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Parikh vectors
5EVK_1 3LVU_1 7UNZ_1 Letter Amino acid
20 17 15 D Aspartic acid
10 11 7 Q Glutamine
10 1 6 H Histidine
6 6 1 M Methionine
19 20 11 T Threonine
43 34 7 A Alanine
16 26 3 R Arginine
2 0 11 C Cysteine
8 7 10 Y Tyrosine
15 8 14 V Valine
9 11 26 I Isoleucine
27 31 29 L Leucine
5 3 0 W Tryptophan
10 10 19 S Serine
6 9 25 N Asparagine
8 14 22 E Glutamic acid
25 23 10 G Glycine
8 1 31 K Lycine
5 12 22 F Phenylalanine
19 14 10 P Proline 

5EVK_1|Chain A|Metallo-beta-lactamase L1|Stenotrophomonas maltophilia (40324)
>3LVU_1|Chains A, B, C, D|ABC transporter, periplasmic substrate-binding protein|Silicibacter pomeroyi (89184)
>7UNZ_1|Chains A[auth B], B[auth D]|Cysteine-rich small secreted protein CSS, putative|Plasmodium falciparum (5833)
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 \(w=f(c)\)
5EVK , Knot 113 271 0.77 40 158 256 
GPAEVPLPQLRAYTVDASWLQPMAPLQIADHTWQIGTEDLTALLVQTPDGAVLLDGGMPQMASHLLDNMKARGVTPRDLRLILLSHAHADHAGPVAELKRRTGAKVAANAESAVLLARGGSDDLHFGDGITYPPANADRIVMDGEVITVGGIVFTAHFMAGHTPGSTAWTWTDTRNGKPVRIAYADSLSAPGYQLQGNPRYPHLIEDYRRSFATVRALPCDVLLTPHPGASNWDYAAGARAGAKALTCKAYADAAEQKFDGQLAKETAGAR
3LVU , Knot 111 258 0.79 38 157 241 
SNAGMTGFVINTRRAPFDDWRLREALLLAFNFEFINDTVTGGVMPRITSYFSGTDLAYRPGTASGREAELLAPFAADLPPGTLEGYALPQGDGTARNRTNLRRAAQFLEQAGFRIEQGQLLGPDGAPLALRFLLRQGDSDMQTVLEIYTRALERLGIAAQIEKVDNAQYTARVAELDFDLTPFRRDLSLSPGNEQRLYWGSHSAGQPGTRNLMGAASPAIDAMIDRMLAATTEDELTAATRALDRVLTAGRYVIPIWR
7UNZ , Knot 126 279 0.84 38 164 265 
GTQDEKSVKNICVCDFTDKLNFLPLEKTKILCELKPQYGEDIKIIANKEYEINCMNNSKVFCPLKDTFINNTNIKLYSPKLHFEIKDITHKGKNAALYYLKIDEEASDIFFSCSIKPKQVSGLLEGEVRVNLKKHINEEYSIFNEEEDVHVCDFSKGNLDITPSAGFYLKNSRNVSCIYRVIPNKLFLIKLPKLDIVTEKLLPSIVNCLSEFSFINFTLKHVQEGDNYISFNVIFGEFKKHFNLACSLDLSDFQQEPCNLGKTANITFIFSKLENLYFQ

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 \(c\).

\(|P_{f(5EVK_1)}(2) \setminus P_{f(3LVU_1)}(2)|=69\), \(|P_{f(3LVU_1)}(2) \setminus P_{f(5EVK_1)}(2)|=68\). 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 1:1110111101010010101101111101100010110001011110010111110111101100110010101101001011110010100111110100001101110100111110110001011011001110100111010110111111010111100110011010000010110110100101110010101001011000000110101110011101011100100111101110110001010110001010110001110
Pair \(Z_2\) Length of longest common subsequence
5EVK_1,3LVU_1 137 4
5EVK_1,7UNZ_1 212 3
3LVU_1,7UNZ_1 191 3

Newick tree

 
[
	7UNZ_1:10.57,
	[
		5EVK_1:68.5,3LVU_1:68.5
	]:41.07
]

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 \((0.85)(0.8)(\frac{529 }{\log_{20} 529}-\frac{258}{\log_{20}258})=77.1\)
Status Protein1 Protein2 d d1/2
Query variables 5EVK_1 3LVU_1 95 92.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]