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Parikh vectors
6LVE_1 7LBQ_1 7HIH_1 Letter Amino acid
24 4 2 Q Glutamine
37 5 6 I Isoleucine
54 11 8 L Leucine
25 16 12 K Lycine
57 7 9 D Aspartic acid
31 5 2 H Histidine
35 0 7 Y Tyrosine
30 5 8 N Asparagine
80 7 12 G Glycine
13 3 5 M Methionine
28 11 3 F Phenylalanine
50 5 11 S Serine
38 7 11 T Threonine
22 3 2 W Tryptophan
48 2 16 V Valine
65 13 17 A Alanine
45 6 9 R Arginine
8 6 4 C Cysteine
46 20 11 E Glutamic acid
39 10 8 P Proline 

6LVE_1|Chains A, C, E, G|N,N-dimethylformamidase large subunit|Paracoccus sp. SSG05 (1130061)
>7LBQ_1|Chain A|Baculoviral IAP repeat-containing protein 5|Homo sapiens (9606)
>7HIH_1|Chains A, B, C, D|Non-structural protein 3|Chikungunya virus (37124)
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 \(w=f(c)\)
6LVE , Knot 298 775 0.85 40 306 716 
MKDIAIRGYCDRPSVATGETIRFYVSANETRGTFDAELVRLIHGDSNPAGPGYKEEAIKSDLEGQYPARFQRTQFGSYVEVADPDAGLQPDGAFSVHLFLWSTTPSRGRQGIASRWNDERQSGWNLAIEDGRVVFTIGDGSGATSSVVSDRPLFQQIWYSITGVYDPEKKQLRLYQKSVVNRTNSRFGLVVPLDSDCAVSADATVKAADSETSLLIAGLGEAAAQDGRTWCIAHYNGKVDAPKIYGCALGQDDAEKLSRGEIVRPISRLAHWDFSAGIGLNGIPTDHVVDASGYGHHGRCMNQPSRGSTGWNWDGHEENFIHCPEQYGALWFHEDCLDDCRWEKDFEFTVPEGLKSDFYAVKIRYEDTEDYIPFFVLPPRGTATAPILVIASTLSYLAYANEQIMHKADIGQAVAGHTPVLNENDVELHKNLSYYGLSTYDGHIDGRGVQYTSWRRPIMNLRPKHRQGFGSIWELPADLHLIDWLNHNGFEYDVATEHDLNDQGAELLRRYKVVLTGSHPAYQTWANADAWEDYLADGGRGMYLAANGMYWIVEVHPEKPWVMEVRKELGVTAWEAPPGEYHYSTNGRRGGRFRGRARATQKIWGTGMSSFGFDHSGYFVQMPDSQDERVAWIMEGIDPEERIGDGGLVGGGAGGYELDRYDLALGTPPNTLLLASSVEHSVVYTVIPDDKAFPHPGMNGGEHPFVRADITYFSTANGGGMFATSSISWLGSLSWNDYDNNVSKMTKNVLNQFIKDEPAPRVKLAAALEHHHHHH
7LBQ , Knot 71 146 0.80 38 109 138 
GSHEMGAPTLPPAWQPFLKDHRISTFKNWPFLEGCACTPERMAEAGFIHCPTENEPDLAQCFFCFKELEGWEPDDDPIEEHKKHSSGCAFLSVKKQFEELTLGEFLKLDRERAKNKIAKETNNKKKEFEETAKKVRRAIEQLAAMD
7HIH , Knot 82 163 0.85 40 130 161 
GAMAPSYRVKRMDIAKNDEECVVNAANPRGLPGDGVCKAVYKKWPESFKNSATPVGTAKTVMCGTYPVIHAVGPNFSNYTESEGDRELAAAYREVAKEVTRLGVNSVAIPLLSTGVYSGGKDRLTQSLNHLFTAMDSTDADVVIYCRDKEWEKKISEAIQMRT

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 \(c\).

\(|P_{f(6LVE_1)}(2) \setminus P_{f(7LBQ_1)}(2)|=214\), \(|P_{f(7LBQ_1)}(2) \setminus P_{f(6LVE_1)}(2)|=17\). 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 1:1001110100001011010010101010000101010110110100011111000011000101001101000011001011010111010111010111100010010011100100000011011100101110110101100011000111001100101100100001010000110000001111111000011010101011000001111111011100100101100010101101010111000100100101101100110101011111011100011010101001001001001001101010000110010001111100001000010001010110110001011010000000011111111010101111111001001101000110010110111100111000010100010001100001010101100001001110101000011101101110101101100011000110000100011011000011101001100011010110001101101101110110111010100111101000111011011110000000100110101010100011101100111000101101100000011111011010001101111111111001000011110110011110010001100111000111011101100111010100100101111110001011101010000001001000110011000111010111110000000
Pair \(Z_2\) Length of longest common subsequence
6LVE_1,7LBQ_1 231 5
6LVE_1,7HIH_1 226 4
7LBQ_1,7HIH_1 161 3

Newick tree

 
[
	6LVE_1:12.47,
	[
		7HIH_1:80.5,7LBQ_1:80.5
	]:42.97
]

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 \((0.85)(0.8)(\frac{921 }{\log_{20} 921}-\frac{146}{\log_{20}146})=215.\)
Status Protein1 Protein2 d d1/2
Query variables 6LVE_1 7LBQ_1 276 162
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]