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Parikh vectors
5LOH_1 1NCP_1 3DVR_1 Letter Amino acid
12 2 12 R Arginine
21 0 11 I Isoleucine
10 0 5 M Methionine
21 1 19 V Valine
23 1 33 A Alanine
22 1 5 E Glutamic acid
25 2 33 G Glycine
22 2 8 K Lycine
21 0 9 P Proline
18 0 37 S Serine
18 1 22 T Threonine
12 0 17 Y Tyrosine
14 2 17 N Asparagine
12 1 4 H Histidine
14 1 6 F Phenylalanine
4 0 2 W Tryptophan
23 0 13 D Aspartic acid
2 3 5 C Cysteine
12 0 7 Q Glutamine
35 0 14 L Leucine 

5LOH_1|Chains A, B|Serine/threonine-protein kinase greatwall,Serine/threonine-protein kinase greatwall|Homo sapiens (9606)
>1NCP_1|Chain A[auth N]|HIV-1 P7 NUCLEOCAPSID PROTEIN|Human immunodeficiency virus 1 (11676)
>3DVR_1|Chain A[auth X]|Proteinase K|Tritirachium album (37998)
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 \(w=f(c)\)
5LOH , Knot 147 341 0.83 40 215 327 
GPHMDPTAGSKKEPGGGAATEEGVNRIAVPKPPSIEEFSIVKPISRGAFGKVYLGQKGGKLYAVKVVKKADMINKNMTHQVQAERDALALSKSPFIVHLYYSLQSANNVYLVMEYLIGGDVKSLLHIYGYFDEEMAVKYISEVALALDYLHRHGIIHRDLKPDNMLISNEGHIKLTDFGLSKVTLNRDINMMDILTTRTFCGTPDYLAPELLLGRAHGPAVDWWALGVCLFEFLTGIPPFNDETPQQVFQNILKRDIPWPEGEEKLSDNAQSAVEILLTIDDTKRAGMKELKRHPLFSDVDWENLQHQTMPFIPQPDDETDTSYFEARNTAQHLTVSGFSL
1NCP , Knot 12 17 0.66 22 15 15 
VKCFNCGKEGHTARNCR
3DVR , Knot 119 279 0.80 40 169 265 
AAQTNAPWGLARISSTSPGTSTYYYDESAGQGSCVYVIDTGIEASHPEFEGRAQMVKTYYYSSRDGNGHGTHCAGTVGSRTYGVAKKTQLFGVKVLDDNGSGQYSTIIAGMDFVASDKNNRNCPKGVVASLSLGGGYSSSVNSAAARLQSSGVMVAVAAGNNNADARNYSPASEPSVCTVGASDRYDRRSSFSNYGSVLDIFGPGTSILSTWIGGSTRSISGTSMATPHVAGLAAYLMTLGKTTAASACRYIADTANKGDLSNIPFGTVNLLAYNNYQA

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 \(c\).

\(|P_{f(5LOH_1)}(2) \setminus P_{f(1NCP_1)}(2)|=205\), \(|P_{f(1NCP_1)}(2) \setminus P_{f(5LOH_1)}(2)|=5\). 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 1:11010101100001111110001100111101101001011011001111010110011010110110010110001000101000111100011110100010010010111001111010011010101000111001001111100100011100010100111000101010011100101000101101100001010100111011110101111011111101101101111100001001100110001111010001000100110111010000011100100011100101001000011111010000000010100010010101101
Pair \(Z_2\) Length of longest common subsequence
5LOH_1,1NCP_1 210 3
5LOH_1,3DVR_1 152 3
1NCP_1,3DVR_1 166 3

Newick tree

 
[
	1NCP_1:10.08,
	[
		5LOH_1:76,3DVR_1:76
	]:24.08
]

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 \((0.85)(0.8)(\frac{358 }{\log_{20} 358}-\frac{17}{\log_{20}17})=111.\)
Status Protein1 Protein2 d d1/2
Query variables 5LOH_1 1NCP_1 142 74
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]