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Parikh vectors
6EWQ_1 4NNH_1 7DCU_1 Letter Amino acid
15 7 10 H Histidine
28 8 5 I Isoleucine
11 5 2 M Methionine
16 9 9 F Phenylalanine
37 5 4 T Threonine
17 6 3 Y Tyrosine
36 17 3 A Alanine
12 5 6 N Asparagine
12 8 8 Q Glutamine
31 23 8 E Glutamic acid
39 8 9 L Leucine
28 8 9 K Lycine
29 13 9 V Valine
24 11 5 D Aspartic acid
4 0 0 C Cysteine
30 6 6 S Serine
4 2 2 W Tryptophan
15 11 5 R Arginine
20 10 6 G Glycine
19 6 4 P Proline 

6EWQ_1|Chains A, B, C, D|Putative capsular polysaccharide biosynthesis protein|Streptococcus pneumoniae serotype 4 (strain ATCC BAA-334 / TIGR4) (170187)
>4NNH_1|Chains A, B|30S ribosomal protein S1|Mycobacterium smegmatis (246196)
>7DCU_1|Chains A, B, C|Heat shock factor protein 2|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 \(w=f(c)\)
6EWQ , Knot 175 427 0.82 40 222 398 
MASMTGMPNYNIPFSPPDITEAEITEVVDTLRSGWITTGPKTKELERRLSLYTQTPKTVCLNSATAALELILRVLEVGPGDEVIVPAMTYTASCSVITHVGATPVMVDIQADTFEMDYDLLEQAITEKTKVIIPVELAGIVCDYDRLFQVVEKKRDFFTASSKWQKAFNRIVIVSDSAHALGSTYKGQPSGSIADFTSFSFHAVKNFTTAEGGSATWKANPVIDDEEMYKEFQILSLHGQTKDALAKMQLGSWEYDIVTPAYKCNMTDIMASLGLVQLDRYPSLLQRRKDIVDRYDSGFAGSRIHPLAHKTETVESSRHLYITRVEGASLEERNLIIQELAKAGIASNVHYKPLPLLTAYKNLGFDMTNYPKAYAFFENEITLPLHTKLSDEEVDYIIETFKTVSEKVLTLSKKKLAAALEHHHHHH
4NNH , Knot 83 168 0.84 38 125 159 
NLYFQHMRHFARTHAIGQIVPGKVTKLVPFGAFVRVEEGIEGLVHISELSERHVEVPDQVVQVGDDAMVKVIDIDLERRRISLSLKQANEDYTEEFDPSKYGMADSYDEQGNYIFPEGFDPETNEWLEGFDKQREEWEARYAEAERRHKMHTAQMEKFAAAEAEAANA
7DCU , Knot 59 113 0.82 38 96 106 
GHHHHHHVPAFLSKLWTLVEETHTNEFITWSQNGQSFLVLDEQRFAKEILPKYFKHNNMASFVRQLNMYGFRKVVHIDSGIVKQERDGPVEFQHPYFKQGQDDLLENIKRKVS

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 \(c\).

\(|P_{f(6EWQ_1)}(2) \setminus P_{f(4NNH_1)}(2)|=134\), \(|P_{f(4NNH_1)}(2) \setminus P_{f(6EWQ_1)}(2)|=37\). 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 1:1101011100011101101001010011001001110011000010001010000100101001011101110110111100111111000100011001110111101010010100011001100000111110111110000011011000001101000100110011110001011100001010101101001010110010010110101010111000010001011010100001110101101000110110000100111011110100010110000011000001111001011100000100000101001011010000111001101111001000111110100011101000101011100010111000100001001100100100011010000111110000000
Pair \(Z_2\) Length of longest common subsequence
6EWQ_1,4NNH_1 171 4
6EWQ_1,7DCU_1 184 6
4NNH_1,7DCU_1 133 3

Newick tree

 
[
	6EWQ_1:95.08,
	[
		4NNH_1:66.5,7DCU_1:66.5
	]:28.58
]

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 \((0.85)(0.8)(\frac{595 }{\log_{20} 595}-\frac{168}{\log_{20}168})=122.\)
Status Protein1 Protein2 d d1/2
Query variables 6EWQ_1 4NNH_1 154 106.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]