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Parikh vectors
8WRL_1 6LWD_1 3AGT_1 Letter Amino acid
32 9 13 D Aspartic acid
8 7 0 C Cysteine
47 21 13 E Glutamic acid
60 35 13 L Leucine
34 11 10 K Lycine
34 20 3 S Serine
27 7 8 Y Tyrosine
16 6 5 H Histidine
31 14 12 V Valine
37 21 13 A Alanine
18 29 13 R Arginine
39 7 4 N Asparagine
27 25 3 P Proline
20 4 3 W Tryptophan
30 18 2 Q Glutamine
32 27 5 G Glycine
22 9 4 I Isoleucine
21 4 3 M Methionine
27 17 4 F Phenylalanine
32 4 5 T Threonine 

8WRL_1|Chain A|Processed angiotensin-converting enzyme 2|Homo sapiens (9606)
>6LWD_1|Chains A, D, G|Endonuclease 8-like 1|Homo sapiens (9606)
>3AGT_1|Chains A, B|Hemerythrin-like domain protein DcrH|Desulfovibrio vulgaris (881)
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 \(w=f(c)\)
8WRL , Knot 245 594 0.87 40 287 567 
STIEEQAKTFLDKFNHEAEDLFYQSSLASWNYNTNITEENVQNMNNAGDKWSAFLKEQSTLAQMYPLQEIQNLTVKLQLQALQQNGSSVLSEDKSKRLNTILNTMSTIYSTGKVCNPDNPQECLLLEPGLNEIMANSLDYNERLWAWESWRSEVGKQLRPLYEEYVVLKNEMARANHYEDYGDYWRGDYEVNGVDGYDYSRGQLIEDVEHTFEEIKPLYEHLHAYVRAKLMNAYPSYISPIGCLPAHLLGDMWGRFWTNLYSLTVPFGQKPNIDVTDAMVDQAWDAQRIFKEAEKFFVSVGLPNMTQGFWENSMLTDPGNVQKAVCHPTAWDLGKGDFRILMCTKVTMDDFLTAHHEMGHIQYDMAYAAQPFLLRNGANEGFHEAVGEIMSLSAATPKHLKSIGLLSPDFQEDNETEINFLLKQALTIVGTLPFTYMLEKWRWMVFKGEIPKDQWMKKWWEMKREIVGVVEPVPHDETYCDPASLFHVSNDYSFIRYYTRTLYQFQFQEALCQAAKHEGPLHKCDISNSTEAGQKLFNMLRLGKSEPWTLALENVVGAKNMNVRPLLNYFEPLFTWLKDQNKNSFVGWSTDWSP
6LWD , Knot 127 295 0.81 40 175 281 
MGQGPELHLASQFVNEACRALVFGGCVEKSSVSRNPEVPFESSAYRISASARGKELRLILSPLPGAQPQQEPLALVFRFGMSGSFQLVPREELPRHAHLRFYTAPPGPRLALCFVDIRRFGRWDLGGKWQPGRGPCVLQEYQQFRENVLRNLADKAFDRPICEALLDQRFFNGIGNYLRAEILYRLKIPPFEKARSVLEALQQHRPSPELTLSQKIRTKLQNPDLLELCHSVPKEVVQLGGRGYGSESGEEDFAAFRAWLRCYGMPGMSSLQDRHGRTIWFQGDPGPLAPKGRKS
3AGT , Knot 64 136 0.77 38 102 133 
GDADVLVKWSEDLANLPSIDTQHKRLVDYINDLYRAARRRDMDKAREVFDALKNYAVEHFGYEERLFADYAYPEATRHKEIHRRFVETVLKWEKQLAAGDPEVVMTTLRGLVDWLVNHIMKEDKKYEAYLRERGVS

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 \(c\).

\(|P_{f(8WRL_1)}(2) \setminus P_{f(6LWD_1)}(2)|=151\), \(|P_{f(6LWD_1)}(2) \setminus P_{f(8WRL_1)}(2)|=39\). 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 1:001000100110010001001100001101000001000010010011001011100000110101100100101010101100010011000000010011001001000101001001000111011100111001000001111001000110010110000111000110100000010010100010110100000101100100010010110001010101011010100101110111011101110110010010111100101010011100110100110010011101111010011100011001101001100101101101010111000101001101000110100011011011110011001100111011010110100100111101010000000101110011011101110011001011110101100011001101000111110111000000011011010000011000000100101001100110001110000100000110011011011000110111001111001010111001011101100000001111000101
Pair \(Z_2\) Length of longest common subsequence
8WRL_1,6LWD_1 190 4
8WRL_1,3AGT_1 221 3
6LWD_1,3AGT_1 167 3

Newick tree

 
[
	8WRL_1:10.77,
	[
		6LWD_1:83.5,3AGT_1:83.5
	]:25.27
]

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 \((0.85)(0.8)(\frac{889 }{\log_{20} 889}-\frac{295}{\log_{20}295})=161.\)
Status Protein1 Protein2 d d1/2
Query variables 8WRL_1 6LWD_1 208 153
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]