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Parikh vectors
4GXZ_1 1PQH_1 5DDE_1 Letter Amino acid
15 5 24 K Lycine
4 3 19 Y Tyrosine
20 18 45 A Alanine
10 8 24 D Aspartic acid
2 2 7 C Cysteine
12 12 18 I Isoleucine
15 4 22 P Proline
7 7 35 S Serine
6 10 27 R Arginine
5 10 12 H Histidine
5 4 19 F Phenylalanine
2 2 8 W Tryptophan
7 6 13 N Asparagine
12 8 33 E Glutamic acid
9 11 34 G Glycine
19 6 60 L Leucine
3 5 9 M Methionine
14 8 19 T Threonine
12 11 39 V Valine
13 3 22 Q Glutamine 

4GXZ_1|Chains A, B, C, D|Suppression of copper sensitivity protein|Salmonella typhimurium (99287)
>1PQH_1|Chains A, B|Aspartate 1-decarboxylase|Escherichia coli (562)
>5DDE_1|Chain A|Menin|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 \(w=f(c)\)
4GXZ , Knot 92 192 0.84 40 139 189 
SNAQETAPFTPDQEKQIENLIHAALFNDPASPRIGAKHPKLTLVNFTDYNCPYCKQLDPMLEKIVQKYPDVAVIIKPLPFKGESSVLAARIALTTWREHPQQFLALHEKLMQKRVYHTDDSIKQAQQKAGATPVTLDEKSMETIRTNLQLARLVGVQGTPATIIGDELIPGAVPWDTLEAVVKEKLASANGG
1PQH , Knot 68 143 0.78 40 106 135 
MRGSHHHHHHGLVPRGSMIRTMLQGKLHRVKVTHADLHYEGTCAIDQDFLDAAGILENEAIDIWNVTNGKRFSTYAIAAERGSRIISVNGAAAHCASVGDIVIIASFVTMPDEEARTWRPNVAYFEGDNEMKRTAKAIPVQVA
5DDE , Knot 198 489 0.83 40 247 466 
GGSSSMGLKAAQKTLFPLRSIDDVVRLFAAELGREEPDLVLLSLVLGFVEHFLAVNRVGLTYFPVADLSIIAALYARFTAQIRGAVDLSLYPREGGVSSRELVKKVSDVIWNSLSRSYFKDRAHIQSLFSFITGTKLDSSGVAFAVVGACQALGLRDVHLALSEDHAWVVFGPNGEQTAEVTWHGKGNEDRRGQTVNAGVAERSWLYLKGSYMRCDRKMEVAFMVCAINPSIDLHTDSLELLQLQQKLLWLLYDLGHLERYPMALGNLADLEELEPTPGRPDPLTLYHKGIASAKTYYRDEHIYPYMYLAGYHCRNRNVREALQAWADTATVIQDYNYCREDEEIYKEFFEVANDVIPNLLKEAASLLEAGSQGSALQDPECFAHLLRFYDGICKWEEGSPTPVLHVGWATFLVQSLGRFEGQVRQKVRIVSVPAPAASPPPEGPVLTFQSEKMKGMKELLVATKINSSAIKLQLTAQSQVQMKKQKVS

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 \(c\).

\(|P_{f(4GXZ_1)}(2) \setminus P_{f(1PQH_1)}(2)|=89\), \(|P_{f(1PQH_1)}(2) \setminus P_{f(4GXZ_1)}(2)|=56\). 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 1:001000111010000010011011110011010111001010110100000100001011100110001011111011110100011110111001000100111100011000100000010010001110110100001001000101101111010110111001111111100101110001101011
Pair \(Z_2\) Length of longest common subsequence
4GXZ_1,1PQH_1 145 3
4GXZ_1,5DDE_1 184 3
1PQH_1,5DDE_1 195 3

Newick tree

 
[
	5DDE_1:10.13,
	[
		4GXZ_1:72.5,1PQH_1:72.5
	]:28.63
]

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 \((0.85)(0.8)(\frac{335 }{\log_{20} 335}-\frac{143}{\log_{20}143})=58.6\)
Status Protein1 Protein2 d d1/2
Query variables 4GXZ_1 1PQH_1 74 62
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]