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Parikh vectors
5UYJ_1 3NBY_1 8ACF_1 Letter Amino acid
11 14 9 N Asparagine
18 23 26 G Glycine
23 28 4 K Lycine
22 21 19 P Proline
10 17 10 T Threonine
28 41 11 L Leucine
14 15 10 A Alanine
13 16 13 R Arginine
19 22 6 D Aspartic acid
4 8 12 C Cysteine
13 13 7 Q Glutamine
19 27 8 E Glutamic acid
20 8 5 I Isoleucine
9 10 1 M Methionine
12 10 7 F Phenylalanine
2 6 4 W Tryptophan
14 31 22 S Serine
21 20 13 V Valine
8 14 3 H Histidine
11 17 7 Y Tyrosine 

5UYJ_1|Chain A|Calcium/calmodulin-dependent protein kinase kinase 2|Homo sapiens (9606)
>3NBY_1|Chains A[auth B], D[auth E]|Snurportin-1|Homo sapiens (9606)
>8ACF_1|Chain A|Complement C2b fragment|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 \(w=f(c)\)
5UYJ , Knot 129 291 0.83 40 189 279 
SMQLNQYTLKDEIGKGSYGVVKLAYNENDNTYYAMKVLSKKKLIRQAGFPRRPPPRGTRPAPGGCIQPRGPIEQVYQEIAILKKLDHPNVVKLVEVLDDPNEDHLYMVFELVNQGPVMEVPTLKPLSEDQARFYFQDLIKGIEYLHYQKIIHRDIKPSNLLVGEDGHIKIADFGVSNEFKGSDALLSNTVGTPAFMAPESLSETRKIFSGKALDVWAMGVTLYCFVFGQCPFMDERIMCLHSKIKSQALEFPDQPDIAEDLKDLITRMLDKNPESRIVVPEIKLHPWVTRH
3NBY , Knot 156 361 0.84 40 208 348 
GSLNELALKLAGLDISQDLNSTAAPHPRLSQYKSKYSSLEQSERRRRLLELQKSKRLDYVNHARRLAEDDWTGMESEEENKKDDEEMDIDTVKKLPKHYANQLMLSEWLIDVPSDLGQEWIVVVCPVGKRALIVASRGSTSAYTKSGYCVNRFSSLLPGGNRRNSTAKDYTILDCIYNEVNQTYYVLDVMCWRGHPFYDCQTDFRFYWMHSKLPEEEGLGEKTKLNPFKFVGLKNFPCTPESLCDVLSMDFPFEVDGLLFYHKQTHYSPGSTPLVGWLRPYMVSDVLGVAVPAGPLTTKPDYAGHQLQQIMEHKKSQKEGMKEKLTHKASENGHYELEHLSTPKLKGSSHSPDHPGCLMEN
8ACF , Knot 90 197 0.80 40 131 189 
APSCPQNVNISGGTFTLSHGWAPGSLLTYSCPQGLYPSPASRLCKSSGQWQTPGATRSLSKAVCKPVRCPAPVSFENGIYTPRLGSYPVGGNVSFECEDGFILRGSPVRQCRPNGMWDGETAVCDNGAGHCPNPGISLGAVRTGFRFGHGDKVRYRCSSNLVLTGSSERECQGNGVWSGTEPICRQPYSYDFPEDVA

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 \(c\).

\(|P_{f(5UYJ_1)}(2) \setminus P_{f(3NBY_1)}(2)|=74\), \(|P_{f(3NBY_1)}(2) \setminus P_{f(5UYJ_1)}(2)|=93\). 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 1:010100001000110100111011000000000110110000110011110011101001111101010111001000111100100101101101100100001011101100111101101011000010101001101100100001100010100111100101011011100010100111000110111111001000001101011011111101001111001110001101000100011011001011001001100110001000111101010111000
Pair \(Z_2\) Length of longest common subsequence
5UYJ_1,3NBY_1 167 4
5UYJ_1,8ACF_1 182 3
3NBY_1,8ACF_1 191 3

Newick tree

 
[
	8ACF_1:96.31,
	[
		5UYJ_1:83.5,3NBY_1:83.5
	]:12.81
]

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 \((0.85)(0.8)(\frac{652 }{\log_{20} 652}-\frac{291}{\log_{20}291})=100.\)
Status Protein1 Protein2 d d1/2
Query variables 5UYJ_1 3NBY_1 124 112
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]