  We consider a leaky integrate-and-fire neuron with deterministic subthreshold
dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process.
The formulation of this minimal model is motivated by the experimentally
observed widespread variation of neural firing thresholds. We show numerically
that the mean first passage time can depend non-monotonically on the noise
amplitude. For sufficiently large values of the correlation time of the
stochastic threshold the mean first passage time is maximal for non-vanishing
noise. We provide an explanation for this effect by analytically transforming
the original model into a first passage time problem for Brownian motion. This
transformation also allows for a perturbative calculation of the first passage
time histograms. In turn this provides quantitative insights into the
mechanisms that lead to the non-monotonic behaviour of the mean first passage
time. The perturbation expansion is in excellent agreement with direct
numerical simulations. The approach developed here can be applied to any
deterministic subthreshold dynamics and any Gauss-Markov processes for the
firing threshold. This opens up the possibility to incorporate biophysically
detailed components into the subthreshold dynamics, rendering our approach a
powerful framework that sits between traditional integrate-and-fire models and
complex mechanistic descriptions of neural dynamics.
