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The Collective Dynamics of Adaptive Neurons: Insights from Single Cell and Network Models
Citation key Ladenbauer2015
Author Ladenbauer, Josef
Year 2015
School Technische Universität Berlin
Abstract Cognitive processing is linked to the activation of neurons in the brain, and specific cognitive tasks are often correlated with certain activity patterns of individual neurons and neuronal networks. Of major relevance are the temporal relationships between successive neuronal spikes and, in particular, the concerted spiking activity across small groups and large populations of coupled neurons, which often exhibit oscillatory overall dynamics due to synchronization. It is therefore important to understand the mechanisms which underlie and control the spiking activity of individual neurons and their collective dynamics in networks. A prominent mechanism which alters neuronal excitability involves adaptation currents through specific types of potassium channels in the neuronal membrane. These currents cause spike rate adaptation in many types of neurons and are regulated by neuromodulators such as acetylcholine. In this thesis, we employ computational models and mathematical methods to shed light on the role of that mechanism in controlling neuronal dynamics at different spatial levels, ranging from single neurons to large networks. Specifically, we characterize how distinct types of adaptation currents affect (i) spike rates, interspike interval variability and phase response properties of single neurons, (ii) spike synchronization and spike-to-spike locking in small networks, and (iii) the dynamics of spike rates across large populations of coupled neurons. We take a bottom-up approach based on an experimentally validated neuron model of the integrate-and-fire type, effectively covering spikes, the fast subthreshold membrane voltage and slow adaptation current dynamics. We use this model across the three spatial levels, which facilitates to relate the respective findings. To obtain robust results in an efficient way we extend different suitable methods from statistical physics and nonlinear dynamics – including mean-field, phase reduction and master stability function techniques – for that model class, and complement them by (stochastic) numerical simulations. This approach allows to examine the relationships between microscopic interactions (neuron biophysics) and macroscopic features (network dynamics) in a direct way and simplifies bridging scales. Applying these tools we demonstrate that at the level of single cells adaptation currents change threshold, gain and variability of spiking, as well as the neuronal phase responses to transient inputs, in type-dependent ways. At the network level adaptation currents engage in mechanisms that generate low-frequency oscillations for excitation dominated synaptic interaction, stabilizing spike synchrony (small networks) or promoting sparse synchronization (large networks), and they can facilitate and modulate faster rhythms which heavily rely on synaptic inhibition. Thereby, we show that neuromodulatory regulation of adaptation currents allows to stabilize biologically relevant synchronized and asynchronous network states and switch between them, by changing the neuronal spiking characteristics in particular ways. This work demonstrates the benefits of unified mathematical bottom-up modeling and analyses in contributing to our understanding of neuronal dynamics across different scales.
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