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Parikh vectors
6YHR_1 6ACW_1 6QER_1 Letter Amino acid
34 20 16 R Arginine
30 13 21 D Aspartic acid
21 20 8 P Proline
9 4 3 W Tryptophan
20 12 15 Y Tyrosine
37 10 24 I Isoleucine
59 15 40 L Leucine
17 11 5 M Methionine
25 14 16 F Phenylalanine
28 32 11 T Threonine
39 9 31 K Lycine
46 21 20 S Serine
30 25 15 A Alanine
23 19 12 N Asparagine
29 12 9 Q Glutamine
37 19 9 G Glycine
17 5 4 H Histidine
19 3 1 C Cysteine
36 12 33 E Glutamic acid
29 22 17 V Valine 

6YHR_1|Chain A|Werner syndrome ATP-dependent helicase|Homo sapiens (9606)
>6ACW_1|Chain A|VP1|Coxsackievirus A10 (42769)
>6QER_1|Chains A, B, C, D|Transcriptional regulator|Streptococcus thermophilus (strain ATCC BAA-491 / LMD-9) (322159)
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 \(w=f(c)\)
6YHR , Knot 238 585 0.86 40 282 561 
MNEGEEDDDKDFLWPAPNEEQVTCLKMYFGHSSFKPVQWKVIHSVLEERRDNVAVMATGYGKSLCFQYPPVYVGKIGLVISPLISLMEDQVLQLKMSNIPACFLGSAQSENVLTDIKLGKYRIVYVTPEYCSGNMGLLQQLEADIGITLIAVDEAHCISEWGHDFRDSFRKLGSLKTALPMVPIVALTATASSSIREDIVRCLNLRNPQITCTGFDRPNLYLEVRRKTGNILQDLQPFLVKTSSHWEFEGPTIIYCPSRKMTQQVTGELRKLNLSCGTYHAGMSFSTRKDIHHRFVRDEIQCVIATIAFGMGINKADIRQVIHYGAPKDMESYYQEIGRAGRDGLQSSCHVLWAPADINLNRHLLTEIRNEKFRLYKLKMMAKMEKYLHSSRCRRQIILSHFEDKQVQKASLGIMGTEKCCDNCRSRLDHCYSMDDSEDTSWDFGPQAFKLLSAVDILGEKFGIGLPILFLRGSNSQRLADQYRRHSLFGTGKDQTESWWKAFSRQLITEGFLVEVSRYNKFMKICALTKKGRNWLHKANTESQSLILQANEELCPKKFLLPSSKTVSSGTKEHCYNQAENLYFQ
6ACW , Knot 129 298 0.82 40 189 288 
GDPVEDIIHDALGNTARRAISSATNVESAANTTPSSHRLETGRVPALQAAETGATSNATDENMIETRCVVNRNGVLETTINHFFSRSGLVGVVNLTDGGTDTTGYATWDIDIMGFVQLRRKCEMFTYMRFNAEFTFVTTTENGGARPYMLQYMYVPPGAPKPTGRDAFQWQTATNPSVFVKLTDPPAQVSVPFMSPASAYQWFYDGYPTFGQHPETSNTTYGLCPNNMMGTFAVRVVSREASQLKLQTRVYMKLKHVRAWVPRPIRSQPYLLKNFPNYDSSKITNSARDRSSIKQANM
6QER , Knot 136 310 0.84 40 184 293 
MNLKDSIGLRIKTERERQQMSREVLCLDGAELTVRQLIRIEKGESLPSLDRLSYIAKRLGKSMTELLDQDNITIPDEYYEMKNRLIKFPTYRNPDRIKSKLTLIEEVYEKFFDILPEEELLTLDILENILSFTSWEESPKVEEIYEDLFEQVKRKRKFSTNDLLVIDYYFFHLYGRKQYDKKLFERIIKRVLNQEIWTDDVYNIVLFNDLMAIAALKIFHNSFSDFLTVVDKALAVIEKSQLYSYKPSVFVLKAKYELLHKENKKEAAENYDKAIVFASVLEDSVLEESIKAGKLADGLGAGWSHPQFEK

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 \(c\).

\(|P_{f(6YHR_1)}(2) \setminus P_{f(6ACW_1)}(2)|=146\), \(|P_{f(6ACW_1)}(2) \setminus P_{f(6YHR_1)}(2)|=53\). 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 1:100100000001111110000100101011000101101011001100000011111010100101001110110111110111011000110101001110111010000110010110001101010000101111001010111011110010010011001000100110100111111111101010001000110010100101000110010101010000101100101111000001010110110010001000101010010100100011101000001000110001001110111111100101001100111001000000110110011000001111110101000110010000101001011101000100000000111001000010010111110000000000010000010000000101110110110110111001111111111010000011000000011101000000110110001100111101000001101011000100110010000001110100010100111100001001000000001001010
Pair \(Z_2\) Length of longest common subsequence
6YHR_1,6ACW_1 199 4
6YHR_1,6QER_1 168 5
6ACW_1,6QER_1 199 5

Newick tree

 
[
	6ACW_1:10.15,
	[
		6YHR_1:84,6QER_1:84
	]:20.15
]

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 \((0.85)(0.8)(\frac{883 }{\log_{20} 883}-\frac{298}{\log_{20}298})=158.\)
Status Protein1 Protein2 d d1/2
Query variables 6YHR_1 6ACW_1 208 155
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]