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Parikh vectors
6QIQ_1 6OFG_1 3QQJ_1 Letter Amino acid
0 3 16 I Isoleucine
0 6 21 K Lycine
3 0 3 C Cysteine
0 5 9 Q Glutamine
3 3 18 G Glycine
0 2 18 E Glutamic acid
0 1 5 M Methionine
0 2 16 R Arginine
0 5 8 N Asparagine
0 8 16 D Aspartic acid
0 4 23 V Valine
0 1 10 H Histidine
0 7 15 S Serine
0 5 17 T Threonine
0 3 21 P Proline
0 1 4 W Tryptophan
0 4 10 Y Tyrosine
2 12 19 A Alanine
0 8 40 L Leucine
0 3 17 F Phenylalanine 

6QIQ_1|Chains A, B|RNA (5'-R(*GP*CP*AP*G)-D(P*(CSL))-R(P*AP*GP*C)-3')|Homo sapiens (9606)
>6OFG_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R|Protein PrgI|Salmonella typhimurium (strain SL1344) (216597)
>3QQJ_1|Chain A|Cyclin-dependent kinase 2|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 \(w=f(c)\)
6QIQ , Knot 4 8 0.34 6 3 3 
GCAGCAGC
6OFG , Knot 47 83 0.83 38 73 80 
GSHMATPWSGYLDDVSAKFDTGVDNLQTQVTEALDKLAAKPSDPALLAAYQSKLSEYNLYRNAQSNTVKAFKDIDAAIIQNFR
3QQJ , Knot 136 306 0.84 40 194 292 
GPLGSPEFMENFQKVEKIGEGTYGVVYKARNKLTGEVVALKKIRLDTETEGVPSTAIREISLLKELNHPNIVKLLDVIHTENKLYLVFEFLHQDLKKFMDASALTGIPLPLIKSYLFQLLQGLAFCHSHRVLHRDLKPQNLLINTEGAIKLADFGLARAFGVPVRTYTHEVVTLWYRAPEILLGCKYYSTAVDIWSLGCIFAEMVTRRALFPGDSEIDQLFRIFRTLGTPDEVVWPGVTSMPDYKPSFPKWARQDFSKVVPPLDEDGRSLLSQMLHYDPNKRISAKAALAHPFFQDVTKPVPHLRL

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 \(c\).

\(|P_{f(6QIQ_1)}(2) \setminus P_{f(6OFG_1)}(2)|=3\), \(|P_{f(6OFG_1)}(2) \setminus P_{f(6QIQ_1)}(2)|=73\). 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 1:10110110
Pair \(Z_2\) Length of longest common subsequence
6QIQ_1,6OFG_1 76 1
6QIQ_1,3QQJ_1 195 2
6OFG_1,3QQJ_1 181 3

Newick tree

 
[
	3QQJ_1:10.37,
	[
		6QIQ_1:38,6OFG_1:38
	]:68.37
]

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 \((0.85)(0.8)(\frac{91 }{\log_{20} 91}-\frac{8}{\log_{20}8})=33.2\)
Status Protein1 Protein2 d d1/2
Query variables 6QIQ_1 6OFG_1 45 24
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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