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Parikh vectors
5XVW_1 8QZG_1 1FHM_1 Letter Amino acid
2 13 1 Q Glutamine
2 12 0 H Histidine
9 13 0 S Serine
4 11 3 Y Tyrosine
10 22 8 D Aspartic acid
6 16 4 K Lycine
2 10 1 M Methionine
9 34 5 P Proline
3 5 1 W Tryptophan
10 37 0 A Alanine
3 1 4 C Cysteine
11 14 5 E Glutamic acid
7 6 2 F Phenylalanine
17 31 1 L Leucine
4 21 3 T Threonine
9 18 5 V Valine
11 18 0 R Arginine
7 7 3 N Asparagine
6 22 6 G Glycine
3 17 2 I Isoleucine 

5XVW_1|Chains A, B, D[auth C], E|PHD finger protein ALFIN-LIKE 2|Arabidopsis thaliana (3702)
>8QZG_1|Chain A[auth 1]|YkuD domain-containing protein|Gluconobacter oxydans (442)
>1FHM_1|Chain A|RUBREDOXIN|Clostridium pasteurianum (1501)
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 \(w=f(c)\)
5XVW , Knot 68 135 0.82 40 106 133 
GSPRTVEEIFKDYSARRAALLRALTKDVDDFYSQCDPEKENLCLYGHPNESWEVNLPAEEVPPELPEPALGINFARDGMQRKDWLSLVAVHSDCWLLSVSFYFGARLNRNERKRLFSLINDLPTLFDVVTGRKAM
8QZG , Knot 141 328 0.83 40 190 314 
MKYLLPTAAAGLLLLAAQPAMAMDIGINSASVPPPASNPPTDTPPQPDLAPPPIDIPDLPVVSDEVAREEASRLAVLMKHNVKGFSTYTPERRKAFLTLAKDAVTQADMPVSRPQLVMVVDRNEKIQHLDYVLALPDAPWESLGGTPVSTGTTGRKYYYITPTGVFQNTADRLGYRAEGTKNKYGIRGIGAKGSRVWDMGWQTAMKGWLPRHETGQIRLEIHATDPQFLEWRLGHPASEGCIRIPATMNKFMDHYGLIDALYEQAASYDPRFQALLPKDRQPTQIAGDLVVVIDSGPLTEPKIDPIADKRPLPAAKLAAALEHHHHHH
1FHM , Knot 31 54 0.76 32 46 52 
MKKYTCTVCGYIYNPEDGDPDNGVNPGTDFKDIPDDWVCPLCGVGKDQFEEVEE

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 \(c\).

\(|P_{f(5XVW_1)}(2) \setminus P_{f(8QZG_1)}(2)|=45\), \(|P_{f(8QZG_1)}(2) \setminus P_{f(5XVW_1)}(2)|=129\). 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 1:101001001100001001111011000100100000100001010101000101011100111011011111011001100001101111000011101010111010000000110110011011011010011
Pair \(Z_2\) Length of longest common subsequence
5XVW_1,8QZG_1 174 4
5XVW_1,1FHM_1 124 3
8QZG_1,1FHM_1 196 4

Newick tree

 
[
	8QZG_1:10.83,
	[
		5XVW_1:62,1FHM_1:62
	]:38.83
]

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 \((0.85)(0.8)(\frac{463 }{\log_{20} 463}-\frac{135}{\log_{20}135})=97.6\)
Status Protein1 Protein2 d d1/2
Query variables 5XVW_1 8QZG_1 122 85.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]