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Parikh vectors
4QEP_1 1TCV_1 5SBU_1 Letter Amino acid
27 17 10 A Alanine
30 17 11 N Asparagine
24 5 6 C Cysteine
45 28 9 G Glycine
42 29 7 L Leucine
23 13 7 P Proline
36 15 10 S Serine
25 13 15 T Threonine
33 9 8 R Arginine
31 11 10 D Aspartic acid
19 9 4 Q Glutamine
27 21 10 I Isoleucine
8 10 3 M Methionine
4 1 0 W Tryptophan
34 17 5 K Lycine
19 9 6 F Phenylalanine
41 31 10 V Valine
29 16 8 E Glutamic acid
11 9 5 H Histidine
25 7 8 Y Tyrosine 

4QEP_1|Chain A|Histone-lysine N-methyltransferase, H3 lysine-9 specific SUVH4|Arabidopsis thaliana (3702)
>1TCV_1|Chains A, B, C|purine-nucleoside phosphorylase|Schistosoma mansoni (6183)
>5SBU_1|Chain A|CD44 antigen|Mus musculus (10090)
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 \(w=f(c)\)
4QEP , Knot 215 533 0.84 40 265 501 
SNGKDVNLEPHLKVTKCLRLFNKQYLLCVQAKLSRPDLKGVTEMIKAKAILYPRKIIGDLPGIDVGHRFFSRAEMCAVGFHNHWLNGIDYMSMEYEKEYSNYKLPLAVSIVMSGQYEDDLDNADTVTYTGQGGHNLTGNKRQIKDQLLERGNLALKHCCEYNVPVRVTRGHNCKSSYTKRVYTYDGLYKVEKFWAQKGVSGFTVYKYRLKRLEGQPELTTDQVNFVAGRIPTSTSEIEGLVCEDISGGLEFKGIPATNRVDDSPVSPTSGFTYIKSLIIEPNVIIPKSSTGCNCRGSCTDSKKCACAKLNGGNFPYVDLNDGRLIESRDVVFECGPHCGCGPKCVNRTSQKRLRFNLEVFRSAKKGWAVRSWEYIPAGSPVCEYIGVVRRTADVDTISDNEYIFEIDCQQTMQGLGGRQRRLRDVAVPMNNGVSQSSEDENAPEFCIDAGSTGNFARFINHSCEPNLFVQCVLSSHQDIRLARVVLFAADNISPMQELTYDYGYALDSVHGPDGKVKQLACYCGALNCRKRLY
1TCV , Knot 132 287 0.86 40 184 276 
MHESVTANIENVKKVAHHIQKLTSIVPEIGIICGSGLGKLADGVKDKITIPYTKIPNFPQTSVVGHSGNLIFGTLSGRKVVVMQGRFHMYEGYSNDTVALPIRVMKLLGVKILMVSNAAGGLNRSLKLGDFVILKDHIYLPGLGLNNILVGPNQEAFGTRFPALSNAYDRDLRKLAVQVAEENGFGNLVHQGVYVMNGGPCYETPAECTMLLNMGCDVVGMSTIPEVVIARHCGIQVFAVSLVTNISVLDVESDLKPNHEEVLATGAQRAELMQSWFEKIIEKLPKD
5SBU , Knot 76 152 0.83 38 122 147 
MNQIDLNVTCRYAGVFHVEKNGRYSISRTEAADLCQAFNSTLPTMDQMKLALSKGFETCRYGFIEGNVVIPRIHPNAICAANHTGVYILVTSNTSHYDTYCFNASAPPEEDCTSVTDLPNSFDGPVTITIVNRDGTRYSKKGEYRTHQEDID

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 \(c\).

\(|P_{f(4QEP_1)}(2) \setminus P_{f(1TCV_1)}(2)|=122\), \(|P_{f(1TCV_1)}(2) \setminus P_{f(4QEP_1)}(2)|=41\). 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 1:00100101010101000101100001101010100101011001101011101001110111101100110010101111000110110010100000000001111101110100000100100100010110010100001000110010111000000011101001000000000010000110010011100110110100001001010101000010111101100000101110001011101011110001000110100110010011101011110000100001000000001010101101101010010110000111001100101100100000001010101100100111100100111101100011110001010010000011010000010111100001001111100110000000011010101100101101100000101110011000001011011111100101100100001011001011010100110001110000010
Pair \(Z_2\) Length of longest common subsequence
4QEP_1,1TCV_1 163 3
4QEP_1,5SBU_1 203 3
1TCV_1,5SBU_1 170 3

Newick tree

 
[
	5SBU_1:97.31,
	[
		4QEP_1:81.5,1TCV_1:81.5
	]:15.81
]

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 \((0.85)(0.8)(\frac{820 }{\log_{20} 820}-\frac{287}{\log_{20}287})=145.\)
Status Protein1 Protein2 d d1/2
Query variables 4QEP_1 1TCV_1 185 142
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]