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Parikh vectors
6VLO_1 8YQQ_1 4AXT_1 Letter Amino acid
14 6 12 A Alanine
6 5 3 Q Glutamine
22 14 12 G Glycine
16 18 3 F Phenylalanine
18 11 7 T Threonine
25 16 6 V Valine
13 11 11 R Arginine
21 19 7 D Aspartic acid
6 22 8 C Cysteine
18 4 2 E Glutamic acid
14 5 1 H Histidine
7 17 2 P Proline
27 22 8 L Leucine
4 0 2 M Methionine
19 42 10 S Serine
29 32 14 N Asparagine
28 16 6 I Isoleucine
20 11 6 K Lycine
3 5 6 W Tryptophan
16 9 3 Y Tyrosine 

6VLO_1|Chains A, B, C, D|Putative dTDP-D-glucose 4,6-dehydratase|Acanthamoeba polyphaga mimivirus (212035)
>8YQQ_1|Chain A|Spike protein S1|Candidatus Accumulibacter adiacens (2954378)
>4AXT_1|Chain A|LYSOZYME C|GALLUS GALLUS (9031)
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 \(w=f(c)\)
6VLO , Knot 142 326 0.84 40 205 314 
GGHMKNILVTGGLGFIGSNFVNHISSKYDNVNIYVYDIGDYCASVENVEWNNRTKLIKGDIRNFDLIMHTLTEHEIDTIVHFAAHSHVDNSFKNSLAFTETNVFGTHVLLECSRMYGKLKLFFHMSTDEVYGEIDTTDTSREVSLLCPTNPYAATKAGAEHIVKSYFLSYKLPIIIARCNNVYGRNQYPEKLIPKFICSLLDGKKLHIQGTGNSRRNFIHAIDVADAVDLVINNGVIGETYNIGVTNEHSVLDVAQILCDIAGVNLENQLEYVPDRLFNDFRYNITNDKIKSLGWEQSRKDFKKELVELFDWYKVNRHRYNIPGSQ
8YQQ , Knot 120 285 0.79 38 159 269 
NLPDCDIDNWLNNVSVPSPLNWERRIFSNCNFNLSTLLRLVHVDSFSCNNLDKSKIFGSCFNSITVDKFAIPNRRRDDLQLGSSGFLQSSNYKIDISSSSCQLYYSLPLVNVTINNFNPSSWNRRYGFGSFNLSSYDVVYSDHCFSVNSDFCPCADPSVVNSCAKSKPPSAICPAGTKYRHCDLDTTLYVKNWCRCSCLPDPISTYSPNTCPQKKVVVGIGEHCPGLGINEEKCGTQLNHSSCFCSPDAFLGWSFDSCISNNRCNIFSNFIFNGINSGTTCSNDL
4AXT , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(6VLO_1)}(2) \setminus P_{f(8YQQ_1)}(2)|=103\), \(|P_{f(8YQQ_1)}(2) \setminus P_{f(6VLO_1)}(2)|=57\). 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 1:11010011101111111001100100000010101001100010100101000001101010010111001000010011011100010001000111000011100111000010101011101000010101000000001011010010110011100110001100011111100001010000100111011001101001010101000001101101101101110011110000111000001101101100111101000100110011001000100001001110000001000110110100100000011100
Pair \(Z_2\) Length of longest common subsequence
6VLO_1,8YQQ_1 160 3
6VLO_1,4AXT_1 181 3
8YQQ_1,4AXT_1 151 3

Newick tree

 
[
	6VLO_1:88.46,
	[
		8YQQ_1:75.5,4AXT_1:75.5
	]:12.96
]

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 \((0.85)(0.8)(\frac{611 }{\log_{20} 611}-\frac{285}{\log_{20}285})=91.3\)
Status Protein1 Protein2 d d1/2
Query variables 6VLO_1 8YQQ_1 120 109
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]