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Parikh vectors
6KYJ_1 7OFG_1 6LQX_1 Letter Amino acid
15 1 4 N Asparagine
10 2 1 C Cysteine
46 1 2 G Glycine
22 0 6 F Phenylalanine
23 1 10 P Proline
30 0 4 T Threonine
45 0 4 A Alanine
29 0 6 R Arginine
19 0 5 S Serine
8 0 3 W Tryptophan
11 1 9 Q Glutamine
37 1 13 L Leucine
23 1 5 I Isoleucine
11 0 4 M Methionine
31 0 7 V Valine
27 0 9 D Aspartic acid
33 0 8 E Glutamic acid
17 1 6 Y Tyrosine
15 0 0 H Histidine
25 0 9 K Lycine 

6KYJ_1|Chains A, C, E, G|Ribulose bisphosphate carboxylase large chain|Oryza sativa (4530)
>7OFG_1|Chain A|Oxytocin|Homo sapiens (9606)
>6LQX_1|Chains A, B, C, D|CREB-binding protein|Homo sapiens (9606)
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 \(w=f(c)\)
6KYJ , Knot 198 477 0.85 40 252 452 
MSPQTETKASVGFKAGVKDYKLTYYTPEYETKDTDILAAFRVTPQPGVPPEEAGAAVAAESSTGTWTTVWTDGLTSLDRYKGRCYHIEPVVGEDNQYIAYVAYPLDLFEEGSVTNMFTSIVGNVFGFKALRALRLEDLRIPPTYSKTFQGPPHGIQVERDKLNKYGRPLLGCTIKPKLGLSAKNYGRACYECLRGGLDFTKDDENVNSQPFMRWRDRFVFCAEAIYKSQAETGEIKGHYLNATAGTCEEMIKRAVFARELGVPIVMHDYLTGGFTANTSLAHYCRDNGLLLHIHRAMHAVIDRQKNHGMHFRVLAKALRMSGGDHIHAGTVVGKLEGEREMTLGFVDLLRDDFIEKDRARGIFFTQDWVSMPGVIPVASGGIHVWHMPALTEIFGDDSVLQFGGGTLGHPWGNAPGAAANRVALEACVQARNEGRDLAREGNEIIRSACKWSPELAAACEIWKAIKFEFEPVDKLDS
7OFG , Knot 9 10 0.69 18 9 8 
CYIQNCPLGX
6LQX , Knot 57 115 0.78 38 98 113 
KKIFKPEELRQALMPTLEALYRQDPESLPFRQPVDPQLLGIPDYFDIVKNPMDLSTIKRKLDTGQYQEPWQYVDDVWLMFNNAWLYNRKTSRVYKFCSKLAEVFEQEIDPVMQSL

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 \(c\).

\(|P_{f(6KYJ_1)}(2) \setminus P_{f(7OFG_1)}(2)|=247\), \(|P_{f(7OFG_1)}(2) \setminus P_{f(6KYJ_1)}(2)|=4\). 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 1:101000001011101110000100001000000001111101010111110011111110000101001100110010000100001011110000011011011011001010011001110111101101101001011100000101110110100001000101111001010111010001010000101110100000010001110100011101011000010010101001010110000110011110011111110001011101000110000001111010011011100000011010111011010110010110111010100010111101100011000010111100011011111111011101101111001110001101111011011101111110011101010100010011001001100100101011110011011010101100100
Pair \(Z_2\) Length of longest common subsequence
6KYJ_1,7OFG_1 251 2
6KYJ_1,6LQX_1 218 3
7OFG_1,6LQX_1 105 2

Newick tree

 
[
	6KYJ_1:13.29,
	[
		6LQX_1:52.5,7OFG_1:52.5
	]:79.79
]

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 \((0.85)(0.8)(\frac{487 }{\log_{20} 487}-\frac{10}{\log_{20}10})=151.\)
Status Protein1 Protein2 d d1/2
Query variables 6KYJ_1 7OFG_1 194 99
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]