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Parikh vectors
8FJZ_1 2KTU_1 7IJQ_1 Letter Amino acid
15 2 5 P Proline
19 6 11 S Serine
9 4 16 N Asparagine
14 9 3 Q Glutamine
14 9 6 H Histidine
14 4 2 R Arginine
41 15 19 L Leucine
18 8 22 V Valine
27 16 13 G Glycine
21 11 6 I Isoleucine
23 13 13 K Lycine
12 8 6 T Threonine
23 4 15 A Alanine
5 2 3 C Cysteine
18 21 6 E Glutamic acid
5 1 0 W Tryptophan
12 9 7 Y Tyrosine
23 13 9 D Aspartic acid
8 4 2 M Methionine
10 11 5 F Phenylalanine 

8FJZ_1|Chains A, B, C, D, E, F|Mitogen-activated protein kinase kinase kinase kinase 1|Homo sapiens (9606)
>2KTU_1|Chain A|Eukaryotic peptide chain release factor subunit 1|Homo sapiens (9606)
>7IJQ_1|Chains A, B|Non-structural protein 3|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 \(w=f(c)\)
8FJZ , Knot 141 331 0.82 40 197 312 
MASHHHHHHDYDGATTENLYFQGSMDVVDPDIFNRDPRDHYDLLQRLGGGTYGEVFKARDKVSGDLVALKMVKMEPDDDVSTLQKEILILKTCRHANIVAYHGSYLWLQKLWICMEFCGAGSLQDIYQVTGSLSELQISYVCREVLQGLAYLHSQKKIHRDIKGANILINDAGEVRLADFGISAQIGAELARRLEFIGTPYWMAPEVAAVALKGGYNELCDIWSLGITAIELAELQPPLFDVHPLRVLFLMTKSGYQPPRLKEKGKWSAAFHNFIKVTLTKSPKKRPSATKMLSHQLVSQPGLNRGLILDLLDKLKNPGKGPSIGDIEDEE
2KTU , Knot 80 170 0.80 40 119 161 
SNVKFIQEKKLIGRYFDEISQDTGKYCFGVEDTLKALEMGAVEILIVYENLDIMRYVLHCQGTEEEKILYLTPEQEKDKSHFTDKETGQEHELIESMPLLEWFANNYKKFGATLEIVTDKSQEGSQFVKGFGGIGGILRYRVDFQGMEYQGGDDEFFDLDDYLEHHHHHH
7IJQ , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL

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 \(c\).

\(|P_{f(8FJZ_1)}(2) \setminus P_{f(2KTU_1)}(2)|=124\), \(|P_{f(2KTU_1)}(2) \setminus P_{f(8FJZ_1)}(2)|=46\). 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 1:1100000000001100001010101011010110001000001100111100101101000101011110110101000100100011110000010111001001110011101010111010010010101001010010001101110100000100010110111001101011011101011101100101110101111011111101100010011011101101101011110101101111100010011010001010111001101010001000101001100011001110011110110010011011011010000
Pair \(Z_2\) Length of longest common subsequence
8FJZ_1,2KTU_1 170 6
8FJZ_1,7IJQ_1 166 3
2KTU_1,7IJQ_1 140 3

Newick tree

 
[
	8FJZ_1:88.18,
	[
		7IJQ_1:70,2KTU_1:70
	]:18.18
]

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 \((0.85)(0.8)(\frac{501 }{\log_{20} 501}-\frac{170}{\log_{20}170})=96.7\)
Status Protein1 Protein2 d d1/2
Query variables 8FJZ_1 2KTU_1 123 92
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]