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Parikh vectors
8VVO_1 5UKA_1 6KOQ_1 Letter Amino acid
9 6 9 Q Glutamine
11 14 15 K Lycine
30 9 28 S Serine
21 13 34 V Valine
18 14 24 T Threonine
8 5 10 N Asparagine
7 14 25 D Aspartic acid
22 13 30 G Glycine
4 12 22 I Isoleucine
6 11 8 F Phenylalanine
4 3 1 W Tryptophan
16 19 23 A Alanine
5 14 32 E Glutamic acid
17 11 36 L Leucine
3 2 4 M Methionine
12 8 20 P Proline
6 6 19 R Arginine
5 2 1 C Cysteine
5 5 18 H Histidine
15 5 9 Y Tyrosine 

8VVO_1|Chains A, C[auth B]|S1CE2 VARIANT OF FAB-EPR-1 heavy chain|Homo sapiens (9606)
>5UKA_1|Chains A, B, C, D, E|Alkyl hydroperoxide reductase subunit C|Salmonella typhimurium (strain LT2 / SGSC1412 / ATCC 700720) (99287)
>6KOQ_1|Chains A, B|DNA-directed RNA polymerase subunit alpha|Mycobacterium tuberculosis H37Rv (83332)
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 \(w=f(c)\)
8VVO , Knot 99 224 0.79 40 145 216 
EVQLVESGGGLVQPGGSLRLSCAASGFNLRSYYMHWVRQAPGKGLEWVASISPYYSYTYYADSVKGRFTISADTSKNTAYLQMNSLRAEDTAVYYCARHGYGAMDYWGQGTLVTVFNQIQGPSVFPLAPSSKSTSGGTAALGCLVKDYFPGPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCDKTHT
5UKA , Knot 88 186 0.82 40 137 177 
SLINTKIKPFKNQAFKNGEFIEVTEKDTEGRWSVFFFYPADFTFVCPTQLGDVADHYEELQKLGVDVYSVSTDTHFTHKAWHSSSETIAKIKYAMIGDPTGALTRNFDNMREDEGLADRATFVVDPQGIIQAIEVTAEGIGRDASDLLRKIKAAQYVAAHPGEVCPAKWKEGEATLAPSLDLVGKI
6KOQ , Knot 151 368 0.80 40 194 353 
MGHHHHHHHHHHSSGHIEGRHMLISQRPTLSEDVLTDNRSQFVIEPLEPGFGYTLGNSLRRTLLSSIPGAAVTSIRIDGVLHEFTTVPGVKEDVTEIILNLKSLVVSSEEDEPVTMYLRKQGPGEVTAGDIVPPAGVTVHNPGMHIATLNDKGKLEVELVVERGRGYVPAVQNRASGAEIGRIPVDSIYSPVLKVTYKVDATRVEQRTDFDKLILDVETKNSISPRDALASAGKTLVELFGLARELNVEAEGIEIGPSPAEADHIASFALPIDDLDLTVRSYNCLKREGVHTVGELVARTESDLLDIRNFGQKSIDEVKIKLHQLGLSLKDSPPSFDPSEVAGYDVATGTWSTEGAYDEQDYAETEQL

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 \(c\).

\(|P_{f(8VVO_1)}(2) \setminus P_{f(5UKA_1)}(2)|=89\), \(|P_{f(5UKA_1)}(2) \setminus P_{f(8VVO_1)}(2)|=81\). 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 1:01011001111101110101001101101000010110011101101110101000000010010101010100000010101001010001100010010111001101011011001011011111100000011011110110001111101010011100110011111000110010011011000110000100100010000100010100000000
Pair \(Z_2\) Length of longest common subsequence
8VVO_1,5UKA_1 170 4
8VVO_1,6KOQ_1 167 4
5UKA_1,6KOQ_1 157 4

Newick tree

 
[
	8VVO_1:86.08,
	[
		6KOQ_1:78.5,5UKA_1:78.5
	]:7.58
]

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 \((0.85)(0.8)(\frac{410 }{\log_{20} 410}-\frac{186}{\log_{20}186})=66.3\)
Status Protein1 Protein2 d d1/2
Query variables 8VVO_1 5UKA_1 85 77
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]