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Parikh vectors
5INE_1 8XNV_1 5MWP_1 Letter Amino acid
25 8 13 A Alanine
30 4 17 N Asparagine
17 6 20 E Glutamic acid
17 4 12 Y Tyrosine
20 4 15 V Valine
17 1 9 R Arginine
14 1 2 C Cysteine
22 4 19 K Lycine
9 6 14 P Proline
31 10 13 T Threonine
8 4 4 W Tryptophan
20 2 9 D Aspartic acid
14 3 21 Q Glutamine
29 3 20 G Glycine
25 9 15 F Phenylalanine
14 0 12 H Histidine
29 11 11 I Isoleucine
41 22 39 L Leucine
17 6 12 M Methionine
39 7 28 S Serine 

5INE_1|Chains A, B|Pre-glycoprotein polyprotein GP complex|Lymphocytic choriomeningitis mammarenavirus (3052303)
>8XNV_1|Chain A|NADH-ubiquinone oxidoreductase chain 3|Mus musculus (10090)
>5MWP_1|Chain A|Mineralocorticoid receptor|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 \(w=f(c)\)
5INE , Knot 188 438 0.87 40 244 423 
MGQIVTMFEALPHIIDEVINIVIIVLIIITSIKAVYNFATCGILALVSFLFLAGRSCGMYGLNGPDIYKGVYQFKSVEFDMSHLNLTMPNACSANNSHHYISMGSSGLELTFTNDSILNHNFCNLTSAFNKKTFDHTLMSIVSSLHLSIRGNSNHKAVSCDFNNGITIQYNLSFSDPQSAISQCRTFRGRVLDMFRTAFGGKYMRSGWGWAGSDGKTTWCSQTSYQYLIIQNRTWENHCRYAGPFGMSRILFAQEKTKFLTRRLAGTFTWTLSDSSGVENPGGYCLTKWMILAAELKCFGNTAVAKCNVNHDEEFCDMLRLIDYNKAALSKFKQDVESALHVFKTTVNSLISDQLLMRNHLRDLMGVPYCNYSKFWYLEHAKTGETSVPKCWLVTNGSYLNETHFSDQIEQEADNMITEMLRKDYIKRQGSTPLALMD
8XNV , Knot 57 115 0.78 38 85 107 
MNLYTVIFINILLSLTLILVAFWLPQMNLYSEKANPYECGFDPTSSARLPFSMKFFLVAITFLLFDLEIALLLPLPWAIQTIKTSTMMIMAFILVTILSLGLAYEWTQKGLEWTE
5MWP , Knot 128 305 0.80 40 187 277 
MHNHNHNHNHNHNGGENLYFQGTPSPVMVLENIEPEIVYAGYDSSKPDTAENLLSTLNRLAGKQMIQVVKWAKVLPGFKNLPLEDQITLIQYSWMSLSSFALSWRSYKHTNSQFLYFAPDLVFNEEKMHQSAMYELCQGMHQISLQFVRLQLTFEEYTIMKVLLLLSTIPKDGLKSQAAFEEMRTNYIKELRKMVTKSPNNSGQSWQRFYQLTKLLDSMHDLVSDLLEFCFYTFRESHALKVEFPAMLVEIISDQLPKVESGNAKPLYFHRKGGSLVPRGSGGGSGGSGGPQAQQKSLLQQLLTE

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 \(c\).

\(|P_{f(5INE_1)}(2) \setminus P_{f(8XNV_1)}(2)|=184\), \(|P_{f(8XNV_1)}(2) \setminus P_{f(5INE_1)}(2)|=25\). 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 1:110110110111011001101111111110010110011001111110111111000110110110100110010010101001010110100100000010110011010100001100010010011000010001101100101010100000110001001101000101001001100000101011011001111001001111110010001000000001110000100000011111100111100000110001110101010000110011100100111111010011001110001000001001101100001110010001001101100010011000111000100111110000001101001001000110011100100100001000100010011001100001000100111110
Pair \(Z_2\) Length of longest common subsequence
5INE_1,8XNV_1 209 3
5INE_1,5MWP_1 169 5
8XNV_1,5MWP_1 182 3

Newick tree

 
[
	8XNV_1:10.08,
	[
		5INE_1:84.5,5MWP_1:84.5
	]:17.58
]

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 \((0.85)(0.8)(\frac{553 }{\log_{20} 553}-\frac{115}{\log_{20}115})=129.\)
Status Protein1 Protein2 d d1/2
Query variables 5INE_1 8XNV_1 171 105
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]