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Parikh vectors
5UUY_1 1XKV_1 7LYZ_1 Letter Amino acid
11 30 3 F Phenylalanine
4 8 6 W Tryptophan
16 53 6 V Valine
6 14 3 Q Glutamine
18 42 8 L Leucine
1 8 2 M Methionine
22 25 7 T Threonine
7 23 3 Y Tyrosine
17 44 12 G Glycine
15 15 6 I Isoleucine
11 40 2 P Proline
13 16 14 N Asparagine
19 20 7 D Aspartic acid
4 13 1 H Histidine
4 45 2 E Glutamic acid
10 20 6 K Lycine
32 24 10 S Serine
19 47 12 A Alanine
8 40 11 R Arginine
0 2 8 C Cysteine 

5UUY_1|Chain A|Dioclea lasiocarpa lectin (DLL)|Dioclea lasiocarpa (3836)
>1XKV_1|Chains A, B|ATP-dependent phosphoenolpyruvate carboxykinase|Thermus thermophilus (300852)
>7LYZ_1|Chain A|HEN EGG WHITE LYSOZYME|Gallus gallus (9031)
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 \(w=f(c)\)
5UUY , Knot 105 237 0.80 38 147 224 
ADTIVAVELDSYPNTDIGDPSYPHIGIDIKSIRSKATARWNMQTGKVGTAHISYNSVAKRLSAVVSYSGTSSTTVSYDVDLNNVLPEWVRVGLSATTGLYKETNTILSWSFTSKLKTNSIADANSLHFSFNQFSQNPKDLILQGDATTDSDGNLQLTRVSSDGSPQGSSVGRALFYAPVHIWEKSAVVASFDATFTFLIKSPDRDPADGITFFIANTDTSIPSGSGGRLLGLFPDAN
1XKV , Knot 211 529 0.83 40 235 487 
MQRLEALGIHPKKRVFWNTVSPVLVEHTLLRGEGLLAHHGPLVVDTTPYTGRSPKDKFVVREPEVEGEIWWGEVNQPFAPEAFEALYQRVVQYLSERDLYVQDLYAGADRRYRLAVRVVTESPWHALFARNMFILPRRFGNDDEVEAFVPGFTVVHAPYFQAVPERDGTRSEVFVGISFQRRLVLIVGTKYAGEIKKSIFTVMNYLMPKRGVFPMHASANVGKEGDVAVFFGLSGTGKTTLSTDPERPLIGDDEHGWSEDGVFNFEGGCYAKVIRLSPEHEPLIYKASNQFEAILENVVVNPESRRVQWDDDSKTENTRSSYPIAHLENVVESGVAGHPRAIFFLSADAYGVLPPIARLSPEEAMYYFLSGYTARVAGTERGVTEPRATFSACFGAPFLPMHPGVYARMLGEKIRKHAPRVYLVNTGWTGGPYGVGYRFPLPVTRALLKAALSGALENVPYRRDPVFGFEVPLEAPGVPQELLNPRETWADKEAYDQQARKLARLFQENFQKYASGVAKEVAEAGPRTE
7LYZ , Knot 66 129 0.82 40 104 127 
KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL

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 \(c\).

\(|P_{f(5UUY_1)}(2) \setminus P_{f(1XKV_1)}(2)|=39\), \(|P_{f(1XKV_1)}(2) \setminus P_{f(5UUY_1)}(2)|=127\). 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 1:100111101000100011010010111010010001010101001011010100001100101110001000001000101001110110111010011000000110101000100001101001010100100010011101010000010101001000101010011011101110110001111010101011100100011011011110000011010110111111010
Pair \(Z_2\) Length of longest common subsequence
5UUY_1,1XKV_1 166 3
5UUY_1,7LYZ_1 161 4
1XKV_1,7LYZ_1 219 3

Newick tree

 
[
	1XKV_1:10.10,
	[
		5UUY_1:80.5,7LYZ_1:80.5
	]:21.60
]

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 \((0.85)(0.8)(\frac{766 }{\log_{20} 766}-\frac{237}{\log_{20}237})=146.\)
Status Protein1 Protein2 d d1/2
Query variables 5UUY_1 1XKV_1 184 131.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]