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Parikh vectors
7EBF_1 2NAS_1 4KMS_1 Letter Amino acid
37 12 19 E Glutamic acid
19 4 8 F Phenylalanine
21 2 5 Y Tyrosine
20 5 8 R Arginine
16 2 21 N Asparagine
35 10 8 D Aspartic acid
26 6 18 V Valine
64 9 26 A Alanine
24 5 8 Q Glutamine
38 10 10 L Leucine
31 6 14 S Serine
33 4 13 T Threonine
12 4 2 W Tryptophan
3 3 4 C Cysteine
50 3 18 K Lycine
12 4 10 M Methionine
21 8 5 P Proline
36 8 19 G Glycine
22 0 9 H Histidine
36 5 24 I Isoleucine 

7EBF_1|Chains A, B, C, D|Isocitrate lyase|Candida albicans (5476)
>2NAS_1|Chain A|Uncharacterized protein|Trypanosoma brucei brucei TREU927 (185431)
>4KMS_1|Chains A, B|Acetoacetyl-CoA reductase|Rickettsia felis (315456)
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 \(w=f(c)\)
7EBF , Knot 223 556 0.84 40 260 524 
HHHHHHMPYTPIDIQKEEADFQKEVAEIKKWWSEPRWRKTKRIYSAEDIAKKRGTLKINHPSSQQADKLFKLLEKHDADKTVSFTFGALDPIHVAQMAKYLDSIYVSGWQCSSTASTSNEPSPDLADYPMDTVPNKVEHLWFAQLFHDRKQREERLTLSKEERAKTPYIDFLRPIIADADTGHGGITAIIKLTKMFIERGAAGIHIEDQAPGTKKCGHMAGKVLVPVQEHINRLVAIRASADIFGSNLLAVARTDSEAATLITSTIDHRDHYFIIGATNPEAGDLAALMAEAESKGIYGNELAAIESEWTKKAGLKLFHEAVIDEIKNGNYSNKDALIKKFTDKVNPLSHTSHKEAKKLAKELTGKDIYFNWDVARAREGYYRYQGGTQCAVMRGRAFAPYADLIWMESALPDYAQAKEFADGVKAAVPDQWLAYNLSPSFNWNKAMPADEQETYIKRLGKLGYVWQFITLAGLHTTALAVDDFSNQYSQIGMKAYGQTVQQPEIEKGVEVVKHQKWSGATYIDGLLKMVSGGVTSTAAMGQGVTEDQFKESKAKA
2NAS , Knot 58 110 0.82 38 88 107 
MIPSFAPGTLVWLKQDRFPWWPGFVMDPDEVRDITLPEGSDVWVCCLPRDSLTLSAANSEDEGQIRYFLPDRDEGMMEEGKLDASCAVAIEEAIQLYEEQLKAQAGGTNE
4KMS , Knot 113 249 0.83 40 167 239 
MAHHHHHHMSEIAIVTGGTRGIGKATALELKNKGLTVVANFFSNYDAAKEMEEKYGIKTKCWNVADFEECRQAVKEIEEEFKKPVSILVNNAGITKDKMLHRMSHQDWNDVINVNLNSCFNMSSSVMEQMRNQDYGRIVNISSINAQAGQVGQTNYSAAKAGIIGFTKALARETASKNITVNCIAPGYIATEMVGAVPEDVLAKIINSIPKKRLGQPEEIARAVAFLVDENAGFITGETISINGGHNMI

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 \(c\).

\(|P_{f(7EBF_1)}(2) \setminus P_{f(2NAS_1)}(2)|=194\), \(|P_{f(2NAS_1)}(2) \setminus P_{f(7EBF_1)}(2)|=22\). 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 1:0000001100110100001010001101001100101000001001001100010101001000010011011000010001010111101101101100100101011000001000001010110011001100100111101100000000010100000100101011011110100101110111010011100111110100011100001011101111100010011110101011100111110000011011000100000011111001011011111101000110100111100010001110110011100100100000011100100010110000000100110010100101010110100100000110001110101111010111100111001010011011011110011100101010100111100000010011011011011011110001111001000000111010100100101001101100001011001011101101110001111011000010000101
Pair \(Z_2\) Length of longest common subsequence
7EBF_1,2NAS_1 216 4
7EBF_1,4KMS_1 181 7
2NAS_1,4KMS_1 175 4

Newick tree

 
[
	7EBF_1:10.36,
	[
		4KMS_1:87.5,2NAS_1:87.5
	]:15.86
]

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 \((0.85)(0.8)(\frac{666 }{\log_{20} 666}-\frac{110}{\log_{20}110})=161.\)
Status Protein1 Protein2 d d1/2
Query variables 7EBF_1 2NAS_1 206 121.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]