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Parikh vectors
5YCV_1 4HDC_1 2FMQ_1 Letter Amino acid
3 1 7 C Cysteine
6 4 0 H Histidine
26 16 0 L Leucine
4 4 0 M Methionine
5 10 0 Y Tyrosine
22 18 0 V Valine
13 10 0 N Asparagine
10 12 0 K Lycine
10 6 0 F Phenylalanine
14 9 0 S Serine
1 0 0 W Tryptophan
26 14 4 G Glycine
3 6 0 P Proline
26 11 4 A Alanine
16 14 0 R Arginine
12 12 0 D Aspartic acid
7 7 0 Q Glutamine
21 23 0 E Glutamic acid
15 19 0 I Isoleucine
18 9 1 T Threonine 

5YCV_1|Chains A, B, C, D|Enoyl-[acyl-carrier-protein] reductase [NADH] FabI|Bacillus cereus (strain ATCC 14579 / DSM 31 / JCM 2152 / NBRC 15305 / NCIMB 9373 / NRRL B-3711) (226900)
>4HDC_1|Chains A, B|Thymidylate kinase|Staphylococcus aureus subsp. aureus (158879)
>2FMQ_1|Chain A[auth B]|5'-D(*CP*CP*GP*AP*CP*AP*GP*CP*GP*CP*AP*TP*CP*AP*GP*C)-3'|
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 \(w=f(c)\)
5YCV , Knot 115 258 0.82 40 157 246 
GSMELLQGKTFVVMGVANQRSIAWGIARSLHNAGAKLIFTYAGERLERNVRELADTLEGQESLVLPCDVTNDEELTACFETIKQEVGTIHGVAHCIAFANRDDLKGEFVDTSRDGFLLAQNISAFSLTAVAREAKKVMTEGGNILTLTYLGGERVVKNYNVMGVAKASLEASVKYLANDLGQHGIRVNAISAGPIRTLSAKGVGDFNSILREIEERAPLRRTTTQEEVGDTAVFLFSDLARGVTGENIHVDSGYHILG
4HDC , Knot 98 205 0.84 38 152 201 
MSAFITFEGPEGSGKTTVINEVYHRLVKDYDVIMTREPGGVPTGEEIRKIVLEGNDMDIRTEAMLFAASRREHLVLKVIPALKEGKVVLCDRYIDSSLAYQGYARGIGVEEVRALNEFAINGLYPDLTIYLNVSAEVGRERIIKNSRDQNRLDQEDLKFHEKVIEGYQEIIHNESQRFKSVNADQPLENVVEDTYQTIIKYLEKI
2FMQ , Knot 8 16 0.46 8 9 12 
CCGACAGCGCATCAGC

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 \(c\).

\(|P_{f(5YCV_1)}(2) \setminus P_{f(4HDC_1)}(2)|=74\), \(|P_{f(4HDC_1)}(2) \setminus P_{f(5YCV_1)}(2)|=69\). 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 1:101011010011111110000111111001001110111001100100010011001010001111001000001010100100011010111001111000010101100000111110010110101110010011001101101001110011000011111010101010011001100110101101111001010111010011001000111000000001100111110011011010010100100111
Pair \(Z_2\) Length of longest common subsequence
5YCV_1,4HDC_1 143 3
5YCV_1,2FMQ_1 160 2
4HDC_1,2FMQ_1 161 1

Newick tree

 
[
	2FMQ_1:82.96,
	[
		5YCV_1:71.5,4HDC_1:71.5
	]:11.46
]

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 \((0.85)(0.8)(\frac{463 }{\log_{20} 463}-\frac{205}{\log_{20}205})=75.2\)
Status Protein1 Protein2 d d1/2
Query variables 5YCV_1 4HDC_1 90 82
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]