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Parikh vectors
1JCV_1 6UHH_1 3UPM_1 Letter Amino acid
1 7 5 Y Tyrosine
13 12 38 A Alanine
22 9 26 G Glycine
1 4 5 M Methionine
6 4 16 F Phenylalanine
6 25 32 L Leucine
10 20 7 K Lycine
8 15 14 P Proline
11 10 24 S Serine
4 11 26 R Arginine
2 3 2 C Cysteine
3 7 11 Q Glutamine
6 6 5 H Histidine
0 4 4 W Tryptophan
8 15 7 N Asparagine
10 15 16 E Glutamic acid
17 11 22 V Valine
9 13 19 D Aspartic acid
6 11 24 I Isoleucine
10 9 24 T Threonine 

1JCV_1|Chain A|CU/ZN SUPEROXIDE DISMUTASE|Saccharomyces cerevisiae (4932)
>6UHH_1|Chains A, B, C, D|Ryanodine receptor 3|Homo sapiens (9606)
>3UPM_1|Chains A, B|Parathion hydrolase|Brevundimonas diminuta (293)
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 \(w=f(c)\)
1JCV , Knot 72 153 0.79 38 107 146 
VQAVAVLKGDAGVSGVVKFEQASESEPTTVSYEIAGNSPNAERGFHIHEFGDATNGCVSAGPHFNPFKKTHGAPTDEVRHVGDMGNVKTDENGVAKGSFKDSLIKLIGPTSVVGRSVVIHAGQDDLGKGDTEESLKTGNAGPRPACGVIGLTN
6UHH , Knot 100 211 0.84 40 146 198 
SNASFIPCPVDTSQVILPPHLEKIRDRLAENIHELWGMNKIELGWTFGKIRDDNKRQHPCLVEFSKLPETEKNYNLQMSTETLKTLLALGCHIAHVNPAAEEDLKKVKLPKNYMMSNGYKPAPLDLSDVKLLPPQEILVDKLAENAHNVWAKDRIKQGWTYGIQQDLKNKRNPRLVPYALLDERTKKSNRDSLREAVRTFVGYGYNIEPSD
3UPM , Knot 140 327 0.82 40 186 302 
DRINTVRGPITISEAGFTLTHEHICGSSAGFLRAWPEFFGSRKALAEKAVRGLRRARAAGVRTIVDVSTFDIGRDVSLLAEVSRAADVHIVAATGLWFDPPLSMRLRSVEELTQFFLREIQYGIEDTGIRAGIIKVATTGKATPFQELVLRAAARASLATGVPVTTHTAASQRDGEQQAAIFESEGLSPSRVCIGHSDDTDDLSYLTALAARGYLIGLDQIPFSAIGLEDNASASALLGNRSWQTRALLIKALIDQGYMKQILVSNDWLFGFSSYVTNIMDVMDRVNPDGMAFIPLRVIPFLREKGVPQETLAGITVTNPARFLSPT

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 \(c\).

\(|P_{f(1JCV_1)}(2) \setminus P_{f(6UHH_1)}(2)|=60\), \(|P_{f(6UHH_1)}(2) \setminus P_{f(1JCV_1)}(2)|=99\). 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 1:101111101011101110100100001001000111001010011010011010010101110101100001110001001101101000001110101000110111100111001110110001101000001001011101101111100
Pair \(Z_2\) Length of longest common subsequence
1JCV_1,6UHH_1 159 3
1JCV_1,3UPM_1 177 3
6UHH_1,3UPM_1 174 3

Newick tree

 
[
	3UPM_1:90.33,
	[
		1JCV_1:79.5,6UHH_1:79.5
	]:10.83
]

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 \((0.85)(0.8)(\frac{364 }{\log_{20} 364}-\frac{153}{\log_{20}153})=63.7\)
Status Protein1 Protein2 d d1/2
Query variables 1JCV_1 6UHH_1 81 69
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]