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Parikh vectors
6UNJ_1 4ZVP_1 5BPG_1 Letter Amino acid
18 5 5 M Methionine
3 0 5 W Tryptophan
25 20 9 D Aspartic acid
15 6 3 Q Glutamine
29 11 7 I Isoleucine
16 4 11 Y Tyrosine
37 11 17 V Valine
7 9 0 C Cysteine
26 13 22 G Glycine
12 3 6 H Histidine
32 11 5 F Phenylalanine
26 11 8 T Threonine
22 9 10 R Arginine
30 12 5 E Glutamic acid
38 20 11 K Lycine
34 5 4 P Proline
30 11 13 S Serine
18 13 15 A Alanine
18 11 11 N Asparagine
51 13 13 L Leucine 

6UNJ_1|Chains A, B|Cytochrome P450 3A4|Homo sapiens (9606)
>4ZVP_1|Chains A, C|Caspase-7|Homo sapiens (9606)
>5BPG_1|Chains A, B, C, D|Fragaceatoxin C|Actinia fragacea (396334)
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 \(w=f(c)\)
6UNJ , Knot 203 487 0.86 40 248 467 
MAYLYGTHSHGLFKKLGIPGPTPLPFLGNILSYHKGFCMFDMECHKKYGKVWGFYDGQQPVLAITDPDMIKTVLVKECYSVFTNRRPFGPVGFMKSAISIAEDEEWKRLRSLLSPTFTSGKLKEMVPIIAQYGDVLVRNLRREAETGKPVTLKDVFGAYSMDVITSTSFGVNIDSLNNPQDPFVENTKKLLRFDFLDPFFLSITVFPFLIPILEVLNICVFPREVTNFLRKSVKRMKESRLEDTQKHRVDFLQLMIDSQNSKETESHKALSDLELVAQSIIFIFAGYETTSSVLSFIMYELATHPDVQQKLQEEIDAVLPNKAPPTYDTVLQMEYLDMVVNETLRLFPIAMRLERVCKKDVEINGMFIPKGVVVMIPSYALHRDPKYWTEPEKFLPERFSKKNKDNIDPYIYTPFGSGPRNCIGMRFALMNMKLALIRVLQNFSFKPCKETQIPLKLSLGGLLQPEKPVVLKVESRDGTVSGAHHHH
4ZVP , Knot 93 198 0.82 38 140 193 
MADDQGCIEEQGVEDSANEDSVDAKPDRSSFVPSLFSKKKKNVTMRSIKTTRDRVPTYQYNMNFEKLGKCIIINNKNFDKVTGMGVRNGTDKDAEALFKCFRSLGFDVIVYNDCSCAKMQDLLKKASEEDHTNAACFACILLSHGEENVIYGKDGVTPIKDLTAHFRGDRCKTLLEKPKLFFIQACRGTELDDGIQAD
5BPG , Knot 82 180 0.78 38 128 175 
MSADVAGAVIDGAGLGFDVLKTVLEALGNVKRKIAVGIDNESGKTWTAMNTYFRSGTSDIVLPHKVAHGKALLYNGQKNRGPVATGVVGVIAYSMSDGNTLAVLFSVPYDYNWYSNWWNVRVYKGQKRADQRMYEELYYHRSPFRGDNGWHSRGLGYGLKSRGFMNSSGHAILEIHVTKA

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 \(c\).

\(|P_{f(6UNJ_1)}(2) \setminus P_{f(4ZVP_1)}(2)|=154\), \(|P_{f(4ZVP_1)}(2) \setminus P_{f(6UNJ_1)}(2)|=46\). 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 1:1101010000111001111110111111011000011011010000001011110010011111001011001110000011000011111111001101100001001001101010010100111111001011100100010010110100111100101100001110100100100111000001101011011110101111111110110101110010011000100100001000000010110111000000000000110010111001111111000000110111001100101000100010111100111000011010010111000101111110100100001010111110111111100110001001001001110010000000101010011101100011101111010111101100101010000011101011111010011110100001010110000
Pair \(Z_2\) Length of longest common subsequence
6UNJ_1,4ZVP_1 200 4
6UNJ_1,5BPG_1 182 4
4ZVP_1,5BPG_1 166 5

Newick tree

 
[
	6UNJ_1:99.45,
	[
		5BPG_1:83,4ZVP_1:83
	]:16.45
]

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 \((0.85)(0.8)(\frac{685 }{\log_{20} 685}-\frac{198}{\log_{20}198})=137.\)
Status Protein1 Protein2 d d1/2
Query variables 6UNJ_1 4ZVP_1 181 126.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]