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Parikh vectors
5FVJ_1 1IJQ_1 1NVP_1 Letter Amino acid
7 26 0 S Serine
7 12 0 E Glutamic acid
7 8 0 H Histidine
2 7 1 C Cysteine
9 10 0 F Phenylalanine
10 22 2 T Threonine
14 23 0 V Valine
18 17 5 A Alanine
6 19 0 N Asparagine
7 14 0 P Proline
8 7 0 Q Glutamine
3 6 0 M Methionine
15 19 9 G Glycine
6 20 0 I Isoleucine
18 33 0 L Leucine
9 13 0 K Lycine
1 9 0 W Tryptophan
2 9 0 Y Tyrosine
10 19 0 R Arginine
7 23 0 D Aspartic acid 

5FVJ_1|Chains A, B|PUTATIVE ACETYLTRANSFERASE|SALMONELLA ENTERICA SUBSP. ENTERICA SEROVAR TYPHIMURIUM (90371)
>1IJQ_1|Chains A, B|LOW-DENSITY LIPOPROTEIN RECEPTOR|Homo sapiens (9606)
>1NVP_1|Chain A[auth E]|5'-D(*GP*GP*GP*GP*GP*GP*GP*CP*TP*AP*TP*AP*AP*AP*AP*GP*G)-3'|
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 \(w=f(c)\)
5FVJ , Knot 82 166 0.84 40 131 158 
GPGGTMGRVTAPEPLSAFHQVAEFVSGEAVLDDWLKQKGLKNQALGAARTFVVCKKDTKQVAGFYSLATGSVNHTEATGNLRRNMPDPIPVIILARLAVDLSFHGKGLGADLLHDAVLRCYRVAENIGVRAIMVHALTEEAKNFFIHHGFKSSQTQQRTLFLRLPQ
1IJQ , Knot 138 316 0.83 40 199 300 
IAYLFFTNRHEVRKMTLDRSEYTSLIPNLRNVVALDTEVASNRIYWSDLSQRMICSTQLDRAHGVSSYDTVISRDIQAPDGLAVDWIHSNIYWTDSVLGTVSVADTKGVKRKTLFRENGSKPRAIVVDPVHGFMYWTDWGTPAKIKKGGLNGVDIYSLVTENIQWPNGITLDLLSGRLYWVDSKLHSISSIDVNGGNRKTILEDEKRLAHPFSLAVFEDKVFWTDIINEAIFSANRLTGSDVNLLAENLLSPEDMVLFHNLTQPRGVNWCERTTLSNGGCQYLCLPAPQINPHSPKFTCACPDGMLLARDMRSCLT
1NVP , Knot 7 17 0.38 8 7 10 
GGGGGGGCTATAAAAGG

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 \(c\).

\(|P_{f(5FVJ_1)}(2) \setminus P_{f(1IJQ_1)}(2)|=55\), \(|P_{f(1IJQ_1)}(2) \setminus P_{f(5FVJ_1)}(2)|=123\). 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 1:1111011010110110110011011010111001100011000111110011100000001111001101010000101010001101111111101110101010111101100111000011001110111101100010011100110000000001110110
Pair \(Z_2\) Length of longest common subsequence
5FVJ_1,1IJQ_1 178 4
5FVJ_1,1NVP_1 128 2
1IJQ_1,1NVP_1 202 3

Newick tree

 
[
	1IJQ_1:10.51,
	[
		5FVJ_1:64,1NVP_1:64
	]:39.51
]

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 \((0.85)(0.8)(\frac{482 }{\log_{20} 482}-\frac{166}{\log_{20}166})=92.7\)
Status Protein1 Protein2 d d1/2
Query variables 5FVJ_1 1IJQ_1 116 88.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]