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Parikh vectors
2DLP_1 7SQH_1 1ZNH_1 Letter Amino acid
1 10 11 N Asparagine
4 14 11 D Aspartic acid
1 5 3 C Cysteine
3 21 4 Q Glutamine
13 14 11 G Glycine
4 19 11 I Isoleucine
8 32 16 L Leucine
4 20 10 R Arginine
5 23 9 F Phenylalanine
16 33 12 S Serine
2 25 10 K Lycine
1 5 1 W Tryptophan
0 7 4 M Methionine
2 24 21 E Glutamic acid
1 4 11 H Histidine
3 28 6 V Valine
7 24 8 A Alanine
2 15 9 T Threonine
2 12 4 Y Tyrosine
6 15 2 P Proline 

2DLP_1|Chain A|KIAA1783 protein|Homo sapiens (9606)
>7SQH_1|Chains A, B, C|Proton-activated chloride channel|Homo sapiens (9606)
>1ZNH_1|Chain A|Major Urinary Protein|Mus musculus (10090)
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 \(w=f(c)\)
2DLP , Knot 45 85 0.78 38 65 76 
GSSGSSGSGYVIALRSYITDNCSLLSFHRGDLIKLLPVATLEPGWQFGSAGGRSGLFPADIVQPAAAPDFSFSKEQRSGSGPSSG
7SQH , Knot 150 350 0.83 40 215 333 
MIRQERSTSYQELSEELVQVVENSELADEQDKETVRVQGPGILPGLDSESASSSIRFSKACLKNVFSVLLIFIYLLLMAVAVFLVYRTITDFREKLKHPVMSVSYKEVDRYDAPGIALYPGQAQLLSCKHHYEVIPPLTSPGQPGDMNCTTQRINYTDPFSNQTVKSALIVQGPREVKKRELVFLQFRLNKSSEDFSAIDYLLFSSFQEFLQSPNRVGFMQACESAYSSWKFSGGFRTWVKMSLVKTKEEDGREAVEFRQETSVVNYIDQRPAAKKSAQLFFVVFEWKDPFIQKVQDIVTANPWNTIALLCGAFLALFKAAEFAKLSIKWMIKIRKRYLKRRGQATSHIS
1ZNH , Knot 81 174 0.80 40 127 167 
MRGSHHHHHHGSEEASSTGRNFNVEKINGEWHTIILASDKREKIEDNGNFRLFLEQIHVLEKSLVLKFHTVRDEECSELSMVADKTEKAGEYSVTYDGFNTFTIPKTDYDNFLMAHLINEKDGETFQLMGLYGREPDLSSDIKERFAQLCEEHGILRENIIDLSNANRCLQARE

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 \(c\).

\(|P_{f(2DLP_1)}(2) \setminus P_{f(7SQH_1)}(2)|=19\), \(|P_{f(7SQH_1)}(2) \setminus P_{f(2DLP_1)}(2)|=169\). 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 1:1001001010111100010000011010010110111110101110110111001111101101111101010000001011001
Pair \(Z_2\) Length of longest common subsequence
2DLP_1,7SQH_1 188 3
2DLP_1,1ZNH_1 142 2
7SQH_1,1ZNH_1 182 3

Newick tree

 
[
	7SQH_1:98.64,
	[
		2DLP_1:71,1ZNH_1:71
	]:27.64
]

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 \((0.85)(0.8)(\frac{435 }{\log_{20} 435}-\frac{85}{\log_{20}85})=106.\)
Status Protein1 Protein2 d d1/2
Query variables 2DLP_1 7SQH_1 133 80.5
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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