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Parikh vectors
6THG_1 1DQR_1 3LPR_1 Letter Amino acid
34 33 8 I Isoleucine
28 54 10 L Leucine
26 11 4 Y Tyrosine
4 38 25 A Alanine
32 28 13 N Asparagine
12 27 9 Q Glutamine
21 29 6 F Phenylalanine
44 33 20 S Serine
25 27 2 D Aspartic acid
14 23 1 H Histidine
27 39 2 K Lycine
31 37 18 T Threonine
4 12 2 W Tryptophan
22 32 19 V Valine
15 20 12 R Arginine
16 5 6 C Cysteine
24 41 32 G Glycine
18 31 4 E Glutamic acid
8 14 1 M Methionine
21 23 4 P Proline 

6THG_1|Chains A, C[auth B], D[auth E], E[auth G], F[auth I]|Attachment glycoprotein|Cedar virus (1221391)
>1DQR_1|Chains A, B|PHOSPHOGLUCOSE ISOMERASE|Oryctolagus cuniculus (9986)
>3LPR_1|Chain A|ALPHA-LYTIC PROTEASE|Lysobacter enzymogenes (69)
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 \(w=f(c)\)
6THG , Knot 173 426 0.82 40 228 393 
ETGKIFCKSVSKDPDFRLKQIDYVIPVQQDRSICMNNPLLDISDGFFTYIHYEGINSCKKSDSFKVLLSHGEIVDRGDYRPSLYLLSSHYHPYSMQVINCVPVTCNQSSFVFCHISNNTKTLDNSDYSSDEYYITYFNGIDRPKTKKIPINNMTADNRYIHFTFSGGGGVCLGEEFIIPVTTVINTDVFTHDYCESFNCSVQTGKSLKEICSESLRSPTNSSRYNLNGIMIISQNNMTDFKIQLNGITYNKLSFGSPGRLSKTLGQVLYYQSSMSWDTYLKAGFVEKWKPFTPNWMNNTVISRPNQGNCPRYHKCPEICYGGTYNDIAPLDLGKDMYVSVILDSDQLAENPEITVFNSTTILYKERVSKDELNTRSTTTSCFLFLDEPWCISVLETNRFNGKSIRPEIYSYKIPKYCGTKHHHHHH
1DQR , Knot 226 557 0.85 40 273 529 
AALTRNPQFQKLQQWHREHGSELNLRHLFDTDKERFNHFSLTLNTNHGHILLDYSKNLVTEEVMHMLLDLAKSRGVEAARESMFNGEKINSTEDRAVLHVALRNRSNTPIVVDGKDVMPEVNKVLDKMKAFCQRVRSGDWKGYTGKTITDVINIGIGGSDLGPLMVTEALKPYSSGGPRVWFVSNIDGTHIAKTLACLNPESSLFIIASKTFTTQETITNAKTAKDWFLLSAKDPSTVAKHFVALSTNTAKVKEFGIDPQNMFEFWDWVGGRYSLWSAIGLSIALHVGFDNFEQLLSGAHWMDQHFRTTPLEKNAPVLLAMLGIWYINCFGCETQAVLPYDQYLHRFAAYFQQGDMESNGKYITKSGARVDHQTGPIVWGEPGTNGQHAFYQLIHQGTKMIPCDFLIPVQTQHPIRKGLHHKILLANFLAQTEALMKGKSTEEARKELQAAGKSPEDLMKLLPHKVFEGNRPTNSIVFTKLTPFILGALIAMYEHKIFVQGVVWDINSFDQWGVELGKQLAKKIEPELDGSSPVTSHDSSTNGLINFIKQQREAKIQ
3LPR , Knot 92 198 0.82 40 127 188 
ANIVGGIEYSINNASLCSVGFSVTRGATKGFVTAGHCGTVNATARIGGAVVGTFAARVFPGNDRAWVSLTSAQTLLPRVANGSSFVTVRGSTEAAVGAAVCRSGRTTGYQCGTITAKNVTANYAEGAVRGLTQGNACAGRGDSGGSWITSAGQAQGVMSGGNVQSNGNNCGIPASQRSSLFERLQPILSQYGLSLVTG

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 \(c\).

\(|P_{f(6THG_1)}(2) \setminus P_{f(1DQR_1)}(2)|=61\), \(|P_{f(1DQR_1)}(2) \setminus P_{f(6THG_1)}(2)|=106\). 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 1:001011000100010101001001111000001010011101001110010001100000000101110010110010001010110000010010110011100000011100100000010000000000010010110010000111001010000101010111110110011111001100011000000010001001001001000010010000000101111100001001010101100001011011010001101100000101000101111001011010110001100100100100000101001100001111011001010111000011001010110000110000100001000000000111100110101100001010010101000011000100000000
Pair \(Z_2\) Length of longest common subsequence
6THG_1,1DQR_1 167 4
6THG_1,3LPR_1 211 4
1DQR_1,3LPR_1 204 4

Newick tree

 
[
	3LPR_1:10.69,
	[
		6THG_1:83.5,1DQR_1:83.5
	]:26.19
]

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 \((0.85)(0.8)(\frac{983 }{\log_{20} 983}-\frac{426}{\log_{20}426})=147.\)
Status Protein1 Protein2 d d1/2
Query variables 6THG_1 1DQR_1 190 164
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]