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Parikh vectors
6VOM_1 4PZI_1 3EZO_1 Letter Amino acid
3 3 10 H Histidine
0 0 2 W Tryptophan
54 3 58 A Alanine
31 7 12 R Arginine
19 3 18 D Aspartic acid
43 2 14 E Glutamic acid
37 3 36 V Valine
13 3 6 M Methionine
31 1 12 T Threonine
18 1 4 Y Tyrosine
1 9 5 C Cysteine
33 2 12 Q Glutamine
39 8 27 G Glycine
41 1 14 I Isoleucine
17 2 16 P Proline
30 2 14 S Serine
15 2 8 N Asparagine
50 3 26 L Leucine
20 11 15 K Lycine
12 1 9 F Phenylalanine 

6VOM_1|Chains A, B, C|ATP synthase subunit alpha, chloroplastic|Spinacia oleracea (3562)
>4PZI_1|Chain A|Histone-lysine N-methyltransferase 2B|Homo sapiens (9606)
>3EZO_1|Chain A|Malonyl CoA-acyl carrier protein transacylase|Burkholderia pseudomallei 1710b (320372)
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 \(w=f(c)\)
6VOM , Knot 197 507 0.80 38 217 473 
MATIRADEISKIIRERIEGYNREVKVVNTGTVLQVGDGIARIHGLDEVMAGELVEFEEGTIGIALNLESNNVGVVLMGDGLMIQEGSSVKATGRIAQIPVSEAYLGRVINALAKPIDGRGEITASESRLIESPAPGIMSRRSVYEPLQTGLIAIDAMIPVGRGQRELIIGDRQTGKTAVATDTILNQQGQNVICVYVAIGQKASSVAQVVTNFQERGAMEYTIVVAETADSPATLQYLAPYTGAALAEYFMYRERHTLIIYDDLSKQAQAYRQMSLLLRRPPGREAYPGDVFYLHSRLLERAAKLSSLLGEGSMTALPIVETQAGDVSAYIPTNVISITDGQIFLSADLFNAGIRPAINVGISVSRVGSAAQIKAMKKVAGKLKLELAQFAELEAFAQFASDLDKATQNQLARGQRLRELLKQPQSAPLTVEEQVMTIYTGTNGYLDSLELDQVRKYLVELRTYVKTNKPEFQEIISSTKTFTEEAEALLKEAIQEQMERFLLQEQA
4PZI , Knot 37 67 0.77 38 56 65 
GSHHGKKMRMARCGHCRGCLRVQDCGSCVNCLDKPKFGGPNTKKQCCVYRKCDKIEARKMERLAKKG
3EZO , Knot 130 318 0.78 40 168 295 
MAHHHHHHMKFAFVFPGQGSQSVGMLNAFADVAVVRETLDEASDALGQDIGKLIADGPADELNLTTNTQPVMLTAAYACYRAWQQAGGAQPSIVAGHSLGEYTALVAAGAIAFRDALPLVRFRAQAMQTAVPVGVGGMAAILGLDDDTVRAVCAEASATGVVEAVNFNAPAQVVIAGTKAGIEKACEIAKEKGAKRALPLPVSAPFHSSLLKPASDKLREYLAGVDVKAPKISVVNNIDVAVVSDPAAIKDALVRQAAGPVRWVECVQHIAREGVTHVIECGPGKVLAGLTKRIDGNLVGASVFDPASLDEALKLAAA

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 \(c\).

\(|P_{f(6VOM_1)}(2) \setminus P_{f(4PZI_1)}(2)|=189\), \(|P_{f(4PZI_1)}(2) \setminus P_{f(6VOM_1)}(2)|=28\). 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 1:110101001001100010100001011001011011011101011001111011010010111110100001111111011110010010101011011100101101101110110101010100001100111111000010011001111101111110100011110000100111000110001001101011110010011011001000111000111100100110100111001111100110000001110001000101000101110011100101101101000110011010011101010111110001101010110011010010111010110111011101110100110110101100111010101101101011101100100100001101001001100100111010001101001001010010100100011010001000010100110000010001011100110001001110001
Pair \(Z_2\) Length of longest common subsequence
6VOM_1,4PZI_1 217 3
6VOM_1,3EZO_1 147 4
4PZI_1,3EZO_1 168 2

Newick tree

 
[
	4PZI_1:10.68,
	[
		6VOM_1:73.5,3EZO_1:73.5
	]:30.18
]

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 \((0.85)(0.8)(\frac{574 }{\log_{20} 574}-\frac{67}{\log_{20}67})=151.\)
Status Protein1 Protein2 d d1/2
Query variables 6VOM_1 4PZI_1 186 105.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]