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Parikh vectors
6BCF_1 4WWB_1 8UCZ_1 Letter Amino acid
31 5 4 I Isoleucine
14 3 3 F Phenylalanine
8 5 8 P Proline
16 6 2 V Valine
10 4 1 Q Glutamine
6 6 7 H Histidine
18 6 8 G Glycine
10 0 1 Y Tyrosine
21 4 2 N Asparagine
3 0 0 C Cysteine
3 1 3 M Methionine
21 3 6 S Serine
21 3 6 T Threonine
17 14 6 R Arginine
32 12 12 L Leucine
21 15 4 E Glutamic acid
27 4 9 K Lycine
4 1 0 W Tryptophan
15 19 3 A Alanine
17 7 5 D Aspartic acid 

6BCF_1|Chains A, D, G, J|Ribosomal protein 3/homing endonuclease-like fusion protein|Leptographium truncatum (330483)
>4WWB_1|Chain A|Nickel and cobalt resistance protein CnrR|Ralstonia metallidurans (266264)
>8UCZ_1|Chains A, B, C|Chloroplastic import inner membrane translocase subunit HP30-1|Arabidopsis thaliana (3702)
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 \(w=f(c)\)
6BCF , Knot 137 315 0.83 40 188 298 
SYSTLANFPVQARNDNISPWTITGFADAESSFMLTVSKDSKRNTGWSVRPRFRIGLHNKDVTILKSIREYLGAGIITSDIDARIRFESLKELEVVINHFDKYPLITQKRADYLLFKKAFYLIKNKEHLTEEGLNQILTLKASLNLGLSEELKEAFPNTIPAERLLVTGQEIPDSNWVAGFTAAEGSFYIRIAKNSTLKTGYQVQSVFQITQDTRDIELMKNLISYLNCGNIRIRKYKGSEGIHDTCVDLVVTNLNDIKEKIIPFFNKNHIIGVKLQDYRDWCKVVTLIDNKEHLTSEGLEKIQKIKEGMNRGRSL
4WWB , Knot 57 118 0.76 36 82 110 
SHRNEAGHGDLHEILHEAVPLDANEREILELKEDAFAQRRREIETRLRAANGKLADAIAKNPAWSPEVEAATQEVERAAGDLQRATLVHVFEMRAGLKPEHRPAFDRVLIDALRRGSQ
8UCZ , Knot 45 90 0.75 36 71 83 
MGSSHHHHHHSSGLVPRGSTEDPFFTRGRTMLVKLGLEKYEKNFKKGLLTDPTLPLLTDSALKAANIPPGPRLMILDHIQRDPEIKGKRK

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 \(c\).

\(|P_{f(6BCF_1)}(2) \setminus P_{f(4WWB_1)}(2)|=140\), \(|P_{f(4WWB_1)}(2) \setminus P_{f(6BCF_1)}(2)|=34\). 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 1:000011011101000010110101110100011101000000001101010101110000101100100011111100010101010010010111001000111000010011100110110000010001100110101010111000100111001110011101001100011111011010101011000010010010011010000001011001100100101010000100110000101110010010001111100001111010000010011011000001000110010010011001001
Pair \(Z_2\) Length of longest common subsequence
6BCF_1,4WWB_1 174 4
6BCF_1,8UCZ_1 167 4
4WWB_1,8UCZ_1 105 3

Newick tree

 
[
	6BCF_1:93.67,
	[
		8UCZ_1:52.5,4WWB_1:52.5
	]:41.17
]

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 \((0.85)(0.8)(\frac{433 }{\log_{20} 433}-\frac{118}{\log_{20}118})=94.9\)
Status Protein1 Protein2 d d1/2
Query variables 6BCF_1 4WWB_1 121 82
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]