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Parikh vectors
1RCL_1 6RUD_1 6JAE_1 Letter Amino acid
2 5 9 H Histidine
4 8 20 F Phenylalanine
0 8 20 M Methionine
11 28 40 T Threonine
6 31 34 V Valine
2 9 32 R Arginine
5 13 21 D Aspartic acid
4 0 13 C Cysteine
14 25 43 G Glycine
1 24 27 K Lycine
5 12 21 P Proline
10 26 34 S Serine
0 1 12 W Tryptophan
12 39 50 A Alanine
5 11 13 Q Glutamine
3 19 33 E Glutamic acid
0 26 46 L Leucine
9 7 10 Y Tyrosine
10 17 15 N Asparagine
3 19 25 I Isoleucine 

1RCL_1|Chain A|RIBONUCLEASE F1|Gibberella fujikuroi (5127)
>6RUD_1|Chains A, B, C, D|L-asparaginase|Wolinella succinogenes (844)
>6JAE_1|Chains A, B, C, D|Glycerol kinase|Trypanosoma brucei gambiense (31285)
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 \(w=f(c)\)
1RCL , Knot 54 106 0.79 34 83 104 
QSATTCGSTNYSASQVRAAANAACQYYQNDDTAGSSTYPHTYNNYEGFDFPVDGPYQEFPIKSGGVYTGGSPGADRVVINTNCEYAGAITHTGASGNNFVGCSGTN
6RUD , Knot 142 328 0.83 38 186 312 
KPQVTILATGGTIAGSGESSVKSSYSAGAVTVDKLLAAVPAINDLATIKGEQISSIGSQEMTGKVWLKLAKRVNELLAQKETEAVIITHGTDTMEETAFFLNLTVKSQKPVVLVGAMRPGSSMSADGPMNLYNAVNVAINKASTNKGVVIVMNDEIHAAREATKLNTTAVNAFASPNTGKIGTVYYGKVEYFTQSVRPHTLASEFDISKIEELPRVDILYAHPDDTDVLVNAALQAGAKGIIHAGMGNGNPFPLTQNALEKAAKSGVVVARSSRVGSGSTTQEAEVDDKKLGFVATESLNPQKARVLLMLALTKTSDREAIQKIFSTY
6JAE , Knot 214 518 0.86 40 254 490 
GIDPFTMKYVGSIDQGTTSTRFIIFDERQRPVSVHQVPHTQHTPHPGWLEHDPMEIFRSACKCMSVAIAKLRQKDASFRKIEAIGITNQRETTVAWDRVTKEPLCYAPVWNDLRTYDITKKVTAELGGGDSMFASKITGLPVSTYFAAFKMRWMLENVPAVADACRRGTLCFGTIDTWLMYKLSGGKAFVTDVTNASRTFLMDLRTRKWSPELCEKLKIPMETLPEIRSNSELFGYVETDECGVAAALNERTPIMGSIGDQQSALFGNMCFEKGEAKNTYGTGCFLLMNVGEEARFSKHGLLSTVGFQVGRDGPCYYALEGAIACAGATVEWMRRNMNLFSHITECEKLARSVPGTQGIVFVPAFSGLLAPYWDPSARGTIVGMTLKTTRAHVIRAALQAIALQLNDVVGSMKRDAGLNLSSLRVDGGLSKNGLLMEIQASLLGVDILVPSMHETTALGAALCAGLAAGVWTSLEEVKAVSRRENSWKTVSPSGSAMEREAMIAEWREALKRTKWAKL

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 \(c\).

\(|P_{f(1RCL_1)}(2) \setminus P_{f(6RUD_1)}(2)|=22\), \(|P_{f(6RUD_1)}(2) \setminus P_{f(1RCL_1)}(2)|=125\). 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 1:0010001000001001011101100000000011000010000000110111011000111001110011011100111000000111100011010011100100
Pair \(Z_2\) Length of longest common subsequence
1RCL_1,6RUD_1 147 3
1RCL_1,6JAE_1 229 3
6RUD_1,6JAE_1 146 5

Newick tree

 
[
	1RCL_1:10.78,
	[
		6RUD_1:73,6JAE_1:73
	]:29.78
]

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 \((0.85)(0.8)(\frac{434 }{\log_{20} 434}-\frac{106}{\log_{20}106})=99.2\)
Status Protein1 Protein2 d d1/2
Query variables 1RCL_1 6RUD_1 121 78
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]