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Parikh vectors
4WZZ_1 4KMW_1 6JJP_1 Letter Amino acid
8 2 2 H Histidine
6 10 6 F Phenylalanine
12 2 13 P Proline
48 12 15 A Alanine
23 12 17 L Leucine
22 11 12 K Lycine
8 6 2 M Methionine
4 1 4 W Tryptophan
18 7 6 Q Glutamine
7 1 5 C Cysteine
33 8 23 G Glycine
31 7 17 T Threonine
14 4 11 Y Tyrosine
1 7 5 R Arginine
26 11 7 D Aspartic acid
14 6 6 E Glutamic acid
27 3 3 I Isoleucine
29 12 37 S Serine
18 8 22 V Valine
22 7 7 N Asparagine 

4WZZ_1|Chain A|Putative sugar ABC transporter, substrate-binding protein|Clostridium phytofermentans (357809)
>4KMW_1|Chains A, B|Dehaloperoxidase A|Amphitrite ornata (129555)
>6JJP_1|Chains A, D|Heavy chain of MW11-h317|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 \(w=f(c)\)
4WZZ , Knot 153 371 0.81 40 202 347 
MHHHHHHSSGVDLGTENLYFQSMGCSSKTDNTSSNKAKTPTTAATTGGDGYATTATYAIIVKSAGNPYNQKESEGYKQVIEANGGKCVIQEPKSATAEDQITCINNAISQGVDCIAIAANDTDALEPALTEAKNQGIHVLSLDSATNANSRKVFVNQAGTTQIAQALMDAILDISGGSGDWAVLSAASTATNQNAWIDGMKTVMQDSKYSKLNLIGVYYGDDEYQASCDQTEAILAADPNIKVICAPTTVGIMAAAKVLQDKGLSGKVKLTGLGLPSEMADYIGDDDQHSCPYMFLWNPIQLGNLAAYASISLVNGTITGAADQSFTVPDKTLGDNGSYKITAAADGGTEIILGAPFKFEPSNIAEWAKVY
4KMW , Knot 68 137 0.81 40 109 134 
GFKQDIATIRGDLRTYAQDIFLAFLNKYPDERRNFKNYVGKSDQELKSMAKFGDHTEKVFNLMMEVADRATDCVPLASDANTLVQMKQHSSLTTGNFEKLFVALVEYMRASGQSFDSQSWDRFGKNLVSALSSAGMK
6JJP , Knot 97 220 0.79 40 134 202 
EVQLVESGGGLVKPGGSLRLSCAASGFTFSSYDMSWVRQAPGKGLEWVATISGGGSYTYYPDSVKGRFTISRDNAKNSLYLQMNSLRAEDTAVYYCASPDSSGVAYWGQGTLVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSC

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 \(c\).

\(|P_{f(4WZZ_1)}(2) \setminus P_{f(4KMW_1)}(2)|=133\), \(|P_{f(4KMW_1)}(2) \setminus P_{f(4WZZ_1)}(2)|=40\). 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 1:10000000011011000101001100000000000010010011001101010010011110011010000000100011010110011001001010001001001100110011111000011011100100011011010010010000111001100011011101110101101011110110010000111011001100000001011110010000010000001111101010110110011111110110001101010101111100110011000000010111101101101110101011010101110001011000110010001011101100111111101010011011010
Pair \(Z_2\) Length of longest common subsequence
4WZZ_1,4KMW_1 173 3
4WZZ_1,6JJP_1 170 4
4KMW_1,6JJP_1 163 3

Newick tree

 
[
	4WZZ_1:87.12,
	[
		6JJP_1:81.5,4KMW_1:81.5
	]:5.62
]

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 \((0.85)(0.8)(\frac{508 }{\log_{20} 508}-\frac{137}{\log_{20}137})=109.\)
Status Protein1 Protein2 d d1/2
Query variables 4WZZ_1 4KMW_1 135 92.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]