The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought.
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Author SummaryA central issue in biology is how do local sub-cellular processes result in global cellular consequences. For neurons this is especially relevant since these spatially extended cells convert local synaptic inputs into action potential output. The dendritic tree of a neuron, which is where most inputs arrive, expresses membrane conductances that can generate intrinsic nonlinearities. The distributions of these membrane conductances are typically highly nonuniform. The non-uniform distribution of membrane conductances can turn the dendritic tree into a network of sparsely spaced active "hot spots". A prominent phenomenon resulting from the dendritic nonlinearities are intrinsic membrane potential oscillations, which are typically recorded at the neuron's soma. Here we analyze whether the active local oscillatory "hot spots" can produce global membrane voltage oscillations. Our mathematical theory shows that indeed, even when local dendritic oscillators are coupled extremely weakly, they still lead to global oscillations. This global effect arises since the oscillators lock to each other. We then show how the biophysical parameters of the dendrites affect this global locking. It becomes clear that when the oscillators are sy...