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Parikh vectors
8SWO_1 6ZCE_1 6FNZ_1 Letter Amino acid
0 8 2 Q Glutamine
3 26 5 G Glycine
0 22 8 L Leucine
0 11 3 P Proline
0 5 0 W Tryptophan
0 22 10 V Valine
0 23 7 D Aspartic acid
2 6 2 C Cysteine
0 16 5 F Phenylalanine
0 16 1 Y Tyrosine
3 20 4 A Alanine
2 14 1 N Asparagine
0 12 2 H Histidine
0 28 10 K Lycine
0 4 0 M Methionine
0 31 2 S Serine
0 8 4 R Arginine
0 26 3 E Glutamic acid
0 24 5 I Isoleucine
0 25 7 T Threonine 

8SWO_1|Chains A, B|RNA (5'-R(*(TLN)P*(LCC)P*(LCC)P*(LCG)P*AP*CP*UP*UP*AP*AP*GP*UP*CP*G*(GA3))-3')|synthetic construct (32630)
>6ZCE_1|Chain A[auth l]|Eukaryotic translation initiation factor 3 subunit I|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>6FNZ_1|Chains A, B, C, D|Neuronal migration protein doublecortin|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 \(w=f(c)\)
8SWO , Knot 9 14 0.56 10 13 12 
UNNGACUUAAGUCG
6ZCE , Knot 148 347 0.83 40 195 329 
MKAIKLTGHERPLTQVKYNKEGDLLFSCSKDSSASVWYSLNGERLGTLDGHTGTIWSIDVDCFTKYCVTGSADYSIKLWDVSNGQCVATWKSPVPVKRVEFSPCGNYFLAILDNVMKNPGSINIYEIERDSATHELTKVSEEPIHKIITHEGLDAATVAGWSTKGKYIIAGHKDGKISKYDVSNNYEYVDSIDLHEKSISDMQFSPDLTYFITSSRDTNSFLVDVSTLQVLKKYETDCPLNTAVITPLKEFIILGGGQEAKDVTTTSANEGKFEARFYHKIFEEEIGRVQGHFGPLNTVAISPQGTSYASGGEDGFIRLHHFEKSYFDFKYDVEKAAEAKEHMQEAN
6FNZ , Knot 44 81 0.79 36 69 79 
KDFVRPKLVTIIRSGVKPRKAVRVLLNKKTAHSFEQVLTDITEAIKLETGVVKKLYTLDGKQVTCLHDFFGDDDVFIACGP

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 \(c\).

\(|P_{f(8SWO_1)}(2) \setminus P_{f(6ZCE_1)}(2)|=8\), \(|P_{f(6ZCE_1)}(2) \setminus P_{f(8SWO_1)}(2)|=190\). 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 1:00011000111001
Pair \(Z_2\) Length of longest common subsequence
8SWO_1,6ZCE_1 198 2
8SWO_1,6FNZ_1 78 2
6ZCE_1,6FNZ_1 178 4

Newick tree

 
[
	6ZCE_1:10.33,
	[
		8SWO_1:39,6FNZ_1:39
	]:67.33
]

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 \((0.85)(0.8)(\frac{361 }{\log_{20} 361}-\frac{14}{\log_{20}14})=114.\)
Status Protein1 Protein2 d d1/2
Query variables 8SWO_1 6ZCE_1 145 76
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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