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Parikh vectors
5SIN_1 7JTH_1 6OVK_1 Letter Amino acid
21 44 32 A Alanine
24 57 9 E Glutamic acid
13 30 7 H Histidine
12 21 5 Y Tyrosine
16 49 14 V Valine
14 24 5 N Asparagine
15 52 10 D Aspartic acid
12 11 1 C Cysteine
15 26 6 F Phenylalanine
22 35 13 T Threonine
7 12 4 W Tryptophan
14 41 19 R Arginine
16 44 16 G Glycine
21 45 6 I Isoleucine
14 26 10 P Proline
24 62 8 S Serine
17 28 20 Q Glutamine
36 73 28 L Leucine
18 34 2 K Lycine
12 25 4 M Methionine 

5SIN_1|Chains A, B, C, D|cAMP and cAMP-inhibited cGMP 3',5'-cyclic phosphodiesterase 10A|Homo sapiens (9606)
>7JTH_1|Chains A, B, C, D, E, F, G, H|Fusicoccadiene synthase|Phomopsis amygdali (1214568)
>6OVK_1|Chain A[auth R]|Siderophore-interacting protein|Pseudomonas capeferrum (1495066)
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 \(w=f(c)\)
5SIN , Knot 152 343 0.86 40 221 334 
GSSICTSEEWQGLMQFTLPVRLCKEIELFHFDIGPFENMWPGIFVYMVHRSCGTSCFELEKLCRFIMSVKKNYRRVPYHNWKHAVTVAHCMYAILQNNHTLFTDLERKGLLIACLCHDLDHRGFSNSYLQKFDHPLAALYSTSTMEQHHFSQTVSILQLEGHNIFSTLSSSEYEQVLEIIRKAIIATDLALYFGNRKQLEEMYQTGSLNLNNQSHRDRVIGLMMTACDLCSVTKLWPVTKLTANDIYAEFWAEGDEMKKLGIQPIPMMDRDKKDEVPQGQLGFYNAVAIPCYTTLTQILPPTEPLLKACRDNLSQWEKVIRGEETATWISSPSVAQKAAASED
7JTH , Knot 284 739 0.84 40 299 685 
MGSSHHHHHHSSGLVPRGSHMEFKYSEVVEPSTYYTEGLCEGIDVRKSKFTTLEDRGAIRAHEDWNKHIGPCGEYRGTLGPRFSFISVAVPECIPERLEVISYANEFAFLHDDVTDHVGHDTGEVENDEMMTVFLEAAHTGAIDTSNKVDIRRAGKKRIQSQLFLEMLAIDPECAKTTMKSWARFVEVGSSRQHETRFVELAKYIPYRIMDVGEMFWFGLVTFGLGLHIPDHELELCRELMANAWIAVGLQNDIWSWPKERDAATLHGKDHVVNAIWVLMQEHQTDVDGAMQICRKLIVEYVAKYLEVIEATKNDESISLDLRKYLDAMLYSISGNVVWSLECPRYNPDVSFNKTQLEWMRQGLPSLESCPVLARSPEIDSDESAVSPTADESDSTEDSLGSGSRQDSSLSTGLSLSPVHSNEGKDLQRVDTDHIFFEKAVLEAPYDYIASMPSKGVRDQFIDALNDWLRVPDVKVGKIKDAVRVLHNSSLLLDDFQDNSPLRRGKPSTHNIFGSAQTVNTATYSIIKAIGQIMEFSAGESVQEVMNSIMILFQGQAMDLFWTYNGHVPSEEEYYRMIDQKTGQLFSIATSLLLNAADNEIPRTKIQSCLHRLTRLLGRCFQIRDDYQNLVSADYTKQKGFCEDLDEGKWSLALIHMIHKQRSHMALLNVLSTGRKHGGMTLEQKQFVLDIIEEEKSLDYTRSVMMDLHVQLRAEIGRIEILLDSPNPAMRLLLELLRV
6OVK , Knot 97 219 0.79 40 135 205 
GAMGQDWRADYHSRIGEQRRLTLADGTQVQLNTDSALNVAFDQQARRLRLVRGEMLITRPALADSRPLWVDTEHGRLESTLAQFNVRLHGQHTQATVYQGSVALQPALHAYPPILLGAGEQASFNQQGLLARQAVAAVAPAWSQGMLVAQGQPLAAFIEDLARYRRGHLACDPALAGLRVSGTFPLENTDKIIAAVAETLQLEVQHFTRYWVTLKPRMA

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 \(c\).

\(|P_{f(5SIN_1)}(2) \setminus P_{f(7JTH_1)}(2)|=49\), \(|P_{f(7JTH_1)}(2) \setminus P_{f(5SIN_1)}(2)|=127\). 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
5SIN_1,7JTH_1 176 4
5SIN_1,6OVK_1 208 4
7JTH_1,6OVK_1 212 3

Newick tree

 
[
	6OVK_1:11.09,
	[
		5SIN_1:88,7JTH_1:88
	]:22.09
]

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 \((0.85)(0.8)(\frac{1082 }{\log_{20} 1082}-\frac{343}{\log_{20}343})=195.\)
Status Protein1 Protein2 d d1/2
Query variables 5SIN_1 7JTH_1 252 184
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]