Reduced models of striatal neurons: dopamine modulation and dynamics

Abstract

Loss of dopamine cells in Parkinson's Disease and its ani-mal models leads to profound motor deficits. An intactdopamine system also seems to be critical for many formsof learning [1]. Much work on understanding these rolesof dopamine has focused on the striatum, the main inputnucleus of the basal ganglia, as the striatum is the mainlocus of dopamine's action in the verterbrate brain [2].Damage to the striatum itself also impairs both motoraction and learning [3]. Thus, the twin problems of under-standing the computational roles of dopamine and thestriatum are inseparably intertwined.Understanding dopamine's effects on the complex striatalmicrocircuit ideally requires large-scale models that repli-cate the neuron types, numbers, and connectivity at one-to-one scale. To build at such scales, we require individualneuron models that are simple enough to be computa-tionally tractable, but sufficiently complex to capture keymembrane properties that contribute to the characteristicbehavior of a neuron species. Our neuron model of choiceis the recent canonical spiking model of Izhikevich [4].However, it has not yet been extended to account for theaction of neuromodulators.We extend the striatal medium spiny (MSN) and fast-spik-ing (FS) interneuron models of [5] to account fordopaminergic modulation of intrinsic ion channels andsynaptic inputs. We use data from a recent 189 compart-ment model of the MSN [3] to tune our simple model ofthat neuron under both current injection and spikinginput regimes with varying activation of dopamine D1-and D2-type receptors. The reduced models capture theinput-output relationships for both current injection andspiking input with remarkable accuracy. We derive a fullset of stability properties for the original and dopaminemodulated forms of the MSN model. We use these toestablish that the dopamine models do not change thestability properties and hence the models predict that theMSN is not bistable in either baseline or dopamine-satu-rated conditions. Our extensions to the simple model ofthe FS interneuron are consistent with the existing data,but tuning the new parameters is made difficult by thelack of quantitative results from experimental work. Ourwork thus establishes reduced yet accurate dopamine-modulated forms of MSN and FS interneuron models,suitable for use in large-scale models of the striatum.Moreover, these also provide a tractable framework forfurther study of dopamine's effects on individual neuroncomputation.