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Parikh vectors
8EEW_1 8AVL_1 3PAQ_1 Letter Amino acid
75 18 11 L Leucine
68 15 7 K Lycine
18 2 5 M Methionine
47 8 8 S Serine
43 6 10 T Threonine
13 5 2 W Tryptophan
47 10 8 D Aspartic acid
8 0 4 C Cysteine
39 6 8 Q Glutamine
26 9 4 F Phenylalanine
20 11 5 P Proline
16 10 10 Y Tyrosine
54 13 9 V Valine
79 13 13 E Glutamic acid
40 8 7 I Isoleucine
43 17 8 A Alanine
48 5 5 R Arginine
35 15 8 N Asparagine
25 15 14 G Glycine
22 6 2 H Histidine 

8EEW_1|Chains A, B|Dynamin-like 120 kDa protein, form S1|Homo sapiens (9606)
>8AVL_1|Chains A, B, C, D, E, F, G, H|Superoxide dismutase [Fe]|Bacteroides fragilis YCH46 (295405)
>3PAQ_1|Chain A|Pulmonary surfactant-associated protein A|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 \(w=f(c)\)
8EEW , Knot 296 766 0.85 40 299 689 
ATDRGSESDKHFRKVSDKEKIDQLQEELLHTQLKYQRILERLEKENKELRKLVLQKDDKGIHHRKLKKSLIDMYSEVLDVLSDYDASYNTQDHLPRVVVVGDQSAGKTSVLEMIAQARIFPRGSGEMMTRSPVKVTLSEGPHHVALFKDSSREFDLTKEEDLAALRHEIELRMRKNVKEGCTVSPETISLNVKGPGLQRMVLVDLPGVINTVTSGMAPDTKETIFSISKAYMQNPNAIILCIQDGSVDAERSIVTDLVSQMDPHGRRTIFVLTKVDLAEKNVASPSRIQQIIEGKLFPMKALGYFAVVTGKGNSSESIEAIREYEEEFFQNSKLLKTSMLKAHQVTTRNLSLAVSDCFWKMVRESVEQQADSFKATRFNLETEWKNNYPRLRELDRNELFEKAKNEILDEVISLSQVTPKHWEEILQQSLWERVSTHVIENIYLPAAQTMNSGTFNTTVDIKLKQWTDKQLPNKAVEVAWETLQEEFSRFMTEPKGKEHDDIFDKLKEAVKEESIKRHKWNDFAEDSLRVIQHNALEDRSISDKQQWDAAIYFMEEALQARLKDTENAIENMVGPDWKKRWLYWKNRTQEQCVHNETKNELEKMLKCNEEHPAYLASDEITTVRKNLESRGVEVDPSLIKDTWHQVYRRHFLKTALNHCNLCRRGFYYYQRHFVDSELECNDVVLFWRIQRMLAITANTLRQQLTNTEVRRLEKNVKEVLEDFAEDGEKKIKLLTGKRVQLAEDLKKVREIQEKLDAFIEALHQEK
8AVL , Knot 91 192 0.83 38 147 186 
MYEMPKLPYANNALEPVISQQTIDYHYGKHLQTYVNNLNSLVPGTEYEGKTVEAIVASAPDGAIFNNAGQVLNHTLYFLQFAPKPAKNEPAGKLGEAIKRDFGSFENFKKEFNAASVGLFGSGWAWLSVDKDGKLHITKEPNGSNPVRAGLKPLLGFDVWEHAYYLDYQNRRADHVNKLWEIIDWDVVEKRL
3PAQ , Knot 71 148 0.80 40 117 144 
AYLDEELQTELYEIKHQILQTMGVLSLQGSMLSVGDKVFSTNGQSVNFDTIKEMCTRAGGNIAVPRTPEENEAIASIAKKYNNYVYLGMIEDQTPGDFHYLDGASVSYTNWYPGEPRGQGKEKCVEMYTDGTWNDRGCLQYRLAVCEF

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 \(c\).

\(|P_{f(8EEW_1)}(2) \setminus P_{f(8AVL_1)}(2)|=178\), \(|P_{f(8AVL_1)}(2) \setminus P_{f(8EEW_1)}(2)|=26\). 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 1:1000100000010010000010010001100010000110010000001001110000011000010001101000110110000100000001101111100011000110111010111010101100011010100110011110000001010000011110001010100010010010100101010111100111101111100100111100000110100101001011110100101010001100110010101000111100101100011010010011010111101110111101010000010110000001100001100011010010000101110001101100010001001010010100010000101001000011001000110011010010100100110001100100011001011110010010100010101001000011001101110010001001100101000001100100110000100001001100010110001100001000001011101100110101000001100111101000110100000000100000001001100000011011000100100010001101010110001001000011001100001000110000001100010000111110100111101001000100001001000100110011001000101101001011001001001000101110110000
Pair \(Z_2\) Length of longest common subsequence
8EEW_1,8AVL_1 204 4
8EEW_1,3PAQ_1 226 3
8AVL_1,3PAQ_1 158 3

Newick tree

 
[
	8EEW_1:11.62,
	[
		8AVL_1:79,3PAQ_1:79
	]:36.62
]

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 \((0.85)(0.8)(\frac{958 }{\log_{20} 958}-\frac{192}{\log_{20}192})=209.\)
Status Protein1 Protein2 d d1/2
Query variables 8EEW_1 8AVL_1 266 164
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]