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Parikh vectors
6JVL_1 5SHD_1 7JZT_1 Letter Amino acid
8 14 7 R Arginine
3 13 13 H Histidine
5 21 24 I Isoleucine
5 12 7 M Methionine
11 15 9 F Phenylalanine
2 12 2 C Cysteine
11 17 11 Q Glutamine
12 24 6 E Glutamic acid
12 15 21 D Aspartic acid
16 16 18 G Glycine
16 36 31 L Leucine
9 18 19 K Lycine
8 22 25 T Threonine
4 7 2 W Tryptophan
4 21 20 A Alanine
1 14 10 N Asparagine
7 14 32 P Proline
5 24 18 S Serine
4 12 4 Y Tyrosine
13 16 18 V Valine 

6JVL_1|Chains A, B|7,8-dihydro-8-oxoguanine triphosphatase|Homo sapiens (9606)
>5SHD_1|Chains A, B, C, D|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>7JZT_1|Chains A, B, C, D|Matrix protein VP40|Zaire ebolavirus (strain Mayinga-76) (128952)
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 \(w=f(c)\)
6JVL , Knot 74 156 0.79 40 119 151 
MGASRLYTLVLVLQPQRVLLGMKKRGFGAGRWNGFGGKVQEGETIEDGARRELQEESGLTVDALHKVGQIVFEFVGEPELMDVHVFCTDSIQGTPVESDEMRPCWFQLDQIPFKDMWPDDSYWFPLLLQKKKFHGYFKFQGQDTILDYTLREVDTV
5SHD , Knot 152 343 0.86 40 221 334 
GSSICTSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
7JZT , Knot 128 297 0.81 40 176 276 
MAHHHHHHVDDDDKGDTPSNPLRPIADDTIDHASHTPGSVSSAFILEAMVNVISGPKVLMKQIPIWLPLGVADQKTYSFDSTTAAIMLASYTITHFGKATNPLVRVNRLGPGIPDHPLRLLRIGNQAFLQEFVLPPVQLPQYFTFDLTALKLITQPLPAATWTDDTPTGSNGALRPGISFHPKLRPILLPNKSGKKGNSADLTSPEKIQAIMTSLQDFKIVPIDPTKNIMGIEVPETLVHKLTGKKVTSKNGQPIIPVLLPKYIGLDPVAPGDLTMVITQDCDTCHSPASLPAVIEK

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 \(c\).

\(|P_{f(6JVL_1)}(2) \setminus P_{f(5SHD_1)}(2)|=55\), \(|P_{f(5SHD_1)}(2) \setminus P_{f(6JVL_1)}(2)|=157\). 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 1:111001001111101001111100011111010111101001001001100010000110101100110111011101011010110000101011000010101101001110011100001111110000101010101000110001001001
Pair \(Z_2\) Length of longest common subsequence
6JVL_1,5SHD_1 212 3
6JVL_1,7JZT_1 169 3
5SHD_1,7JZT_1 175 4

Newick tree

 
[
	5SHD_1:10.06,
	[
		6JVL_1:84.5,7JZT_1:84.5
	]:16.56
]

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 \((0.85)(0.8)(\frac{499 }{\log_{20} 499}-\frac{156}{\log_{20}156})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 6JVL_1 5SHD_1 136 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]