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Parikh vectors
7RBH_1 3EVY_1 8ORG_1 Letter Amino acid
12 10 11 N Asparagine
13 7 17 Q Glutamine
19 7 31 T Threonine
12 11 5 Y Tyrosine
18 15 29 A Alanine
21 20 27 D Aspartic acid
23 17 14 I Isoleucine
7 8 6 M Methionine
14 7 39 P Proline
21 19 45 S Serine
22 6 46 G Glycine
36 16 43 K Lycine
14 10 3 F Phenylalanine
1 0 0 W Tryptophan
19 11 14 R Arginine
3 0 2 C Cysteine
27 28 24 E Glutamic acid
15 9 11 H Histidine
26 27 20 L Leucine
18 11 25 V Valine 

7RBH_1|Chain A|DNA polymerase beta|Homo sapiens (9606)
>3EVY_1|Chains A, B|Putative type I restriction enzyme R protein|Bacteroides fragilis NCTC 9343 (272559)
>8ORG_1|Chains A, B, C|Microtubule-associated protein tau|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 \(w=f(c)\)
7RBH , Knot 147 341 0.83 40 200 324 
MSKRKAPQETLNGGITDMLTELANFEKNVSQAIHKYNAYRKAASVIAKYPHKIKSGAEAKKLPGVGTKIAEKIDEFLATGKLRKLEKIRQDDTSSSINFLTRVSGIGPSAARKFVDEGIKTLEDLRKNEDKLNHHQRIGLKYFGDFEKRIPREEMLQMQDIVLNEVKKVDSEYIATVCGSFRRGAESSGDMDVLLTHPSFTSESTKQPKLLHQVVEQLQKVHFITDTLSKGETKFMGVCQLPSKNDEKEYPHRRIDIRLIPKDQYYCGVLYFTGSDIFNKNMRAHALEKGFTINEYTIRPLGVTGVAGEPLPVDSEKDIFDYIQWKYREPKDRSEHHHHHH
3EVY , Knot 107 239 0.81 36 152 230 
MSLSSEVVLMKPYEKLVERFNEMAAEFLSYFPTVKSVGNLESELDKRRFVILFRAMLRLRNEVKGYNEFDAEDLTIEEQRFADYQSKYLDMSNEFAITSEKEDAESILQDIDFELELVHRDIINVMYILALLQDLKPESSSYPKDRKAVLDTMDSNPELRSKIALIDNFIKLHIDGRQSNDLPADMESDLDKYIATQKAIAIEQVATEEGIDSTLLHEYISEYEYLGKPKNEGHHHHHH
8ORG , Knot 159 412 0.77 38 183 356 
MAEPRQEFEVMEDHAGTYGLGDRKDQGGYTMHQDQEGDTDAGLKESPLQTPTEDGSEEPGSETSDAKSTPTAEAEEAGIGDTPSLEDEAAGHVTQARMVSKSKDGTGSDDKKAKGADGKTKIATPRGAAPPGQKGQANATRIPAKTPPAPKTPPSSGEPPKSGDRSGYSSPGSPGTPGSRSRTPSLPTPPTREPKKVAVVRTPPKSPSSAKSRLQTAPVPMPDLKNVKSKIGSTENLKHQPGGGKVQIINKKLDLSNVQSKCGSKDNIKHVPGGGSVQIVYKPVDLSKVTSKCGSLGNIHHKPGGGQVEVKSEKLDFKDRVQSKIGSLDNITHVPGGGNKKIETHKLTFRENAKAKTDHGAEIVYKSPVVSGDTSPRHLSNVSSTGSIDMVDSPQLATLADEVSASLAKQGL

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 \(c\).

\(|P_{f(7RBH_1)}(2) \setminus P_{f(3EVY_1)}(2)|=95\), \(|P_{f(3EVY_1)}(2) \setminus P_{f(7RBH_1)}(2)|=47\). 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 1:10000110001011100110011010001001100001000110111001001001101001111100110010011101010010010000000010110010111101100110011001001000000100000111001101000110001101001110010010000110101010011000101011100101000000010110011001001011000100100011110011000000001000101011100000011101010011000101011001101000010111101111011110000011001010000100000000000
Pair \(Z_2\) Length of longest common subsequence
7RBH_1,3EVY_1 142 6
7RBH_1,8ORG_1 135 4
3EVY_1,8ORG_1 157 3

Newick tree

 
[
	3EVY_1:77.13,
	[
		7RBH_1:67.5,8ORG_1:67.5
	]:9.63
]

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 \((0.85)(0.8)(\frac{580 }{\log_{20} 580}-\frac{239}{\log_{20}239})=96.7\)
Status Protein1 Protein2 d d1/2
Query variables 7RBH_1 3EVY_1 120 101
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]