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Parikh vectors
6OCV_1 3TKF_1 1JYC_1 Letter Amino acid
3 3 0 C Cysteine
22 23 7 E Glutamic acid
4 9 6 H Histidine
10 29 15 I Isoleucine
7 8 11 P Proline
11 19 19 T Threonine
7 31 18 A Alanine
4 21 14 N Asparagine
23 32 18 L Leucine
9 31 12 K Lycine
13 11 11 F Phenylalanine
14 21 31 S Serine
7 9 6 R Arginine
13 22 18 D Aspartic acid
11 15 16 G Glycine
0 3 4 W Tryptophan
8 8 7 Y Tyrosine
12 28 17 V Valine
7 14 5 Q Glutamine
5 8 2 M Methionine 

6OCV_1|Chain A|Heme NO binding domain protein|Shewanella woodyi (60961)
>3TKF_1|Chains A, B|Transaldolase|Francisella tularensis subsp. tularensis (119856)
>1JYC_1|Chains A, B, C, D|Concanavalin-Br|Canavalia ensiformis (3823)
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 \(w=f(c)\)
6OCV , Knot 90 190 0.82 38 142 185 
MMGMVFTGLMELIEDEFGYETLDTLLESCELQSEGIYTSVGSYDHQELLQLVVKLSEVSSVPVTELVRLFGKKLFVELIEGHPEIANEMKDSFDLLSKIDSFIHVEVYKLYPQAELPKFTCDRLGDNDIRLHYQSKRPFASFAEGLLDGCAEYFKEDFTISRTPETQDSETDVIFNITRAPRGAENLYFQ
3TKF , Knot 146 345 0.82 40 197 329 
MHHHHHHSSGVDLGTENLYFQSNAMQKSVLEQLKQVTMVVADTGDFELIKKYKPVDATTNPSLILKAVKEQKYSNLVAETISKVKANNPDLNSDDLVKEIAIEILVSFGIKILDVIEGKVSSEVDARVSFNSATTIDYAKRIIARYESNGIPKDRVLIMIAATWEGIKAAKLLQKEGINCNLTLIFDKAQAKACAEAGVYLVSPFVGRITDWQMQQNNLKTFPAIADDDGVNSVKAIYKLYKSHGFKTIVMGASFRNVEQVIALAGCDALTISPVLLEELKNRDEHLEVKLTKNDDVVTQSPQISEADFRWLMNENAMATHKLAEGIRLFTKDTIELENIIKQNL
1JYC , Knot 104 237 0.80 38 151 226 
ADTIVAVELDTYPNTDIGDPSYPHIGIDIKSVRSKKTAKWNMQNGKVGTAHIIYNSVDKRLSAVVSYPNADSATVSYDVDLDNVLPEWVRVGLSASTGLYKETNTILSWSFTSKLKSNSTHETNALHFMFNQFSKDQKDLILQGDATTGTDGNLELTRVSSNGSPQGSSVGRALFYAPVHIWESSAVVASFEATFTFLIKSPDSHPADGIAFFISNIDSSIPSGSTGRLLGLFPDAN

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 \(c\).

\(|P_{f(6OCV_1)}(2) \setminus P_{f(3TKF_1)}(2)|=51\), \(|P_{f(3TKF_1)}(2) \setminus P_{f(6OCV_1)}(2)|=106\). 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 1:1111110111011000110001001100001000110001100000011011101001001110011011100111011010101100100010110010011010100101010110100001100010100000011101101110101001000101000100000000111010011011001010
Pair \(Z_2\) Length of longest common subsequence
6OCV_1,3TKF_1 157 6
6OCV_1,1JYC_1 159 3
3TKF_1,1JYC_1 158 4

Newick tree

 
[
	1JYC_1:79.49,
	[
		6OCV_1:78.5,3TKF_1:78.5
	]:0.99
]

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 \((0.85)(0.8)(\frac{535 }{\log_{20} 535}-\frac{190}{\log_{20}190})=99.7\)
Status Protein1 Protein2 d d1/2
Query variables 6OCV_1 3TKF_1 127 97.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]