Modern naturally occurring proteins have been produced by a lengthy selecti
ve evolutionary process. While, in general, they are all composed of the sa
me 20 amino acids there is a distinct bias in their average amino acid comp
osition. This bias may have arisen due to evolutionary mechanisms, the dege
neracy of the genetic code, the primordial availability of suitable monomer
s, their relative reactivity or a number of other, equally speculative, cau
ses. Mathematics appears to dictate that Nature could not have sampled all
possible amino acid sequences and selected the most suitable for a particul
ar function, suggesting that the protei ns observed today may have evolved
from a relatively small number of precursors. If this is true it would impl
y that there is a vast set of possible proteins that have simply never exis
ted and that may possess interesting or useful properties. This article inv
estigates whether the structural space occupied by proteins that do not cur
rently exist can be sampled. One approach suggests itself - random polypept
ide synthesis in which all possible residue types are inserted at all possi
ble positions of an amino acid sequence of a given length. It is abundantly
clear that the truly random synthesis of even a small set of such protein
sequences is precluded by simple mathematics. The issues that this raises a
re discussed and different practical approaches to the problem described.