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Parikh vectors
5UOG_1 8TDH_1 7HOC_1 Letter Amino acid
20 16 14 S Serine
14 19 5 N Asparagine
0 6 6 C Cysteine
9 11 6 H Histidine
15 21 5 I Isoleucine
41 32 12 L Leucine
7 15 2 M Methionine
12 16 3 F Phenylalanine
38 34 14 V Valine
37 37 10 A Alanine
25 23 9 R Arginine
23 23 6 T Threonine
6 12 5 Q Glutamine
5 31 2 K Lycine
15 35 9 D Aspartic acid
19 21 7 E Glutamic acid
30 39 14 G Glycine
21 30 4 P Proline
3 13 3 W Tryptophan
4 17 8 Y Tyrosine 

5UOG_1|Chains A, B, C, D|NADPH-dependent glyoxylate/hydroxypyruvate reductase|Rhizobium meliloti (strain 1021) (266834)
>8TDH_1|Chains A, B, C, D|Predicted dehydrogenases and related proteins|Alistipes (239759)
>7HOC_1|Chains A, B|Protease 2A|Coxsackievirus A16 (31704)
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 \(w=f(c)\)
5UOG , Knot 140 344 0.79 38 171 319 
MHHHHHHSSGVDLGTENLYFQSMSRPRILVPGKINPRVLERLPEMFETVRIERADAALVTADMRDVSGIAVSGKLPVPLMDAFPSLEIVANFGVGYDGVDVSRAAARGIVVTNTPDVLTEEVADTAIGLLLNTLRLLPQAEQWLRQGRWVREGAFPLSPLSLRGRTVGLFGLGRIGLAIARRLEAFGVSIAYHTRTPREGLGFTYHPTLVGMAEAVDTLIVIVPGTASTLKAVNADVLSALGPKGVLINVGRGSTVDEAALVTALQNGTIAGAGLDVFENEPNVPEALLSFPNVSLLPHVASASVVTRNAMSDLVVDNLKAWFSTGEALTPVAETPFRRRAIQN
8TDH , Knot 188 451 0.85 40 245 431 
DKLNILGVGIGGRGSSVLRGLESQNIIGLCDVDWKYADHVFKRYPAAKKYNDYRKMFDEMLKSADAVMVATADHTHAIIAADAMTAGKHVYVEKPLTHTVYESRLLTKLADKYKVATQMGNQGASDEGVRKVCEWIWNGEIGEVRKVETFTDRPIWPQGLSRPEDDQRIPKTLNWDAFIGPAPYRPYNAIYTPWNFRGWWDFGTGALGDMACHILHPVFKGLKLGYPTKVQGSSTLLLNESAPMAQTVKFVFPARDNMPKVAMPEVEVYWYDGGLKPARPEGLPAGKDLNMAGGGVIFYGTKDTLICGCYGVNPYLVSGRVPNAPKVLREIKESHQMDWVRACKEDADDRVPSASDFSEAGPFNEMVVMGVLAVRLQNLNRELLWDGPNMRFTNIPDDATISAVIKDGFHIKDGHPTFDKTWTDPVNAQQFAQELIKHTYRDGWKLPDMPR
7HOC , Knot 70 144 0.80 40 112 139 
SGAIYVGNYRVVNRHLATHNDWANLVWEDSSRDLLVSSTTAQGCDTIARCDCQTGVYYCSSRRKHYPVSFSKPSLIFVEASEYYPARYQSHLMLAVGHSEPGDCGGILRCQHGVVGIVSTGGNGLVGFADVRDLLWLDEEAMEQ

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 \(c\).

\(|P_{f(5UOG_1)}(2) \setminus P_{f(8TDH_1)}(2)|=50\), \(|P_{f(8TDH_1)}(2) \setminus P_{f(5UOG_1)}(2)|=124\). 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 1:10000000011011000101001001011111010101100110110010100101111010100101111010111111011101011101111001101001110111100010110001100111111001011101001100101100111110110101001111111011111100101111011000001001111000101111101100111111101001011010110111101111011010010011110110010111111011000101101110110101110110101100011001110010111001011011100110001100
Pair \(Z_2\) Length of longest common subsequence
5UOG_1,8TDH_1 174 4
5UOG_1,7HOC_1 169 3
8TDH_1,7HOC_1 205 3

Newick tree

 
[
	8TDH_1:98.33,
	[
		5UOG_1:84.5,7HOC_1:84.5
	]:13.83
]

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 \((0.85)(0.8)(\frac{795 }{\log_{20} 795}-\frac{344}{\log_{20}344})=122.\)
Status Protein1 Protein2 d d1/2
Query variables 5UOG_1 8TDH_1 161 138
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]