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Parikh vectors
5LTA_1 5OQN_1 6JES_1 Letter Amino acid
59 68 16 E Glutamic acid
30 24 9 G Glycine
19 15 3 H Histidine
39 83 10 I Isoleucine
72 105 14 L Leucine
43 52 5 K Lycine
41 61 9 S Serine
6 6 1 W Tryptophan
25 38 4 F Phenylalanine
39 22 10 P Proline
43 55 20 V Valine
48 44 9 R Arginine
35 62 5 D Aspartic acid
9 14 2 C Cysteine
45 38 3 T Threonine
29 23 4 Y Tyrosine
58 53 14 A Alanine
22 62 8 N Asparagine
33 30 6 Q Glutamine
19 16 7 M Methionine 

5LTA_1|Chain A|Pre-mRNA-splicing factor ATP-dependent RNA helicase PRP43|Chaetomium thermophilum var. thermophilum DSM 1495 (759272)
>5OQN_1|Chain A|Condensin complex subunit 3|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>6JES_1|Chains A, B|Peptide deformylase|Acinetobacter baumannii (470)
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 \(w=f(c)\)
5LTA , Knot 280 714 0.86 40 291 665 
MATTAKQAEAVEDSDINPWTGQRHSERYFKILKARRKLPVNKQRQEFLDLYHNNQILVFVGETGSGKTTQIPQYVLYDELPHQTGKLIACTQPRRVAAMSVAQRVADELDVKLGEEVGYSIRFENKTSSKTLLKYMTDGQLLREAMHDRDMSRYSCIILDEAHERTLATDILMALLKQLSERRKDLKIIVMSATLDAQKFQSYFFNAPLLAVPGRTHPVEIFYTPEAERDYVEAAIRTVLQIHACEPEGDILLFLTGEEEIEDACRRISLEVDEMIRESDAGPMSVYPLYGTLPPHQQQRIFEKAPQPFRPGGRPGRKCIVATNIAETSLTIDGIVYVVDPGFSKQKIYNPRTRVESLLVSPISKASAQQRAGRAGRTRPGKCFRLYTEEAFKKELIEQTYPEILRSNLSNTVLELKKLGVEDLVHFDLMDPPAPETMMRALEELNYLACLDDDGELTPLGNLASEFPLDPALAVMLISSPEFYCSNEILSITSLLSVPQIWVRPANARKRADEMKAQFAHPDGDHLTLLNAYHAYKGAEARGEDMKKWCHEHFLSYRHLSSADNVRAQLKKIMETHGIELVSTPFHDKNYYTNIRRALLAGFFMQVAMRESSNSKVYKTVKDEQLVLIHPSTTVTTPYEWVVYNEFVLTTKQYVRTVTNIRPEWLLEIAPVYYDLSTFQKGEIKNALTRVAEKIRRQQAMKASKAWSHPQFEK
5OQN , Knot 326 871 0.84 40 296 785 
MGIDINTKIFNSVAEVFQKAQGSYAGHRKHIAVLKKIQSKAVEQGYEDAFNFWFDKLVTKILPLKKNEIIGDRIVKLVAAFIASLERELILAKKQNYKLTNDEEGIFSRFVDQFIRHVLRGVESPDKNVRFRVLQLLAVIMDNIGEIDESLFNLLILSLNKRIYDREPTVRIQAVFCLTKFQDEEQTEHLTELSDNEENFEATRTLVASIQNDPSAEVRRAAMLNLINDNNTRPYILERARDVNIVNRRLVYSRILKSMGRKCFDDIEPHIFDQLIEWGLEDRELSVRNACKRLIAHDWLNALDGDLIELLEKLDVSRSSVCVKAIEALFQSRPDILSKIKFPESIWKDFTVEIAFLFRAIYLYCLDNNITEMLEENFPEASKLSEHLNHYILLRYHHNDISNDSQSHFDYNTLEFIIEQLSIAAERYDYSDEVGRRSMLTVVRNMLALTTLSEPLIKIGIRVMKSLSINEKDFVTMAIEIINDIRDDDIEKQESESDIINNLPPEKEASSATIVLCLTRSSYMLELVNTPLTENILIASLMDTLITPAVRNTAPNIRELGVKNLGLCCLLDVKLAIDNMYILGMCVSKGNASLKYIALQVIVDIFSVHGNTVVDGEGKVDSISLHKIFYKVLKNNGLPECQVIAAEGLCKLFLADVFTDDDLFETLVLSYFSPINSSNEALVQAFAFCIPVYCFSHPAHQQRMSRTAADILLRLCVLWDDLQSSVIPEVDREAMLKPNIIFQQLLFWTDPRNLVNQTGSTKKDTVQLTFLIDVLKIYAQIEKKEIKKMIITNINAIFLSSEQDYSTLKELLEYSDDIAENDNLDNVSKNALDKLRNNLNSLIEEINERSETQTKDENNTANDQYSSILGN
6JES , Knot 77 159 0.81 40 119 153 
SVVLPVAKRGEDILKLIAAPVSANELNSNWLYQLADAMHATMLERNGVGIAAPQVYISKRVIIVASRPNPRYPDAPEMNAVVMVNPEILEFSSEMCLGEEGCLSVPDERGQVERAEMVKVKYLTLQGEMVETVFQGFPARIVQHEVDHLNGILFVERIS

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 \(c\).

\(|P_{f(5LTA_1)}(2) \setminus P_{f(5OQN_1)}(2)|=54\), \(|P_{f(5OQN_1)}(2) \setminus P_{f(5LTA_1)}(2)|=59\). 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 1:110010010110000101101000000010110100011100000011010000011111100101000011001100011000101110001001111011001100101011001100101000000001100100101100110000100000111001000011001111110010000001011110101010010001101111111100011011001010000101110011010100101011111010001001000101010011000011110101101011100000110011011011101100011100110001010111011011100001001000100111011001010001101100011001010000110001100001011000100011010011100110101101111001101100100110100010101110110011101111111100101000001101001101101110110100010010101101010010110100100110101001001000011000010010010101001100011011001100000000100111111110111000000010001000011110100010010011100011100000100100101011101111000100100101001100110010000110100110010100
Pair \(Z_2\) Length of longest common subsequence
5LTA_1,5OQN_1 113 5
5LTA_1,6JES_1 200 4
5OQN_1,6JES_1 209 3

Newick tree

 
[
	6JES_1:11.50,
	[
		5LTA_1:56.5,5OQN_1:56.5
	]:57.00
]

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 \((0.85)(0.8)(\frac{1585 }{\log_{20} 1585}-\frac{714}{\log_{20}714})=216.\)
Status Protein1 Protein2 d d1/2
Query variables 5LTA_1 5OQN_1 275 250.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]