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Parikh vectors
7JUZ_1 6UIX_1 4XHA_1 Letter Amino acid
19 14 20 I Isoleucine
10 3 20 M Methionine
21 23 38 S Serine
12 11 46 T Threonine
4 8 10 C Cysteine
15 11 27 Q Glutamine
18 8 18 H Histidine
14 21 29 F Phenylalanine
11 11 28 Y Tyrosine
20 25 54 V Valine
18 36 58 A Alanine
17 8 44 D Aspartic acid
23 21 48 E Glutamic acid
14 17 35 P Proline
9 6 12 W Tryptophan
31 42 65 L Leucine
22 8 44 K Lycine
20 23 42 R Arginine
11 18 18 N Asparagine
25 17 49 G Glycine 

7JUZ_1|Chain A|Kinase suppressor of Ras 1|Homo sapiens (9606)
>6UIX_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V|Calcium homeostasis modulator protein 2|Homo sapiens (9606)
>4XHA_1|Chains A, B|RNA-dependent RNA polymerase|Thosea asigna virus (83810)
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 \(w=f(c)\)
7JUZ , Knot 144 334 0.83 40 210 321 
MSYYHHHHHHDYDIPTTENLYFQGAPISRKASQTSVYLQEWDIPFEQVELGEPIGQGRWGRVHRGRWHGEVAIRLLEMDGHNQDHLKLFKKEVMNYRQTRHENVVLFMGACMNPPHLAIITSFCKGRTLHSFVRDPKTSLDINKTRQIAQEIIKGMGYLHAKGIVHKDLKSKNVFYDNGKVVITDFGLFGISGVVREGRRENQLKLSHDWLCYLAPEIVREMTPGKDEDQLPFSKAADVYAFGTVWYELQARDWPLKNQAAEASIWQIGSGEGMKRVLTSVSLGKEVSEILSACWAFDLQERPSFSLLMDMLEKLPKLNRRLSHPGHFWKSAEI
6UIX , Knot 145 331 0.84 40 193 312 
MAALIAENFRFLSLFFKSKDVMIFNGLVALGTVGSQELFSVVAFHCPCSPARNYLYGLAAIGVPALVLFIIGIILNNHTWNLVAECQHRRTKNCSAAPTFLLLSSILGRAAVAPVTWSVISLLRGEAYVCALSEFVDPSSLTAREEHFPSAHATEILARFPCKENPDNLSDFREEVSRRLRYESQLFGWLLIGVVAILVFLTKCLKHYCSPLSYRQEAYWAQYRANEDQLFQRTAEVHSRVLAANNVRRFFGFVALNKDDEELIANFPVEGTQPRPQWNAITGVYLYRENQGLPLYSRLHKWAQGLAGNGAAPDNVEMALLPSFESRLVPR
4XHA , Knot 269 705 0.83 40 291 647 
MSYYHHHHHHDYDIPTTENLYFQGAMGAMGIMEASNPVIAPTRLSLEAMLAERAMVARQDLAGLKRKLAGADRVLAPQSPEQCGRESAQAQARSVTSELKSAVKEAQGLEHQTLDFLEQLGEYPVCGILHGDHPVHPSGTHNNNGKVSVKRQFAAGVNTSDALTCAFRFEDSDLVRETALKTTYTDGTWAGFVQRLKMQTTRKCVQEKVSRKLLKQLFPYDPQKLVDVSGELSELVLGIKTNAIASAGPPYWRTKRDALPDMLDCVLPLLYDHIVRKDLTTLRNKHPELFLAECKNKTDRYEVESLGEKTRPYFSHPFHLSALVSVLSQSFSGALKIMTEDSTSFNAYGFSWTNGGAEDLAIWARQAGEAGKKPPRIACYGDDTDIYYRKDGKLYRICPDFKQMDGSVDATTIEAVVDYVVDAHVKQYPTARQFWEEVGKLWVEMATQSPFLIDGTKVYRKMQKDGLMTGVVGTTLFDTVKSALAYNDWADQLMFGSLNLLEEKYAIEFFKNKHGLVIKEGTWKPALVNEDPGFGELWTEQKFLGLQLKVVRRENEKVYVPNLPFEDWLTMWVTPRSKYRSKETETMRERTLFDRARGLLVTGAVFDERARGLMGAVINSTAPEVVCMRVQEGGGRGAPPAYAFLTRDGVFEFPISDGYPSYDWVVSLYSRDHPCDMPRVFPEAATLIASYRKQVMDTRVVIKEE

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 \(c\).

\(|P_{f(7JUZ_1)}(2) \setminus P_{f(6UIX_1)}(2)|=99\), \(|P_{f(6UIX_1)}(2) \setminus P_{f(7JUZ_1)}(2)|=82\). 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 1:1000000000000110000101011110001000010100101110010110111010110100101010111011010100000101100011000000000111111101011011110010010010011001000101000001100110111010101110001000011000101110011111101110010000010100011001110110010110000011100110101110110010100111000110101101101011001100101100100110101110100010101110110011010001001101100101
Pair \(Z_2\) Length of longest common subsequence
7JUZ_1,6UIX_1 181 4
7JUZ_1,4XHA_1 171 25
6UIX_1,4XHA_1 176 4

Newick tree

 
[
	6UIX_1:90.47,
	[
		7JUZ_1:85.5,4XHA_1:85.5
	]:4.97
]

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 \((0.85)(0.8)(\frac{665 }{\log_{20} 665}-\frac{331}{\log_{20}331})=92.2\)
Status Protein1 Protein2 d d1/2
Query variables 7JUZ_1 6UIX_1 119 118
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]