Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron's 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.