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Parikh vectors
6UFH_1 7BJJ_1 5RVG_1 Letter Amino acid
0 18 6 I Isoleucine
0 29 19 L Leucine
0 22 13 K Lycine
0 8 5 F Phenylalanine
0 18 5 P Proline
0 13 11 S Serine
0 22 6 E Glutamic acid
25 18 13 G Glycine
0 10 7 Y Tyrosine
0 9 6 T Threonine
16 19 15 A Alanine
0 17 2 R Arginine
0 16 6 H Histidine
0 8 2 M Methionine
0 6 0 W Tryptophan
0 18 9 D Aspartic acid
21 5 3 C Cysteine
0 21 22 V Valine
0 13 16 N Asparagine
0 7 3 Q Glutamine 

6UFH_1|Chain A[auth B]|RNA (77-MER)|Mycobacterium tuberculosis (1773)
>7BJJ_1|Chain A|Serine/threonine-protein kinase Chk1|Homo sapiens (9606)
>5RVG_1|Chains A, B|Non-structural protein 3|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 \(w=f(c)\)
6UFH , Knot 23 77 0.43 8 16 42 
GGGCCUAUAGCUCAGGCGGUUAGAGCGCUUCGCUGAUAACGAAGAGGUCGGAGGUUCAAGUCCUCCUAGGCCCGCCA
7BJJ , Knot 130 297 0.83 40 182 283 
MAVPFVEDWDLVQTLGEGAYGEVQLAVNRVTEEAVAVKIVDMKRAVDCPENIKKEICILKMLNHENVIKFYGHRREGNIQYLFMELASGGSLFDRIEPDIGMPEPDAQRFFHQLMAGVVYLHGIGITHRDIKPHNLLLDERDNLKIADYSLATVFRYNNRERLLNKMCGTLPYVAPELLKRREFHAEPVDVWSCGIVLTAMLAGELPWDQPSDSCQEYSDWKEKKTYLNPWKKIDSAPLALLHKILVENPSARITIPDIKKDRWYNKPLKKGAKRPRVTSGGVSESPSGHHHHHHHH
5RVG , Knot 80 169 0.81 38 119 162 
SMVNSFSGYLKLTDNVYIKNADIVEEAKKVKPTVVVNAANVYLKHGGGVAGALNKATNNAMQVESDDYIATNGPLKVGGSCVLSGHNLAKHCLHVVGPNVNKGEDIQLLKSAYENFNQHEVLLAPLLSAGIFGADPIHSLRVCVDTVRTNVYLAVFDKNLYDKLVSSFL

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 \(c\).

\(|P_{f(6UFH_1)}(2) \setminus P_{f(7BJJ_1)}(2)|=12\), \(|P_{f(7BJJ_1)}(2) \setminus P_{f(6UFH_1)}(2)|=178\). 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 1:11100010110001110110011110100001001101101111111001111100011100000001110001001
Pair \(Z_2\) Length of longest common subsequence
6UFH_1,7BJJ_1 190 2
6UFH_1,5RVG_1 127 3
7BJJ_1,5RVG_1 167 3

Newick tree

 
[
	7BJJ_1:96.54,
	[
		6UFH_1:63.5,5RVG_1:63.5
	]:33.04
]

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 \((0.85)(0.8)(\frac{374 }{\log_{20} 374}-\frac{77}{\log_{20}77})=92.4\)
Status Protein1 Protein2 d d1/2
Query variables 6UFH_1 7BJJ_1 128 75
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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