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Parikh vectors
4JBZ_1 6WAB_1 5DAV_1 Letter Amino acid
21 8 14 N Asparagine
30 17 13 G Glycine
3 4 13 H Histidine
15 11 6 F Phenylalanine
56 6 27 A Alanine
1 1 3 C Cysteine
21 10 22 P Proline
13 9 24 S Serine
6 9 17 R Arginine
24 6 16 D Aspartic acid
15 6 7 Q Glutamine
30 3 19 E Glutamic acid
34 11 35 L Leucine
10 1 7 M Methionine
19 8 23 T Threonine
15 4 4 Y Tyrosine
22 10 22 I Isoleucine
39 6 12 K Lycine
8 1 4 W Tryptophan
21 9 20 V Valine 

4JBZ_1|Chains A, B, C|MALTOSE-BINDING PERIPLASMIC PROTEIN FUSED WITH XENOPUS LAEVIS MCM10 COILED-COIL REGION|Escherichia coli (749527)
>6WAB_1|Chains A, B, C, D|Galectin-4|Homo sapiens (9606)
>5DAV_1|Chain A|Phytanoyl-CoA dioxygenase family protein (AFU_orthologue AFUA_8G00230)|Aspergillus nidulans FGSC A4 (227321)
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 \(w=f(c)\)
4JBZ , Knot 162 403 0.80 40 201 372 
MKIEEGKLVIWINGDKGYNGLAEVGKKFEKDTGIKVTVEHPDKLEEKFPQVAATGDGPDIIFWAHDRFGGYAQSGLLAEITPAAAFQDKLYPFTWDAVRYNGKLIAYPIAVEALSLIYNKDLLPNPPKTWEEIPALDKELKAKGKSALMFNLQEPYFTWPLIAADGGYAFKYAAGKYDIKDVGVDNAGAKAGLTFLVDLIKNKHMNADTDYSIAEAAFNKGETAMTINGPWAWSNIDTSAVNYGVTVLPTFKGQPSKPFVGVLSAGINAASPNKELAKEFLENYLLTDEGLEAVNKDKPLGAVALKSYEEELAKDPRIAATMENAQKGEIMPNIPQMSAFWYAVRTAVINAASGRQTVDAALAAAQTNAAAMGVCQEKSKDELEDELRKMQAQMKKLQEQLQK
6WAB , Knot 68 140 0.80 40 112 136 
GPPTFNPPVPYFGRLQGGLTARRTIIIKGYVPPTGKSFAINFKVGSSGDIALHINPRMGNGTVVRNSLLNGSWGSEEKKITHNPFGPGQFFDLSIRCGLDRFKVYANGQHLFDFAHRLSAFQRVDTLEIQGDVTLSYVQI
5DAV , Knot 134 308 0.83 40 180 294 
STSKDHVKSQIPRLSAINDLHKIWPTVEEHGAAIIESFLSLDIVRRLNEEVDPFVKIEPIPAAKTKDHPNHVLSTTTRLVNVLAPISKAYREDVLNSKVLHRICSDAFHVYGDYWVLMGAVMELAPSNPAQPLHRDMRFSHPIVEYLKPDAPATSINFLVALSPFTAENGATHVILGSHKWQNLSNVSMDATVRALMNPGDALLITDSTIHCGGAETTGTETRRLLTITMGISQLTPLESNLAVPRPVIESLTPLAQRLLGWASQRSAAPRDIGLLTIRGNSIEKTMNLKAEQPLHDDEAEPLCRETI

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 \(c\).

\(|P_{f(4JBZ_1)}(2) \setminus P_{f(6WAB_1)}(2)|=136\), \(|P_{f(6WAB_1)}(2) \setminus P_{f(4JBZ_1)}(2)|=47\). 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 1:1010010111110100100111011001000011010100100100011011101011011111000111010011110101111100010110101100010111011110110110000111011001001111000101010011110100101011111101101100111000100111001110111011101100001010000011011100100110101111100100011001101110101010011111101110110100011001100011000110110000111111100000011001011101001001011101101011101100111011010001011111100011111100000000100010010101001000100
Pair \(Z_2\) Length of longest common subsequence
4JBZ_1,6WAB_1 183 3
4JBZ_1,5DAV_1 169 3
6WAB_1,5DAV_1 176 4

Newick tree

 
[
	6WAB_1:91.45,
	[
		4JBZ_1:84.5,5DAV_1:84.5
	]:6.95
]

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 \((0.85)(0.8)(\frac{543 }{\log_{20} 543}-\frac{140}{\log_{20}140})=117.\)
Status Protein1 Protein2 d d1/2
Query variables 4JBZ_1 6WAB_1 147 100
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]