Purkinje cells have been previously modeled as a system undergoing a saddle-node bifurcation of fixed points from rest to firing and a saddle homoclinic orbit bifurcation from firing to rest. In vitro, this dynamical structure is a result of the neuron’s intrinsic membrane properties and is associated with bistability within a limited range of low firing frequencies, where a unidirectional climbing fiber (CF) input is able to toggle the cell between a firing (“up”) and rest (“down”) state. We identified several factors that contribute to bistability and the ability for a unidirectional input (CF) to toggle cell output, including a slow K+ current activated during spike discharge or following synaptic depolarizations. However, input conditions that determine the probability for a Purkinje cell to express bistability in vivo have not been determined. A key difference in vivo is the presence of tonic background input to the dendrites from parallel fiber (PF) and stellate cell inputs. We tested the hypothesis that dendritic inputs control the dynamics of Purkinje cell firing, and can thus regulate the ability for CFs to induce toggling of Purkinje cell output.
Presentation of mixed excitatory and inhibitory dendritic current noise (I-noise) or conductance noise (g-noise) to a two-compartment 5-equation model of the Purkinje neuron had differing effects on spike output. Mixed I-noise increased the probability of observing CF-evoked transitions to a down state whether the model was in the low frequency-bistable regime or not. The size and time course of the currents associated with different state transitions suggested that properly timed PF and/or stellate cell inputs could affect the ability for CFs to invoke Purkinje cell transitions. However, conductance noise prevented any CF-evoked transitions and the model was highly sensitive to the E:I ratio. Spike trains with physiological mean frequencies and high coefficient of variation (CV) were also found. Spike triggered averages during g-noise revealed that the spikes were being driven by synaptic inputs and not intrinsic dynamics, indicating a shift in computational properties between high and low conductance states.
Here we show that bistability in a Purkinje neuron can be controlled by the amount of synaptic input it receives. Of the two types of noise we used, I-noise could cause spontaneous state transitions, but g-noise could not, suggesting that CF-associated toggling would not occur in high conductance states. These results could explain the discrepancy between in vivo and in vitro recordings regarding CF-induced state transitions.