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Parikh vectors
6VLB_1 5TBC_1 4RAS_1 Letter Amino acid
27 21 29 S Serine
26 18 41 V Valine
21 18 87 A Alanine
14 21 52 D Aspartic acid
17 15 17 H Histidine
15 23 65 G Glycine
41 26 55 L Leucine
11 19 63 R Arginine
2 3 14 C Cysteine
30 27 46 E Glutamic acid
11 12 19 Y Tyrosine
15 13 18 Q Glutamine
35 23 29 I Isoleucine
12 14 21 F Phenylalanine
21 14 45 P Proline
27 19 24 T Threonine
2 1 9 W Tryptophan
20 12 17 N Asparagine
25 36 27 K Lycine
8 8 26 M Methionine 

6VLB_1|Chains A, B|UDP-N-acetylglucosamine 2-epimerase|Neisseria meningitidis serogroup A / serotype 4A (strain Z2491) (122587)
>5TBC_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>4RAS_1|Chains A, B, C|Oxidoreductase, NAD-binding/iron-sulfur cluster-binding protein|Nitratireductor pacificus pht-3B (391937)
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 \(w=f(c)\)
6VLB , Knot 158 380 0.82 40 208 356 
MKVLTVFGTRPEAIKMAPVILELQKHNTITSKVCITAQHREMLDQVLSLFEIKADYDLNIMKPNQSLQEITTNIISSLTDVLEDFKPDCVLVHGDTTTTFAASLAAFYQKIPVGHIEAGLRTYNLYSPWPEEANRRLTSVLSQWHFAPTEDSKNNLLSESIPSDKVIVTGNTVIDALMVSLEKLKITTIKKQMEQAFPFIQDNSKVILITAHRRENHGEGIKNIGLSILELAKKYPTFSFVIPLHLNPNVRKPIQDLLSSVHNVHLIEPQEYLPFVYLMSKSHIILSDSGGIQEEAPSLGKPVLVLRDTTERPEAVAAGTVKLVGSETQNIIESFTQLIEYPEYYEKMANIENPYGIGNASKIIVETLLKNRLEHHHHHH
5TBC , Knot 148 343 0.84 40 201 326 
MGMSKRKAPQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEKGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSEHHHHHH
4RAS , Knot 268 704 0.83 40 276 628 
MRLYSNRDRPNHLGPLALERLARVDDVVAQPARQPEDGFAASEDSLLGDVEEYARLFTRFLDGPVAPLGDAIPDDPARRAENLKASAYFLDASMVGICRLDPDDRAGDCDPSHTHALVFAVQFGREPEAGEAGAEWIRGTNAARTDMRCAEIAAILSGYVRWMGFPARGHFSGDAQVDLARLAVRAGLARVVDGVLVAPFLRRGFRLGVVTTGYALAADRPLAPEGDLGETAPEVMLGIDGTRPGWEDAEEEKRPLHMGRYPMETIRRVDEPTTLVVRQEIQRVAKRGDFFKRAEAGDLGEKAKQEKKRFPMKHPLALGMQPLIQNMVPLQGTREKLAPTGKGGDLSDPGRNAEAIKALGYYLGADFVGICRAEPWMYYASDEVEGKPIEAYHDYAVVMLIDQGYETMEGASGDDWISASQSMRAYMRGAEIAGVMAAHCRRMGYSARSHSNAHSEVIHNPAILMAGLGEVSRIGDTLLNPFIGPRSKSIVFTTDLPMSVDRPIDFGLQDFCNQCRKCARECPCNAISFGDKVMFNGYEIWKADVEKCTKYRVTQMKGSACGRCMKMCPWNREDTVEGRRLAELSIKVPEARAAIIAMDDALQNGKRNLIKRWWFDLEVIDGVAGAPRMGTNERDLSPDRGDKIGANQKLAMYPPRLQPPPGTTLDAVLPVDRSGGLAEYAAAETPAAARARLKSSAGHHHHHH

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 \(c\).

\(|P_{f(6VLB_1)}(2) \setminus P_{f(5TBC_1)}(2)|=80\), \(|P_{f(5TBC_1)}(2) \setminus P_{f(6VLB_1)}(2)|=73\). 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 1:10110111001011011111101000001000101010000110011011010100010110100010010001100100110010100111010000011101111000111101011100001001110010001001100101110000000110001100011101001101111010010100100010011111000001111010000001011001110110110001010111110101010011001100100101101000111101100001110001110001101101111100000010111110101110000011001001100100000110100101110100111001100010000000
Pair \(Z_2\) Length of longest common subsequence
6VLB_1,5TBC_1 153 7
6VLB_1,4RAS_1 154 6
5TBC_1,4RAS_1 161 6

Newick tree

 
[
	4RAS_1:79.51,
	[
		6VLB_1:76.5,5TBC_1:76.5
	]:3.01
]

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 \((0.85)(0.8)(\frac{723 }{\log_{20} 723}-\frac{343}{\log_{20}343})=104.\)
Status Protein1 Protein2 d d1/2
Query variables 6VLB_1 5TBC_1 130 124.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]