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Parikh vectors
6YIM_1 2UWO_1 3ATN_1 Letter Amino acid
7 15 11 R Arginine
9 9 3 Q Glutamine
10 9 2 P Proline
6 14 10 S Serine
3 4 6 W Tryptophan
4 7 14 N Asparagine
1 9 8 C Cysteine
0 6 1 H Histidine
5 14 6 I Isoleucine
8 20 2 E Glutamic acid
3 23 12 G Glycine
13 15 8 L Leucine
9 20 6 K Lycine
4 15 12 A Alanine
9 11 7 D Aspartic acid
5 5 2 M Methionine
6 12 3 F Phenylalanine
4 21 7 T Threonine
6 8 3 Y Tyrosine
7 17 6 V Valine 

6YIM_1|Chain A|CREBBP|Homo sapiens (9606)
>2UWO_1|Chain A|COAGULATION FACTOR X|HOMO SAPIENS (9606)
>3ATN_1|Chain A|Lysozyme C|Gallus gallus (9031)
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 \(w=f(c)\)
6YIM , Knot 59 119 0.79 38 100 117 
SMRKKIFKPEELRQALMPTLEALYRQDPESLPFRQPVDPQLLGIPDYFDIVKNPMDLSTIKRKLDTGQYQEPWQYVDDVWLMFNNAWLYNRKTSRVYKFCSKLAEVFEQEIDPVMQSLG
2UWO , Knot 116 254 0.84 40 181 246 
IVGGQECKDGECPWQALLINEENEGFCGGTILSEFYILTAAHCLYQAKRFKVRVGDRNTEQEEGGEAVHEVEVVIKHNRFTKETYDFDIAVLRLKTPITFRMNVAPACLPERDWAESTLMTQKTGIVSGFGRTHEKGRQSTRLKMLEVPYVDRNSCKLSSSFIITQNMFCAGYDTKQEDACQGDSGGPHVTRFKDTYFVTGIVSWGEGCARKGKYGIYTKVTAFLKWIDRSMKTRGLPKAKSHAPEVITSSPLK
3ATN , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(6YIM_1)}(2) \setminus P_{f(2UWO_1)}(2)|=51\), \(|P_{f(2UWO_1)}(2) \setminus P_{f(6YIM_1)}(2)|=132\). 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 1:01000110100100111101011000010011100110101111100101100110100100010010000110010011111001110000000100100011011000101110011
Pair \(Z_2\) Length of longest common subsequence
6YIM_1,2UWO_1 183 3
6YIM_1,3ATN_1 144 3
2UWO_1,3ATN_1 199 3

Newick tree

 
[
	2UWO_1:10.24,
	[
		6YIM_1:72,3ATN_1:72
	]:30.24
]

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 \((0.85)(0.8)(\frac{373 }{\log_{20} 373}-\frac{119}{\log_{20}119})=77.5\)
Status Protein1 Protein2 d d1/2
Query variables 6YIM_1 2UWO_1 99 72
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]