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Parikh vectors
5TRG_1 2JND_1 9DLL_1 Letter Amino acid
21 7 0 R Arginine
13 6 0 D Aspartic acid
21 9 4 G Glycine
9 4 0 I Isoleucine
8 3 0 F Phenylalanine
8 7 0 P Proline
13 12 0 T Threonine
35 7 3 A Alanine
1 6 4 C Cysteine
19 8 0 E Glutamic acid
20 8 0 L Leucine
17 2 0 V Valine
10 5 0 Q Glutamine
2 4 0 H Histidine
7 5 0 K Lycine
3 2 0 M Methionine
16 6 0 S Serine
0 2 0 W Tryptophan
7 7 0 N Asparagine
10 9 0 Y Tyrosine 

5TRG_1|Chains A, B, C, D, E, F, G, O, P, Q, R, S, T, U|Proteasome subunit alpha|Mycobacterium tuberculosis (1773)
>2JND_1|Chain A|Corticotropin-releasing factor receptor 2|Mus musculus (10090)
>9DLL_1|Chains A, B|CAG 13-mer RNA (5'-R(*GP*AP*CP*AP*GP*CP*AP*GP*CP*UP*GP*UP*C)-3')|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 \(w=f(c)\)
5TRG , Knot 107 240 0.81 38 148 225 
MEQAMRERSELARKGIARAKSVVALAYAGGVLFVAENPSRSLQKISELYDRVGFAAAGKFNEFDNLRRGGIQFADTRGYAYDRRDVTGRQLANVYAQTLGTIFTEQAKPYEVELCVAEVAHYGETKRPELYRITYDGSIADEPHFVVMGGTTEPIANALKESYAENASLTDALRIAVAALRAGSADTSGGDQPTLGVASLEVAVLDANRPRRAFRRITGSALQALLVDQESPQSDGESSG
2JND , Knot 60 119 0.80 40 101 115 
GSGMKETAAAKFERQHMDSPDLGTTLLEQYCHRTTIGNFSGPYTYCNTTLDQIGTCWPQSAPGALVERPCPEYFNGIKYNTTRNAYRECLENGTWASRVNYSHCEPILDDKQRKYDLHY
9DLL , Knot 7 13 0.46 8 9 9 
GACAGCAGCUGUC

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 \(c\).

\(|P_{f(5TRG_1)}(2) \setminus P_{f(2JND_1)}(2)|=102\), \(|P_{f(2JND_1)}(2) \setminus P_{f(5TRG_1)}(2)|=55\). 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 1:100110000011001110100111110111111110010001001001000111111101001001001110110001010000010100110101001101100010100101011011001000010100100010110010111111000111011000010010100110111111011010001100101111010111101001001100101011011110000100010001
Pair \(Z_2\) Length of longest common subsequence
5TRG_1,2JND_1 157 3
5TRG_1,9DLL_1 155 2
2JND_1,9DLL_1 108 2

Newick tree

 
[
	5TRG_1:84.50,
	[
		9DLL_1:54,2JND_1:54
	]:30.50
]

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 \((0.85)(0.8)(\frac{359 }{\log_{20} 359}-\frac{119}{\log_{20}119})=73.5\)
Status Protein1 Protein2 d d1/2
Query variables 5TRG_1 2JND_1 94 69.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]