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Parikh vectors
8XPT_1 7CFO_1 7HAU_1 Letter Amino acid
5 2 1 W Tryptophan
19 4 0 C Cysteine
11 6 9 Q Glutamine
16 20 26 E Glutamic acid
19 33 19 L Leucine
5 10 17 T Threonine
15 12 20 I Isoleucine
7 13 17 K Lycine
16 9 8 N Asparagine
6 9 10 H Histidine
7 8 7 M Methionine
13 10 10 F Phenylalanine
24 17 16 S Serine
11 4 7 Y Tyrosine
19 14 11 V Valine
13 22 15 A Alanine
26 12 8 R Arginine
21 12 16 D Aspartic acid
15 12 15 G Glycine
17 14 5 P Proline 

8XPT_1|Chains A, B, C, D|Histone-lysine N-methyltransferase EHMT1|Homo sapiens (9606)
>7CFO_1|Chains A, B, C, D|Retinoic acid receptor RXR-alpha|Homo sapiens (9606)
>7HAU_1|Chain A|Heat shock protein HSP 90-alpha|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 \(w=f(c)\)
8XPT , Knot 124 285 0.82 40 196 276 
NSQVWSALQMSKALQDSAPDRPSPVERIVSRDIARGYERIPIPCVNAVDSEPCPSNYKYVSQNCVTSPMNIDRNITHLQYCVCIDDCSSSNCMCGQLSMRCWYDKDGRLLPEFNMAEPPLIFECNHACSCWRNCRNRVVQNGLRARLQLYRTRDMGWGVRSLQDIPPGTFVCEYVGELISDSEADVREEDSYLFDLDNKDGEVYCIDARFYGNVSRFINHHCEPNLVPVRVFMAHQDLRFPRIAFFSTRLIEAGEQLGFDYGERFWDIKGKLFSCRCGSPKCRHS
7CFO , Knot 112 243 0.84 40 168 231 
GSSHSSANEDMPVERILEAELAVEPKTETYVEANMGLNPSSPNDPVTNICQAADKQLFTLVEWAKRIPHFSELPLDDQVILLRAGWNELLIASFSHRSIAVKDGILLATGLHVHRNSAHSAGVGAIFDRVLTELVSKMRDMQMDKTELGCLRAIVLFNPDSKGLSNPAEVEALREKVYASLEAYCKHKYPEQPGRFAKLLLRLPALRSIGLKCLEHLFFFKLIGDTPIDTFLMEMLEAPHQMT
7HAU , Knot 105 237 0.80 38 157 225 
MDQPMEEEEVETFAFQAEIAQLMSLIINTFYSNKEIFLRELISNSSDALDKIRYESLTDPSKLDSGKELHINLIPNKQDRTLTIVDTGIGMTKADLINNLGTIAKSGTKAFMEALQAGADISMIGQFGVGFYSAYLVAEKVTVITKHNDDEQYAWESSAGGSFTVRTDTGEPMGRGTKVILHLKEDQTEYLEERRIKEIVKKHSQFIGYPITLFVEKERDKEVSDDEAELEHHHHHH

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 \(c\).

\(|P_{f(8XPT_1)}(2) \setminus P_{f(7CFO_1)}(2)|=104\), \(|P_{f(7CFO_1)}(2) \setminus P_{f(8XPT_1)}(2)|=76\). 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 1:000110110100110001100101100110001101000111101011000101000001000010011010001001000101000000001010101001000010111010110111110000100010000001100110101010000011111001001111011000110110000101000000110100001010010101010100110000010111101111000101101111000110110011100100110101011000010100000
Pair \(Z_2\) Length of longest common subsequence
8XPT_1,7CFO_1 180 5
8XPT_1,7HAU_1 177 4
7CFO_1,7HAU_1 151 4

Newick tree

 
[
	8XPT_1:93.38,
	[
		7HAU_1:75.5,7CFO_1:75.5
	]:17.88
]

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 \((0.85)(0.8)(\frac{528 }{\log_{20} 528}-\frac{243}{\log_{20}243})=81.4\)
Status Protein1 Protein2 d d1/2
Query variables 8XPT_1 7CFO_1 106 97
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]