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Parikh vectors
4OQS_1 9EOQ_1 3EEJ_1 Letter Amino acid
22 0 15 I Isoleucine
25 11 12 T Threonine
7 0 8 Y Tyrosine
34 0 14 V Valine
29 0 9 D Aspartic acid
15 0 13 Q Glutamine
28 0 17 E Glutamic acid
2 9 1 C Cysteine
16 0 9 F Phenylalanine
34 0 11 P Proline
11 0 7 M Methionine
43 7 6 A Alanine
9 0 11 N Asparagine
15 0 16 K Lycine
49 0 24 L Leucine
19 0 14 S Serine
4 0 4 W Tryptophan
28 0 12 R Arginine
25 15 14 G Glycine
18 0 10 H Histidine 

4OQS_1|Chain A|CYP105AS1|Amycolatopsis orientalis (31958)
>9EOQ_1|Chain A|DNA (42-MER)|synthetic construct (32630)
>3EEJ_1|Chains A, B|Dihydrofolate reductase|Candida glabrata (5478)
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 \(w=f(c)\)
4OQS , Knot 179 433 0.83 40 222 403 
MRVDSENMNEPVTLPTGRAVGYPFDPPPDLVKLPPVSPMRFPDGHIGWLVTSHAAARTVMIDPRFSNRPEHKHPVFSVIPRPGGATKAPAPGWFINMDAPEHTRYRRMLISQFTVRRIKELEPRIVQITEDHLDAMAKAGPPVDLVQAFALPVPSLVICELLGVSYADHAFFQEQTTIMASVDKTQDEVTTALGKLTRYIAELVATKRLSPKDDLLGSLITDTDLTDEELTNIALLLLVAGHETTANMLGLGTFALLQHPEQIAALDSPDAVEELLRYLSIVHLGTPNRAALEDVELEGQMIRKGDTVAIGLPAVNRDPKVFDEPDILQLDRVDARKHAAFGGGIHQCLGQQLARVEMRIGFTRLFARFPSLRLAVPAEEIKLREKSAAYGVWALPVAWDARPSFLVQSGYVEQKLISEEDLNSAVDHHHHHH
9EOQ , Knot 17 42 0.50 8 15 29 
ACTTCCAGTCCGTGGTAGGGCAGGTTGGGGTGACCGCTATAT
3EEJ , Knot 104 227 0.82 40 154 214 
MSKVPVVGIVAALLPEMGIGFQGNLPWRLAKEMKYFREVTTLTNDNSKQNVVIMGRKTWESIPQKFRPLPKRINVVVSRSFDGELRKVEDGIYHSNSLRNCLTALQSSLANENKIERIYIIGGGEIYRQSMDLADHWLITKIMPLPETTIPQMDTFLQKQELEQRFYDNSDKLVDFLPSSIQLEGRLTSQEWNGELVKGLPVQEKGYQFYFTLYTKKLEHHHHHHHH

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 \(c\).

\(|P_{f(4OQS_1)}(2) \setminus P_{f(9EOQ_1)}(2)|=214\), \(|P_{f(9EOQ_1)}(2) \setminus P_{f(4OQS_1)}(2)|=7\). 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 1:1010000100110110101110110111011011110110110101111100011100111010100010000111011101111001111111101011000000011100101001001010110100001011101111101101111111011100111100100111000001110100000010011101000110111000101000111011000010000100111111111000010111110111100100111100101100110010110110100111001010101100100111111110001011001011010010100011111110001100110101011100111011010111110010100001101111111110101011100101000110000100110000000
Pair \(Z_2\) Length of longest common subsequence
4OQS_1,9EOQ_1 221 3
4OQS_1,3EEJ_1 178 6
9EOQ_1,3EEJ_1 163 3

Newick tree

 
[
	4OQS_1:10.86,
	[
		3EEJ_1:81.5,9EOQ_1:81.5
	]:24.36
]

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 \((0.85)(0.8)(\frac{475 }{\log_{20} 475}-\frac{42}{\log_{20}42})=134.\)
Status Protein1 Protein2 d d1/2
Query variables 4OQS_1 9EOQ_1 175 94.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]