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Parikh vectors
9FWS_1 7TZI_1 7KIE_1 Letter Amino acid
7 28 21 D Aspartic acid
13 1 6 C Cysteine
4 7 8 Q Glutamine
13 35 19 G Glycine
9 42 21 V Valine
13 50 19 A Alanine
3 35 26 E Glutamic acid
6 36 30 L Leucine
8 7 23 K Lycine
1 36 16 R Arginine
7 17 13 N Asparagine
3 13 5 H Histidine
7 15 17 P Proline
5 5 13 Y Tyrosine
4 38 13 I Isoleucine
3 13 16 M Methionine
5 13 10 F Phenylalanine
6 34 11 S Serine
13 22 16 T Threonine
1 4 5 W Tryptophan 

9FWS_1|Chain A|Non-structural protein 10|Severe acute respiratory syndrome coronavirus 2 (2697049)
>7TZI_1|Chains A, B|Mur ligase family protein|Methanothermobacter thermautotrophicus (145262)
>7KIE_1|Chains A, B|Fibroblast growth factor receptor 2|Homo sapiens (9606)
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 \(w=f(c)\)
9FWS , Knot 66 131 0.81 40 109 128 
AGNATEVPANSTVLSFCAFAVDAAKAYKDYLASGGQPITNCVKMLCTHTGTGQAITVTPEANMDQESFGGASCCLYCRCHIDHPNPKGFCDLKGKYVQIPTTCANDPVGFTLKNTVCTVCGMWKGYGCSCD
7TZI , Knot 179 451 0.80 40 210 421 
ASISGIFTTLGAAEAGDIVIRHWIDEKGIEIASERGVSAIITQDLRGKSSRLAEEHGLPVILVDRIENANALALSWTIERFAPSSRRVVVTGTNGKSTTTHMIHHIIETTGASSYTNTDSRSEFNTLIDPVVSQQIAEASSDGAPEFMVIEVSEVQGWLGRVMRDHARMMTAAIGPEVVVITNVAMDHIGLVESVEDVFREVAGALRAIESGVAVLNADDERVRAMAHVNPGLSVVFYGSDSPVRYDGEGIHIGGDLIIPAEELPFRSEHFIQNTLAAAAACLELGFSPEDIRMGVKTYRPLKRRFSVLMTEPLVIDDFAHNPSGIRFTVRSAAANLRGRLWVVNAIRGSRGEDINVMNAAALADSLRGLNAELIVTSSSDVVDEQNRVLENERRAFLGVLDERGASYIHVEKLRDALRMVLDAAKPHDTILLLGAQGMDPAAGIIDEIRM
7KIE , Knot 133 308 0.82 40 194 290 
AGVSEYELPEDPKWEFPRDKLTLGKPLGEGCFGQVVMAEAVGIDKDKPKEAVTVAVKMLKDDATEKDLSDLVSEMEMMKMIGKHKNIINLLGACTQDGPLYVIFEYASKGNLREYLRARRPPGMEYSYDINRVPEEQMTFKDLVSCTYQLARGMEYLASQKCIHRDLAARNVLVTENNVMKIADFGLARDINNIDYYKKTTNGRLPVKWMAPEALFDRVYTHQSDVWSFGVLMWEIFTLGGSPYPGIPVEELFKLLKEGHRMDKPANCTNELYMMMRDCWHAVPSQRPTFKQLVEDLDRILTLTTNEE

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 \(c\).

\(|P_{f(9FWS_1)}(2) \setminus P_{f(7TZI_1)}(2)|=54\), \(|P_{f(7TZI_1)}(2) \setminus P_{f(9FWS_1)}(2)|=155\). 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 1:11010011100011010111101101000011011011000101100001010110101010100001111000100000100101011001010010110001001111010001001011101010000
Pair \(Z_2\) Length of longest common subsequence
9FWS_1,7TZI_1 209 4
9FWS_1,7KIE_1 191 4
7TZI_1,7KIE_1 168 4

Newick tree

 
[
	9FWS_1:10.92,
	[
		7KIE_1:84,7TZI_1:84
	]:20.92
]

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 \((0.85)(0.8)(\frac{582 }{\log_{20} 582}-\frac{131}{\log_{20}131})=131.\)
Status Protein1 Protein2 d d1/2
Query variables 9FWS_1 7TZI_1 165 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]