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Parikh vectors
8HXC_1 4KUC_1 2KIA_1 Letter Amino acid
11 2 10 K Lycine
5 24 10 A Alanine
7 21 12 R Arginine
10 17 7 G Glycine
4 14 5 F Phenylalanine
15 14 4 Y Tyrosine
9 2 2 C Cysteine
12 15 11 E Glutamic acid
17 17 4 T Threonine
13 8 7 D Aspartic acid
4 14 12 Q Glutamine
18 23 9 I Isoleucine
15 22 10 L Leucine
6 3 5 M Methionine
6 15 9 P Proline
15 19 2 S Serine
1 1 4 W Tryptophan
16 17 3 N Asparagine
7 4 2 H Histidine
12 15 1 V Valine 

8HXC_1|Chains A, B, C, D, E, F, G|NFkB inhibitor|Monkeypox virus (10244)
>4KUC_1|Chains A, D[auth I]|Ricin|Ricinus communis (3988)
>2KIA_1|Chain A|Myosin-VI|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 \(w=f(c)\)
8HXC , Knot 96 203 0.83 40 144 198 
VEYKNTICPPRQDYRYWYFVAELTIGVNYDINSTIIGECHMSESYIDRNANIVLTGYGLKINMTIMDTDQRFVAAAEGVGKDNKLSVLLFTTQRLDKVHHNISVTITCMEMNCGTTKYNSDLPESIHKSSSCDITINGSCVTCVNLETDPTKINPHYLHPKNKYLYHNSEYSMRGSYGVTFIDELNQCLLDIKELSYDICYRE
4KUC , Knot 116 267 0.81 40 171 259 
IFPKQYPIINFTTAGATVQSYTNFIRAVRGRLTTGADVRHEIPVLPNRVGLPINQRFILVELSNHAELSVTLALDVTNAYVVGYRAGNSAYFFHPDNQEDAEAITHLFTDVQNRYTFAFGGNYDRLEQLAGNLRENIELGNGPLEEAISALYYYSTGGTQLPTLARSFIICIQMISEAARFQYIEGEMRTRIRYNRRSAPDPSVITLENSWGRLSTAIQESNQGAFASPIQLQRRNGSKFSVYDVSILIPIIALMVYRCAPPPSSQF
2KIA , Knot 63 129 0.79 40 105 125 
ARQQEIDMKRQQRFFRIPFIRPADQYKDPQNKKKGWWYAHFDGPWIARQMELHPDKPPILLVAGKDDMEMCEKNLEETGLTRKRGAEILPRQFEEIWERCGGIQYLQSAIESRQARPTYATAMLQNLLK

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 \(c\).

\(|P_{f(8HXC_1)}(2) \setminus P_{f(4KUC_1)}(2)|=76\), \(|P_{f(4KUC_1)}(2) \setminus P_{f(8HXC_1)}(2)|=103\). 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 1:10000010110000001011101011100010001110001000010001011101011010101100000111110111000010111100001001000101010010100100000001100100000001010100100101000100101001010000100000001010011011001000110100100010000
Pair \(Z_2\) Length of longest common subsequence
8HXC_1,4KUC_1 179 3
8HXC_1,2KIA_1 175 3
4KUC_1,2KIA_1 176 3

Newick tree

 
[
	4KUC_1:89.16,
	[
		8HXC_1:87.5,2KIA_1:87.5
	]:1.66
]

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 \((0.85)(0.8)(\frac{470 }{\log_{20} 470}-\frac{203}{\log_{20}203})=77.7\)
Status Protein1 Protein2 d d1/2
Query variables 8HXC_1 4KUC_1 99 88
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]