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Parikh vectors
6STM_1 1WIS_1 6XPN_1 Letter Amino acid
8 5 10 N Asparagine
5 7 15 E Glutamic acid
40 15 23 G Glycine
0 7 19 I Isoleucine
5 7 17 R Arginine
0 1 9 H Histidine
5 2 4 K Lycine
1 2 5 M Methionine
9 19 12 S Serine
5 7 14 T Threonine
1 2 2 W Tryptophan
12 2 66 A Alanine
34 1 3 C Cysteine
9 7 6 Q Glutamine
4 3 12 F Phenylalanine
7 14 12 P Proline
7 3 20 D Aspartic acid
8 9 23 L Leucine
9 2 10 Y Tyrosine
1 9 19 V Valine 

6STM_1|Chains A, B|Arundo donax Lectin (ADL)|Arundo donax (35708)
>1WIS_1|Chain A|KIAA1514 protein|Homo sapiens (9606)
>6XPN_1|Chains A, B|Periplasmic solute binding protein|Paracoccus denitrificans (strain Pd 1222) (318586)
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 \(w=f(c)\)
6STM , Knot 66 170 0.66 36 83 132 
AYECGKQGGGALCPNNKCCSRYGYCGFGPAYCGTGCQSGGCCPGKRCGDQANGETCPNNLCCSEDGYCGFGSEYCGAGCQGGPCRADKLCGTLAGGQLCPDNLCCSQWGFCGLGVEFCGDGCQSGACCSMRCGRQADGAKCTNNYCCGASGYCGLGGDYCGAGCQSGPCT
1WIS , Knot 58 124 0.75 40 89 117 
GSSGSSGTISSGVPPELPGPPTNLGISNIGPRSVTLQFRPGYDGKTSISRWLVEAQVGVVGEGEEWLLIHQLSNEPDARSMEVPDLNPFTCYSFRMRQVNIVGTSPPSQPSRKIQTLQSGPSSG
6XPN , Knot 123 301 0.77 40 157 265 
MKDWLFRIATCSIMTFSSLAAAQAEPLDVVATFSIIGDFAAKVGGDRIRLNVLVGPDSDTHVYEPRPADAIALAGADVVLTNGLEFEGFLTRLIAASGTDAAVATLTDGVETMEEPGGGHYHYIDGKAVFHAGAHDPHAWQAVPNAKVYVQNIAAAFCAADAEGCAAYQANAARYIGELDALDTEIRAAIAALPQDRRTVVVAHNAFRYFEAAYGVHFLSPAAAADVAGLIREIRARNASAIFAENISDTRLLEQIAREAGLPLAGTLYSDALSGPDGPASNYIAMMRHNAGAIAAALAAR

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 \(c\).

\(|P_{f(6STM_1)}(2) \setminus P_{f(1WIS_1)}(2)|=59\), \(|P_{f(1WIS_1)}(2) \setminus P_{f(6STM_1)}(2)|=65\). 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 1:10001001111101000000001001111100101000110011000100101000100100000100111000011100111001001010111101010010000111011110101010001100010010010110000000011010011110001110001100
Pair \(Z_2\) Length of longest common subsequence
6STM_1,1WIS_1 124 4
6STM_1,6XPN_1 158 3
1WIS_1,6XPN_1 158 3

Newick tree

 
[
	6XPN_1:83.90,
	[
		6STM_1:62,1WIS_1:62
	]:21.90
]

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 \((0.85)(0.8)(\frac{294 }{\log_{20} 294}-\frac{124}{\log_{20}124})=52.9\)
Status Protein1 Protein2 d d1/2
Query variables 6STM_1 1WIS_1 55 51.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]