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Parikh vectors
5DAX_1 6HCT_1 6EOX_1 Letter Amino acid
3 4 0 C Cysteine
13 6 19 G Glycine
35 0 9 L Leucine
7 0 4 M Methionine
24 0 9 S Serine
17 0 7 R Arginine
14 0 7 N Asparagine
16 0 14 D Aspartic acid
12 0 7 K Lycine
22 0 6 P Proline
7 0 2 Q Glutamine
19 0 4 E Glutamic acid
4 0 7 Y Tyrosine
4 0 3 W Tryptophan
20 0 9 V Valine
27 6 12 A Alanine
13 0 9 H Histidine
22 0 11 I Isoleucine
6 0 10 F Phenylalanine
23 0 10 T Threonine 

5DAX_1|Chain A|Phytanoyl-CoA dioxygenase family protein (AFU_orthologue AFUA_8G00230)|Aspergillus nidulans FGSC A4 (227321)
>6HCT_1|Chains A, B|RNA (5'-R(*GP*CP*CP*GP*AP*UP*GP*AP*AP*UP*GP*CP*AP*UP*GP*AP*AP*GP*C)-3')|Archaeoglobus fulgidus DSM 4304 (224325)
>6EOX_1|Chain A|Macrophage metalloelastase|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 \(w=f(c)\)
5DAX , Knot 134 308 0.83 40 180 294 
STSKDHVKSQIPRLSAINDLHKIWPTVEEHGAAIIESFLSLDIVRRLNEEVDPFVKIEPIPAAKTKDHPNHVLSTTTRLVNVLAPISKAYREDVLNSKVLHRICSDAFHVYGDYWVLMGAVMELAPSNPAQPLHRDMRFSHPIVEYLKPDAPATSINFLVALSPFTAENGATHVILGSHKWQNLSNVSMDATVRALMNPGDALLITDSTIHCGGAETTGTETRRLLTITMGISQLTPLESNLAVPRPVIESLTPLAQRLLGWASQRSAAPRDIGLLTIRGNSIEKTMNLKAEQPLHDDEAEPLCRETI
6HCT , Knot 9 19 0.46 8 9 13 
GCCGAUGAAUGCAUGAAGC
6EOX , Knot 79 159 0.84 38 120 154 
MGPVWRKHYITYRINNYTPDMNREDVDYAIRKAFQVWSNVTPLKFSKINTGMADILVVFARGAHGDDHAFDGKGGILAHAFGPGSGIGGDAHFDEDEFWTTHSGGTNLFLTAVHEIGHSLGLGHSSDPKAVMFPTYKYVDINTFRLSADDIRGIQSLYG

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 \(c\).

\(|P_{f(5DAX_1)}(2) \setminus P_{f(6HCT_1)}(2)|=177\), \(|P_{f(6HCT_1)}(2) \setminus P_{f(5DAX_1)}(2)|=6\). 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 1:00000010001101011001001110100011111001101011001000101110101111100000100110000011011111001000011000110010001101010011111111011100110110001010011100101011100101111101101001100111100010010010101010111011011110000100111000100000110101110010110001111011100101110011111000011100111101010010001010100110000101100001
Pair \(Z_2\) Length of longest common subsequence
5DAX_1,6HCT_1 183 3
5DAX_1,6EOX_1 174 4
6HCT_1,6EOX_1 127 2

Newick tree

 
[
	5DAX_1:96.35,
	[
		6EOX_1:63.5,6HCT_1:63.5
	]:32.85
]

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 \((0.85)(0.8)(\frac{327 }{\log_{20} 327}-\frac{19}{\log_{20}19})=101.\)
Status Protein1 Protein2 d d1/2
Query variables 5DAX_1 6HCT_1 131 68.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]