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Parikh vectors
6CRB_1 2EAL_1 3FEM_1 Letter Amino acid
36 3 24 K Lycine
14 16 8 F Phenylalanine
14 8 11 P Proline
12 4 1 Y Tyrosine
19 6 11 R Arginine
21 6 18 D Aspartic acid
13 11 6 Q Glutamine
27 3 25 E Glutamic acid
22 16 25 G Glycine
21 15 22 S Serine
1 1 2 W Tryptophan
18 14 30 V Valine
18 5 30 A Alanine
7 4 13 M Methionine
26 8 21 L Leucine
3 2 5 C Cysteine
9 4 6 H Histidine
23 6 22 I Isoleucine
19 8 11 T Threonine
12 8 6 N Asparagine 

6CRB_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>2EAL_1|Chains A, B|Galectin-9|Homo sapiens (9606)
>3FEM_1|Chains A, B, C, D, E, F|Pyridoxine biosynthesis protein SNZ1|Saccharomyces cerevisiae (4932)
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 \(w=f(c)\)
6CRB , Knot 146 335 0.84 40 199 321 
MSKRKAPQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEKGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSE
2EAL , Knot 66 148 0.74 40 103 135 
MAFSGSQAPYLSPAVPFSGTIQGGLQDGLQITVNGTVLSSSGTRFAVNFQTGFSGNDIAFHFNPRFEDGGYVVCNTRQNGSWGPEERKTHMPFQKGMPFDLCFLVQSSDFKVMVNGILFVQYFHRVPFHRVDTISVNGSVQLSYISFQ
3FEM , Knot 127 297 0.81 40 164 274 
MTGEDFKIKSGLAQMLKGGVIMDVVTPEQAKIAEKSGACAVMALESIPADMRKSGKVCRMSDPKMIKDIMNSVSIPVMAKVRIGHFVEAQIIEALEVDYIDESEVLTPADWTHHIEKDKFKVPFVCGAKDLGEALRRINEGAAMIRTKGEAGTGDVSEAVKHIRRITEEIKACQQLKSEDDIAKVAEEMRVPVSLLKDVLEKGKLPVVNFAAGGVATPADAALLMQLGCDGVFVGSGIFKSSNPVRLATAVVEATTHFDNPSKLLEVSSDLGELMGGVSIESISHASNGVRLSEIGW

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 \(c\).

\(|P_{f(6CRB_1)}(2) \setminus P_{f(2EAL_1)}(2)|=141\), \(|P_{f(2EAL_1)}(2) \setminus P_{f(6CRB_1)}(2)|=45\). 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 1:10000110001011100110011010001001100001000110111001001001101001111100110010011101010010010000000010110010111101100110011001001000000100000111001101000110001101001110010010000110101010011000101011100101000000010110011001001011000100100011110011000000001000101011100000011101010011000101011001101000010111101111011110000011001010000100000
Pair \(Z_2\) Length of longest common subsequence
6CRB_1,2EAL_1 186 3
6CRB_1,3FEM_1 139 5
2EAL_1,3FEM_1 169 3

Newick tree

 
[
	2EAL_1:94.42,
	[
		6CRB_1:69.5,3FEM_1:69.5
	]:24.92
]

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 \((0.85)(0.8)(\frac{483 }{\log_{20} 483}-\frac{148}{\log_{20}148})=98.8\)
Status Protein1 Protein2 d d1/2
Query variables 6CRB_1 2EAL_1 126 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]