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Parikh vectors
3IGT_1 6HIQ_1 4MYY_1 Letter Amino acid
0 13 0 W Tryptophan
0 40 0 V Valine
0 14 6 N Asparagine
2 18 6 G Glycine
0 15 10 K Lycine
0 30 10 S Serine
0 28 2 D Aspartic acid
4 7 0 C Cysteine
0 35 7 I Isoleucine
0 7 1 M Methionine
0 17 0 Y Tyrosine
0 21 9 E Glutamic acid
0 11 1 H Histidine
0 58 14 L Leucine
0 30 1 P Proline
2 23 3 T Threonine
2 20 5 A Alanine
0 28 1 R Arginine
0 16 8 Q Glutamine
0 21 1 F Phenylalanine

3IGT_1|Chain A|5'-D(*CP*CP*GP*AP*GP*TP*CP*CP*TP*A)-3'|
>6HIQ_1|Chains A, B, C, D, E|5-hydroxytryptamine receptor 3A|Mus musculus (10090)
>4MYY_1|Chains A, B|CurG, CurH fusion protein|Moorea producens 3L (489825)
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 \(w=f(c)\)
3IGT , Knot 6 10 0.46 8 8 8
CCGAGTCCTA
6HIQ , Knot 184 452 0.83 40 231 421
QPALLRLSDHLLANYKKGVRPVRDWRKPTTVSIDVIMYAILNVDEKNQVLTTYIWYRQYWTDEFLQWTPEDFDNVTKLSIPTDSIWVPDILINEFVDVGKSPNIPYVYVHHRGEVQNYKPLQLVTACSLDIYNFPFDVQNCSLTFTSWLHTIQDINITLWRSPEEVRSDKSIFINQGEWELLEVFPQFKEFSIDISNSYAEMKFYVIIRRRPLFYAVSLLLPSIFLMVVDIVGFCLPPDSGERVSFKITLLLGYSVFLIIVSDTLPATAIGTPLIGVYFVVCMALLVISLAETIFIVRLVHKQDLQRPVPDWLRHLVLDRIAWILCLGEQPMAHRPPATFQANKTDDCSGSDLLPAMGNHCSHVGGPQDLEKTPRGRGSPLPPPREASLAVRGLLQELSSIRHFLEKRDEMREVARDWLRVGYVLDRLLFRIYLLAVLAYSITLVTLWSIWH
4MYY , Knot 43 85 0.75 32 60 78
NSALEAKLLDEIKQSSNQELESSIDQILESIINGGGSGGGSMLNKFTKKEQILSEKQQIKQLSPLQRAALALKKLETKLNNTLHE

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 \(c\).

\(|P_{f(3IGT_1)}(2) \setminus P_{f(6HIQ_1)}(2)|=6\), \(|P_{f(6HIQ_1)}(2) \setminus P_{f(3IGT_1)}(2)|=229\). 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 1:0011100001
Pair \(Z_2\) Length of longest common subsequence
3IGT_1,6HIQ_1 235 2
3IGT_1,4MYY_1 68 1
6HIQ_1,4MYY_1 209 3

Newick tree

 
[
	6HIQ_1:12.88,
	[
		3IGT_1:34,4MYY_1:34
	]:92.88
]

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 \((0.85)(0.8)(\frac{462 }{\log_{20} 462}-\frac{10}{\log_{20}10})=144.\)
Status Protein1 Protein2 d d1/2
Query variables 3IGT_1 6HIQ_1 182 93.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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