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Parikh vectors
2WWG_1 2QEB_1 7HIO_1 Letter Amino acid
6 9 9 R Arginine
11 11 9 D Aspartic acid
6 6 8 P Proline
13 7 7 Y Tyrosine
14 10 16 V Valine
17 4 8 N Asparagine
5 5 2 Q Glutamine
10 6 12 G Glycine
16 13 8 L Leucine
22 15 12 K Lycine
2 7 4 C Cysteine
19 13 11 E Glutamic acid
16 8 6 I Isoleucine
5 5 5 M Methionine
8 5 3 F Phenylalanine
14 4 11 S Serine
7 5 17 A Alanine
7 6 2 H Histidine
9 6 11 T Threonine
5 0 2 W Tryptophan 

2WWG_1|Chains A, B, C|THYMIDILATE KINASE, PUTATIVE|PLASMODIUM FALCIPARUM (36329)
>2QEB_1|Chains A, B|D7R4 Protein|Anopheles gambiae (7165)
>7HIO_1|Chains A, B, C, D|Non-structural protein 3|Chikungunya virus (37124)
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 \(w=f(c)\)
2WWG , Knot 99 212 0.83 40 151 206 
SHMTDDKKKGKFIVFEGLDRSGKSTQSKLLVEYLKNNNVEVKHLYFPNRETGIGQIISKYLKMENSMSNETIHLLFSANRWEHMNEIKSLLLKGIWVVCDRYAYSGVAYSSGALNLNKTWCMNPDQGLIKPDVVFYLNVPPNYAQNRSDYGEEIYEKVETQKKIYETYKHFAHEDYWINIDATRKIEDIHNDIVKEVTKIKVEPEEFNFLWS
2QEB , Knot 72 145 0.82 38 113 141 
METVQDCENKLPPSLKSRLCEIRRYEIIEGPEMDKHIHCVMRALDFVYEDGRGDYHKLYDPLNIIELDKRHDVNLEKCIGECVQVPTSERAHVFYKCLLKSTTGRTFKKVFDLMELKKAGKVPQHQRYTAEFVQIMKDYDKALNC
7HIO , Knot 82 163 0.85 40 130 161 
GAMAPSYRVKRMDIAKNDEECVVNAANPRGLPGDGVCKAVYKKWPESFKNSATPVGTAKTVMCGTYPVIHAVGPNFSNYTESEGDRELAAAYREVAKEVTRLGVNSVAIPLLSTGVYSGGKDRLTQSLNHLFTAMDSTDADVVIYCRDKEWEKKISEAIQMRT

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 \(c\).

\(|P_{f(2WWG_1)}(2) \setminus P_{f(2QEB_1)}(2)|=107\), \(|P_{f(2QEB_1)}(2) \setminus P_{f(2WWG_1)}(2)|=69\). 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 1:00100000010111101100010000001110010000101001011000011101100010100010000101110100100100100111011111000010011100011101000101010011101011101011100100000010010001000001000000110000110101000100100011001001010100101110
Pair \(Z_2\) Length of longest common subsequence
2WWG_1,2QEB_1 176 3
2WWG_1,7HIO_1 169 4
2QEB_1,7HIO_1 165 3

Newick tree

 
[
	2WWG_1:87.48,
	[
		7HIO_1:82.5,2QEB_1:82.5
	]:4.98
]

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 \((0.85)(0.8)(\frac{357 }{\log_{20} 357}-\frac{145}{\log_{20}145})=64.3\)
Status Protein1 Protein2 d d1/2
Query variables 2WWG_1 2QEB_1 86 70.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]