Abstract
The classical model of basal ganglia has been refined in recent years with discoveries of subpopulations within a nucleus and previously unknown projections. One such discovery is the presence of subpopulations of arkypallidal and prototypical neurons in external globus pallidus, which was previously considered to be a primarily homogeneous nucleus. Developing a computational model of these multiple interconnected nuclei is challenging, because the strengths of the connections are largely unknown. We therefore use a genetic algorithm to search for the unknown connectivity parameters in a firing rate model. We apply a binary cost function derived from empirical firing rate and phase relationship data for the physiological and Parkinsonian conditions. Our approach generates ensembles of over 1,000 configurations, or homologies, for each condition, with broad distributions for many of the parameter values and overlap between the two conditions. However, the resulting effective weights of connections from or to prototypical and arkypallidal neurons are consistent with the experimental data. We investigate the significance of the weight variability by manipulating the parameters individually and cumulatively, and conclude that the correlation observed between the parameters is necessary for generating the dynamics of the two conditions. We then investigate the response of the networks to a transient cortical stimulus, and demonstrate that networks classified as physiological effectively suppress activity in the internal globus pallidus, and are not susceptible to oscillations, whereas parkinsonian networks show the opposite tendency. Thus, we conclude that the rates and phase relationships observed in the globus pallidus are predictive of experimentally observed higher level dynamical features of the physiological and parkinsonian basal ganglia, and that the multiplicity of solutions generated by our method may well be indicative of a natural diversity in basal ganglia networks. We propose that our approach of generating and analyzing an ensemble of multiple solutions to an underdetermined network model provides greater confidence in its predictions than those derived from a unique solution, and that projecting such homologous networks on a lower dimensional space of sensibly chosen dynamical features gives a better chance than a purely structural analysis at understanding complex pathologies such as Parkinson's disease.
Highlights
IntroductionOur understanding of the circuitry of the basal ganglia has been much refined in recent years due to the discovery of distinct sub-populations of neurons within nuclei previously assumed to be homogeneous (Gertler et al, 2008; Taverna et al, 2008; Planert et al, 2010; Mallet et al, 2012; Mastro et al, 2014) and additional projections between nuclei previously thought to be unconnected (Nadjar et al, 2006; Calabresi et al, 2014; Saunders et al, 2015)
These nuclei were chosen with the purpose of modeling a minimal basal ganglia circuit implementing the three main functional pathways, i.e., the direct pathway (D1→ globus pallidus internus (GPi)), the indirect pathway (D2→Globus pallidus externus (GPe)→GPi) and the hyperdirect pathway (STN→GPi)
It has been suggested that GPe-tonically active (TA) populations projects upstream to striatum much more than GPe-tonically inactive (TI) population, here both are included as free parameters in order to include the possibility of few but strong projections from prototypical neurons to striatum
Summary
Our understanding of the circuitry of the basal ganglia has been much refined in recent years due to the discovery of distinct sub-populations of neurons within nuclei previously assumed to be homogeneous (Gertler et al, 2008; Taverna et al, 2008; Planert et al, 2010; Mallet et al, 2012; Mastro et al, 2014) and additional projections between nuclei previously thought to be unconnected (Nadjar et al, 2006; Calabresi et al, 2014; Saunders et al, 2015). Empirical data has been gathered on the strengths of many of the connections in the basal ganglia circuit, such as lateral inhibition in striatum (Taverna et al, 2008; Planert et al, 2010), many others remain uncertain (e.g., afferent and efferent projections of the GPe-arkypallidal neurons) Faced with this high degree of under-specification, modelers typically choose one of two alternatives: make simplifying assumptions on the unknown parameters, or strive for a unique or locally optimal solution by performing an extensive and computationally demanding parameter fit with respect to a cost function based on desired model dynamics. While the robustness of obtained results with respect to the parameter choice has been extensively studied in the context of single-cell (e.g., Achard and De Schutter, 2006) and small network models (e.g., Prinz et al, 2004), this has hardly been done for large-scale networks, basal ganglia
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