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Parikh vectors
7UPM_1 5GTY_1 1AOW_1 Letter Amino acid
2 6 1 W Tryptophan
14 23 14 V Valine
17 16 24 R Arginine
21 26 21 E Glutamic acid
11 18 2 P Proline
27 16 22 S Serine
14 21 23 A Alanine
16 25 19 I Isoleucine
30 33 32 L Leucine
14 8 10 F Phenylalanine
9 12 18 T Threonine
10 6 4 C Cysteine
11 8 2 H Histidine
3 14 11 M Methionine
16 22 22 G Glycine
14 23 20 K Lycine
10 13 13 Y Tyrosine
5 8 9 N Asparagine
15 21 29 D Aspartic acid
5 12 13 Q Glutamine 

7UPM_1|Chain A|Tribbles homolog 2|Homo sapiens (9606)
>5GTY_1|Chains A, B, C, D, E, F, G, H|Epidermal growth factor receptor|Homo sapiens (9606)
>1AOW_1|Chain A|ANNEXIN IV|Bos taurus (9913)
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 \(w=f(c)\)
7UPM , Knot 122 264 0.86 40 180 256 
GPGNLSHCVSCIGKYLLLEPLEGDHVFRAVHLHSGEELVCKVFDISCYQESLAPCFCLSAHSNINQITEIILGETKAYVFFERSYGDMHSFVRTCKKLREEEAARLFYQIASAVAHCHDGGLVLRDLKLRKFIFKDEERTRVKLESLEDAYILRGDDDSLSDKHGCPAYVSPEILNTSGSYSGKAADVWSLGVMLYTMLVGRYPFHDIEPSSLFSKIRRGQFNIPETLSPKAKCLIRSILRREPSERLTSQEILDHPWFSTDFS
5GTY , Knot 147 331 0.86 40 212 325 
GAMGGEAPNQALLRILKETEFKKIKVLGSGAFGTVYKGLWIPEGEKVKIPVAIKELREATSPKANKEILDEAYVMASVDNPHVCRLLGICLTSTVQLIMQLMPFGCLLDYVREHKDNIGSQYLLNWCVQIAKGMNYLEDRRLVHRDLAARNVLVKTPQHVKITDFGLAKLLGAEEKEYHAEGGKVPIKWMALESILHRIYTHQSDVWSYGVTVWELMTFGSKPYDGIPASEISSILEKGERLPQPPICTIDVYMIMVKCWMIDADSRPKFRELIIEFSKMARDPQRYLVIQGDERMHLPSPTDSNFYRALMDEEDMDDVVDADEYLIPQQG
1AOW , Knot 129 309 0.79 40 173 282 
ASGFNAAEDAQTLRKAMKGLGTDEDAIINVLAYRSTAQRQEIRTAYKTTIGRDLMDDLKSELSGNFEQVILGMMTPTVLYDVQEVRKAMKGAGTDEGCLIEILASRTPEEIRRINQTYQLQYGRSLEDDIRSDTSFMFQRVLVSLSAGGRDESNYLDDALMRQDAQDLYEAGEKKWGTDEVKFLTVLCSRNRNHLLHVFDEYKRIAQKDIEQSIKSETSGSFEDALLAIVKCMRNKSAYFAERLYKSMKGLGTDDDTLIRVMVSRAEIDMLDIRANFKRLYGKSLYSFIKGDTSGDYRKVLLILCGGDD

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 \(c\).

\(|P_{f(7UPM_1)}(2) \setminus P_{f(5GTY_1)}(2)|=69\), \(|P_{f(5GTY_1)}(2) \setminus P_{f(7UPM_1)}(2)|=101\). 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 1:111010001001100111011010011011010010011001101000000111010101000100100111100010111000010100110000010000110110011011100001111100101001110000000101001001011010000100001011010101100010001011011011111001111001100101001100100101011001010100110011000100010000110011100010
Pair \(Z_2\) Length of longest common subsequence
7UPM_1,5GTY_1 170 4
7UPM_1,1AOW_1 161 4
5GTY_1,1AOW_1 163 3

Newick tree

 
[
	5GTY_1:84.17,
	[
		7UPM_1:80.5,1AOW_1:80.5
	]:3.67
]

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 \((0.85)(0.8)(\frac{595 }{\log_{20} 595}-\frac{264}{\log_{20}264})=93.2\)
Status Protein1 Protein2 d d1/2
Query variables 7UPM_1 5GTY_1 120 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]