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Parikh vectors
6HWV_1 5DVP_1 7VJY_1 Letter Amino acid
13 8 17 F Phenylalanine
21 20 16 S Serine
15 11 11 Y Tyrosine
15 8 14 Q Glutamine
13 8 7 H Histidine
19 32 24 T Threonine
22 41 27 V Valine
25 30 17 A Alanine
43 17 29 L Leucine
27 23 17 D Aspartic acid
4 1 12 C Cysteine
23 13 9 E Glutamic acid
16 39 26 G Glycine
22 15 11 I Isoleucine
10 7 10 M Methionine
19 16 11 R Arginine
14 21 21 N Asparagine
5 10 3 W Tryptophan
19 10 11 K Lycine
17 20 13 P Proline 

6HWV_1|Chain A|Mitogen-activated protein kinase 14|Homo sapiens (9606)
>5DVP_1|Chains A, B|L,D-transpeptidase 2|Mycobacterium tuberculosis (83332)
>7VJY_1|Chain A|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
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 \(w=f(c)\)
6HWV , Knot 159 362 0.86 40 224 348 
GSHSQERPTFYRQELNKTIWEVPERYQNLSPVGSGAYGSVCAAFDTKTGLRVAVKKLSRPFQSIIHAKRTYRELRLLKHMKHENVIGLLDVFTPARSLEEFNDVYLVTHLMGADLNNIVKCQKLTDDHVQFLIYQILRGLKYIHSADIIHRDLKPSNLAVNEDCELKILDFGLARHTDDEMTGYVATRWYRAPEIMLNWMHYNQTVDIWSVGCIMAELLTGRTLFPGTDHIDQLKLILRLVGTPGAELLKKISSESARNYIQSLTQMPKMNFANVFIGANPLAVDLLEKMLVLDSDKRITAAQALAHAYFAQYHDPDDEPVADPYDQSFESRDLLIDEWKSLTYDEVISFVPPPLDQEEMES
5DVP , Knot 149 350 0.83 40 203 335 
LVPKLTASVTDGAVGVTVDAPVSVTAADGVLAAVTMVNDNGRPVAGRLSPDGLRWSTTEQLGYNRRYTLNATALGLGGAATRQLTFQTSSPAHLTMPYVMPGDGEVVGVGEPVAIRFDENIADRGAAEKAIKITTNPPVEGAFYWLNNREVRWRPEHFWKPGTAVDVAVNTYGVDLGEGMFGEDNVQTHFTIGDEVIATADDNTKILTVRVNGEVVKSMPTSMGKDSTPTANGIYIVGSRYKHIIMDSSTYGVPVNSPNGYRTDVDWATQISYSGVFVHSAPWSVGAQGHTNTSHGCLNVSPSNAQWFYDHVKRGDIVEVVNTVGGTLPGIDGLGDWNIPWDQWRAGNAK
7VJY , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ

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 \(c\).

\(|P_{f(6HWV_1)}(2) \setminus P_{f(5DVP_1)}(2)|=91\), \(|P_{f(5DVP_1)}(2) \setminus P_{f(6HWV_1)}(2)|=70\). 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 1:10000001010000100011011000001011101101010111000011011100100110011010000001011001000011111011011001001001011001111010011000010000101110011011001001011000101001110000010110111100000010101100100110111011000001011011011101101001111000100101110111011101100100001000100100110101101111101111011001111000001011011101011000010001110100001000011100100100001101111110000100
Pair \(Z_2\) Length of longest common subsequence
6HWV_1,5DVP_1 161 4
6HWV_1,7VJY_1 184 4
5DVP_1,7VJY_1 181 3

Newick tree

 
[
	7VJY_1:94.56,
	[
		6HWV_1:80.5,5DVP_1:80.5
	]:14.06
]

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 \((0.85)(0.8)(\frac{712 }{\log_{20} 712}-\frac{350}{\log_{20}350})=99.1\)
Status Protein1 Protein2 d d1/2
Query variables 6HWV_1 5DVP_1 125 123
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]