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Parikh vectors
7PKW_1 7DGM_1 2EVX_1 Letter Amino acid
7 4 18 P Proline
14 5 32 S Serine
1 2 6 W Tryptophan
21 7 34 V Valine
0 0 4 C Cysteine
9 9 23 I Isoleucine
1 2 9 M Methionine
10 14 38 G Glycine
23 7 13 T Threonine
18 17 30 A Alanine
17 13 42 E Glutamic acid
14 7 21 F Phenylalanine
20 6 31 Q Glutamine
6 11 7 H Histidine
20 17 33 L Leucine
27 18 14 K Lycine
20 2 12 Y Tyrosine
3 2 48 R Arginine
17 2 21 N Asparagine
20 8 23 D Aspartic acid 

7PKW_1|Chain A|Putative transfer protein|Streptococcus thermophilus (1308)
>7DGM_1|Chains A, B|Myoglobin|Equus caballus (9796)
>2EVX_1|Chain A|11S globulin beta subunit|Cucurbita maxima (3661)
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 \(w=f(c)\)
7PKW , Knot 118 268 0.82 38 163 253 
SNKVGTLQAQVEATQKQKAQPIDANRKYDYKLQYYLNDYVYAYFTLPQEGDKQQAQVEHLNSFYNFVPDVKAQGQVRNPSTLLDSQLVTVEGKVATYKVKYKEMIQHDKDTEEKELVTGFNIPFDEKEGKYYVSGLPWFSAIESSQAGYFSEDDQLQLTANDHVSDSQHKKVEKFLKVFFTNYTTNQDNLNLIAKNVAIVANTTFKTIDYTYLKKDRADLIAYVQATFEVGGTTHSENFTFTLSEKDKSYYVTKLEHTIPLNYANDKD
7DGM , Knot 74 153 0.81 38 114 147 
GLSDGEWQQVLNVWGKVEADIAGHGQEVLIRLFTGHPETLEKFDKFKHLKTEAEMKASEDLKKHGTVVLTALGGILKKHAAHEAELKPLAQSHATKHKIPIKYLEFISDAIIHVLHSKHPGDFGADAQGAMTKALELFRNDIAAKYKELGFQG
2EVX , Knot 181 459 0.80 40 218 426 
QIEQQSPWEFQGSEVWQQHRYQSPRACRLENLRAQDPVRRAEAEAGFTEVWDQDNDEFQCAGVNMIRHTIRPKGLLLPGFSNAPKLIFVAQGFGIRGIAIPGCAETYQTDLRRSQSAGSAFKDQHQKIRPFREGDLLVVPAGVSHWMYNRGQSDLVLIVFADTRNVANQIDPYLRKFYLAGRPEQVERGVEEWERSSRKGSSGEKSGNIFSGFADEFLEEAFQIDGGLVRKLKGEDDERDRIVQVDEDFEVLLPEKDEEERSRGRYIESESESENGLEETICTLRLKQNIGRSERADVFNPRGGRISTANYHTLPILRQVRLSAERGVLYSNAMVAPHYTVNSHSVMYATRGNARVQVVDNFGQSVFDGEVREGQVLMIPQNFVVIKRASDRGFEWIAFKTNDNAITNLLAGRVSQMRMLPLGVLSNMYRISREEAQRLKYGQQEMRVLSPGRSQGRRE

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 \(c\).

\(|P_{f(7PKW_1)}(2) \setminus P_{f(7DGM_1)}(2)|=99\), \(|P_{f(7DGM_1)}(2) \setminus P_{f(7PKW_1)}(2)|=50\). 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 1:0001101010101000001011010000000100010001010101100100001010010010011101010101001001100011010101100010000110000000000110110111000010001011111011000011010000010101000100000001001101110000000001011100111110001001000010000101110101010111000000101010000000010010001110010000
Pair \(Z_2\) Length of longest common subsequence
7PKW_1,7DGM_1 149 4
7PKW_1,2EVX_1 161 3
7DGM_1,2EVX_1 182 3

Newick tree

 
[
	2EVX_1:89.39,
	[
		7PKW_1:74.5,7DGM_1:74.5
	]:14.89
]

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 \((0.85)(0.8)(\frac{421 }{\log_{20} 421}-\frac{153}{\log_{20}153})=79.9\)
Status Protein1 Protein2 d d1/2
Query variables 7PKW_1 7DGM_1 100 78
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]