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Parikh vectors
6DZO_1 7QSC_1 5QKI_1 Letter Amino acid
16 14 12 E Glutamic acid
18 10 5 I Isoleucine
5 3 6 M Methionine
17 24 7 P Proline
8 12 17 K Lycine
12 13 11 F Phenylalanine
16 10 8 S Serine
40 16 17 A Alanine
15 8 3 R Arginine
10 20 14 Q Glutamine
20 9 13 G Glycine
7 16 9 T Threonine
0 1 2 W Tryptophan
11 13 7 N Asparagine
13 10 12 D Aspartic acid
5 7 3 H Histidine
28 34 12 L Leucine
3 0 2 C Cysteine
7 6 8 Y Tyrosine
17 18 21 V Valine 

6DZO_1|Chain A|Tryptophan synthase alpha chain|Salmonella typhimurium (strain LT2 / SGSC1412 / ATCC 700720) (99287)
>7QSC_1|Chains A, C|Rho GTPase-activating protein 1|Homo sapiens (9606)
>5QKI_1|Chains A, B|Thiol:disulfide interchange protein|Escherichia coli K-12 (83333)
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 \(w=f(c)\)
6DZO , Knot 116 268 0.80 38 165 253 
MERYENLFAQLNDRREGAFVPFVTLGDPGIEQSLKIIDTLIDAGADALELGVPFSDPLADGPTIQNANLRAFAAGVTPAQCFEMLALIREKHPTIPIGLLMYANLVFNNGIDAFYARCEQVGVDSVLVADVPVEESAPFRQAALRHNIAPIFICPPNADDDLLRQVASYGRGYTYLLSRSGVTGAENRGALPLHHLIEKLKEYHAAPALQGFGISSPEQVSAAVRAGAAGAISGSAIVKIIEKNLASPKQMLAELRSFVSAMKAASRA
7QSC , Knot 113 244 0.84 38 162 236 
GSHVKLEQLGIPRQVLKYDDFLKSTQKSPATAPKPMPPRPPLPNQQFGVSLQHLQEKNPEQEPIPIVLRETVAYLQAHALTTEGIFARSANTQVVREVQQKYNMGLPVDFDQYNELHLPAVILKTFLRELPEPLLTFDLYPHVVGFLNIDESQRVPATLQVLQTLPEENYQVLRFLTAFLVQISAHSDQNKMTNTNLAVVFGPNLLWAKDAAITLKAINPINTFTKFLLDHQGELFPSPDPSGL
5QKI , Knot 86 189 0.79 40 134 185 
AQYEDGKQYTTLEKPVAGAPQVLEFFSFFCPHCYQFEEVLHISDNVKKKLPEGVKMTKYHVNFMGGDLGKDLTQAWAVAMALGVEDKVTVPLFEGVQKTQTIRSASDIRDVFINAGIKGEEYDAAWNSFVVKSLVAQQEKAAADVQLRGVPAMFVNGKYQLNPQGMDTSNMDVFVQQYADTVKYLSEKK

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 \(c\).

\(|P_{f(6DZO_1)}(2) \setminus P_{f(7QSC_1)}(2)|=82\), \(|P_{f(7QSC_1)}(2) \setminus P_{f(6DZO_1)}(2)|=79\). 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 1:1000001110100000111111101101110001011001101110110111110011101101001010111111011001011111000010111111101011100110110100001110011110111000111001110001111110110100011001100101000110001101100011111001100100001111101111001001011101111111010111011000110100111010011011011001
Pair \(Z_2\) Length of longest common subsequence
6DZO_1,7QSC_1 161 3
6DZO_1,5QKI_1 157 3
7QSC_1,5QKI_1 152 3

Newick tree

 
[
	6DZO_1:80.64,
	[
		5QKI_1:76,7QSC_1:76
	]:4.64
]

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 \((0.85)(0.8)(\frac{512 }{\log_{20} 512}-\frac{244}{\log_{20}244})=76.7\)
Status Protein1 Protein2 d d1/2
Query variables 6DZO_1 7QSC_1 99 94
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]