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Parikh vectors
1YWG_1 1LDZ_1 8IGU_1 Letter Amino acid
19 0 53 I Isoleucine
6 0 24 M Methionine
8 0 16 Y Tyrosine
11 0 31 R Arginine
15 0 57 E Glutamic acid
9 0 4 H Histidine
26 0 24 K Lycine
14 0 24 P Proline
21 0 35 D Aspartic acid
8 8 3 C Cysteine
14 0 17 F Phenylalanine
19 0 46 S Serine
16 0 34 T Threonine
4 0 8 W Tryptophan
35 0 47 V Valine
8 0 30 Q Glutamine
30 0 39 L Leucine
29 12 53 G Glycine
28 7 34 A Alanine
17 0 17 N Asparagine 

1YWG_1|Chains A[auth O], B[auth P], C[auth Q], D[auth R]|glyceraldehyde-3-phosphate dehydrogenase|Plasmodium falciparum (5833)
>1LDZ_1|Chain A|LEAD-DEPENDENT RIBOZYME|null
>8IGU_1|Chains A, B, C|V-type sodium ATPase catalytic subunit A|Enterococcus hirae ATCC 9790 (768486)
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 \(w=f(c)\)
1YWG , Knot 146 337 0.84 40 195 322 
MAVTKLGINGFGRIGRLVFRAAFGRKDIEVVAINDPFMDLNHLCYLLKYDSVHGQFPCEVTHADGFLLIGEKKVSVFAEKDPSQIPWGKCQVDVVCESTGVFLTKELASSHLKGGAKKVIMSAPPKDDTPIYVMGINHHQYDTKQLIVSNASCTTNCLAPLAKVINDRFGIVEGLMTTVHASTANQLVVDGPSKGGKDWRAGRCALSNIIPASTGAAKAVGKVLPELNGKLTGVAFRVPIGTVSVVDLVCRLQKPAKYEEVALEIKKAAEGPLKGILGYTEDEVVSQDFVHDNRSSIFDMKAGLALNDNFFKLVSWYDNEWGYSNRVLDLAVHITNN
1LDZ , Knot 12 30 0.45 8 13 22 
GCGACCGAGCCAGCGAAAGUUGGGAGUCGC
8IGU , Knot 233 596 0.83 40 255 559 
SSGMQIGKIIKVSGPLVMAENMSEASIQDMCLVGDLGVIGEIIEMRQDVASIQVYEETSGIGPGEPVRSTGEALSVELGPGIISQMFDGIQRPLDTFMEVTQSNFLGRGVQLPALDHEKQWWFEATIEEGTEVSAGDIIGYVDETKIIQHKIMVPNGIKGTVQKIESGSFTIDDPICVIETEQGLKELTMMQKWPVRRGRPIKQKLNPDVPMITGQRVIDTFFPVTKGGAAAVPGPFGAGKTVVQHQIAKWSDVDLVVYVGCGERGNEMTDVVNEFPELIDPNTGESLMERTVLIANTSNMPVAAREASIYTGITIAEYFRDMGYDVAIMADSTSRWAEALREMSGRLEEMPGDEGYPAYLGSRLAEYYERSGRVIALGSDQREGSITAISAVSPSGGDISEPVTQNTLRVVKVFWGLDSSLAQKRHFPSINWIQSYSLYSTEVGRYMDQILQQDWSDMVTEGMRILQEEEQLNEIVRLVGIDSLSDNDRLTLEVAKSIREDYLQQNAFDDVDTFTSREKQFNMLKVILTFGKEARKALSLGAYFNEIMEGTVAVRERISRSKYIPEEELAKISSINEEIKETIQLIVSEGGMTDD

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 \(c\).

\(|P_{f(1YWG_1)}(2) \setminus P_{f(1LDZ_1)}(2)|=190\), \(|P_{f(1LDZ_1)}(2) \setminus P_{f(1YWG_1)}(2)|=8\). 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 1:1110011101110110111011110001011110011101001001100001010110010010111111000101110001001111000101100001111000110001011100111011100001101111000000000111001000000111110110001111011100101001001110110011001011001100111100111011101110101010111101111010110110010011000011101001101110111100000110001100000011010111110001101101000011000011011101000
Pair \(Z_2\) Length of longest common subsequence
1YWG_1,1LDZ_1 198 3
1YWG_1,8IGU_1 164 5
1LDZ_1,8IGU_1 256 4

Newick tree

 
[
	1LDZ_1:12.35,
	[
		1YWG_1:82,8IGU_1:82
	]:41.35
]

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 \((0.85)(0.8)(\frac{367 }{\log_{20} 367}-\frac{30}{\log_{20}30})=108.\)
Status Protein1 Protein2 d d1/2
Query variables 1YWG_1 1LDZ_1 142 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]