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Parikh vectors
2ADU_1 5THB_1 1DAT_1 Letter Amino acid
15 8 6 Y Tyrosine
16 26 6 N Asparagine
25 10 12 D Aspartic acid
27 14 15 E Glutamic acid
14 26 10 S Serine
23 17 15 A Alanine
15 9 2 C Cysteine
29 33 11 G Glycine
26 29 6 T Threonine
8 8 3 M Methionine
19 15 3 P Proline
4 5 1 W Tryptophan
18 18 11 R Arginine
10 10 6 H Histidine
25 24 27 L Leucine
25 14 9 K Lycine
10 11 11 Q Glutamine
26 21 4 I Isoleucine
11 8 8 F Phenylalanine
23 17 8 V Valine 

2ADU_1|Chain A|Methionine aminopeptidase 2|Homo sapiens (9606)
>5THB_1|Chains A, C, E|Hemagglutinin HA1 chain|Influenza A virus (11320)
>1DAT_1|Chain A|L FERRITIN|Equus caballus (9796)
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 \(w=f(c)\)
2ADU , Knot 159 369 0.85 40 223 352 
KVQTDPPSVPICDLYPNGVFPKGQECEYPPTQDGRTAAWRTTSEEKKALDQASEEIWNDFREAAEAHRQVRKYVMSWIKPGMTMIEICEKLEDCSRKLIKENGLNAGLAFPTGCSLNNCAAHYTPNAGDTTVLQYDDICKIDFGTHISGRIIDCAFTVTFNPKYDTLLKAVKDATNTGIKCAGIDVRLCDVGEAIQEVMESYEVEIDGKTYQVKPIRNLNGHSIGQYRIHAGKTVPIIKGGEATRMEEGEVYAIETFGSTGKGVVHDDMECSHYMKNFDVGHVPIRLPRTKHLLNVINENFGTLAFCRRWLDRLGESKYLMALKNLCDLGIVDPYPPLCDIKGSYTAQFEHTILLRPTCKEVVSRGDDY
5THB , Knot 141 323 0.84 40 199 308 
ADPGDKICLGHHAVANGTIVKTLTNEQEEVTNATETVESTGINRLCMKGRKHKDLGNCHPIGMLIGTPACDLHLTGMWDTLIERENAIAYCYPGATVNVEALRQKIMESGGINKISTGFTYGSSINSAGTTRACMRNGGNSFYAELKWLVSKSKGQNFPQTTNTYRNTDTAEHLIMWGIHHPSSTQEKNTLYGTQSLSISVGSSTYRNNFVPVVGARPQVNGLSSRIDFHWTLVQPGDNITFSHNGGLIAPSRVSKLIGRGLGIQSDAPIDNNCESKCFWRGGSINTRLPFQNLSPRTVGQCPKYVNRRSLMLATGMRNVPEL
1DAT , Knot 83 174 0.82 40 129 170 
SSQIRQNYSTEVEAAVNRLVNLYLRASYTYLSLGFYFDRDDVALEGVCHFFRELAEEKREGAERLLKMQNQRGGRALFQDLQKPSQDEWGTTPDAMKAAIVLEKSLNQALLDLHALGSAQADPHLCDFLESHFLDEEVKLIKKMGDHLTNIQRLVGSQAGLGEYLFERLTLKHD

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 \(c\).

\(|P_{f(2ADU_1)}(2) \setminus P_{f(5THB_1)}(2)|=97\), \(|P_{f(5THB_1)}(2) \setminus P_{f(2ADU_1)}(2)|=73\). 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 1:010001101110010101111010000011000100111000000001100100011001001101000100011011011101101000100000011000110111111010010001100010110001100001001011001010110011010101000011011001000110011101010011011001100001010100001011001010011000101100111101101001001010110011001011100010000010010110111011000011011000110111000110011000011110010011110101110010100010100011101000011001000
Pair \(Z_2\) Length of longest common subsequence
2ADU_1,5THB_1 170 3
2ADU_1,1DAT_1 188 4
5THB_1,1DAT_1 176 3

Newick tree

 
[
	1DAT_1:92.97,
	[
		2ADU_1:85,5THB_1:85
	]:7.97
]

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 \((0.85)(0.8)(\frac{692 }{\log_{20} 692}-\frac{323}{\log_{20}323})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 2ADU_1 5THB_1 129 121
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]