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Parikh vectors
5SJA_1 5GPI_1 1GBW_1 Letter Amino acid
16 19 8 V Valine
24 10 3 E Glutamic acid
18 12 5 K Lycine
7 5 5 W Tryptophan
16 26 11 G Glycine
21 7 6 I Isoleucine
36 14 8 L Leucine
12 3 2 M Methionine
22 11 5 T Threonine
21 12 14 A Alanine
14 8 14 R Arginine
14 3 10 N Asparagine
15 11 8 D Aspartic acid
12 6 6 Y Tyrosine
15 2 2 F Phenylalanine
14 10 2 P Proline
24 9 6 S Serine
12 2 8 C Cysteine
17 6 6 Q Glutamine
13 2 1 H Histidine 

5SJA_1|Chains A, B, C, D|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>5GPI_1|Chains A[auth B], F[auth D], G[auth F], H|NS3 protease|Zika virus (64320)
>1GBW_1|Chain A|LYSOZYME|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 \(w=f(c)\)
5SJA , Knot 152 343 0.86 40 221 334 
GSSICTSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
5GPI , Knot 86 178 0.83 40 127 175 
GSGALWDVPAPKEVKKGETTDGVYRVMTRRLLGSTQVGVGVMQEGVFHTMWHVTKGAALRSGEGRLDPYWGDVKQDLVSYCGPWKLDAAWDGLSEVQLLAVPPGERAKNIQTLPGIFKTKDGDIGAVALDYPAGTSGSPILDKCGRVIGLYGNGVVIKNGSYVSAITQGKREEETPVE
1GBW , Knot 68 130 0.84 40 109 128 
KVFERCELARTLKRLGMDGYRGISLANWMCLAKWESGYNTRATNYNAGDRSTDYGIFQINSRYWCNDGKTPGAVNACHLSCSALLQDNIADAVACAKRVVRDPQGIRAWIAWRNRCQNRDVRQYVQGCGV

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 \(c\).

\(|P_{f(5SJA_1)}(2) \setminus P_{f(5GPI_1)}(2)|=142\), \(|P_{f(5GPI_1)}(2) \setminus P_{f(5SJA_1)}(2)|=48\). 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
5SJA_1,5GPI_1 190 5
5SJA_1,1GBW_1 218 3
5GPI_1,1GBW_1 142 3

Newick tree

 
[
	5SJA_1:11.71,
	[
		5GPI_1:71,1GBW_1:71
	]:39.71
]

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 \((0.85)(0.8)(\frac{521 }{\log_{20} 521}-\frac{178}{\log_{20}178})=99.6\)
Status Protein1 Protein2 d d1/2
Query variables 5SJA_1 5GPI_1 127 95
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]