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Parikh vectors
3CRD_1 6BKP_1 4CRV_1 Letter Amino acid
5 17 12 D Aspartic acid
0 9 7 C Cysteine
11 10 18 E Glutamic acid
6 22 9 G Glycine
1 7 8 H Histidine
18 22 23 L Leucine
3 10 8 F Phenylalanine
6 23 14 T Threonine
2 12 6 Y Tyrosine
5 16 14 V Valine
7 16 29 A Alanine
2 24 8 N Asparagine
4 27 12 I Isoleucine
3 3 13 M Methionine
4 20 16 P Proline
6 12 20 Q Glutamine
6 18 11 K Lycine
3 32 11 S Serine
7 18 18 R Arginine
1 5 1 W Tryptophan 

3CRD_1|Chain A|RAIDD|Homo sapiens (9606)
>6BKP_1|Chain A|Hemagglutinin|Influenza A virus (1731408)
>4CRV_1|Chain A|CCR4-NOT TRANSCRIPTION COMPLEX SUBUNIT 1|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 \(w=f(c)\)
3CRD , Knot 53 100 0.81 38 80 98 
MEARDKQVLRSLRLELGAEVLVEGLVLQYLYQEGILTENHIQEINAQTTGLRKTMLLLDILPSRGPKAFDTFLDSLQEFPWVREKLKKAREEAMTDLPAG
6BKP , Knot 142 323 0.84 40 207 309 
ADPGATLCLGHHAVPNGTIVKTITNDRIEVTNATELVQNSSIGEICDSPHQILDGENCTLIDALLGDPQCDGFQNKKWDLFVERSKAYSNCYPYDVPDYASLRSLVASSGTLEFNNESFNWTGVTQNGTSSACIRRSSSSFFSRLNWLTHLNYKYPALNVTMPNNEQFDKLYIWGVHHPGTDKDQIFLYAQSSGRITVSTKRSQQAVIPNIGSRPKIRDIPSRISIYWTIVKPGDILLINSTGNLIAPRGYFKIRSGKSSIMRSDAPIGKCKSECITPNGSIPNDKPFQNVNRITYGACPRYVKHSTLKLATGMRNVPEKQTR
4CRV , Knot 119 258 0.85 40 175 251 
GPHMLEQYSYHDINVYSLAGLAPHITLNPTIPLFQAHPQLKQCVRQAIERAVQELVHPVVDRSIKIAMTTCEQIVRKDFALDSEESRMRIAAHHMMRNLTAGMAMITCREPLLMSISTNLKNSFASALRTASPQQREMMDQAAAQLAQDNCELACCFIQKTAVEKAGPEMDKRLATEFELRKHARQEGRRYCDPVVLTYQAERMPEQIRLKVGGVDPKQLAVYEEFARNVPGFLPTNDLSQPTGFLAQPMKQAWATDD

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 \(c\).

\(|P_{f(3CRD_1)}(2) \setminus P_{f(6BKP_1)}(2)|=34\), \(|P_{f(6BKP_1)}(2) \setminus P_{f(3CRD_1)}(2)|=161\). 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 1:1010000110010101110111011110010001110000100101000110001111011100110110011001001111000100100011001111
Pair \(Z_2\) Length of longest common subsequence
3CRD_1,6BKP_1 195 4
3CRD_1,4CRV_1 155 3
6BKP_1,4CRV_1 186 4

Newick tree

 
[
	6BKP_1:10.50,
	[
		3CRD_1:77.5,4CRV_1:77.5
	]:23.00
]

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 \((0.85)(0.8)(\frac{423 }{\log_{20} 423}-\frac{100}{\log_{20}100})=98.2\)
Status Protein1 Protein2 d d1/2
Query variables 3CRD_1 6BKP_1 125 81
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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