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Parikh vectors
5SKF_1 5NHO_1 2DLH_1 Letter Amino acid
15 24 5 D Aspartic acid
16 21 11 G Glycine
36 46 6 L Leucine
18 23 4 K Lycine
12 10 3 M Methionine
14 20 5 N Asparagine
14 20 9 P Proline
24 17 17 S Serine
22 14 12 T Threonine
7 3 2 W Tryptophan
16 14 10 V Valine
14 19 3 R Arginine
21 28 7 I Isoleucine
15 14 1 F Phenylalanine
21 25 5 A Alanine
17 13 11 Q Glutamine
24 23 4 E Glutamic acid
13 20 2 H Histidine
12 20 4 Y Tyrosine
12 7 0 C Cysteine 

5SKF_1|Chains A, B, C, D|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>5NHO_1|Chain A|Mitogen-activated protein kinase 1|Homo sapiens (9606)
>2DLH_1|Chain A|Receptor-type tyrosine-protein phosphatase delta|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 \(w=f(c)\)
5SKF , Knot 152 343 0.86 40 221 334 
GSSICTSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
5NHO , Knot 163 381 0.84 40 240 366 
MHHHHHHGGGENLYFQGSHMAAAAAAGAGPEMVRGQVFDVGPRYTNLSYIGEGAYGMVCSAYDNLNKVRVAIKKISPFEHQTYCQRTLREIKILLRFRHENIIGINDIIRAPTIEQMKDVYIVQDLMETDLYKLLKTQHLSNDHICYFLYQILRGLKYIHSANVLHRDLKPSNLLLNTTCDLKICDFGLARVADPDHDHTGFLTEYVATRWYRAPEIMLNSKGYTKSIDIWSVGCILAEMLSNRPIFPGKHYLDQLNHILGILGSPSQEDLNCIINLKARNYLLSLPHKNKVPWNRLFPNADSKALDLLDKMLTFNPHKRIEVEQALAHPYLEQYYDPSDEPIAEAPFKFDMELDDLPKEKLKELIFEETARFQPGYRSLE
2DLH , Knot 60 121 0.79 38 90 111 
GSSGSSGPVLTQTSEQAPSSAPRDVQARMLSSTTILVQWKEPEEPNGQIQGYRVYYTMDPTQHVNNWMKHNVADSQITTIGNLVPQKTYSVKVLAFTSIGDGPLSSDIQVITQTGSGPSSG

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 \(c\).

\(|P_{f(5SKF_1)}(2) \setminus P_{f(5NHO_1)}(2)|=87\), \(|P_{f(5NHO_1)}(2) \setminus P_{f(5SKF_1)}(2)|=106\). 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 1:1001000001011101011101000101101011110011111110110000100010100100111010000001100010011011001011100000110010001111101000100011000010010011111000001000010001011010100110010000000110110011110011101100001001000101010000000011111101001001001111001010010101110100100111011111000000011010111001111100001001111001110100001001001101000101100101100111000
Pair \(Z_2\) Length of longest common subsequence
5SKF_1,5NHO_1 193 4
5SKF_1,2DLH_1 191 4
5NHO_1,2DLH_1 214 3

Newick tree

 
[
	5NHO_1:10.92,
	[
		5SKF_1:95.5,2DLH_1:95.5
	]:8.42
]

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 \((0.85)(0.8)(\frac{724 }{\log_{20} 724}-\frac{343}{\log_{20}343})=104.\)
Status Protein1 Protein2 d d1/2
Query variables 5SKF_1 5NHO_1 133 128
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]