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Parikh vectors
6LJV_1 8IXQ_1 3FOZ_1 Letter Amino acid
2 9 8 Y Tyrosine
7 49 24 R Arginine
2 1 2 C Cysteine
8 18 8 H Histidine
2 22 17 P Proline
6 79 40 A Alanine
4 6 2 N Asparagine
8 9 19 I Isoleucine
6 7 8 M Methionine
6 14 9 F Phenylalanine
14 17 20 S Serine
2 7 5 W Tryptophan
2 8 18 Q Glutamine
13 37 20 G Glycine
6 43 37 L Leucine
14 4 10 K Lycine
11 29 17 D Aspartic acid
9 30 24 E Glutamic acid
12 19 12 T Threonine
18 43 16 V Valine 

6LJV_1|Chain A|Fatty acid-binding protein, adipocyte|Homo sapiens (9606)
>8IXQ_1|Chains A, B, C, D|Glycosyltransferase|Streptomyces lincolnensis (1915)
>3FOZ_1|Chains A, B|tRNA delta(2)-isopentenylpyrophosphate transferase|Escherichia coli K-12 (83333)
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 \(w=f(c)\)
6LJV , Knot 74 152 0.81 40 112 143 
MGSSHHHHHHSSGLVPRGSHMCDAFVGTWKLVSSENFDDYMKEVGVGFATRKVAGMAKPNMIISVNGDVITIKSESTFKNTEISFILGQEFDEVTADDRKVKSTITLDGGVLVHVQKWDGKSTTIKRKREDDKLVVECVMKGVTSTRVYERA
8IXQ , Knot 172 451 0.77 40 184 390 
MTARTERGRALAFVWLMVEGAQVAAGGVAGYVRNLLDEQDALRDHLAERGWSVEFVLGEPFYDPGAPGYDEERWRRVREHLAARGGRAVRLVSDSDGLDGWGEERFFHALSATGAQLVLDTAERCDAVVAVSGTSAFARVPGMVQRQGGELAAKVLHVHTFGLATHDTAHVPSPAEIAADGDVAFWTRQSDRVSVGYISRYTAELYARTYAIPAAALLPNRSAIPRHAPRFGVLTEERINERIAGLGLPAEGEFVVMWGRNSAPGLDKGYHLLLEAARDLPGVVPVIATRRPDPGLRRLADRYAVPAVLLDDQPFTHLSALLQSPRTLAAAFLGEAEPGAVSPMEAMWVARESGALVIAADTGNLPEVVDDGAAGIVTRRTAADVADAVRRVRKLTADERRRMRAAAAARVRARFDFAANVRELADAAVDRLAEVSKLAAALEHHHHHHHH
3FOZ , Knot 134 316 0.81 40 174 297 
MSDISKASLPKAIFLMGPTASGKTALAIELRKILPVELISVDSALIYKGMDIGTAKPNAEELLAAPHRLLDIRDPSQAYSAADFRRDALAEMADITAAGRIPLLVGGTMLYFKALLEGLSPLPSADPEVRARIEQQAAEQGWESLHRQLQEVDPVAAARIHPNDPQRLSRALEVFFISGKTLTELTQTSGDALPYQVHQFAIAPASRELLHQRIEQRFHQMLASGFEAEVRALFARGDLHTDLPSIRCVGYRQMWSYLEGEISYDEMVYRGVCATRQLAKRQITWLRGWEGVHWLDSEKPEQARDEVLQVVGAIAG

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 \(c\).

\(|P_{f(6LJV_1)}(2) \setminus P_{f(8IXQ_1)}(2)|=49\), \(|P_{f(8IXQ_1)}(2) \setminus P_{f(6LJV_1)}(2)|=121\). 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 1:11000000000011110100100111101011000010001001111110001111101011101010110100000100001011110010010100001000101011111010010100001000000001110011011000010001
Pair \(Z_2\) Length of longest common subsequence
6LJV_1,8IXQ_1 170 6
6LJV_1,3FOZ_1 180 4
8IXQ_1,3FOZ_1 154 4

Newick tree

 
[
	6LJV_1:90.77,
	[
		8IXQ_1:77,3FOZ_1:77
	]:13.77
]

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 \((0.85)(0.8)(\frac{603 }{\log_{20} 603}-\frac{152}{\log_{20}152})=130.\)
Status Protein1 Protein2 d d1/2
Query variables 6LJV_1 8IXQ_1 158 106
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]