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Parikh vectors
2RKB_1 7WPX_1 3FHP_1 Letter Amino acid
39 28 0 A Alanine
7 32 0 D Aspartic acid
10 20 0 H Histidine
5 17 0 M Methionine
16 27 0 P Proline
17 34 2 S Serine
33 34 1 V Valine
8 26 2 N Asparagine
17 18 2 Q Glutamine
31 31 1 G Glycine
14 35 2 I Isoleucine
13 25 1 T Threonine
12 18 0 R Arginine
21 42 2 E Glutamic acid
14 33 0 K Lycine
5 9 0 W Tryptophan
2 30 2 Y Tyrosine
10 0 4 C Cysteine
38 47 2 L Leucine
6 24 0 F Phenylalanine 

2RKB_1|Chains A, B, C, D, E|Serine dehydratase-like|Homo sapiens (9606)
>7WPX_1|Chain A|Methionine--tRNA ligase|Staphylococcus aureus subsp. aureus COL (93062)
>3FHP_1|Chains A, C|Insulin|Sus scrofa (9823)
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 \(w=f(c)\)
2RKB , Knot 136 318 0.82 40 185 303 
QEPFHVVTPLLESWALSQVAGMPVFLKCENVQPSGSFKIRGIGHFCQEMAKKGCRHLVCSSGGNAGIAAAYAARKLGIPATIVLPESTSLQVVQRLQGEGAEVQLTGKVWDEANLRAQELAKRDGWENVPPFDHPLIWKGHASLVQELKAVLRTPPGALVLAVGGGGLLAGVVAGLLEVGWQHVPIIAMETHGAHCFNAAITAGKLVTLPDITSVAKSLGAKTVAARALECMQVCKIHSEVVEDTEAVSAVQQLLDDERMLVEPACGAALAAIYSGLLRRLQAEGCLPPSLTSVVVIVCGGNNINSRELQALKTHLGQ
7WPX , Knot 215 530 0.84 38 260 497 
MGSSHHHHHHSAKETFYITTPIYYPSGNLHIGHAYSTVAGDVIARYKRMQGYDVRYLTGTDEHGQKIQEKAQKAGKTEIEYLDEMIAGIKQLWAKLEISNDDFIRTTEERHKHVVEQVFERLLKQGDIYLGEYEGWYSVPDETYYTESQLVDPQYENGKIIGGKSPDSGHEVELVKEESYFFNISKYTDRLLEFYDQNPDFIQPPSRKNEMINNFIKPGLADLAVSRTSFNWGVHVPSNPKHVVYVWIDALVNYISALGYLSDDESLFNKYWPADIHLMAKEIVRFHSIIWPILLMALDLPLPKKVFAHGWILMKDGKMSKSKGNVVDPNILIDRYGLDATRYYLMRELPFGSDGVFTPEAFVERTNFDLANDLGNLVNRTISMVNKYFDGELPAYQGPLHELDEEMEAMALETVKSYTESMESLQFSVALSTVWKFISRTNKYIDETTPWVLAKDDSQKDMLGNVMAHLVENIRYAAVLLRPFLTHAPKEIFEQLNINNPQFMEFSSLEQYGVLNESIMVTGQPKPIFP
3FHP , Knot 15 21 0.72 22 20 19 
GIVEQCCTSICSLYQLENYCN

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 \(c\).

\(|P_{f(2RKB_1)}(2) \setminus P_{f(7WPX_1)}(2)|=50\), \(|P_{f(7WPX_1)}(2) \setminus P_{f(2RKB_1)}(2)|=125\). 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 1:001101101110011100111111110000101010101011101000110010001100011011111101100111110111100001011001010110101010110010101001100011001111001111010101100101110011111111111111111111111011100111111000110010111011011011010011001110011101100101001000110000110110011000011101101111111001110010101011101001111101100100001011000110
Pair \(Z_2\) Length of longest common subsequence
2RKB_1,7WPX_1 175 3
2RKB_1,3FHP_1 187 2
7WPX_1,3FHP_1 256 3

Newick tree

 
[
	3FHP_1:11.15,
	[
		2RKB_1:87.5,7WPX_1:87.5
	]:31.65
]

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 \((0.85)(0.8)(\frac{848 }{\log_{20} 848}-\frac{318}{\log_{20}318})=143.\)
Status Protein1 Protein2 d d1/2
Query variables 2RKB_1 7WPX_1 183 145
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]