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Parikh vectors
9BOZ_1 6QCN_1 6RJZ_1 Letter Amino acid
27 14 10 I Isoleucine
19 3 8 N Asparagine
19 24 33 E Glutamic acid
7 8 3 H Histidine
40 39 24 L Leucine
25 20 17 K Lycine
18 9 9 M Methionine
28 23 20 S Serine
25 19 27 A Alanine
26 15 13 R Arginine
28 17 15 D Aspartic acid
8 11 2 C Cysteine
15 11 9 Q Glutamine
23 16 7 P Proline
7 3 2 W Tryptophan
16 20 17 G Glycine
28 17 5 F Phenylalanine
23 11 10 T Threonine
16 11 10 Y Tyrosine
24 13 12 V Valine 

9BOZ_1|Chains A, B, C, D|Glycine receptor subunit alpha-3|Homo sapiens (9606)
>6QCN_1|Chains A, B|NAD-dependent protein deacetylase sirtuin-2|Homo sapiens (9606)
>6RJZ_1|Chain A|14-3-3 protein sigma|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 \(w=f(c)\)
9BOZ , Knot 178 422 0.85 40 248 406 
ARSRSAPMSPSDFLDKLMGRTSGYDARIRPNFKGPPVNVTCNIFINSFGSIAETTMDYRVNIFLRQKWNDPRLAYSEYPDDSLDLDPSMLDSIWKPDLFFANEKGANFHEVTTDNKLLRIFKNGNVLYSIRLTLTLSCPMDLKNFPMDVQTCIMQLESFGYTMNDLIFEWQDEAPVQVAEGLTLPQFLLKEEKDLRYCTKHYNTGKFTCIEVRFHLERQMGYYLIQMYIPSLLIVILSWVSFWINMDAAPARVALGITTVLTMTTQSSGSRASLPKVSYVKAIDIWMAVCLLFVFSALLEYAAVNFVSRQHKELLRFRRKRKNKTEAFDMDDEVRESRFSFTAYGMGPCLQAKDGMTPKGPNHPVQVMPKSPDEMRKVFIDRAKKIDTISRACFPLAFLIFNIFYWVIYKILRHEDIHQQQD
6QCN , Knot 134 304 0.84 40 191 288 
HMKERLLDELTLEGVARYMQSERCRRVICLVGAGISTSAGIPDFRSPSTGLYDNLEKYHLPYPEAIFEISYFKKHPEPFFALAKELYPGQFKPTICHYFMRLLKDKGLLLRCYTQNIDTLERIAGLEQEDLVEAHGTFYTSHCVSASCRHEYPLSWMKEKIFSEVTPKCEDCQSLVKPDIVFFGESLPARFFSCMQSDFLKVDLLLVMGTSLQVQPFASLISKAPLSTPRLLINKEKAGQSDPFLGMIMGLGGGMDFDSKKAYRDVAWLGECDQGCLALAELLGWKKELEDLVRREHASIDAQS
6RJZ , Knot 114 253 0.83 40 170 244 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWTADNAGEEGGEAPQEPQS

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 \(c\).

\(|P_{f(9BOZ_1)}(2) \setminus P_{f(6QCN_1)}(2)|=117\), \(|P_{f(6QCN_1)}(2) \setminus P_{f(9BOZ_1)}(2)|=60\). 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 1:10000111010011001110001001010101011110100011100110110001000101110001001011000010001010101100110101111000110100100000110110010110010101010011010011101000110100110010011101000111011011011011100000100000000010100101010100011001101011011111101101110101111011111001101000001001011010010110111110111110111001110110000001101000000000110100010000101010111101010011010110011011100100100111001001001001011111111011011100110000100000
Pair \(Z_2\) Length of longest common subsequence
9BOZ_1,6QCN_1 177 4
9BOZ_1,6RJZ_1 178 4
6QCN_1,6RJZ_1 161 4

Newick tree

 
[
	9BOZ_1:91.33,
	[
		6QCN_1:80.5,6RJZ_1:80.5
	]:10.83
]

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 \((0.85)(0.8)(\frac{726 }{\log_{20} 726}-\frac{304}{\log_{20}304})=116.\)
Status Protein1 Protein2 d d1/2
Query variables 9BOZ_1 6QCN_1 148 125.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]