0.8)(\frac{568 }{\log_{20} 568}-\frac{242}{\log_{20}242})=92.6\)
Status Protein1 Protein2 d d1/2
Query variables 6QPW_1 3GQL_1 116 101.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]