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Parikh vectors
6AGX_1 3IEG_1 7KJR_1 Letter Amino acid
17 41 13 A Alanine
9 10 15 F Phenylalanine
17 7 12 P Proline
8 19 10 Q Glutamine
23 36 11 K Lycine
12 14 17 Y Tyrosine
13 15 21 I Isoleucine
30 40 32 L Leucine
10 20 24 S Serine
16 20 6 R Arginine
21 29 13 D Aspartic acid
6 7 7 C Cysteine
23 40 12 E Glutamic acid
16 11 24 T Threonine
5 1 6 W Tryptophan
21 16 26 V Valine
12 8 9 N Asparagine
18 11 14 G Glycine
5 8 8 H Histidine
16 6 4 M Methionine 

6AGX_1|Chains A, B, C, D|Fibroblast growth factor receptor 2|Homo sapiens (9606)
>3IEG_1|Chains A, B|DnaJ homolog subfamily C member 3|Mus musculus (10090)
>7KJR_1|Chains A, B|ORF3a protein|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 \(w=f(c)\)
6AGX , Knot 129 298 0.82 40 192 283 
ELPEDPKWEFPRDKLTLGKPLGEGCFGQVVMAEAVGIDKDKPKEAVTVAVKMLKDDATEKDLSDLVSEMEMMKMIGKHKNIINLLGACTQDGPLYVIVEYASKGNLREYLRARRPPGMEYSYDINRVPEEQMTFKDLVSCTYQLARGMEYLASQKCIHRDLTARNVLVTENNVMKIADFGLARDINNIDYYKKTTNGRLPVKWMAPEALFDRVYTHQSDVWSFGVLMWEIFTLGGSPYPGIPVEELFKLLKEGHRMDKPANCTNELYMMMRDCWHAVPSQRPTFKQLVEDLDRILTLT
3IEG , Knot 151 359 0.82 40 194 339 
ADVEKHLELGKKLLAAGQLADALSQFHAAVDGDPDNYIAYYRRATVFLAMGKSKAALPDLTKVIALKMDFTAARLQRGHLLLKQGKLDEAEDDFKKVLKSNPSEQEEKEAESQLVKADEMQRLRSQALDAFDGADYTAAITFLDKILEVCVWDAELRELRAECFIKEGEPRKAISDLKAASKLKSDNTEAFYKISTLYYQLGDHELSLSEVRECLKLDQDHKRCFAHYKQVKKLNKLIESAEELIRDGRYTDATSKYESVMKTEPSVAEYTVRSKERICHCFSKDEKPVEAIRICSEVLQMEPDNVNALKDRAEAYLIEEMYDEAIQDYEAAQEHNENDQQIREGLEKAQRLLKQSQKR
7KJR , Knot 124 284 0.82 40 178 271 
MDLFMRIFTIGTVTLKQGEIKDATPSDFVRATATIPIQASLPFGWLIVGVALLAVFQSASKIITLKKRWQLALSKGVHFVCNLLLLFVTVYSHLLLVAAGLEAPFLYLYALVYFLQSINFVRIIMRLWLCWKCRSKNPLLYDANYFLCWHTNCYDYCIPYNSVTSSIVITSGDGTTSPISEHDYQIGGYTEKWESGVKDCVVLHSYFTSDYYQLYSTQLSTDTGVEHVTFFIYNKIVDEPEEHVQIHTIDGSSGVVNPVMEPIYDEPTTTTSVPLSNSLEVLFQ

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 \(c\).

\(|P_{f(6AGX_1)}(2) \setminus P_{f(3IEG_1)}(2)|=85\), \(|P_{f(3IEG_1)}(2) \setminus P_{f(6AGX_1)}(2)|=87\). 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 1:0110010101100010110111010110111101111000010011011101100010000100110010110111000011011110000111011100100101000101001111000001001100010100110000011011001100001000101001110000110110111100100100000000101110111101110010000001101111110110111010111110011011001001001100000101110001011100010100110010011010
Pair \(Z_2\) Length of longest common subsequence
6AGX_1,3IEG_1 172 3
6AGX_1,7KJR_1 174 3
3IEG_1,7KJR_1 186 4

Newick tree

 
[
	7KJR_1:91.36,
	[
		6AGX_1:86,3IEG_1:86
	]:5.36
]

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 \((0.85)(0.8)(\frac{657 }{\log_{20} 657}-\frac{298}{\log_{20}298})=99.7\)
Status Protein1 Protein2 d d1/2
Query variables 6AGX_1 3IEG_1 124 115.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]