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Parikh vectors
7HSK_1 3FFV_1 3KVH_1 Letter Amino acid
23 22 34 L Leucine
6 9 10 F Phenylalanine
9 9 10 P Proline
28 17 6 T Threonine
11 12 19 A Alanine
19 7 14 R Arginine
21 16 13 E Glutamic acid
8 4 4 Y Tyrosine
12 6 5 N Asparagine
21 7 17 G Glycine
13 6 14 H Histidine
21 8 13 S Serine
15 9 3 I Isoleucine
14 8 9 K Lycine
7 2 8 M Methionine
7 4 2 W Tryptophan
22 10 16 V Valine
19 10 6 D Aspartic acid
4 4 3 C Cysteine
15 11 8 Q Glutamine 

7HSK_1|Chains A, B|Oleoyl-acyl carrier protein thioesterase 1, chloroplastic|Arabidopsis thaliana (3702)
>3FFV_1|Chains A, B|Protein syd|Escherichia coli (83333)
>3KVH_1|Chain A|Protein syndesmos|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 \(w=f(c)\)
7HSK , Knot 131 295 0.84 40 189 276 
MGSLTEDGLSYKEKFVVRSYEVGSNKTATVETIANLLQEVGCNHAQSVGFSTDGFATTTTMRKLHLIWVTARMHIEIYKYPAWGDVVEIETWCQSEGRIGTRRDWILKDSVTGEVTGRATSKWVMMNQDTRRLQKVSDDVRDEYLVFCPQEPRLAFPEENNRSLKKIPKLEDPAQYSMIGLKPRRADLDMNQHVNNVTYIGWVLESIPQEIVDTHELQVITLDYRRECQQDDVVDSLTTTTSEIGGTNGSATSGTQGHNDSQFLHLLRLSGDGQEINRGTTLWRKKPSSHHHHHH
3FFV , Knot 88 181 0.84 40 138 178 
MDDLTAQALKDFTARYCDAWHEEHKSWPLSEELYGVPSPCIISTTEDAVYWQPQPFTGEQNVNAVERAFDIVIQPTIHTFYTTQFAGDMHAQFGDIKLTLLQTWSEDDFRRVQENLIGHLVTQKRLKLPPTLFIATLEEELEVISVCNLSGEVCKETLGTRKRTHLASNLAEFLNQLKPLL
3KVH , Knot 94 214 0.78 40 130 197 
MVPELKQISRVEAMRLGPGWSHSCHAMLYAANPGQLFGRIPMRFSVLMQMRFDGLLGFPGGFVDRRFWSLEDGLNRVLGLGLGCLRLTEADYLSSHLTEGPHRVVAHLYARQLTLEQLHAVEISAVHSRDHGLEVLGLVRVPLYTQKDRVGGFPNFLSNAFVSTAKCQLLFALKVLNMMPEEKLVEALAAATEKQKKALEKLLPASSAHHHHHH

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 \(c\).

\(|P_{f(7HSK_1)}(2) \setminus P_{f(3FFV_1)}(2)|=117\), \(|P_{f(3FFV_1)}(2) \setminus P_{f(7HSK_1)}(2)|=66\). 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 1:1101000110000011100001100001010011011001100010011100011100001001011110101010100011110110100100001011000011100010101010100011110000001001000100001110100101111000000100110100110001111010010101000100100111110011001100001011010000000000110010000001110010100100100000110110101010010010011000100000000
Pair \(Z_2\) Length of longest common subsequence
7HSK_1,3FFV_1 183 3
7HSK_1,3KVH_1 173 6
3FFV_1,3KVH_1 168 3

Newick tree

 
[
	7HSK_1:90.65,
	[
		3KVH_1:84,3FFV_1:84
	]:6.65
]

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 \((0.85)(0.8)(\frac{476 }{\log_{20} 476}-\frac{181}{\log_{20}181})=86.3\)
Status Protein1 Protein2 d d1/2
Query variables 7HSK_1 3FFV_1 109 88
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]