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Parikh vectors
5MBQ_1 1JIG_1 1KKD_1 Letter Amino acid
29 4 3 I Isoleucine
6 12 7 T Threonine
18 18 5 E Glutamic acid
23 8 6 N Asparagine
34 9 15 K Lycine
3 5 4 M Methionine
12 2 0 P Proline
20 8 1 S Serine
21 14 8 A Alanine
8 4 7 Q Glutamine
19 7 1 G Glycine
1 6 11 H Histidine
12 5 2 F Phenylalanine
1 3 1 W Tryptophan
21 12 7 V Valine
4 1 7 R Arginine
0 0 0 C Cysteine
32 17 12 L Leucine
7 7 1 Y Tyrosine
20 4 4 D Aspartic acid 

5MBQ_1|Chains A, B, C|Enterochelin uptake periplasmic binding protein|Campylobacter jejuni (197)
>1JIG_1|Chains A, B, C, D|Dlp-2|Bacillus anthracis (1392)
>1KKD_1|Chain A|Small conductance calcium-activated potassium channel protein 2|Rattus norvegicus (10116)
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 \(w=f(c)\)
5MBQ , Knot 123 291 0.80 38 161 265 
GPAMLPISMSDEGDSFLVKDSLGENKIPKNPSKVVILDLGILDTFDALKLNDKVVGVPAKNLPKYLQQFKNKPSVGGVQQVDFEAINALKPDLIIISGRQSKFYDKLKEIAPTLFVGLDNANFLSSFENNVLSVAKLYGLEKEALEKISDIKNEIEKAKSIVDEDKKALIILTNSNKISAFGPQSRFGIIHDVLGINAVDENIKVGTAGKSINSEFILEKNPDYIFVVDRNVILGNKERAQGILDNALVAKTKAAQNKKIIYLDPEYWYLASGNGLESLKTMILEIKNAVK
1JIG , Knot 71 146 0.80 38 109 141 
STKTNVVEVLNKQVANWNVLYVKLHNYHWYVTGPHFFTLHEKFEEFYNEAGTYIDELAERILALEGKPLATMKEYLATSSVNEGTSKESAEEMVQTLVNDYSALIQELKEGMEVAGEAGDATSADMLLAIHTTLEQHVWMLSAFLK
1KKD , Knot 49 102 0.74 36 72 93 
MGRKLELTKAEKHVHNFMMDTQLTKRVKNAAANVLRETWLIYKNTKLVKKIDHAKVRKHQRKFLQAIHQLRSVKMEQRKLNDQANTLVDLAKTQLEHHHHHH

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 \(c\).

\(|P_{f(5MBQ_1)}(2) \setminus P_{f(1JIG_1)}(2)|=101\), \(|P_{f(1JIG_1)}(2) \setminus P_{f(5MBQ_1)}(2)|=49\). 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 1:111111101000100111000110001100100111101111001011010001111110011001001000101111001010110110101111010000100010011101111100101100100011011010110001100100100010010011000001111100000101111000111100111101100010110110010001110001001111000111100001011100111100011000011010100101101011001001110100110
Pair \(Z_2\) Length of longest common subsequence
5MBQ_1,1JIG_1 150 3
5MBQ_1,1KKD_1 161 4
1JIG_1,1KKD_1 127 3

Newick tree

 
[
	5MBQ_1:82.01,
	[
		1JIG_1:63.5,1KKD_1:63.5
	]:18.51
]

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 \((0.85)(0.8)(\frac{437 }{\log_{20} 437}-\frac{146}{\log_{20}146})=86.7\)
Status Protein1 Protein2 d d1/2
Query variables 5MBQ_1 1JIG_1 107 81
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]