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Parikh vectors
9CNU_1 6UMM_1 2IYT_1 Letter Amino acid
5 2 0 C Cysteine
11 13 10 E Glutamic acid
18 31 18 L Leucine
20 16 9 P Proline
15 43 25 A Alanine
12 18 9 D Aspartic acid
8 3 3 M Methionine
12 27 11 T Threonine
11 28 21 R Arginine
20 7 3 Q Glutamine
14 9 7 I Isoleucine
5 8 0 W Tryptophan
7 3 3 Y Tyrosine
16 34 18 V Valine
13 3 3 N Asparagine
9 5 9 H Histidine
11 5 5 K Lycine
4 3 2 F Phenylalanine
8 9 9 S Serine
21 18 19 G Glycine 

9CNU_1|Chain A|Capsid protein p24|Human immunodeficiency virus 2 (11709)
>6UMM_1|Chains A, F|ESX-3 secretion system protein EccE3|Mycobacterium smegmatis (strain ATCC 700084 / mc(2)155) (246196)
>2IYT_1|Chain A|SHIKIMATE KINASE|MYCOBACTERIUM TUBERCULOSIS (83332)
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 \(w=f(c)\)
9CNU , Knot 110 240 0.83 40 175 233 
PVQQTGGGNYIHVPLSPRTLNAWVKLVEDKKFGAEVVPGFQALSEGCTPYDINQMLNCVGDHQAAMQIIREIINDEAADWDAQHPIPGPLPAGQLRDPRGSDIAGTTSTVEEQIQWMYRPQNPVPVGNIYRRWIQIGLQKCVRMYNPTNILDVKQGPKEPFQSYVDRFYKSLRAEQTDPAVKNWMTQTLLIQNANPDCKLVLKGLGMNPTLEEMLTACQGVGGPGQKARLMGSSHHHHHH
6UMM , Knot 117 285 0.77 40 153 263 
MTARIALASLFVVAAVLAQPWQTTTQRWVLGVSIAAVIVLLAWWKGMFLTTRIGRALAMVRRNRAEDTVETDAHRATVVLRVDPAAPAQLPVVVGYLDRYGITCDKVRITHRDAGGTRRSWISLTVDAVDNLAALQARSARIPLQDTTEVVGRRLADHLREQGWTVTVVEGVDTPLPVSGKETWRGVADDAGVVAAYRVKVDDRLDEVLAEIGHLPAEETWTALEFTGSPAEPLLTVCAAVRTSDRPAAKAPLAGLTPARGRHRPALAALNPLSTERLDGTAVPL
2IYT , Knot 80 184 0.75 36 113 169 
MAPKAVLVGLPGSGKSTIGRRLAKALGVGLLDTDVAIEQRTGRSIADIFATDGEQEFRRIEEDVVRAALADHDGVLSLGGGAVTSPGVRAALAGHTVVYLEISAAEGVRRTGGNTVRPLLAGPDRAEKYRALMAKRAPLYRRVATMRVDTNRRNPGAVVRHILSRLQVPSPSEAATLEHHHHHH

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 \(c\).

\(|P_{f(9CNU_1)}(2) \setminus P_{f(6UMM_1)}(2)|=89\), \(|P_{f(6UMM_1)}(2) \setminus P_{f(9CNU_1)}(2)|=67\). 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 1:110001110010111010010111011000011101111101100100100100110011000111011001100011010100111111111010010100111000010001011001001111101000110111000101001001101001100110001001000101000011100110001110010100011101111010100110100111111001011100000000
Pair \(Z_2\) Length of longest common subsequence
9CNU_1,6UMM_1 156 3
9CNU_1,2IYT_1 158 6
6UMM_1,2IYT_1 122 5

Newick tree

 
[
	9CNU_1:83.52,
	[
		6UMM_1:61,2IYT_1:61
	]:22.52
]

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 \((0.85)(0.8)(\frac{525 }{\log_{20} 525}-\frac{240}{\log_{20}240})=81.5\)
Status Protein1 Protein2 d d1/2
Query variables 9CNU_1 6UMM_1 99 94.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]