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Parikh vectors
6UNP_1 5WNJ_1 2EGO_1 Letter Amino acid
26 21 5 A Alanine
19 6 4 N Asparagine
22 22 10 G Glycine
13 15 6 I Isoleucine
27 24 5 S Serine
33 31 9 E Glutamic acid
17 13 1 M Methionine
14 7 2 Y Tyrosine
25 18 9 V Valine
18 18 3 D Aspartic acid
10 7 6 Q Glutamine
14 15 4 H Histidine
34 39 9 L Leucine
11 13 3 F Phenylalanine
15 23 2 P Proline
14 10 8 T Threonine
26 21 7 R Arginine
7 9 0 C Cysteine
13 23 3 K Lycine
5 7 0 W Tryptophan 

6UNP_1|Chains A, B|Bone morphogenetic protein receptor type-2|Homo sapiens (9606)
>5WNJ_1|Chain A|Receptor-interacting serine/threonine-protein kinase 4|Mus musculus (10090)
>2EGO_1|Chains A, B|General receptor for phosphoinositides 1-associated scaffold protein|Rattus norvegicus (10116)
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 \(w=f(c)\)
6UNP , Knot 157 363 0.85 40 219 347 
MGSSHHHHHHSSGENLYFQGHMMEAAASEPSLDLDNLKLLELIGRGRYGAVYKGSLDERPVAVKVFSFANRQNFINEKNIYRVPLMEHDNIARFIVGDERVTADGRMEYLLVMEYYPNGSLCKYLSLHTSDWVSSCRLAHSVTRGLAYLHTELPRGDHYKPAISHRDLNSRNVLVKNDGTCVISDFGLSMRLTGNRLVRPGEEDNAAISEVGTIRYMAPEVLEGAVNLRDCESALKQVDMYALGLIYWEIFMRCTDLFPGESVPEYQMAFQTEVGNHPTFEDMQVLVSREKQRPKFPEAWKENSLAVRSLKETIEDCWGQDAEARLTAQCAEERMAELMMIWERNKSVSPTVNPMSTAMQNER
5WNJ , Knot 149 342 0.84 40 212 332 
MEGEGRGRWALGLLRTFDAGEFAGWEKVGSGGFGQVYKVRHVHWKTWLAIKCSPSLHVDDRERMELLEEAKKMEMAKFRYILPVYGICQEPVGLVMEYMETGSLEKLLASEPLPWDLRFRIVHETAVGMNFLHCMSPPLLHLNLKPANILLDAHYHVKISDFGLAKCNGMSHSHDLSMDGLFGTIAYLPPERIREKSRLFDTKHDVYSFAIVIWGVLTQKKPFADEKNILHIMMKVVKGHRPELPPICRPRPRACASLIGLMQRCWHADPQVRPTFQEITSETEDLCEKPDEEVKDLAHEPGEKSSLESKSEARPESSRLKRASAPPFDNDCSLSELLSQLD
2EGO , Knot 50 96 0.79 36 77 93 
GSQQRKVLTLEKGDNQTFGFEIQTYGLHHREEQRVEMVTFVARVHESSPAQLAGLTPGDTIASVNGLNVEGIRHREIVDIIKASGNVLRLETLYGT

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 \(c\).

\(|P_{f(6UNP_1)}(2) \setminus P_{f(5WNJ_1)}(2)|=81\), \(|P_{f(5WNJ_1)}(2) \setminus P_{f(6UNP_1)}(2)|=74\). 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 1:110000000000100101010110111001010100101101110100111001010001111011011000011000010011110000110111100010101010011110001010100010100001100001100100111010001101000011100001000011100010011001110101010011011000011100110100111011011101000001100101011111010111000011110011000111000110010100101110000001011011000011100100010001100101010100100011011111000001010101100110000
Pair \(Z_2\) Length of longest common subsequence
6UNP_1,5WNJ_1 155 6
6UNP_1,2EGO_1 192 3
5WNJ_1,2EGO_1 189 3

Newick tree

 
[
	2EGO_1:10.47,
	[
		6UNP_1:77.5,5WNJ_1:77.5
	]:22.97
]

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 \((0.85)(0.8)(\frac{705 }{\log_{20} 705}-\frac{342}{\log_{20}342})=99.5\)
Status Protein1 Protein2 d d1/2
Query variables 6UNP_1 5WNJ_1 123 119
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]