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Parikh vectors
8IQN_1 5EVB_1 6MOE_1 Letter Amino acid
36 27 23 L Leucine
10 6 4 M Methionine
12 19 8 T Threonine
8 8 3 Y Tyrosine
8 2 0 C Cysteine
12 10 12 H Histidine
15 16 3 R Arginine
18 19 3 P Proline
18 9 10 I Isoleucine
10 5 2 F Phenylalanine
24 20 15 D Aspartic acid
14 10 3 Q Glutamine
18 8 10 E Glutamic acid
12 25 14 G Glycine
14 8 8 K Lycine
41 10 3 S Serine
12 43 25 A Alanine
8 6 9 N Asparagine
1 5 1 W Tryptophan
15 15 12 V Valine 

8IQN_1|Chain A|Vitamin D3 receptor|Homo sapiens (9606)
>5EVB_1|Chain A|Metallo-beta-lactamase L1|Stenotrophomonas maltophilia (40324)
>6MOE_1|Chains A, B|E2 DARPin|synthetic construct (32630)
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 \(w=f(c)\)
8IQN , Knot 132 306 0.82 40 184 287 
DSLRPKLSEEQQRIIAILLDAHHKTYDPTYSDFCQFRPPVRVNDGGGSHPSRPNSRHTPSFSGDSSSSCSDHCITSSDMMDSSSFSNLDLSEEDSDDPSVTLELSQLSMLPHLADLVSYSIQKVIGFAKMIPGFRDLTSEDQIVLLKSSAIEVIMLRSNESFTMDDMSWTCGNQDYKYRVSDVTKAGHSLELIEPLIKFQVGLKKLNLHEEEHVLLMAICIVSPDRPGVQDAALIEAIQDRLSNTLQTYIRCRHPPPGSHLLYAKMIQKLADLRSLNEEHSKQYRCLSFQPECSMKLTPLVLEVFG
5EVB , Knot 113 271 0.77 40 158 256 
GPAEVPLPQLRAYTVDASWLQPMAPLQIADHTWQIGTEDLTALLVQTPDGAVLLDGGMPQMASHLLDNMKARGVTPRDLRLILLSHAHADHAGPVAELKRRTGAKVAANAESAVLLARGGSDDLHFGDGITYPPANADRIVMDGEVITVGGIVFTAHFMAGHTPGSTAWTWTDTRNGKPVRIAYADSLSAPGYQLQGNPRYPHLIEDYRRSFATVRALPCDVLLTPHPGASNWDYAAGARAGAKALTCKAYADAAEQKFDGQLAKETAGAR
6MOE , Knot 59 168 0.60 38 86 116 
MGSDLGKKLLKAARAGQDDEVRILMANGADVNATDIWDATPLHLAALIGHLEIVEVLLKNGADVNASDITGTTPLHLAATMGHLEIVEVLLKYGADVNAYDLNGATPLHLAARMGHVEIVEVLLKYGADVNAQDKFGKTAFDISIDNGNEDLAEILQAAALEHHHHHH

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 \(c\).

\(|P_{f(8IQN_1)}(2) \setminus P_{f(5EVB_1)}(2)|=93\), \(|P_{f(5EVB_1)}(2) \setminus P_{f(8IQN_1)}(2)|=67\). 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 1:001010100000011111101000000100001001011101001110010010000010101000000000010000110000100101000000010101010010111011011000100111110111110010000011110001101111000001010010100100000001001001100101101110101110010100000111111011010011100111101100010001000100001111001101011001101001000000000010101000101011110111
Pair \(Z_2\) Length of longest common subsequence
8IQN_1,5EVB_1 160 4
8IQN_1,6MOE_1 170 4
5EVB_1,6MOE_1 138 4

Newick tree

 
[
	8IQN_1:86.58,
	[
		5EVB_1:69,6MOE_1:69
	]:17.58
]

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 \((0.85)(0.8)(\frac{577 }{\log_{20} 577}-\frac{271}{\log_{20}271})=86.3\)
Status Protein1 Protein2 d d1/2
Query variables 8IQN_1 5EVB_1 109 101
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]