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Parikh vectors
8FVK_1 6AYY_1 5HOO_1 Letter Amino acid
12 14 16 P Proline
8 19 15 T Threonine
7 8 12 Y Tyrosine
5 40 25 A Alanine
6 27 20 D Aspartic acid
8 17 29 E Glutamic acid
1 14 12 H Histidine
12 10 29 K Lycine
5 31 21 V Valine
3 23 28 R Arginine
12 9 11 N Asparagine
2 6 5 C Cysteine
5 13 6 M Methionine
3 1 10 W Tryptophan
13 23 28 L Leucine
2 22 18 S Serine
9 4 21 Q Glutamine
2 40 13 G Glycine
7 20 9 I Isoleucine
5 6 17 F Phenylalanine 

8FVK_1|Chains A, B|Bromodomain-containing protein 4|Homo sapiens (9606)
>6AYY_1|Chains A, B|Fructose-1,6-bisphosphatase class 2|Mycobacterium tuberculosis (83331)
>5HOO_1|Chains A, B|Mariner Mos1 transposase|Drosophila mauritiana (7226)
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 \(w=f(c)\)
8FVK , Knot 66 127 0.84 40 110 123 
SMNPPPPETSNPNKPKRQTNQLQYLLRVVLKTLWKHQFAWPFQQPVDAVKLNLPDYYKIIKTPMDMGTIKKRLENNYYWNAQECIQDFNTMFTNCYIYNKPGDDIVLMAEALEKLFLQKINELPTEE
6AYY , Knot 145 347 0.81 40 197 326 
GSSHHHHHHSSGLVPRGSHMELVRVTEAGAMAAGRWVGRGDKEGGDGAAVDAMRELVNSVSMRGVVVIGEGEKDHAPMLYNGEEVGNGDGPECDFAVDPIDGTTLMSKGMTNAISVLAVADRGTMFDPSAVFYMNKIAVGPDAAHVLDITAPISENIRAVAKVKDLSVRDMTVCILDRPRHAQLIHDVRATGARIRLITDGDVAGAISACRPHSGTDLLAGIGGTPEGIIAAAAIRCMGGAIQAQLAPRDDAERRKALEAGYDLNQVLTTEDLVSGENVFFCATGVTDGDLLKGVRYYPGGCTTHSIVMRSKSGTVRMIEAYHRLSKLNEYSAIDFTGDSSAVYPLP
5HOO , Knot 150 345 0.84 40 210 331 
MSSFVPNKEQTRTVLIFCFHLKKTAAESHRMLVEAFGEQVPTVKTCERWFQRFKSGDFDVDDKEHGKPPKRYEDAELQALLDEDDAQTQKQLAEQLEVSQQAVSNRLREMGKIQKVGRWVPHELNERQMERRKNTCEILLSRYKRKSFLHRIVTGDEKWIFFVNPKRKKSYVDPGQPATSTARPNRFGKKTMLCVWWDQSGVIYYELLKPGETVNAARYQQQLINLNRALQRKRPEYQKRQHRVIFLHDNAPSHTARAVRDTLETLNWEVLPHAAYSPDLAPSDYHLFASMGHALAEQRFDSYESVKKWLDEWFAAKDDEFYWRGIHKLPERWEKCVASDGKYFE

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 \(c\).

\(|P_{f(8FVK_1)}(2) \setminus P_{f(6AYY_1)}(2)|=52\), \(|P_{f(6AYY_1)}(2) \setminus P_{f(8FVK_1)}(2)|=139\). 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 1:0101111000010010000001001101110011000111110011011010110000110011011010001000001010001001001100001000110011111011001110010011000
Pair \(Z_2\) Length of longest common subsequence
8FVK_1,6AYY_1 191 3
8FVK_1,5HOO_1 186 3
6AYY_1,5HOO_1 183 4

Newick tree

 
[
	8FVK_1:95.15,
	[
		5HOO_1:91.5,6AYY_1:91.5
	]:3.65
]

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 \((0.85)(0.8)(\frac{474 }{\log_{20} 474}-\frac{127}{\log_{20}127})=103.\)
Status Protein1 Protein2 d d1/2
Query variables 8FVK_1 6AYY_1 132 90.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]