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Parikh vectors
9MVZ_1 6RZW_1 8EKD_1 Letter Amino acid
40 52 6 E Glutamic acid
23 44 8 K Lycine
119 58 7 A Alanine
4 6 2 C Cysteine
40 33 4 Q Glutamine
47 13 2 M Methionine
37 22 4 F Phenylalanine
52 49 12 S Serine
13 3 4 W Tryptophan
23 22 2 N Asparagine
18 15 0 H Histidine
83 76 10 L Leucine
86 43 11 V Valine
49 45 6 R Arginine
61 43 17 G Glycine
63 41 3 I Isoleucine
28 16 8 Y Tyrosine
62 43 8 D Aspartic acid
47 36 5 P Proline
72 35 12 T Threonine 

9MVZ_1|Chains A[auth D], D[auth E], E[auth F]|MmpL5 protein|Mycolicibacterium smegmatis (1772)
>6RZW_1|Chains A, B, C, D, E, F, G, H, I, J|Putative mitochondrial dynamin protein|Chaetomium thermophilum var. thermophilum DSM 1495 (759272)
>8EKD_1|Chain A[auth E]|Fab LLNL-199 HC|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 \(w=f(c)\)
9MVZ , Knot 355 967 0.84 40 300 835 
MSAPTDDTPTDAIAAPRHSAPPRPRLPWFLRTFAVPIILAWVAVVAILNTVVPTLDEVGEMRAVSMAPNDAPSTLAIKRVGQVFEEYDTSSSVMIVLEGEEPLGIEAHAFYDKMVADLRADTEHVQHVQDFWGDTLTASGAQSVDGKAAYVQVYIAGDQGESLANESVEAVRKIATERETPSGVKAYVTGAAATSADQRAEGDASMKLIEGVTFAVITVMLLAVYRSVITTLIVLAMVVLGLSGARGIVAFLGFYNVFGLTTFATNMVVTLAIAAATDYAIFLIGRYQEARRAGEDRESAYYTMFHGTAHVVLASGLTIAGATLCLHFTRLPYFQTMGVPLAIGMLIVVAAALTAGPAVISVVSRFGKTLEPKRFSRSPGWHRVGTATVRWPGAILVCAVVAALIGLLALPGYYTTYDDRRYLPDDVPANVGYDAAFRHFSQAKMNPDLMMVETDRDLRNPADFLVIDKIAKALKNVHGIAQVQTITRPDGDPIEHSTIPYTIGQSGTTQIMNNDYMQTNLDNLLKQADDLQTSIDSMTEMMNIQTELAAVSQSMADKMAQTSDDTADVRDHLADFDDFFRPIRNYLYWEPHCYDIPMCWSMRSIFESIDGINTMSDDFQELVPEMRRMADLMPRMVAVMPAQIQSMKNQKQTLLNQYQVQKAQQDQNMAMQENATAMSQAFDAAKNDDSFYLPPEAFETDDFQRGMKLFMSPDGHAVRFTIIHQGDPLTEEGTARMDELKVAAADAIKGTPFEGARIYLGGSAATYNDMQIGADYDLIIVAASALILIFIIMMVLTRAVVAAAVIVGTVVLSLASAFGLSVLLWQHIVGIPLHWMVLPMSVIVLLAVGADYNLLLVSRMKEEIHAGIRTGIIRAMVGTGAVVTAAGLVFAFTMASMAVSSLITIGQVGTTIGLGLLFDTLVVRSLMTPSIATLLGRWFWWPQRVRERPVPSKWPTPIQRTPEEALS
6RZW , Knot 267 695 0.83 40 271 631 
EEIMRDDNMMFITKKMIEIRNLLQKVGQGSTVTLPSIVVIGSQSSGKSSVLEAIVGHEFLPKGSNMITRRPIELTLVNDPEAKVDYGEFPDLGLARVTDFSLIQKTLTELNQSVPESECVTDDPIRLTIHSPNIPDLSLIDLPGYIQVAGENQPRELKRKITELCDKYIRGPNIILAISAADTDLANSTALQASRRVDPRGERTIGVITKMDLVEPEKGAAILSDRQYPLKLGYVGVISKLPPQSGLFRRDTGNLLASINRNEKNYFGSHPTEFGPDSGVSTGVMTLRKKLLQVLEQQMSSKLNETTEAIQRELEETTYQFKVQYNEQPMSAESYLAASLDDFKHQFHEFASSFGRPQLQTLLKDALDQKVLDQLAARYWNRPIEDLSPAPREPDNIIDLPKADPDSPYWHRQLDTACSGLTRLGVGRLAATVAASAIQQHVEKLLDKSSFAKHPSARKVISDAAATVLADRSYATSDGIEISLKPYKFDPDIQPNEWAQGREHVVGVLQAELEQCQAAMKALENSVGGRKKLKEVMSFVDKARKGEIIVEGDHPSGAGGFSAALLARGREAVFLRDRADILSLRIQAAKSRQCKTLTNKYYCPEVFLDAVATKLAQTAVLFLNVEMLNDFYVRFPREVEAKLHEHMHAGGGLEKFAREDPKVRRHLDLIRRKELLETVLGKIEELHRISSGTAG
8EKD , Knot 66 131 0.81 38 99 129 
EVQLVESGGGLVKPGGSLRLSCAASGFTFRDVWMSWVRQAPGKGLEWVGRIKSKIDGGTTDYAAPVKGRFTISRDDSKNTLYLQMNSLKTEDTAVYYCTTAGSYYYDTVGPELPEGKFDYWGQGTLVTVSS

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 \(c\).

\(|P_{f(9MVZ_1)}(2) \setminus P_{f(6RZW_1)}(2)|=77\), \(|P_{f(6RZW_1)}(2) \setminus P_{f(9MVZ_1)}(2)|=48\). 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 1:1011000010011111000111010111110011111111111111110011101001101011011100110011100110110000000011111010011110101100011101010000100100111001010110010101101010111001001100010110011000001011010101111001000101010101101101111011111100011001111111111101101111111100111100110011101111110001111110000100110000010001101010111101101111010101001101001111111111111111101111110110011001010010001110011010101111111011111111111111000000000011001110110011100100101010111100000100110111100110110010111010010010101100001100110010001100001000100110010010001001001101000111100011001100000010100011010011011000101010000111010100110010110010001001110100110111011111110100100000011000010010000011100010110011011000001011101100001001101110101011010110010110001010100101111011010110110101110110000101110001111110111111111111001111111111011101101111011110011111101111110111111111000111100100010111001110111101111011111111011011100110110110011111110011100110101101110111110010001110011011000100110
Pair \(Z_2\) Length of longest common subsequence
9MVZ_1,6RZW_1 125 5
9MVZ_1,8EKD_1 229 4
6RZW_1,8EKD_1 210 4

Newick tree

 
[
	8EKD_1:12.60,
	[
		9MVZ_1:62.5,6RZW_1:62.5
	]:59.10
]

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 \((0.85)(0.8)(\frac{1662 }{\log_{20} 1662}-\frac{695}{\log_{20}695})=240.\)
Status Protein1 Protein2 d d1/2
Query variables 9MVZ_1 6RZW_1 302 260.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]