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Parikh vectors
7CHD_1 6STD_1 5CZC_1 Letter Amino acid
14 7 40 A Alanine
10 16 21 D Aspartic acid
10 13 24 G Glycine
2 7 4 W Tryptophan
4 1 5 C Cysteine
7 4 8 Q Glutamine
11 6 10 H Histidine
10 8 8 I Isoleucine
9 13 3 K Lycine
2 5 12 M Methionine
6 5 15 P Proline
25 11 30 L Leucine
9 9 16 F Phenylalanine
6 7 7 Y Tyrosine
9 11 29 R Arginine
8 1 4 N Asparagine
11 12 24 E Glutamic acid
10 8 15 S Serine
11 10 27 T Threonine
9 10 26 V Valine 

7CHD_1|Chains A, B, C, D, E, F, G, H|N-acetyltransferase domain-containing protein|Escherichia coli O157:H7 (83334)
>6STD_1|Chains A, B, C|Scytalone dehydratase|Magnaporthe grisea (148305)
>5CZC_1|Chains A, B|Malonyl-CoA-[acyl-carrier-protein] transacylase|Streptomyces halstedii (1944)
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 \(w=f(c)\)
7CHD , Knot 83 183 0.78 40 131 176 
MDDLTIEILTDDADYDLQRFDCGEEALNLFLTTHLVRQHRNKILRAYILCRNTPERQVLGYYTLCGSCFERAALPSKSKQKKIPYKNIPSVTLGRLAIDRSLQGQGWDATLVAHAMNVVWSASLAVGIHGLFVEALNEKAHTFYKSLGFIPLVGENENALFFPTKSIELLFTQSDLEHHHHHH
6STD , Knot 82 164 0.85 40 130 159 
GEITFSDYLGLMTCVYEWADSYDSKDWDRLRKVIAPTLRIDYRSFLDKLWEAMPAEEFVGMVSSKQVLGDPTLRTQHFIGGTRWEKVSEDEVIGYHQLRVPHQRYKDTTMKEVTMKGHAHSANLHWYKKIDGVWKFAGLKPDIRWGEFDFDRIFEDGRETFGDK
5CZC , Knot 139 328 0.81 40 187 314 
HMNATVETTQHDVEGTGAAGATAMLFPGMGPAAFSDVGRFMVTNRYTRELLAEADDTLGYSLVDRFRQAEGDYSEYAQIAFLVNCVALARWAEQTMDLTPRICAGASFGEKSVAAYSGALTFADAVRMTAGLARCMDEYFRTEHLGVVTHSFVRAPRERLDEILAELDERGEWHEISCHIDHDFFMLTLHERNSVWLEGRLRSVGAMPLYAMRPPMHAAAFGGLRDKAEEEVIAPLTFHDPTLPVVADQDGKVLTTGDEVRTMLLESFVRPLRWPDVISSLQDQGVTRVCVAGPDSLFGRVGTTTRAFEVIAATPRLALQPRARTTSR

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 \(c\).

\(|P_{f(7CHD_1)}(2) \setminus P_{f(6STD_1)}(2)|=85\), \(|P_{f(6STD_1)}(2) \setminus P_{f(7CHD_1)}(2)|=84\). 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 1:100101011000100010010010011011100011000000110101100001000111000101001001111000000011000110101101110001010110101110110111010111110111101100010010001111111100001111100010111000010000000
Pair \(Z_2\) Length of longest common subsequence
7CHD_1,6STD_1 169 4
7CHD_1,5CZC_1 164 3
6STD_1,5CZC_1 163 4

Newick tree

 
[
	7CHD_1:83.83,
	[
		5CZC_1:81.5,6STD_1:81.5
	]:2.33
]

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 \((0.85)(0.8)(\frac{347 }{\log_{20} 347}-\frac{164}{\log_{20}164})=55.3\)
Status Protein1 Protein2 d d1/2
Query variables 7CHD_1 6STD_1 71 68
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]