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Parikh vectors
4FTI_1 7VXK_1 3RHB_1 Letter Amino acid
7 64 7 Q Glutamine
17 72 3 I Isoleucine
17 78 3 A Alanine
18 63 3 D Aspartic acid
28 103 12 L Leucine
22 58 9 K Lycine
9 95 10 T Threonine
10 56 2 Y Tyrosine
21 95 12 V Valine
14 89 5 N Asparagine
6 30 4 C Cysteine
23 48 8 E Glutamic acid
16 85 11 G Glycine
9 98 6 S Serine
6 10 1 W Tryptophan
17 40 5 R Arginine
7 25 2 H Histidine
6 11 3 M Methionine
9 78 3 F Phenylalanine
17 60 4 P Proline 

4FTI_1|Chain A|Serine/threonine-protein kinase Chk1|Homo sapiens (9606)
>7VXK_1|Chains A, C[auth B], D|Spike glycoprotein|Severe acute respiratory syndrome coronavirus 2 (2697049)
>3RHB_1|Chain A|Glutaredoxin-C5, chloroplastic|Arabidopsis thaliana (3702)
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 \(w=f(c)\)
4FTI , Knot 124 279 0.83 40 175 268 
AVPFVEDWDLVQTLGEGAYGEVQLAVNRVTEEAVAVKIVDMKRAVDCPENIKKEICINKMLNHENVVKFYGHRREGNIQYLFLEYCSGGELFDRIEPDIGMPEPDAQRFFHQLMAGVVYLHGIGITHRDIKPENLLLDERDNLKISDFGLATVFRYNNRERLLNKMCGTLPYVAPELLKRREFHAEPVDVWSCGIVLTAMLAGELPWDQPSDSCQEYSDWKEKKTYLNPWKKIDSAPLALLHKILVENPSARITIPDIKKDRWYNKPLKKGAKRPRVTS
7VXK , Knot 446 1258 0.84 40 324 1088 
MFVFLVLLPLVSSQCVNFTTRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFANPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLGVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVRGLPQGFSALEPLVDLPIGINITRFQTLHISYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGNIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVKGFNCYFPLQSYGFQPTYGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQGVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSPGSASSVASQSIIAYTMSLGVENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSFIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGAALQIPFAMQMAYRFNGIGVTQNVLYENQKLIANQFNSAIGKIQDSLSSTASALGKLQDVVNQNAQALNTLVKQLSSNFGAISSVLNDILSRLDPPEAEVQIDRLITGRLQSLQTYVTQQLIRAAEIRASANLAATKMSECVLGQSKRVDFCGKGYHLMSFPQSAPHGVVFLHVTYVPAQEKNFTTAPAICHDGKAHFPREGVFVSNGTHWFVTQRNFYEPQIITTDNTFVSGNCDVVIGIVNNTVYDPLQPELDSFKEELDKYFKNHTSPDVDLGDISGINASVVNIQKEIDRLNEVAKNLNESLIDLQELGKYEQGSGYIPEAPRDGQAYVRKDGEWVLLSTFLENLYFQGDYKDDDDKHHHHHHHHH
3RHB , Knot 59 113 0.82 40 92 110 
MASFGSRMEESIRKTVTENTVVIYSKTWCSYCTEVKTLFKRLGVQPLVVELDQLGPQGPQLQKVLERLTGQHTVPNVFVCGKHIGGCTDTVKLNRKGDLELMLAEANGKNGQS

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 \(c\).

\(|P_{f(4FTI_1)}(2) \setminus P_{f(7VXK_1)}(2)|=27\), \(|P_{f(7VXK_1)}(2) \setminus P_{f(4FTI_1)}(2)|=176\). 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 1:111110010110011011010101110010001111011010011001001000101001100001101010000101001110000110110010101111010100110011111101011110000101001110000010100111101100000001100101011011101100001010110110011110111110111001000000000100000010110010011111100111001010101101000010001100110010100
Pair \(Z_2\) Length of longest common subsequence
4FTI_1,7VXK_1 203 4
4FTI_1,3RHB_1 169 3
7VXK_1,3RHB_1 242 4

Newick tree

 
[
	7VXK_1:11.36,
	[
		4FTI_1:84.5,3RHB_1:84.5
	]:34.86
]

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 \((0.85)(0.8)(\frac{1537 }{\log_{20} 1537}-\frac{279}{\log_{20}279})=325.\)
Status Protein1 Protein2 d d1/2
Query variables 4FTI_1 7VXK_1 416 254
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]