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Parikh vectors
5XZF_1 1OSP_1 6LIP_1 Letter Amino acid
3 5 1 C Cysteine
10 2 8 M Methionine
8 8 9 F Phenylalanine
17 11 12 P Proline
8 9 4 Y Tyrosine
1 5 4 W Tryptophan
21 13 17 D Aspartic acid
14 10 12 Q Glutamine
14 10 6 E Glutamic acid
12 12 24 G Glycine
11 2 9 H Histidine
17 10 13 I Isoleucine
34 13 17 L Leucine
28 34 12 S Serine
11 21 16 T Threonine
12 10 36 A Alanine
12 8 9 R Arginine
7 9 10 N Asparagine
16 12 8 K Lycine
15 10 15 V Valine 

5XZF_1|Chain A|Vitamin D3 receptor|Rattus norvegicus (10116)
>1OSP_1|Chain A[auth L]|FAB 184.1|Mus musculus (10090)
>6LIP_1|Chain A|Metallo-beta-lactamase type 2|Klebsiella pneumoniae (573)
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 \(w=f(c)\)
5XZF , Knot 119 271 0.82 40 172 256 
GSHMGSPNSPLKDSLRPKLSEEQQHIIAILLDAHHKTYDPTYADFRDFRPPVRMDGSTGSVTLDLSPLSMLPHLADLVSYSIQKVIGFAKMIPGFRDLTSDDQIVLLKSSAIEVIMLRSNQSFTMDDMSWDCGSQDYKYDVTDVSKAGHTLELIEPLIKFQVGLKKLNLHEEEHVLLMAICIVSPDRPGVQDAKLVEAIQDRLSNTLQTYIRCRHPPPGSHQLYAKMIQKLADLRSLNEEHSKQYRSLSFQPENSMKLTPLVLEVFGNEIS
1OSP , Knot 97 214 0.81 40 151 209 
DIQMSQSSSSFSVSLGDRVTITCKASEDIYSRLAWYQQKPGNAPRLLISGATSLETWVPSRFSGSDSGKDYTLSITSLQTEDVATYFCQQYWSPPPTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC
6LIP , Knot 111 242 0.84 40 165 234 
GEIRPTIGQQMETGDQRFGDLVFRQLAPNVWQHTSYLDMPGFGAVASNGLIVRDGGRVLVVDTAWTDDQTAQILNWIKQEINLPVALAVVTHAHQDKMGGMDALHAAGIATYANALSNQLAPQEGMVAAQHSLTFAANGWVEPATAPNFGPLKVFYPGPGHTSDNITVGIDGTDIAFGGCLIKDSKAKSLGNLGDADTEHYAASARAFGAAFPKASMIVMSHSAPDSRAAITHTARMADKLR

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 \(c\).

\(|P_{f(5XZF_1)}(2) \setminus P_{f(1OSP_1)}(2)|=101\), \(|P_{f(1OSP_1)}(2) \setminus P_{f(5XZF_1)}(2)|=80\). 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 1:1001101001100010101000000111111010000001001010010111010100101010101101110110110001001111101111100100000111100011011110000010100101001000000010010011001011011101011100101000001111110110100111001011011000100010001000011110001010110011010010000000000101010001010111101110010
Pair \(Z_2\) Length of longest common subsequence
5XZF_1,1OSP_1 181 3
5XZF_1,6LIP_1 155 3
1OSP_1,6LIP_1 168 3

Newick tree

 
[
	1OSP_1:90.34,
	[
		5XZF_1:77.5,6LIP_1:77.5
	]:12.84
]

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 \((0.85)(0.8)(\frac{485 }{\log_{20} 485}-\frac{214}{\log_{20}214})=78.5\)
Status Protein1 Protein2 d d1/2
Query variables 5XZF_1 1OSP_1 100 90
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]