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Parikh vectors
6MPW_1 9EOC_1 6JJB_1 Letter Amino acid
0 69 7 E Glutamic acid
10 64 13 L Leucine
1 62 1 S Serine
1 34 5 A Alanine
0 36 12 N Asparagine
1 33 2 G Glycine
1 44 3 R Arginine
1 34 6 D Aspartic acid
0 19 5 M Methionine
3 16 5 F Phenylalanine
0 15 7 Y Tyrosine
3 45 5 V Valine
0 25 9 Q Glutamine
3 39 7 I Isoleucine
1 48 12 K Lycine
0 34 12 P Proline
0 37 8 T Threonine
1 7 3 W Tryptophan
0 17 2 C Cysteine
0 28 1 H Histidine 

6MPW_1|Chains A, B, C, D, E|mini-eVgL membrane protein|synthetic construct (32630)
>9EOC_1|Chain A|Integrator complex subunit 13|Homo sapiens (9606)
>6JJB_1|Chain A|Bromodomain-containing protein 4|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 \(w=f(c)\)
6MPW , Knot 15 27 0.61 24 17 21 
DSLKWIVFLLFLIVLLLLAIVFLLRGX
9EOC , Knot 276 706 0.85 40 290 653 
MKIFSESHKTVFVVDHCPYMAESCRQHVEFDMLVKNRTQGIIPLAPISKSLWTCSVESSMEYCRIMYDIFPFKKLVNFIVSDSGAHVLNSWTQEDQNLQELMAALAAVGPPNPRADPECCSILHGLVAAVETLCKITEYQHEARTLLMENAERVGNRGRIICITNAKSDSHVRMLEDCVQETIHEHNKLAANSDHLMQIQKCELVLIHTYPVGEDSLVSDRSKKELSPVLTSEVHSVRAGRHLATKLNILVQQHFDLASTTITNIPMKEEQHANTSANYDVELLHHKDAHVDFLKSGDSHLGGGSREGSFKETITLKWCTPRTNNIELHYCTGAYRISPVDVNSRPSSCLTNFLLNGRSVLLEQPRKSGSKVISHMLSSHGGEIFLHVLSSSRSILEDPPSISEGCGGRVTDYRITDFGEFMRENRLTPFLDPRYKIDGSLEVPLERAKDQLEKHTRYWPMIISQTTIFNMQAVVPLASVIVKESLTEEDVLNCQKTIYNLVDMERKNDPLPISTVGTRGKGPKRDEQYRIMWNELETLVRAHINNSEKHQRVLECLMACRSKPPEEEERKKRGRKREDKEDKSEKAVKDYEQEKSWQDSERLKGILERGKEELAEAEIIKDSPDSPEPPNKKPLVEMDETPQVEKSKGPVSLLSLWSNRINTANSRKHQEFAGRLNSVNNRAELYQHLKEENGMETTENGKASRQ
6JJB , Knot 65 125 0.83 40 108 121 
MNPPPPETSNPNKPKRQTNQLQYLLRVVLKTLWKHQFAWPFQQPVDAVKLNLPDYYKIIKTPMDMGTIKKRLENNYYWNAQECIQDFNTMFTNCYIYNKPGDDIVLMAEALEKLFLQKINELPTE

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 \(c\).

\(|P_{f(6MPW_1)}(2) \setminus P_{f(9EOC_1)}(2)|=5\), \(|P_{f(9EOC_1)}(2) \setminus P_{f(6MPW_1)}(2)|=278\). 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 1:001011111111111111111111010
Pair \(Z_2\) Length of longest common subsequence
6MPW_1,9EOC_1 283 3
6MPW_1,6JJB_1 111 3
9EOC_1,6JJB_1 222 3

Newick tree

 
[
	9EOC_1:14.30,
	[
		6MPW_1:55.5,6JJB_1:55.5
	]:87.80
]

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 \((0.85)(0.8)(\frac{733 }{\log_{20} 733}-\frac{27}{\log_{20}27})=209.\)
Status Protein1 Protein2 d d1/2
Query variables 6MPW_1 9EOC_1 267 137.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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