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Parikh vectors
5SDY_1 3STN_1 6ZPP_1 Letter Amino acid
14 2 18 R Arginine
14 7 6 N Asparagine
15 4 13 D Aspartic acid
16 13 6 G Glycine
13 1 3 H Histidine
22 13 5 T Threonine
21 4 27 A Alanine
24 13 9 E Glutamic acid
21 12 9 I Isoleucine
12 4 3 M Methionine
14 1 9 P Proline
24 8 23 S Serine
12 1 2 C Cysteine
36 8 21 L Leucine
7 0 2 W Tryptophan
12 1 2 Y Tyrosine
17 7 9 Q Glutamine
18 15 4 K Lycine
15 8 7 F Phenylalanine
16 10 12 V Valine 

5SDY_1|Chain A|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>3STN_1|Chain A|Fatty acid-binding protein, liver|Homo sapiens (9606)
>6ZPP_1|Chain A|virulence factor|Drechmeria coniospora (98403)
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 \(w=f(c)\)
5SDY , Knot 152 343 0.86 40 221 334 
GSSICTSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
3STN , Knot 61 132 0.75 38 97 126 
MAGSSFSGKYQLQSQENFEAFMKAIGLPEELIQKGKDIKGVSEIVQNGKHFKFTITAGSKVIQNEFTVGEECELETMTGEKVKTVVQLEGDNKLVTTFKNIKSVTELNGDIITNTMTLGDIVFKRISKRIGT
6ZPP , Knot 85 190 0.78 40 121 180 
SRLSNAFVLATTASAAAVPSPALPADDILLAINQSLRLVDSRAAMLVSQVRHGAINNVGSLADSYHELIFSLRGAVRAVDDVWRPLPKDAPMRIVESLRPFQKIPASLRSALKERLDAIAERPGGCQAVDDNNRQLGLDFDRLYWEIASSSSFSAIHETVSSQQKQFETAMRELTDEFSSRCLRRAQASA

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 \(c\).

\(|P_{f(5SDY_1)}(2) \setminus P_{f(3STN_1)}(2)|=160\), \(|P_{f(3STN_1)}(2) \setminus P_{f(5SDY_1)}(2)|=36\). 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 1:1001000001011101011101000101101011110011111110110000100010100100111010000001100010011011001011100000110010001111101000100011000010010011111000001000010001011010100110010000000110110011110011101100001001000101010000000011111101001001001111001010010101110100100111011111000000011010111001111100001001111001110100001001001101000101100101100111000
Pair \(Z_2\) Length of longest common subsequence
5SDY_1,3STN_1 196 4
5SDY_1,6ZPP_1 192 3
3STN_1,6ZPP_1 158 4

Newick tree

 
[
	5SDY_1:10.30,
	[
		6ZPP_1:79,3STN_1:79
	]:23.30
]

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 \((0.85)(0.8)(\frac{475 }{\log_{20} 475}-\frac{132}{\log_{20}132})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 5SDY_1 3STN_1 133 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]