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Parikh vectors
6QMD_1 3DEF_1 3VNG_1 Letter Amino acid
16 10 15 N Asparagine
11 2 8 C Cysteine
9 12 6 Q Glutamine
9 6 8 M Methionine
15 8 14 P Proline
22 24 22 L Leucine
4 11 4 F Phenylalanine
17 15 18 T Threonine
18 20 20 A Alanine
16 14 16 D Aspartic acid
38 18 38 G Glycine
16 9 16 H Histidine
12 15 11 I Isoleucine
17 5 17 Y Tyrosine
28 26 28 V Valine
23 11 23 R Arginine
14 17 13 E Glutamic acid
3 19 2 K Lycine
27 17 24 S Serine
6 3 6 W Tryptophan 

6QMD_1|Chain A|Kelch-like ECH-associated protein 1|Mus musculus (10090)
>3DEF_1|Chain A|T7I23.11 protein|Arabidopsis thaliana (3702)
>3VNG_1|Chain A|Kelch-like ECH-associated protein 1|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 \(w=f(c)\)
6QMD , Knot 128 321 0.76 40 179 273 
MGSSHHHHHHSSGLVPRGPKVGRLIYTAGGYFRQSLSYLEAYNPSNGSWLRLADLQVPRSGLAGCVVGGLLYAVGGRNNSPDGNTDSSALDCYNPMTNQWSPCASMSVPRNRIGVGVIDGHIYAVGGSHGCIHHSSVERYEPERDEWHLVAPMLTRRIGVGVAVLNRLLYAVGGFDGTNRLNSAECYYPERNEWRMITPMNTIRSGAGVCVLHNCIYAAGGYDGQDQLNSVERYDVETETWTFVAPMRHHRSALGITVHQGKIYVLGGYDGHTFLDSVECYDPDSDTWSEVTRMTSGRSGVGVAVTMEPCRKQIDQQNCTC
3DEF , Knot 114 262 0.80 40 164 249 
MGSLVREWVGFQQFPAATQEKLIEFFGKLKQKDMNSMTVLVLGKGGVGKSSTVNSLIGEQVVRVSPFQAEGLRPVMVSRTMGGFTINIIDTPGLVEAGYVNHQALELIKGFLVNRTIDVLLYVDRLDVYAVDELDKQVVIAITQTFGKEIWCKTLLVLTHAQFSPPDELSYETFSSKRSDSLLKTIRAGSKMRKQEFEDSAIAVVYAENSGRCSKNDKDEKALPNGEAWIPNLVKAITDVATNQRKAIHVDAAALEHHHHHH
3VNG , Knot 122 309 0.75 40 162 259 
GSSHHHHHHSSGLVPRGSHMAPKVGRLIYTAGGYFRQSLSYLEAYNPSDGTWLRLADLQVPRSGLAGCVVGGLLYAVGGRNNSPDGNTDSSALDCYNPMTNQWSPCAPMSVPRNRIGVGVIDGHIYAVGGSHGCIHHNSVERYEPERDEWHLVAPMLTRRIGVGVAVLNRLLYAVGGFDGTNRLNSAECYYPERNEWRMITAMNTIRSGAGVCVLHNCIYAAGGYDGQDQLNSVERYDVETETWTFVAPMKHRRSALGITVHQGRIYVLGGYDGHTFLDSVECYDPDTDTWSEVTRMTSGRSGVGVAVT

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 \(c\).

\(|P_{f(6QMD_1)}(2) \setminus P_{f(3DEF_1)}(2)|=102\), \(|P_{f(3DEF_1)}(2) \setminus P_{f(6QMD_1)}(2)|=87\). 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 1:110000000000111101101101100111010001001010010010110110101100111101111110111100001010000011000011000101010101100011111101010111100101000010000100001011111100011111111001101111101000100100001000010110110010011110110001011110010001001000010000101111100000111101001010111100100110010000100001001001001001111110101000010000000
Pair \(Z_2\) Length of longest common subsequence
6QMD_1,3DEF_1 189 6
6QMD_1,3VNG_1 27 63
3DEF_1,3VNG_1 192 6

Newick tree

 
[
	3DEF_1:10.71,
	[
		6QMD_1:13.5,3VNG_1:13.5
	]:96.21
]

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 \((0.85)(0.8)(\frac{583 }{\log_{20} 583}-\frac{262}{\log_{20}262})=90.6\)
Status Protein1 Protein2 d d1/2
Query variables 6QMD_1 3DEF_1 104 100
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]