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Parikh vectors
2LNQ_1 5IXH_1 7GUW_1 Letter Amino acid
3 4 6 E Glutamic acid
2 5 15 L Leucine
1 3 3 Y Tyrosine
6 18 10 V Valine
1 1 9 R Arginine
2 6 7 N Asparagine
0 0 5 C Cysteine
2 6 9 I Isoleucine
0 6 3 P Proline
3 21 8 A Alanine
1 9 4 Q Glutamine
6 12 5 G Glycine
3 2 3 H Histidine
3 9 7 F Phenylalanine
0 2 0 W Tryptophan
2 10 9 S Serine
0 14 7 T Threonine
2 12 8 D Aspartic acid
2 17 4 K Lycine
1 4 6 M Methionine 

2LNQ_1|Chains A, B, C, D, E, F, G, H|P3(40)|Homo sapiens (9606)
>5IXH_1|Chains A, B|YceI-like domain protein|Burkholderia cenocepacia BC7 (985077)
>7GUW_1|Chain A|B-cell lymphoma 6 protein|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 \(w=f(c)\)
2LNQ , Knot 25 40 0.76 32 37 38 
DAEFRHDSGYEVHHQKLVFFAENVGSNKGAIIGLMVGGVV
5IXH , Knot 75 161 0.79 38 112 157 
HMDVDLAKSKVSAVSKQMNVPTEGAFKKFSAQVKFDPAKAAQGSAQMTIDVASFDLGDKMYNDQVAGKDWFDAKTYPQATFVSSAIAPAGGNKYNVTGKLTIKGKAETVTVPVTVAQNGATQTFDGVLPIKRSAFNVGTGEWKDTSIVADEVQIKFHLVAT
7GUW , Knot 65 128 0.82 38 98 125 
GPGADSCIQFTRHASDVLLNLNRLRSRDILTDVVIVVSREQFRAHKTVLMACSGLFYSIFTDQLKCNLSVINLDPEINPEGFCILLDFMYTSRLNLREGNIMAVMATAMYLQMEHVVDTCRKFIKASE

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 \(c\).

\(|P_{f(2LNQ_1)}(2) \setminus P_{f(5IXH_1)}(2)|=23\), \(|P_{f(5IXH_1)}(2) \setminus P_{f(2LNQ_1)}(2)|=98\). 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 1:0101000010010000111110011000111111111111
Pair \(Z_2\) Length of longest common subsequence
2LNQ_1,5IXH_1 121 3
2LNQ_1,7GUW_1 119 2
5IXH_1,7GUW_1 158 2

Newick tree

 
[
	5IXH_1:73.62,
	[
		2LNQ_1:59.5,7GUW_1:59.5
	]:14.12
]

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 \((0.85)(0.8)(\frac{201 }{\log_{20} 201}-\frac{40}{\log_{20}40})=55.1\)
Status Protein1 Protein2 d d1/2
Query variables 2LNQ_1 5IXH_1 68 42
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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