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Parikh vectors
3CNB_1 1STP_1 5AOG_1 Letter Amino acid
15 8 32 L Leucine
9 10 24 V Valine
11 25 32 A Alanine
11 8 24 D Aspartic acid
2 0 8 C Cysteine
3 6 14 Q Glutamine
8 2 6 H Histidine
7 5 5 E Glutamic acid
7 18 24 G Glycine
5 4 20 P Proline
6 14 22 S Serine
10 19 20 T Threonine
11 8 10 K Lycine
0 6 0 W Tryptophan
2 6 4 Y Tyrosine
2 4 25 R Arginine
7 10 11 N Asparagine
12 4 7 I Isoleucine
7 0 1 M Methionine
8 2 18 F Phenylalanine 

3CNB_1|Chains A, B, C|DNA-binding response regulator, merR family|Colwellia psychrerythraea (167879)
>1STP_1|Chain A|STREPTAVIDIN COMPLEX WITH BIOTIN|Streptomyces avidinii (1895)
>5AOG_1|Chain A|CATIONIC PEROXIDASE SPC4|SORGHUM BICOLOR (4558)
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 \(w=f(c)\)
3CNB , Knot 71 143 0.82 38 116 137 
MSLNVKNDFSILIIEDDKEFADMLTQFLENLFPYAKIKIAYNPFDAGDLLHTVKPDVVMLDLMMVGMDGFSICHRIKSTPATANIIVIAMTGALTDDNVSRIVALGAETCFGKPLNFTLLEKTIKQLVEQKKATSEGHHHHHH
1STP , Knot 74 159 0.78 36 108 151 
DPSKDSKAQVSAAEAGITGTWYNQLGSTFIVTAGADGALTGTYESAVGNAESRYVLTGRYDSAPATDGSGTALGWTVAWKNNYRNAHSATTWSGQYVGGAEARINTQWLLTSGTTEANAWKSTLVGHDTFTKVKPSAASIDAAKKAGVNNGNPLDAVQQ
5AOG , Knot 129 307 0.80 38 164 288 
QPPLAPGLSFDFYKRSCPKAESIVRSFVQDAVRRDVGLAAGLLRLHFHDCFVQGCDASVLLDGSATGPGEQQAPPNLTLRPTAFKAINDIHDRLHKECGGTVVSCSDVLALAARDSVVVSGGPSYRVPLGRRDSASFATQQDVLSGLPPPTAAVPALLAVLSKINLDATDLVALSGGHTIGLGHCTSFEDRLFPRPDPTLNATFAGQLRRTCPAKGTDRRTPLDVRTPNAFDNKYYVNLVNREGLFTSDQDLFSNARTRALVDKFARSQRDFFDQFAFSVVKMGQIKVLTGTQGQIRTNCSARNAAG

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 \(c\).

\(|P_{f(3CNB_1)}(2) \setminus P_{f(1STP_1)}(2)|=73\), \(|P_{f(1STP_1)}(2) \setminus P_{f(3CNB_1)}(2)|=65\). 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 1:10101000101111000001101100110011101010110011011011001010111101111110110100010001101011111101110000100111111000110110101100010011000010001000000
Pair \(Z_2\) Length of longest common subsequence
3CNB_1,1STP_1 138 4
3CNB_1,5AOG_1 162 3
1STP_1,5AOG_1 152 4

Newick tree

 
[
	5AOG_1:81.47,
	[
		3CNB_1:69,1STP_1:69
	]:12.47
]

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 \((0.85)(0.8)(\frac{302 }{\log_{20} 302}-\frac{143}{\log_{20}143})=49.0\)
Status Protein1 Protein2 d d1/2
Query variables 3CNB_1 1STP_1 60 58.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]