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Parikh vectors
6TOV_1 4KYT_1 1ATU_1 Letter Amino acid
0 36 19 N Asparagine
0 50 19 D Aspartic acid
0 45 16 P Proline
0 13 2 W Tryptophan
2 22 6 Y Tyrosine
3 68 22 G Glycine
0 53 32 K Lycine
0 57 19 S Serine
0 48 8 R Arginine
0 24 1 C Cysteine
0 78 31 E Glutamic acid
0 72 20 I Isoleucine
0 37 26 F Phenylalanine
0 62 26 T Threonine
0 82 24 V Valine
0 86 24 A Alanine
0 23 15 Q Glutamine
0 12 10 H Histidine
0 93 46 L Leucine
0 33 8 M Methionine 

6TOV_1|Chain A|Teicoplanin Aglycone|synthetic construct (32630)
>4KYT_1|Chain A|SERCA1a|Oryctolagus cuniculus (9986)
>1ATU_1|Chain A|ALPHA-1-ANTITRYPSIN|Homo sapiens (9606)
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 \(w=f(c)\)
6TOV , Knot 5 7 0.46 6 4 4 
GYXGGYX
4KYT , Knot 367 994 0.85 40 320 881 
MEAAHSKSTEECLAYFGVSETTGLTPDQVKRHLEKYGHNELPAEEGKSLWELVIEQFEDLLVRILLLAACISFVLAWFEEGEETITAFVEPFVILLILIANAIVGVWQERNAENAIEALKEYEPEMGKVYRADRKSVQRIKARDIVPGDIVEVAVGDKVPADIRILSIKSTTLRVDQSILTGESVSVIKHTEPVPDPRAVNQDKKNMLFSGTNIAAGKALGIVATTGVSTEIGKIRDQMAATEQDKTPLQQKLDEFGEQLSKVISLICVAVWLINIGHFNDPVHGGSWIRGAIYYFKIAVALAVAAIPEGLPAVITTCLALGTRRMAKKNAIVRSLPSVETLGCTSVICSDKTGTLTTNQMSVCKMFIIDKVDGDFCSLNEFSITGSTYAPEGEVLKNDKPIRSGQFDGLVELATICALCNDSSLDFNETKGVYEKVGEATETALTTLVEKMNVFNTEVRNLSKVERANACNSVIRQLMKKEFTLEFSRDRKSMSVYCSPAKSSRAAVGNKMFVKGAPEGVIDRCNYVRVGTTRVPMTGPVKEKILSVIKEWGTGRDTLRCLALATRDTPPKREEMVLDDSSRFMEYETDLTFVGVVGMLDPPRKEVMGSIQLCRDAGIRVIMITGDNKGTAIAICRRIGIFGENEEVADRAYTGREFDDLPLAEQREACRRACCFARVEPSHKSKIVEYLQSYDEITAMTGDGVNDAPALKKAEIGIAMGSGTAVAKTASEMVLADDNFSTIVAAVEEGRAIYNNMKQFIRYLISSNVGEVVCIFLTAALGLPEALIPVQLLWVNLVTDGLPATALGFNPPDLDIMDRPPRSPKEPLISGWLFFRYMAIGGYVGAATVGAAAWWFMYAEDGPGVTYHQLTHFMQCTEDHPHFEGLDCEIFEAPEPMTMALSVLVTIEMCNALNSLSENQSLMRMPPWVNIWLLGSICLSMSLHFLILYVDPLPMIFKLKALDLTQWLMVLKISLPVIGLDEILKFIARNYLEG
1ATU , Knot 158 374 0.83 40 210 348 
PTFNKITPNLAEFAFSLYRQLAHQSNSTNILFSPVSIAAAFAMLSLGAKGDTHDEILEGLNFNLTEIPEAQIHEGFQELLRTLNQPDSQLQLTTGNGLFLSEGLKLVDKFLEDVKKLYHSEAFTVNFGDTEEAKKQINDYVEKGTQGKIVDLVKELDRDTVFALVNYIFFKGKWERPFEVKDTEEEDFHVDQVTTVKVPMMKRLGMFNIQHCKKLSSWVLLMKYLGNATAIFFLPDEGKLQHLENELTHDIITKFLENEDRRSASLHLPKLSITGTYDLKSVLGQLGITKVFSNGADLSGVTEEAPLKLSKAVHKAVLTIDEKGTEAAGAMFLEAIPMSIPPEVKFNKPFVFLIIEQNTKAPLFMGRVVNPTQK

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 \(c\).

\(|P_{f(6TOV_1)}(2) \setminus P_{f(4KYT_1)}(2)|=2\), \(|P_{f(4KYT_1)}(2) \setminus P_{f(6TOV_1)}(2)|=318\). 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 1:1001100
Pair \(Z_2\) Length of longest common subsequence
6TOV_1,4KYT_1 320 3
6TOV_1,1ATU_1 214 1
4KYT_1,1ATU_1 162 4

Newick tree

 
[
	6TOV_1:15.04,
	[
		1ATU_1:81,4KYT_1:81
	]:69.04
]

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 \((0.85)(0.8)(\frac{1001 }{\log_{20} 1001}-\frac{7}{\log_{20}7})=287.\)
Status Protein1 Protein2 d d1/2
Query variables 6TOV_1 4KYT_1 365 183.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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