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Parikh vectors
6ERG_1 1TXA_1 5OVB_1 Letter Amino acid
30 3 3 R Arginine
27 3 7 I Isoleucine
39 4 2 S Serine
23 9 8 T Threonine
2 2 3 W Tryptophan
26 3 5 A Alanine
22 2 9 Q Glutamine
19 2 7 Y Tyrosine
26 5 2 G Glycine
8 1 1 H Histidine
63 1 13 L Leucine
15 0 5 M Methionine
28 2 5 F Phenylalanine
28 6 12 P Proline
18 2 12 N Asparagine
37 7 6 D Aspartic acid
4 10 2 C Cysteine
49 0 8 E Glutamic acid
49 8 12 K Lycine
31 3 5 V Valine 

6ERG_1|Chains A, D|X-ray repair cross-complementing protein 6|Homo sapiens (9606)
>1TXA_1|Chain A|TOXIN B|Ophiophagus hannah (8665)
>5OVB_1|Chains A, B|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 \(w=f(c)\)
6ERG , Knot 213 544 0.82 40 242 506 
MSGWESYYKTEGDEEAEEEQEENLEASGDYKYSGRDSLIFLVDASKAMFESQSEDELTPFDMSIQCIQSVYISKIISSDRDLLAVVFYGTEKDKNSVNFKNIYVLQELDNPGAKRILELDQFKGQQGQKRFQDMMGHGSDYSLSEVLWVCANLFSDVQFKMSHKRIMLFTNEDNPHGNDSAKASRARTKAGDLRDTGIFLDLMHLKKPGGFDISLFYRDIISIAEDEDLRVHFEESSKLEDLLRKVRAKETRKRALSRLKLKLNKDIVISVGIYNLVQKALKPPPIKLYRETNEPVKTKTRTFNTSTGGLLLPSDTKRSQIYGSRQIILEKEETEELKRFDDPGLMLMGFKPLVLLKKHHYLRPSLFVYPEESLVIGSSTLFSALLIKCLEKEVAALCRYTPRRNIPPYFVALVPQEEELDDQKIQVTPPGFQLVFLPFADDKRKMPFTEKIMATPEQVGKMKAIVEKLRFTYRSDSFENPVLQQHFRNLEALALDLMEPEQAVDLTLPKVEAMNKRLGSLVDEFKELVYPPDYNPEGKVTKRK
1TXA , Knot 40 73 0.78 36 60 70 
TKCYVTPDATSQTCPDGQDICYTKTWCDGFCSSRGKRIDLGCAATCPKVKPGVDIKCCSTDNCNPFPTWKRKH
5OVB , Knot 66 127 0.84 40 110 123 
SMNPPPPETSNPNKPKRQTNQLQYLLRVVLKTLWKHQFAWPFQQPVDAVKLNLPDYYKIIKTPMDMGTIKKRLENNYYWNAQECIQDFNTMFTNCYIYNKPGDDIVLMAEALEKLFLQKINELPTEE

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 \(c\).

\(|P_{f(6ERG_1)}(2) \setminus P_{f(1TXA_1)}(2)|=204\), \(|P_{f(1TXA_1)}(2) \setminus P_{f(6ERG_1)}(2)|=22\). 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 1:1011000000010001000000010101000001000111110100111000000010110101001001010011000001111110100000001010010110010011100110100101001000100111010000100111101011001010100001111000001010001010010001101000111101101001111010110001101100001010100000100110010100000011001010100011101110011001101111010000001100000010000111111000000010100011100000001001001111111101111100000101011101000111100011011110010001111000010001110111111000010000101011110111111100000111000111010011010111001010000001001110001001011110110100110101101011000110110010011011000101010000
Pair \(Z_2\) Length of longest common subsequence
6ERG_1,1TXA_1 226 3
6ERG_1,5OVB_1 186 3
1TXA_1,5OVB_1 126 3

Newick tree

 
[
	6ERG_1:11.82,
	[
		5OVB_1:63,1TXA_1:63
	]:50.82
]

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 \((0.85)(0.8)(\frac{617 }{\log_{20} 617}-\frac{73}{\log_{20}73})=160.\)
Status Protein1 Protein2 d d1/2
Query variables 6ERG_1 1TXA_1 202 114.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]