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Parikh vectors
7NHT_1 1DDJ_1 6NEV_1 Letter Amino acid
7 7 25 D Aspartic acid
20 25 36 G Glycine
19 24 33 V Valine
11 9 14 Q Glutamine
4 7 17 H Histidine
12 10 29 I Isoleucine
8 9 23 F Phenylalanine
14 5 11 Y Tyrosine
11 13 34 R Arginine
7 8 15 N Asparagine
2 12 9 C Cysteine
20 21 29 L Leucine
14 13 17 K Lycine
5 2 12 M Methionine
14 15 24 S Serine
13 13 12 T Threonine
23 14 50 A Alanine
18 16 30 E Glutamic acid
10 18 19 P Proline
2 6 8 W Tryptophan 

7NHT_1|Chain A|Proteasome subunit alpha type-2|Homo sapiens (9606)
>1DDJ_1|Chains A, B, C, D|PLASMINOGEN|Homo sapiens (9606)
>6NEV_1|Chains A, B|FAD-dependent monooxygenase tropB|Talaromyces stipitatus (strain ATCC 10500 / CBS 375.48 / QM 6759 / NRRL 1006) (441959)
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 \(w=f(c)\)
7NHT , Knot 106 234 0.82 40 160 226 
MAERGYSFSLTTFSPSGKLVQIEYALAAVAGGAPSVGIKAANGVVLATEKKQKSILYDERSVHKVEPITKHIGLVYSGMGPDYRVLVHRARKLAQQYYLVYQEPIPTAQLVQRVASVMQEYTQSGGVRPFGVSLLICGWNEGRPYLFQSDPSGAYFAWKATAMGKNYVNGKTFLEKRYNEDLELEDAIHTAILTLKESFEGQMTEDNIEVGICNEAGFRRLTPTEVKDYLAAIA
1DDJ , Knot 113 247 0.84 40 169 238 
SFDCGKPQVEPKKCPGRVVGGCVAHPHSWPWQVSLRTRFGMHFCGGTLISPEWVLTAAHCLEKSPRPSSYKVILGAHQEVNLEPHVQEIEVSRLFLEPTRKDIALLKLSSPAVITDKVIPACLPSPNYVVADRTECFITGWGETQGTFGAGLLKEAQLPVIENKVCNRYEFLNGRVQSTELCAGHLAGGTDSCQGDAGGPLVCFEKDKYILQGVTSWGLGCARPNKPGVYVRVSRFVTWIEGVMRNN
6NEV , Knot 182 447 0.82 40 236 418 
MPGSLIDTRQQPLSVGIVGGGIIGVILAAGLVRRGIDVKVFEQARGFREIGAGMAFTANAVRCMEMLDPAIVWALRSSGAVPISIGDHQAEARDYLRWVDGYHESSKRLYQLDAGIRGFEACRRDQFLEALVKVLPEGIVECQKRLQKIHEKNETEKVTLEFADGTFAHVDCVIGADGIRSRVRQHLFGEDSPYSHPHYSHKFAFRGLITMENAISALGEDKARTLNMHVGPNAHLIHFPVANETMVNIAAFVSDPEEWPDKLSLVGPATREEAMGYFANWNPGLRAVLGFMPENIDRWAMFDTYDYPAPFFSRGKICLVGDAAHAAVPHHGAGACIGIEDALCATVLLAEVFVSTRGKSSIVRNRAIAAAFGSFNAVRRVRAQWFVDSSRRVCDLYQQPEWADPQKRIKAENCFEEIKDRSHKIWHFDYNSMLQEAIEKYRHNMGS

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 \(c\).

\(|P_{f(7NHT_1)}(2) \setminus P_{f(1DDJ_1)}(2)|=82\), \(|P_{f(1DDJ_1)}(2) \setminus P_{f(7NHT_1)}(2)|=91\). 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 1:110010010100101010110100111111111101110110111110000000110000010010110001111001111000111001001100001100011101011001101100000011101111011101100101011000101101110101110001010011000000010100110011101000101010000101110001110010100100011111
Pair \(Z_2\) Length of longest common subsequence
7NHT_1,1DDJ_1 173 3
7NHT_1,6NEV_1 184 4
1DDJ_1,6NEV_1 183 3

Newick tree

 
[
	6NEV_1:93.43,
	[
		7NHT_1:86.5,1DDJ_1:86.5
	]:6.93
]

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 \((0.85)(0.8)(\frac{481 }{\log_{20} 481}-\frac{234}{\log_{20}234})=71.2\)
Status Protein1 Protein2 d d1/2
Query variables 7NHT_1 1DDJ_1 90 89.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]