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Parikh vectors
7RKP_1 7QJI_1 8PSH_1 Letter Amino acid
4 4 2 C Cysteine
9 47 0 L Leucine
15 21 0 S Serine
7 6 0 Y Tyrosine
9 58 0 V Valine
3 9 0 Q Glutamine
12 2 0 H Histidine
8 19 0 M Methionine
2 9 0 W Tryptophan
9 9 0 D Aspartic acid
21 19 0 E Glutamic acid
11 28 0 F Phenylalanine
14 35 0 I Isoleucine
14 19 0 K Lycine
5 14 0 P Proline
13 26 1 T Threonine
10 62 1 A Alanine
15 11 0 R Arginine
6 9 0 N Asparagine
10 31 4 G Glycine 

7RKP_1|Chain A|Polymerase acidic protein|Influenza A virus (strain swl A/California/04/2009 H1N1) (641501)
>7QJI_1|Chains A, D[auth E]|Divalent metal cation transporter|Vicugna pacos (30538)
>8PSH_1|Chain A|DNA (5'-D(*DGP*(SC)P*(GS)P*(PST)P*(SC)P*(AS)P*(GS)P*(GS))-3')|
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 \(w=f(c)\)
7RKP , Knot 93 197 0.83 40 147 190 
MGSSHHHHHHSSGLVPRGSHMEDFVRQCFNPMIVELAEKAMKEYGEDPKIETNKFAATCTHLEVCFMYSDGGSKHRFEIIEGRDRIMAWTVVNSICNTTGVEKPKFLPDLYDYKENRFIEIGVTRREVHIYYLEKANKIKSEKTHIHIFSFTGEEMATKADYTLDEESRARIKTRLFTIRQEMASRSLWDSFRQSER
7QJI , Knot 176 438 0.81 40 201 390 
MMMKKNEKLELRDVAVDAAESTELVEVPEKKQPKKIWLLLAALGPGIVTAMAGNDAGGISTYSTVGAKFGFATLWVIPIMCVLLIVVQMTAARMGAVTGKGFAALIRERFGIRLTALAMLALLIGNVATTFSEFAGIASGMEMFGVSKYLSVPVAAVAVWLLVVGGSYKRVEKVFLILSLVFVTYIVAAFMAQPNWEEALTSTVVPHIVNDQSFVSLVIAMIGTTIAPWMMFFNQSNVVEKGVTVKDLFSQKVDVVAGTIAACLVAWFIIVTTGAVLFPQGIEIESAADAARALAPFAGHYAEALFAIGLIAASFLAACVLPLTTAFVICEAFGWEAGVSFKWKEAPLFKSIFTFVIAFSAVVVLIPNIDLMGVMLTAQFVNGLILPVLLVFMAIIAADKRVMGAYRSRIVSRVLIWLTVGIVTVLTAALLVMQVLGI
8PSH , Knot 5 8 0.43 8 7 6 
GCGTCAGG

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 \(c\).

\(|P_{f(7RKP_1)}(2) \setminus P_{f(7QJI_1)}(2)|=65\), \(|P_{f(7QJI_1)}(2) \setminus P_{f(7RKP_1)}(2)|=119\). 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 1:11000000000011110100100110001011110110011000100101000011100001010110001100001011010001111011001000011001011101000000011011100001010010010010000001011010100110010001000001010001101000110001100100000
Pair \(Z_2\) Length of longest common subsequence
7RKP_1,7QJI_1 184 3
7RKP_1,8PSH_1 150 2
7QJI_1,8PSH_1 202 3

Newick tree

 
[
	7QJI_1:10.80,
	[
		7RKP_1:75,8PSH_1:75
	]:27.80
]

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 \((0.85)(0.8)(\frac{635 }{\log_{20} 635}-\frac{197}{\log_{20}197})=124.\)
Status Protein1 Protein2 d d1/2
Query variables 7RKP_1 7QJI_1 153 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]