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Parikh vectors
2ZKO_1 4JCR_1 6AGO_1 Letter Amino acid
0 4 7 H Histidine
0 5 14 Y Tyrosine
5 13 7 A Alanine
0 10 15 Q Glutamine
0 20 18 E Glutamic acid
4 13 19 G Glycine
0 12 20 K Lycine
0 5 6 M Methionine
0 5 9 F Phenylalanine
0 10 13 V Valine
0 9 17 R Arginine
4 0 16 C Cysteine
0 25 14 I Isoleucine
0 13 16 N Asparagine
0 13 16 L Leucine
0 5 10 P Proline
0 12 12 S Serine
0 14 7 T Threonine
0 3 5 W Tryptophan
0 10 15 D Aspartic acid 

2ZKO_1|Chains A[auth C], B[auth D]|RNA (5'-R(P*AP*GP*AP*CP*AP*GP*CP*AP*UP*UP*AP*UP*GP*CP*UP*GP*UP*CP*UP*UP*U)-3')|
>4JCR_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N|ATP-dependent Clp protease proteolytic subunit|Listeria monocytogenes (169963)
>6AGO_1|Chains A, B|Histone-lysine N-methyltransferase ASH1L|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 \(w=f(c)\)
2ZKO , Knot 11 21 0.53 8 12 19 
AGACAGCAUUAUGCUGUCUUU
4JCR , Knot 88 201 0.77 38 139 191 
MAENTKNENITNILTQKLIDTRTVLIYGEINQELAEDVSKQLLLLESISNDPITIFINSQGGHVEAGDTIHDMIKFIKPTVKVVGTGWVASAGITIYLAAEKENRFSLPNTRYMIHQPAGGVQGQSTEIEIEAKEIIRMRERINRLIAEATGQSYEQISKDTDRDFWLSVNEAKDYGIVNEIIENRDGLKMASWSHPQFEK
6AGO , Knot 118 256 0.85 40 184 245 
GSGKYLRQKRIDFQLPYDILWQWKHNQLYKKPDVPLYKKIRSNVYVDVKPLSGYEATTCNCKKPDDDTRKGCVDDCLNRMIFAECSPNTCPCGEQCCNQRIQRHEWVQCLERFRAEEKGWGIRTKEPLKAGQFIIEYLGEVVSEQEFRNRMIEQYHNHSDHYCLNLDSGMVIDSYRMGNEARFINHSCDPNCEMQKWSVNGVYRIGLYALKDMPAGTELTYDYNFHSFNVEKQQLCKCGFEKCRGIIGGKSQRVNG

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 \(c\).

\(|P_{f(2ZKO_1)}(2) \setminus P_{f(4JCR_1)}(2)|=11\), \(|P_{f(4JCR_1)}(2) \setminus P_{f(2ZKO_1)}(2)|=138\). 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 1:111011010010100100000
Pair \(Z_2\) Length of longest common subsequence
2ZKO_1,4JCR_1 149 2
2ZKO_1,6AGO_1 192 2
4JCR_1,6AGO_1 179 3

Newick tree

 
[
	6AGO_1:98.15,
	[
		2ZKO_1:74.5,4JCR_1:74.5
	]:23.65
]

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 \((0.85)(0.8)(\frac{222 }{\log_{20} 222}-\frac{21}{\log_{20}21})=69.6\)
Status Protein1 Protein2 d d1/2
Query variables 2ZKO_1 4JCR_1 86 48
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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