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Parikh vectors
2EDK_1 5NBN_1 1IFP_1 Letter Amino acid
1 7 0 C Cysteine
5 44 3 L Leucine
2 28 0 P Proline
3 35 5 T Threonine
6 24 2 D Aspartic acid
2 27 0 N Asparagine
7 14 4 Q Glutamine
1 6 0 H Histidine
4 17 2 F Phenylalanine
1 9 1 W Tryptophan
4 25 6 A Alanine
2 16 0 Y Tyrosine
13 28 6 V Valine
6 37 1 K Lycine
12 44 0 E Glutamic acid
10 30 4 G Glycine
5 30 7 I Isoleucine
3 5 1 M Methionine
7 43 1 S Serine
7 20 1 R Arginine 

2EDK_1|Chain A|Myosin-binding protein C, fast-type|Homo sapiens (9606)
>5NBN_1|Chains A, B|Actin-related protein 4|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>1IFP_1|Chain A|MAJOR COAT PROTEIN ASSEMBLY|Pseudomonas phage Pf3 (10872)
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 \(w=f(c)\)
2EDK , Knot 54 101 0.82 40 81 96 
GSSGSSGPVLIVTPLEDQQVFVGDRVEMAVEVSEEGAQVMWMKNGVELTREDSFKARYRFKKDGKRHILIFSDVVQEDRGRYQVITNGGQCEAELIVEEKQ
5NBN , Knot 198 489 0.83 40 240 460 
MSNAALQVYGGDEVSAVVIDPGSYTTNIGYSGSDFPQSILPSVYGKYTADEGNKKIFSEQSIGIPRKDYELKPIIENGLVIDWDTAQEQWQWALQNELYLNSNSGIPALLTEPVWNSTENRKKSLEVLLEGMQFEACYLAPTSTCVSFAAGRPNCLVVDIGHDTCSVSPIVDGMTLSKSTRRNFIAGKFINHLIKKALEPKEIIPLFAIKQRKPEFIKKTFDYEVDKSLYDYANNRGFFQECKETLCHICPTKTLEETKTELSSTAKRSIESPWNEEIVFDNETRYGFAEELFLPKEDDIPANWPRSNSGVVKTWRNDYVPLKRTKPSGVNKSDKKVTPTEEKEQEAVSKSTSPAANSADTPNETGKRPLEEEKPPKENNELIGLADLVYSSIMSSDVDLRATLAHNVVLTGGTSSIPGLSDRLMTELNKILPSLKFRILTTGHTIERQYQSWLGGSILTSLGTFHQLWVGKKEYEEVGVERLLNDRFR
1IFP , Knot 27 44 0.77 28 40 42 
MQSVITDVTGQLTAVQADITTIGGAIIVLAAVVLGIRWIKAQFF

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 \(c\).

\(|P_{f(2EDK_1)}(2) \setminus P_{f(5NBN_1)}(2)|=24\), \(|P_{f(5NBN_1)}(2) \setminus P_{f(2EDK_1)}(2)|=183\). 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 1:10010011111101100001111001011101000110111100110100000101000100010001111001100001000110011000101110000
Pair \(Z_2\) Length of longest common subsequence
2EDK_1,5NBN_1 207 3
2EDK_1,1IFP_1 91 3
5NBN_1,1IFP_1 218 3

Newick tree

 
[
	5NBN_1:11.88,
	[
		2EDK_1:45.5,1IFP_1:45.5
	]:74.38
]

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 \((0.85)(0.8)(\frac{590 }{\log_{20} 590}-\frac{101}{\log_{20}101})=143.\)
Status Protein1 Protein2 d d1/2
Query variables 2EDK_1 5NBN_1 180 108
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]