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Parikh vectors
8FBX_1 5IHL_1 5ACW_1 Letter Amino acid
21 11 6 Q Glutamine
5 8 6 K Lycine
6 0 2 M Methionine
54 5 29 A Alanine
17 11 14 D Aspartic acid
8 4 14 I Isoleucine
4 6 7 F Phenylalanine
10 17 16 T Threonine
11 15 16 E Glutamic acid
30 16 23 G Glycine
23 11 14 P Proline
25 14 24 S Serine
5 2 10 Y Tyrosine
6 20 1 C Cysteine
43 11 27 L Leucine
18 6 9 H Histidine
5 3 3 W Tryptophan
23 12 27 V Valine
30 8 11 R Arginine
7 3 7 N Asparagine 

8FBX_1|Chains A, B, C|Selenosugar synthase SenB|Variovorax paradoxus (34073)
>5IHL_1|Chains A, C[auth D], E[auth F], G[auth H]|Tumor necrosis factor receptor superfamily member 5|Homo sapiens (9606)
>5ACW_1|Chains A, B|BETA-LACTAMASE|PSEUDOMONAS AERUGINOSA (287)
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 \(w=f(c)\)
8FBX , Knot 145 351 0.80 40 180 317 
MGSSHHHHHHSSGLVPRGSHMSNPSLVIVSPALPGANNGNWRTAQRWKALLSPVCSARVVQQWPDADASADTVMLALHARRSAESIAHWAHAHPGRGLGVVLTGTDLYQDIGSDPQAQRSLQLAQRLVVLQALGAEALPPECRAKARVVYQSTSARAELPKSARQLRAVMVGHLRQVKSPQTLFDAARLLCGREDIRIDHIGDAGDAGLGELARALASDCPGYRWLGALPHAQTRQRIQRAHVLVHTSALEGGAHVIMEAVRSGTPVLASRVPGNVGMLGNDYAGYFPHGDAAALAALLEACRAGQGSKDRAAGLLDSLRTQCALRAPLFDPRAEQAALFQLLNELQPPPP
5IHL , Knot 86 183 0.81 38 127 174 
PTACREKQYLINSQCCSLCQPGQKLVSDCTEFTETECLPCGESEFLDTWNRETHCHQHKYCDPNLGLRVQQKGTSETDTICTCEEGWHCTSEACESCVLHRSCSPGFGVKQIATGVSDTICEPCPVGFFSDVSSAFEKCHPWTSCETKDLVVQQAGTDKTDVVCGPQDRLRDPGGGGGRLVPR
5ACW , Knot 117 266 0.81 40 161 257 
MFKLLSKLLVYLTASIMAIASPLAFSVDSSGEYPTVSEIPVGEVRLYQIADGVWSHIATQSFDGAVYPSNGLIVRDGDELLLIDTAWGAKNTAALLAEIEKQIGLPVTRAVSTHFHDDRVGGVDVLRAAGVATYASPSTRRLAEVEGNEIPTHSLEGLSSSGDAVRFGPVELFYPGAAHSTDNLVVYVPSASVLYGGCAIYELSRTSAGNVADADLAEWPTSIERIQQHYPEAQFVIPGHGLPGGLDLLKHTTNVVKAHTNRSVVE

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 \(c\).

\(|P_{f(8FBX_1)}(2) \setminus P_{f(5IHL_1)}(2)|=118\), \(|P_{f(5IHL_1)}(2) \setminus P_{f(8FBX_1)}(2)|=65\). 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 1:110000000000111101001001011110111111001010010010111011001011001101010100111110100010011011010110111111010010001100101000101100111101111011110001010110000010101100100101111101001001001101101101000101001101101111011011100011001111110100000100101110001101110111011001011110011101111100011011010111111110100110100001111100100001101111010100111101100101111
Pair \(Z_2\) Length of longest common subsequence
8FBX_1,5IHL_1 183 4
8FBX_1,5ACW_1 149 4
5IHL_1,5ACW_1 182 3

Newick tree

 
[
	5IHL_1:96.18,
	[
		8FBX_1:74.5,5ACW_1:74.5
	]:21.68
]

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 \((0.85)(0.8)(\frac{534 }{\log_{20} 534}-\frac{183}{\log_{20}183})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 8FBX_1 5IHL_1 126 96
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]