  Gene expression has a stochastic component owing to the single molecule
nature of the gene and the small number of copies of individual DNA binding
proteins in the cell. We show how the statistics of such systems can be mapped
on to quantum many body problems. The dynamics of a single gene switch
resembles the spin boson model of a two site polaron or an electron transfer
reaction. Networks of switches can be approximately described as quantum spin
systems by using an appropriate variational principle. In this way the concept
of frustration for magnetic systems can be taken over into gene networks. The
landscape of stable attractors depends on the degree and style of frustration,
much as for neural networks. We show the number of attractors, which may
represent cell types, is much smaller for appropriately designed, weakly
frustrated stochastic networks than for randomly connected networks.
