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Parikh vectors
7LHR_1 3LSL_1 3ASY_1 Letter Amino acid
28 18 25 A Alanine
3 10 7 M Methionine
6 7 6 F Phenylalanine
6 13 9 Y Tyrosine
25 18 19 V Valine
8 9 2 N Asparagine
6 4 0 C Cysteine
14 7 16 P Proline
21 17 7 T Threonine
18 13 13 D Aspartic acid
5 3 5 Q Glutamine
24 23 13 G Glycine
6 16 6 I Isoleucine
24 20 30 L Leucine
8 28 9 K Lycine
18 10 21 R Arginine
17 20 13 E Glutamic acid
11 2 6 H Histidine
9 16 4 S Serine
5 4 0 W Tryptophan 

7LHR_1|Chains A, B|Phosphoadenosine phosphosulfate reductase|Mycobacterium tuberculosis (1773)
>3LSL_1|Chains A, B[auth D], C[auth G]|Glutamate receptor 2|Rattus norvegicus (10116)
>3ASY_1|Chains A, B|Uridine kinase|Thermus thermophilus (300852)
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 \(w=f(c)\)
7LHR , Knot 116 262 0.82 40 162 247 
MSGETTRLTEPQLRELAARGAAELDGATATDMLRWTDETFGDIGGAGGGVSGHRGWTTCNYVVASNMADAVLVDLAAKVRPGVPVIFLDTGYHFVETIGTRDAIESVYDVRVLNVTPEHTVAEQDELLGKDLFARNPHECCRLRKVVPLGKTLRGYSAWVTGLRRVDAPTRANAPLVSFDETFKLVKVNPLAAWTDQDVQEYIADNDVLVNPLVREGYPSIGCAPCTAKPAEGADPRSGRWQGLAKTECGLHASLEHHHHHH
3LSL , Knot 119 258 0.85 40 172 248 
KTVVVTTILESPYVMMKKNHEMLEGNERYEGYCVDLAAEIAKHCGFKYKLTIVGDGKYGARDADTKIWNGMVGELVYGKADIAIAPLTITLVREEVIDFSKPFMSLGISIMIKKGTPIESAEDLSKQTEIAYGTLDSGSTKEFFRRSKIAVFDKMWTYMRSAEPSVFVRTTAEGVARVRKSKGKYAYLLESTMNEYIEQRKPCDTMKVGGNLDSKGYGIATPKGSSLGNAVNLAVLKLNEQGLLDKLKNKWWYDKGEC
3ASY , Knot 96 211 0.81 36 130 199 
MSAPKPFVIGIAGGTASGKTTLAQALARTLGERVALLPMDHYYKDLGHLPLEERLRVNYDHPDAFDLALYLEHAQALLRGLPVEMPVYDFRAYTRSPRRTPVRPAPVVILEGILVLYPKELRDLMDLKVFVDADADERFIRRLKRDVLERGRSLEGVVAQYLEQVKPMHLHFVEPTKRYADVIVPRGGQNPVALEMLAAKALARLARMGAA

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 \(c\).

\(|P_{f(7LHR_1)}(2) \setminus P_{f(3LSL_1)}(2)|=75\), \(|P_{f(3LSL_1)}(2) \setminus P_{f(7LHR_1)}(2)|=85\). 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 1:1010000100101001110111010110100110100001101111111101001100000111001101111011101011111111001001100110001100100101101010001100001110011100100000100111110010100111011001011001011110100010110101111100001000110001110111001010110110010110110100101011100001101010000000
Pair \(Z_2\) Length of longest common subsequence
7LHR_1,3LSL_1 160 5
7LHR_1,3ASY_1 132 4
3LSL_1,3ASY_1 154 3

Newick tree

 
[
	3LSL_1:82.26,
	[
		7LHR_1:66,3ASY_1:66
	]:16.26
]

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 \((0.85)(0.8)(\frac{520 }{\log_{20} 520}-\frac{258}{\log_{20}258})=74.7\)
Status Protein1 Protein2 d d1/2
Query variables 7LHR_1 3LSL_1 94 93
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]