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Parikh vectors
5CNS_1 8VNO_1 7AWK_1 Letter Amino acid
62 3 14 A Alanine
33 0 6 Q Glutamine
20 0 4 H Histidine
50 0 7 I Isoleucine
42 0 10 K Lycine
49 0 3 S Serine
35 0 3 N Asparagine
51 0 8 D Aspartic acid
28 0 9 F Phenylalanine
31 0 11 P Proline
39 0 6 V Valine
40 0 10 R Arginine
46 0 5 E Glutamic acid
75 0 11 L Leucine
16 0 3 M Methionine
5 0 4 W Tryptophan
11 3 0 C Cysteine
48 1 8 G Glycine
39 6 6 T Threonine
41 0 2 Y Tyrosine 

5CNS_1|Chains A, B, C, D|Ribonucleoside-diphosphate reductase 1 subunit alpha|Escherichia coli (strain K12) (83333)
>8VNO_1|Chains A[auth C], C[auth D]|DNA (5'-D(*TP*TP*GP*AP*CP*TP*CP*TP*CP*TP*TP*AP*A)-3')|synthetic construct (32630)
>7AWK_1|Chain A|Probable endoribonuclease HigB1|Mycobacterium tuberculosis (strain ATCC 25618 / H37Rv) (83332)
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 \(w=f(c)\)
5CNS , Knot 292 761 0.84 40 294 703 
MNQNLLVTKRDGSTERINLDKIHRVLDWAAEGLHNVSISQVELRSHIQFYDGIKTSDIHETIIKAAADLISRDAPDYQYLAARLAIFHLRKKAYGQFEPPALYDHVVKMVEMGKYDNHLLEDYTEEEFKQMDTFIDHDRDMTFSYAAVKQLEGKYLVQNRVTGEIYESAQFLYILVAACLFSNYPRETRLQYVKRFYDAVSTFKISLPTPIMSGVRTPTRQFSSCVLIECGDSLDSINATSSAIVKYVSQRAGIGINAGRIRALGSPIRGGEAFHTGCIPFYKHFQTAVKSCSQGGVRGGAATLFYPMWHLEVESLLVLKNNRGVEGNRVRHMDYGVQINKLMYTRLLKGEDITLFSPSDVPGLYDAFFADQEEFERLYTKYEKDDSIRKQRVKAVELFSLMMQERASTGRIYIQNVDHCNTHSPFDPAIAPVRQSNLCLEIALPTKPLNDVNDENGEIALCTLSAFNLGAINNLDELEELAILAVRALDALLDYQDYPIPAAKRGAMGRRTLGIGVINFAYYLAKHGKRYSDGSANNLTHKTFEAIQYYLLKASNELAKEQGACPWFNETTYAKGILPIDTYKKDLDTIANEPLHYDWEALRESIKTHGLRNSTLSALMPSETSSQISNATNGIEPPRGYVSIKASKDGILRQVVPDYEHLHDAYELLWEMPGNDGYLQLVGIMQKFIDQSISANTNYDPSRFPSGKVPMQQLLKDLLTAYKFGVKTLYYQNTRDGAEDAQDDLVPSIQDDGCESGACKI
8VNO , Knot 7 13 0.46 8 8 9 
TTGACTCTCTTAA
7AWK , Knot 65 130 0.81 38 100 126 
GSHMPPPDPAAMGTWKFFRASVDGRPVFKKEFDKLPDQARAALIVLMQRYLVGDLAAGSIKPIRGDILELRWHEANNHFRVLFFRWGQHPVALTAFYANQQKTPKTKIETALDRQKIWKRAFGDTPPILE

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 \(c\).

\(|P_{f(5CNS_1)}(2) \setminus P_{f(8VNO_1)}(2)|=287\), \(|P_{f(8VNO_1)}(2) \setminus P_{f(5CNS_1)}(2)|=1\). 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 1:10001110000100001010010011011101100101001010001010011000010001101110110001100001110111101000101010111100011011011000001100000001001001100000101001110010100110001010100010110111110110001000010010010011001010110111011001000100011100100100101000111001000111110110101110110110110010111000100110000011101111011011101010011110000110100100100110100110001101001011010011110011110000100100000000010000101101101110001001010100100000001101111110000101011110011001000010111001011011110010010011111101101110000011111001111000111111011001100100000101001000010110001101000110001101110000010111110000001001100110001011000100011000010111100000010010011011010101010001110011100001001001110111001010111110011000101000001001101011100110011010011100100000001100100011101000100011001
Pair \(Z_2\) Length of longest common subsequence
5CNS_1,8VNO_1 288 3
5CNS_1,7AWK_1 222 4
8VNO_1,7AWK_1 104 2

Newick tree

 
[
	5CNS_1:14.38,
	[
		7AWK_1:52,8VNO_1:52
	]:93.38
]

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 \((0.85)(0.8)(\frac{774 }{\log_{20} 774}-\frac{13}{\log_{20}13})=226.\)
Status Protein1 Protein2 d d1/2
Query variables 5CNS_1 8VNO_1 288 145.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]