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Parikh vectors
5ORZ_1 7TZG_1 9JPK_1 Letter Amino acid
12 8 2 F Phenylalanine
2 4 0 C Cysteine
9 15 18 Q Glutamine
23 5 15 E Glutamic acid
15 39 16 G Glycine
10 0 8 H Histidine
7 5 5 N Asparagine
10 11 11 D Aspartic acid
3 5 3 M Methionine
13 9 7 I Isoleucine
34 17 30 L Leucine
17 10 2 K Lycine
14 9 5 P Proline
16 30 15 S Serine
13 20 11 T Threonine
4 4 0 W Tryptophan
12 14 6 Y Tyrosine
17 21 43 A Alanine
20 8 23 R Arginine
14 14 18 V Valine 

5ORZ_1|Chain A|Aurora kinase A|Homo sapiens (9606)
>7TZG_1|Chains A, B|scFvF7|Homo sapiens (9606)
>9JPK_1|Chains A, B|Pyruvate dehydrogenase complex repressor|Achromobacter denitrificans (32002)
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 \(w=f(c)\)
5ORZ , Knot 119 265 0.83 40 166 258 
QWALEDFEIGRPLGKGKFGNVYLAREKQSKFILALKVLFKAQLEKAGVEHQLRREVEIQSHLRHPNILRLYGYFHDATRVYLILEYAPLGTVYRELQKLSKFDEQRTATYITELANALSYCHSKRVIHRDIKPENLLLGSAGELKIADFGWSVHAPSSRRTTLAGTLDYLPPEMIEGRMHDEKVDLWSLGVLCYEFLVGKPPFEANTYQETYKRISRVEFTFPDFVTEGARDLISRLLKHNPSQRPMLREVLEHPWITANSSKPS
7TZG , Knot 104 248 0.77 38 149 224 
MAQVQLVESGGGLVQPGGSLRLSCAASGFTFSSYAMNWVRQAPGKGLEWVSGISAGGTGTYYADSVKGRFTISRDNSKNTLYLQMNSLRAEDTAVYYCAKDQDGGKKTDAFDIWGQGTMVTVSSGGGGSGGGGSGGGGSDIVMTQSPSLLSASVGDRVTITCRASQGINYYLAWYQQKPGKAPKLLIYAASTLQSGVPSRFSGSGSGTEFTLTISSLQPEDFATYYCQQTGYYPLTFGPGTKVDIAAA
9JPK , Knot 100 238 0.76 36 127 218 
MLSKSLTLTEQVARQIAGDIAEGVHSVGAKLPPGRVLAEQYGVSAAVIREATERLRAQGLIQSRQGSGSVVVSRTGAQGFQVSAGLDDREQLASVYELRMELEGGAAALAARRRNATDLAAMAEALAALEANLDHPEQGVEHDIAFHVAIAAATHNRYYQDLLQYLNLQLRLAVSTARTNSRRQEGLTAVVHQEHVAVYDAILAGDPDRARLAATRHLQQAASRLRLDLLSPAARQTS

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 \(c\).

\(|P_{f(5ORZ_1)}(2) \setminus P_{f(7TZG_1)}(2)|=96\), \(|P_{f(7TZG_1)}(2) \setminus P_{f(5ORZ_1)}(2)|=79\). 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 1:0111001011011101011010110000001111101110101001110001000101000100101101010100100101110011110100010010010000010010011011000000011000101001111011010110111010110000001110100111011010100001011011110001111011101000000000100101011011001100110011000100011100110011101000010
Pair \(Z_2\) Length of longest common subsequence
5ORZ_1,7TZG_1 175 3
5ORZ_1,9JPK_1 145 4
7TZG_1,9JPK_1 144 4

Newick tree

 
[
	5ORZ_1:82.94,
	[
		9JPK_1:72,7TZG_1:72
	]:10.94
]

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 \((0.85)(0.8)(\frac{513 }{\log_{20} 513}-\frac{248}{\log_{20}248})=75.8\)
Status Protein1 Protein2 d d1/2
Query variables 5ORZ_1 7TZG_1 98 91.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]