Complex Parameter Landscape for a Complex Neuron Model

Abstract

The electrical activity of a neuron is strongly dependent on the ionic channels present in its membrane. Modifying the maximal conductances from these channels can have a dramatic impact on neuron behavior. But the effect of such modifications can also be cancelled out by compensatory mechanisms among different channels. We used an evolution strategy with a fitness function based on phase-plane analysis to obtain 20 very different computational models of the cerebellar Purkinje cell. All these models produced very similar outputs to current injections, including tiny details of the complex firing pattern. These models were not completely isolated in the parameter space, but neither did they belong to a large continuum of good models that would exist if weak compensations between channels were sufficient. The parameter landscape of good models can best be described as a set of loosely connected hyperplanes. Our method is efficient in finding good models in this complex landscape. Unraveling the landscape is an important step towards the understanding of functional homeostasis of neurons. Neurons are believed to be electrical information processors. But how many models of a neuron can have similar input/output behavior? How precisely must the model parameters be tuned? These questions are crucial for models of the cerebellar Purkinje cell, a neuron with a huge dendritic arborization and a complex range of electrical outputs, for which recent experiments have demonstrated that dissimilar sets of ionic channel densities can produce similar activities. The authors have therefore used a detailed model of a Purkinje cell, released its 24 channel density parameters, and let them be optimized through an evolution strategy algorithm. They obtained 20 sets of parameters (20 models) that reproduce very precisely the original electrical waveforms. Therefore, model parameters are not uniquely identifiable. The parameters obtained vary several fold whereas small variations of these can also lead to drastically different results. Therefore, the authors have examined in more details the parameter space to gain better understanding of compensatory mechanisms in such complex models. They demonstrate that the 20 models are neither completely isolated nor fully connected, but rather, they belong to thin hyperplanes of good solutions that grid searches or random searches are likely to miss.