  Proteins can sometimes be knotted, and for many reasons the study of knotted
proteins is rapidly becoming very important. For example, it has been proposed
that a knot increases the stability of a protein. Knots may also alter
enzymatic activities and enhance binding. Moreover, knotted proteins may even
have some substantial biomedical significance in relation to illnesses such as
Parkinson's disease. But to a large extent the biological role of knots remains
a conundrum. In particular, there is no explanation why knotted proteins are so
scarce. Here we argue that knots are relatively rare because they tend to cause
swelling in proteins that are too short, and presently short proteins are
over-represented in the Protein Data Bank (PDB). Using Monte Carlo simulations
we predict that the figure-8 knot leads to the most compact protein
configuration when the number of amino acids is in the range of 200-600. For
the existence of the simplest knot, the trefoil, we estimate a theoretical
upper bound of 300-400 amino acids, in line with the available PDB data.
