Pyramidal Neuron as Two-Layer Neural Network

Poirazi, Panayiota; Brannon, Terrence; Mel, Bartlett W.

doi:10.1016/s0896-6273(03)00149-1

Cited by 715 publications

(884 citation statements)

References 30 publications

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“…In turn, the cable yields the current flux through its ends into (and thereby perturbing) the two oscillators: the terms ε p A,B in equation (3). It is clear that it is next to impossible to solve equations (1)-(3) directly.…”

Section: Resultsmentioning

confidence: 99%

“…Such active conductances can underlie a wide variety of dynamical behaviors, amongst others dendritic spikes and ongoing oscillations of the dendritic membrane potential [2]. Such active dendritic phenomena have been suggested as mechanisms endowing single neurons with significant computational power [3] and flexibility in the way the dendritic tree processes its inputs: whether as a global element, effectively collapsing the tree into a single functional compartment or with various parts of the tree acting as independent processing elements [4,5]. While the possibility of powerful and flexible dendritic processing is indeed of great interest, the precise conditions under which dendrites can act independently or globally remain largely to be determined.…”

Section: Introductionmentioning

confidence: 99%

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The role of ongoing dendritic oscillations in single-neuron dynamics

2009

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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. 1 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...

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The role of ongoing dendritic oscillations in single-neuron dynamics

2009

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“…The simplicity of the IF model contrasts with the complexity of the dendritic arborization of some pyramidal neurons, with their regenerative membrane currents and clustered synaptic inputs (Spruston 2008). The extended geometry of cortical neurons and their nonlinear dentritic properties may offer additional computational power by exploiting nonlinear dendritic properties (Poirazi et al 2003;Polsky et al 2004), like the multiplicative gain modulation of the somatic response function reviewed here.…”

Section: Discussionmentioning

confidence: 99%

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

et al. 2008

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The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

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“…Apparently, each dendritic branch integrates its input independently through a local nonlinearity. This suggests a two step process: first, synchrony decoding occurs in the dendritic branches, and then global integration with the inputs from other dendritic branches at the soma follows 90 .…”

Section: Decoding Synchronous Inputs In Spatially Extended Neuronsmentioning

confidence: 99%

Regulation of spike timing in visual cortical circuits

2008

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A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.Reliability and precision are two different quantities. When you make an appointment with your friend, she can either keep the appointment or not show up at all. If she does show up, she might or might not be on time. The former uncertainty is related to reliability, whereas the latter is related to precision. When the same stimulus waveform is repeatedly injected at the soma of a neuron in vitro (FIG. 1a), a similar spike train is obtained on each trial 1,2 (FIG. 1b). When approximately the same number of spikes occur on each trial the neuron is said to be reliable, whereas when the spikes occur almost at the same time across trials it is said to be precise (FIG. 1c). For a single neuron, the potential information content of precise and reliable spike times is many times larger than that which is contained in the firing rate, which is averaged across a typical interval of a hundred milliseconds [3][4][5][6] . The information contained in spike timing is available immediately, rather than after an averaging period. Furthermore, the timing of patterns of spikes can potentially transmit even more information than the timing of the individual constituent spikes 3,7 . The potential relevance of spike patterns becomes apparent when we consider neurons at the population level: when a group of similar neurons (a 'pool') produces precise and reliable spike trains, the neurons they project to receive volleys of synchronous spikes 8,9 . This opens up the possibility of communicating between different cortical areas through synchronous spike volleys.In contrast to the in vitro situation described above, in the intact cortex most excitatory synaptic inputs arrive at the dendrites rather than at the soma (FIG. 1d), and synaptic transmission is typically unreliable [10][11][12][13] . Furthermore, most of these dendritic inputs are not directly related to ongoing sensory stimulation; rather, they reflect spatiotemporally structured internal activity. Therefore, when the same stimulus is presented repeatedly, the resulting spike trains are usually neither precise nor reliable when they are aligned to the stimulus onset 6 . Instead, HHMI Author ManuscriptHHMI Author Manuscript HHMI Author Manuscript neural activity in vivo might be dominated by internally generated complex reverberations or rhythmic oscillations, and precise and reliable sp...

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Pyramidal Neuron as Two-Layer Neural Network

Cited by 715 publications

References 30 publications

The role of ongoing dendritic oscillations in single-neuron dynamics

The role of ongoing dendritic oscillations in single-neuron dynamics

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

Regulation of spike timing in visual cortical circuits

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