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Parikh vectors
8ZBV_1 4AUW_1 4QGL_1 Letter Amino acid
50 12 8 R Arginine
36 10 5 Q Glutamine
40 3 8 H Histidine
49 11 9 K Lycine
32 2 9 F Phenylalanine
41 7 15 V Valine
64 3 9 G Glycine
40 2 15 I Isoleucine
72 10 13 L Leucine
64 4 12 A Alanine
12 1 0 C Cysteine
23 2 1 M Methionine
44 0 6 P Proline
26 0 2 W Tryptophan
41 4 10 N Asparagine
55 4 11 D Aspartic acid
44 8 18 E Glutamic acid
52 7 10 S Serine
36 3 8 T Threonine
27 3 5 Y Tyrosine 

8ZBV_1|Chain A|Alpha-L-fucosidase|Pontiella sulfatireligans (2750658)
>4AUW_1|Chains A, B, E, F|TRANSCRIPTION FACTOR MAFB|MUS MUSCULUS (10090)
>4QGL_1|Chain A|Acireductone dioxygenase|Bacillus anthracis (261594)
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 \(w=f(c)\)
8ZBV , Knot 326 848 0.86 40 322 783 
HHHHHHMEKTSAHVVPSMVRRNFCQLMTAATAAPFMGGALSAHAAAGHSAAFLKMDRSEEPSLLLRYDRSAANWNEALPIGNGRIGGMVWGNVSEEIIDLNEETLWSGHPRETDNPNAKQHLPQIRKAVFDKNYERANDLAYKIQGTYNENYQPLGQLHLSMSHAGESTNYARALDIGNAVSTVDYEVDGVKYHRDYFVSAPDNSMCIRLTASEPGKISCRLKMDSPLKHVSFSRGNSCIMQGQAPSHADRASIKADQVIFYDPKEEGLSFYSQLQVVPEGGRFWKYENGMRVEHADSLVLVFSAATNFDGFDVFPRKSRIDPCKVVKETFRKIGPVDFKELQKRHIADYRTLFDRVGIQLGKGASISKTTDQRIKDYARDEDPDLVALTFQYGRYMLISSSRPGTLPANLQGIWNPLMRPPWMSNWTNDLNTQMNYWLSWTTNLPECEKALIDWVDNLRPNGRKTARTNYGAKGWLCHNTTDLWMQTAPAGIERPRWCILPLGGVWLCQHLWMHYVFHGDREFLEKRSYPIMREAAEFCLDWLIKDSDGYYVTCPSVSPENWFATAGDKQLSISKASTYDMQLIRDLFTNCIQAAKVLNTDKEFSAKLQERMDHLYPQKIGQYGQLQEWSEDWDKPEDQHRHISHLFGLFPGDQLTPNKNPEGWKGARQSLLMRSGEMAKGGKGKNDADTGWSINWKIGWWARLHDAEQAQNMLRKIFRFAPSGNTLSSQKGGRYANLLNAGPPFQIDGVLGFTAGVVELLLQSHDGFIHLLPALPKNWPDGRVTGLKARGGFIVDIEWKDGKLLEAVIHPGHEKEVRVHYQDDVHVFAKIEKPVRITRHDHHHHHH
4AUW , Knot 48 96 0.76 36 77 93 
MFSDDQLVSMSVRELNRHLRGFTKDEVIRLKQKRRTLKNRGYAQSCRYKRVQQKHHLENEKTQLIQQVEQLKQEVSRLARERDAYKVKSEKLANSG
4QGL , Knot 85 174 0.84 38 136 171 
GAAAMAQIRIHEVNTRIENEVKVSKFLQEEGVLYEKWNISKLPPHLNENYSLTDENKAEILAVFSKEIADVSARRGYKAHDVISLSNSTPNLDELLINFQKEHHHTDDEVRFIVSGHGIFAIEGKDGTFFDVELEPGDLISVPENARHYFTLQDDRQVVAIRIFVTTEGWVPIY

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 \(c\).

\(|P_{f(8ZBV_1)}(2) \setminus P_{f(4AUW_1)}(2)|=250\), \(|P_{f(4AUW_1)}(2) \setminus P_{f(8ZBV_1)}(2)|=5\). 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 1:00000010000101110110001001101101111111110101111001111010000010111000001101001111101011111110100011010000110101000001010001101001110000001001100101000000011101010100110000010110110110010001011000000110110001010101001101000101001100101001000110101100100101010011100100011010001011101101100001101001001111101100101101110000101001100010011110100100001100001100111011011010000000100010000101111010010011100001101110101110111011110010001000100110100011000011101100101010001000011011100000011100111110010101111111110001110011010001100000111001101010111000010010010101001110110001010010000101100110001011011000001010100010010100110010100100010010000001001111111001010001011011000111001011011010001001101010111110100100100110011011101001000011001011011111010111110111101110000111011111100110101011010111110101001011011101100001010000010111010011010000000000
Pair \(Z_2\) Length of longest common subsequence
8ZBV_1,4AUW_1 255 3
8ZBV_1,4QGL_1 208 4
4AUW_1,4QGL_1 137 3

Newick tree

 
[
	8ZBV_1:12.39,
	[
		4QGL_1:68.5,4AUW_1:68.5
	]:59.89
]

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 \((0.85)(0.8)(\frac{944 }{\log_{20} 944}-\frac{96}{\log_{20}96})=237.\)
Status Protein1 Protein2 d d1/2
Query variables 8ZBV_1 4AUW_1 303 166.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]