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Parikh vectors
2MXG_1 4GJV_1 5ZBI_1 Letter Amino acid
0 4 29 I Isoleucine
1 6 5 W Tryptophan
1 2 16 F Phenylalanine
1 9 35 V Valine
1 23 33 A Alanine
0 10 22 N Asparagine
1 0 8 C Cysteine
4 21 45 G Glycine
1 8 41 L Leucine
0 11 34 S Serine
0 20 30 T Threonine
0 3 21 H Histidine
3 6 37 K Lycine
0 3 13 M Methionine
1 3 24 P Proline
2 5 19 R Arginine
0 7 38 D Aspartic acid
0 7 22 Q Glutamine
0 5 32 E Glutamic acid
0 6 28 Y Tyrosine 

2MXG_1|Chain A|antimicrobial peptide|
>4GJV_1|Chain A|Streptavidin|Streptomyces avidinii (1895)
>5ZBI_1|Chains A, B|Peptide asparaginyl ligase|Viola canadensis (97421)
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 \(w=f(c)\)
2MXG , Knot 13 16 0.75 20 15 14 
VARGWKRKCPLFGKGG
4GJV , Knot 74 159 0.78 38 110 154 
MASMTGGQQMGRDEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTHGTTEANAWKSTLVGHDTFTKVKPSAASIDAAKKAGVNNGNPLDAVQQ
5ZBI , Knot 217 532 0.85 40 268 507 
MAHHHHHHMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGRDITGDGFLRLPSHGNGNSGDVDSKAGTKWAVLIAGSKGYQNYRHQADVCHAYQILRKGGVKDENIIVFMYDDIAYDIRNPYPGTIINSPDKKDVYKGVPKDYTGEDVNVQNFLAVILGNKTALTGGSGKVLDTRPNDHIFIYYTDHGYPGVLGMPTEPYLYANDLIDTLKKKHALGTYEGLVFYVEACESASIFEGLLPDGLNIYVSTAAKAGEGSWVAYCPSQEPPVPAEYGTCVGDLYSVTWMEDSDVYNLRTQTLHQQYELVKNKIAYASTVSQFGDFPISKDSLFEYMGTDPANEKRQYEDEEKSSSPHVGAVHQREADLHHFWDKYQKASEGSRNKVDARKQLVEVMLHRMHVDDSIESIAKLLFGSGAKASEMMNTIRPPGQPLVSDWDCLKTMVRTFETHCGSLSEYGMKYTRFLANICNSGIQKEKMGEASAQVCLNFP

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 \(c\).

\(|P_{f(2MXG_1)}(2) \setminus P_{f(4GJV_1)}(2)|=9\), \(|P_{f(4GJV_1)}(2) \setminus P_{f(2MXG_1)}(2)|=104\). 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 1:1101100001111011
Pair \(Z_2\) Length of longest common subsequence
2MXG_1,4GJV_1 113 2
2MXG_1,5ZBI_1 259 3
4GJV_1,5ZBI_1 206 4

Newick tree

 
[
	5ZBI_1:13.10,
	[
		2MXG_1:56.5,4GJV_1:56.5
	]:74.60
]

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 \((0.85)(0.8)(\frac{175 }{\log_{20} 175}-\frac{16}{\log_{20}16})=57.2\)
Status Protein1 Protein2 d d1/2
Query variables 2MXG_1 4GJV_1 71 38.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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