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Parikh vectors
7SIY_1 5VMN_1 7FVG_1 Letter Amino acid
15 5 6 A Alanine
17 10 10 R Arginine
14 3 10 D Aspartic acid
17 12 8 I Isoleucine
6 3 1 W Tryptophan
11 3 8 Y Tyrosine
4 2 3 C Cysteine
9 3 5 M Methionine
11 5 5 V Valine
18 9 12 E Glutamic acid
18 9 3 G Glycine
24 2 8 K Lycine
16 4 6 P Proline
17 15 17 S Serine
19 9 7 T Threonine
13 10 5 N Asparagine
12 5 5 Q Glutamine
7 1 8 H Histidine
35 16 14 L Leucine
21 6 8 F Phenylalanine 

7SIY_1|Chain A|E3 ubiquitin-protein ligase CBL|Homo sapiens (9606)
>5VMN_1|Chain A|Bak protein|Grouper iridovirus (127569)
>7FVG_1|Chain A|PH-interacting protein|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 \(w=f(c)\)
7SIY , Knot 133 304 0.83 40 194 292 
PGTVDKKMVEKCWKLMDKVVRLCQNPKLALKNSPPYILDLLPDTYQHLRTILSRYEGKMETLGENEYFRVFMENLMKKTKQTISLFKEGKERMYEENSQPRRNLTKLSLIFSHMLAELKGIFPSGLFQGDTFRITKADAAEFWRKAFGEKTIVPWKSFRQALHEVHPISSGLEAMALKSTIDLTCNDYISVFEFDIFTRLFQPWSSLLRNWNSLAVTHPGYMAFLTYDEVKARLQKFIHKPGSYIFRLSCTRLGQWAIGYVTADGNILQTIPHNKPLFQALIDGFREGFYLFPDGRNQNPDLTG
5VMN , Knot 63 132 0.77 40 100 127 
GPLGSMTNINFSALLRGERMCPLTREIHSQMLIVTKSYSLVETFRAFPRLPNILEIGNNIVSDGNLNWGRILILLGISQLYFTKSESESERTQITEQLERFFRQDAISNWIASNGGWVTCASLDLRNYSSVT
7FVG , Knot 73 149 0.81 40 117 140 
MHHHHHHSSGVDLGTENLYFQSMSYDIQAWKKQCEELLNLIFQCEDSEPFRQPVDLLEYPDYRDIIDTPMDFATVRETLEAGNYESPMELCKDVRLIFSNSKAYTPSKRSRIYSMSLRLSAFFEEHISSVLSDYKSALRFHKRNTITKR

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 \(c\).

\(|P_{f(7SIY_1)}(2) \setminus P_{f(5VMN_1)}(2)|=137\), \(|P_{f(5VMN_1)}(2) \setminus P_{f(7SIY_1)}(2)|=43\). 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 1:1101000110001011001101000101110001101101110000010011000010100110000101110011000000101100100010000001000100101110011101011110111010010100101101100111000111100100110010110011011110001010000010110101100110110011001001110011011110000101010011001100110100001101111010101011001100011101110110011011101000010101
Pair \(Z_2\) Length of longest common subsequence
7SIY_1,5VMN_1 180 3
7SIY_1,7FVG_1 183 4
5VMN_1,7FVG_1 135 3

Newick tree

 
[
	7SIY_1:97.27,
	[
		5VMN_1:67.5,7FVG_1:67.5
	]:29.77
]

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 \((0.85)(0.8)(\frac{436 }{\log_{20} 436}-\frac{132}{\log_{20}132})=91.0\)
Status Protein1 Protein2 d d1/2
Query variables 7SIY_1 5VMN_1 120 84
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]