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Parikh vectors
6HVQ_1 4JBA_1 5HWO_1 Letter Amino acid
8 12 32 V Valine
3 7 32 R Arginine
8 7 13 I Isoleucine
4 6 16 P Proline
4 2 17 Y Tyrosine
17 25 41 L Leucine
8 3 10 M Methionine
10 2 4 F Phenylalanine
6 10 23 S Serine
7 6 5 N Asparagine
0 1 7 C Cysteine
16 8 27 E Glutamic acid
8 7 41 G Glycine
10 9 19 T Threonine
2 1 4 W Tryptophan
5 6 13 Q Glutamine
9 9 71 A Alanine
12 8 23 D Aspartic acid
6 3 9 H Histidine
13 12 13 K Lycine 

6HVQ_1|Chains A, B, C, D, F|DNA protection during starvation protein|Listeria innocua serovar 6a (strain ATCC BAA-680 / CLIP 11262) (272626)
>4JBA_1|Chains A, B|Multiple antibiotic resistance protein MarR|Escherichia coli (83333)
>5HWO_1|Chain A|Hydroxymethylglutaryl-CoA synthase|Myxococcus xanthus (strain DK 1622) (246197)
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 \(w=f(c)\)
6HVQ , Knot 78 156 0.84 38 123 151 
MKTINSVDTKEFLNHQVANLNVFTVKIHQIHWYMRGHNFFTLHEKMDDLYSEFGEQMDEVAERLLAIGGSPFSTLKEFLENASVEEAPYTKPKTMDQLMEDLVGTLELLRDEYKQGIELTDKEGDDVTNDMLIAFKASIDKHIWMFKAFLGKAPLE
4JBA , Knot 69 144 0.79 40 104 135 
MKSTSDLFNEIIPLGRLIHMVNQKKDRLLNEYLSPLDITAAQFKVLSSIRSAASITPVELKKVLSVDLGALTRMLDRLVCKGWVERLPNPNDKRGVLVKLTTGGAAISEQSHQLVGQDLHQELTKNLTADEVATLEYLLKKVLP
5HWO , Knot 165 420 0.79 40 198 371 
GHMKKRVGIEALAVAVPSRYVDIEDLARARGVDPAKYTAGLGAREMAVTDPGEDTVALAATAAARLIRQQDVDPSRIGMLVVGTETGIDHSKPVASHVQGLLKLPRTMRTYDTQHACYGGTAGLMAAVEWIASGAGAGKVAVVVCSDIARYGLNTAGEPTQGGGAVALLVSEQPDLLAMDVGLNGVCSMDVYDFWRPVGRREALVDGHYSITCYLEALSGAYRGWREKALAAGLVRWSDALPGEQLARIAYHVPFCKMARKAHTQLRLCDLEDAADAAASTPESREAQAKSAASYDAQVATSLGLNSRIGNVYTASLYLALAGLLQHEAGALAGQRIGLLSYGSGCAAEFYSGTVGEKAAERMAKADLEAVLARRERVSIEEYERLMKLPADAPEAVAPSPGAFRLTEIRDHRRQYAEGN

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 \(c\).

\(|P_{f(6HVQ_1)}(2) \setminus P_{f(4JBA_1)}(2)|=80\), \(|P_{f(4JBA_1)}(2) \setminus P_{f(6HVQ_1)}(2)|=61\). 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 1:100100100001100011010110101001010101001101000100100011001001100111111011001001100101001100010010011001110101100000011010000100100011111010100011110111101110
Pair \(Z_2\) Length of longest common subsequence
6HVQ_1,4JBA_1 141 4
6HVQ_1,5HWO_1 181 3
4JBA_1,5HWO_1 176 4

Newick tree

 
[
	5HWO_1:94.68,
	[
		6HVQ_1:70.5,4JBA_1:70.5
	]:24.18
]

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 \((0.85)(0.8)(\frac{300 }{\log_{20} 300}-\frac{144}{\log_{20}144})=48.1\)
Status Protein1 Protein2 d d1/2
Query variables 6HVQ_1 4JBA_1 61 57
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]