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Parikh vectors
3SNF_1 6FVT_1 4CGX_1 Letter Amino acid
6 14 9 I Isoleucine
6 12 3 F Phenylalanine
10 10 10 T Threonine
8 4 6 C Cysteine
1 4 4 M Methionine
3 8 6 Y Tyrosine
3 14 15 E Glutamic acid
3 18 10 G Glycine
3 2 7 H Histidine
12 13 8 K Lycine
4 7 5 P Proline
1 1 6 W Tryptophan
3 14 9 A Alanine
8 7 5 N Asparagine
6 13 13 D Aspartic acid
3 5 8 Q Glutamine
5 19 14 L Leucine
8 16 14 S Serine
8 15 15 V Valine
3 8 10 R Arginine 

3SNF_1|Chain A|Protein P-30|Rana pipiens (8404)
>6FVT_10|Chains J[auth 3], X[auth j]|Proteasome subunit beta type-3|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
>4CGX_1|Chains A, B|POLYMERASE ACIDIC PROTEIN|THOGOTO VIRUS (11569)
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 \(w=f(c)\)
3SNF , Knot 52 104 0.77 40 85 100 
QDWLTFQKKHITNTRDVDCDNIMSTNLFHCKDKNTFIYSRPEPVKAICKGIIASKNVLTTSEFYLSDCNVTSRPCKYKLKKSTNKFCVTCENQAPVHFVGVGSC
6FVT , Knot 96 204 0.83 40 152 198 
SDPSSINGGIVVAMTGKDCVAIACDLRLGSQSLGVSNKFEKIFHYGHVFLGITGLATDVTTLNEMFRYKTNLYKLKEERAIEPETFTQLVSSSLYERRFGPYFVGPVVAGINSKSGKPFIAGFDLIGCIDEAKDFIVSGTASDQLFGMCESLYEPNLEPEDLFETISQALLNAADRDALSGWGAVVYIIKKDEVVKRYLKMRQD
4CGX , Knot 83 177 0.81 40 134 172 
GMGSGMAMTDRPDHIDSRVWELSETQEDWITQVHGHVRRVVECWKYTICCLISNMHTHRGAPQYDVFKWQDRSTIEWICSKKKVQYPERDTPDLYDNERAVAYKVLLVSDLSDHSPTSGIYHDLAFNLEGEAEESCALVLRGSQLQDIKGFLCRALEWVVSNNLTQEVVETISGEAK

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 \(c\).

\(|P_{f(3SNF_1)}(2) \setminus P_{f(6FVT_1)}(2)|=43\), \(|P_{f(6FVT_1)}(2) \setminus P_{f(3SNF_1)}(2)|=110\). 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 1:00110100001000001000011000110000000110001011011001111000110000101000010001000010000001010000011101111100
Pair \(Z_2\) Length of longest common subsequence
3SNF_1,6FVT_1 153 4
3SNF_1,4CGX_1 159 3
6FVT_1,4CGX_1 170 4

Newick tree

 
[
	4CGX_1:84.13,
	[
		3SNF_1:76.5,6FVT_1:76.5
	]:7.63
]

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 \((0.85)(0.8)(\frac{308 }{\log_{20} 308}-\frac{104}{\log_{20}104})=63.8\)
Status Protein1 Protein2 d d1/2
Query variables 3SNF_1 6FVT_1 80 59
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]