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Parikh vectors
7SIT_1 6QHM_1 7ETJ_1 Letter Amino acid
21 17 11 K Lycine
25 27 20 A Alanine
18 13 20 R Arginine
8 5 10 F Phenylalanine
8 2 3 W Tryptophan
6 3 10 H Histidine
23 10 15 I Isoleucine
12 9 13 M Methionine
12 7 17 P Proline
25 20 13 S Serine
12 8 8 N Asparagine
15 9 14 Q Glutamine
26 33 15 E Glutamic acid
28 17 13 G Glycine
34 24 50 L Leucine
14 10 20 T Threonine
12 10 5 Y Tyrosine
20 12 26 V Valine
9 15 17 D Aspartic acid
5 2 6 C Cysteine 

7SIT_1|Chains A, C|Voltage-gated potassium channel subunit beta-2|Rattus norvegicus (10116)
>6QHM_1|Chain A|14-3-3 protein sigma|Homo sapiens (9606)
>7ETJ_1|Chains A[auth I], B[auth h], E[auth n], F[auth o]|Triplex capsid protein 2|Human cytomegalovirus (10359)
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 \(w=f(c)\)
7SIT , Knot 145 333 0.84 40 204 321 
MLQFYRNLGKSGLRVSCLGLGTWVTFGGQITDEMAEHLMTLAYDNGINLFDTAEVYAAGKAEVVLGNIIKKKGWRRSSLVITTKIFWGGKAETERGLSRKHIIEGLKASLERLQLEYVDVVFANRPDPNTPMEETVRAMTHVINQGMAMYWGTSRWSSMEIMEAYSVARQFNLIPPICEQAEYHMFQREKVEVQLPELFHKIGVGAMTWSPLACGIVSGKYDSGIPPYSRASLKGYQWLKDKILSEEGRRQQAKLKELQAIAERLGCTLPQLAIAWCLRNEGVSSVLLGASNAEQLMENIGAIQVLPKLSSSIVHEIDSILGNKPYSKKDYRS
6QHM , Knot 114 253 0.83 40 170 244 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWTADNAGEEGGEAPQEPQS
7ETJ , Knot 133 306 0.83 40 193 290 
MAAMEANIFCTFDHKLSIADVGKLTKLVAAVVPIPQRLHLIKHYQLGLHQFVDHTRGYVRLRGLLRNMTLTLMRRVEGNQILLHVPTHGLLYTVLNTGPVTWEKGDALCVLPPLFHGPLARENLLTLGQWELVLPWIVPMPLALEINQRLLIMGLFSLDRSYEEVKAAVQQLQTITFRDATFTIPDPVIDQHLLIDMKTACLSMSMVANLASELTMTYVRKLALEDSSMLLVKCQELLMRLDRERSVGEPRTPARPQHVSPDDEIARLSALFVMLRQLDDLIREQVVFTVCDVSPDNKSATCIFKG

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 \(c\).

\(|P_{f(7SIT_1)}(2) \setminus P_{f(6QHM_1)}(2)|=96\), \(|P_{f(6QHM_1)}(2) \setminus P_{f(7SIT_1)}(2)|=62\). 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 1:110100011001101001111011011101000110011011000110110010101110101111011000110000111000111110100001100001101101010010100101111001010011000101100110011110110001001011010011001011111000100011000010101101100111111010111011101000011110001010100110001100010000101001011100110011011111010001100111110010011001111011101000110010011100100000000
Pair \(Z_2\) Length of longest common subsequence
7SIT_1,6QHM_1 158 5
7SIT_1,7ETJ_1 155 3
6QHM_1,7ETJ_1 157 4

Newick tree

 
[
	6QHM_1:79.16,
	[
		7SIT_1:77.5,7ETJ_1:77.5
	]:1.66
]

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 \((0.85)(0.8)(\frac{586 }{\log_{20} 586}-\frac{253}{\log_{20}253})=94.1\)
Status Protein1 Protein2 d d1/2
Query variables 7SIT_1 6QHM_1 118 103
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]