  Cells use genetic switches to shift between alternate stable gene expression
states, e.g., to adapt to new environments or to follow a developmental
pathway. Conceptually, these stable phenotypes can be considered as attractive
states on an epigenetic landscape with phenotypic changes being transitions
between states. Measuring these transitions is challenging because they are
both very rare in the absence of appropriate signals and very fast. As such, it
has proven difficult to experimentally map the epigenetic landscapes that are
widely believed to underly developmental networks. Here, we introduce a new
nonequilibrium perturbation method to help reconstruct a regulatory network's
epigenetic landscape. We derive the mathematical theory needed and then use the
method on simulated data to reconstruct the landscapes. Our results show that
with a relatively small number of perturbation experiments it is possible to
recover an accurate representation of the true epigenetic landscape. We propose
that our theory provides a general method by which epigenetic landscapes can be
studied. Finally, our theory suggests that the total perturbation impulse
required to induce a switch between metastable states is a fundamental quantity
in developmental dynamics.
