Nonlinear interactions in a dendritic tree: localization, timing, and role in information processing.

Koch, Christof; Poggio, Tomaso; Torre, Vincent

doi:10.1073/pnas.80.9.2799

Cited by 455 publications

(352 citation statements)

References 18 publications

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“…Our theoretical understanding of dendritic inhibition is largely grounded on Cable theory and shunting effects of GABA. For example, Koch et al proposed the proximal (on-path) inhibition could yield the strongest effects on the excitation (43). In contrast, Gidon and Segev predicted that distal inhibition could better "shunt" a group of excitatory synapses (56).…”

Section: Discussionmentioning

confidence: 99%

Cell-type–specific inhibition of the dendritic plateau potential in striatal spiny projection neurons

Lindroos

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Striatal spiny projection neurons (SPNs) receive convergent excitatory synaptic inputs from the cortex and thalamus. Activation of spatially clustered and temporally synchronized excitatory inputs at the distal dendrites could trigger plateau potentials in SPNs. Such supralinear synaptic integration is crucial for dendritic computation. However, how plateau potentials interact with subsequent excitatory and inhibitory synaptic inputs remains unknown. By combining computational simulation, two-photon imaging, optogenetics, and dualcolor uncaging of glutamate and GABA, we demonstrate that plateau potentials can broaden the spatiotemporal window for integrating excitatory inputs and promote spiking. The temporal window of spiking can be delicately controlled by GABAergic inhibition in a celltype-specific manner. This subtle inhibitory control of plateau potential depends on the location and kinetics of the GABAergic inputs and is achieved by the balance between relief and reestablishment of NMDA receptor Mg 2+ block. These findings represent a mechanism for controlling spatiotemporal synaptic integration in SPNs.O ne of the principal functions of neurons is to integrate excitatory and inhibitory synaptic inputs and transform subthreshold membrane potential fluctuations into suprathreshold spiking activities. Both theoretical and experimental works have proposed that a single neuron can process inputs as a multilayer computational device in which individual dendritic branches function as a computational unit and can generate dendritic spikes or plateau potentials (1-4). In vivo studies have demonstrated that dendritic plateau potentials evoked by coincident inputs can amplify excitatory signals and enhance the capacity of learning and information storage at a specific branch (5-7). However, a majority of the understanding of dendritic computation is based on studies focusing on pyramidal cells of hippocampal and cortical areas. It is relatively less known whether these conclusions apply to the striatal neurons (8).The striatum, the main input nucleus of the basal ganglia, receives convergent glutamatergic inputs from the cortex and thalamus (9-11). The integration of these functionally distinct inputs is critical for fine movement control and action selection (12, 13). The principal neurons in the striatum-spiny projection neurons (SPNs)-display hyperpolarized membrane potentials (∼−80 mV) at rest, often referred to as the "down-state" (14, 15). It is generally believed that coherent cortical inputs can effectively depolarize SPNs and promote membrane potential transitions from a hyperpolarized down-state to a depolarized "up-state" (∼−55 mV), at which point action potentials can be generated (14-16). To achieve this ∼20-to 30-mV state transition, it has been estimated that a large number (hundreds to thousands) of active inputs would be required (14-17). Interestingly, striatal SPNs are capable of producing long-lasting plateau potentials following activation of spatially clustered and temporally synchronized excit...

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Section: Discussionmentioning

confidence: 99%

Cell-type–specific inhibition of the dendritic plateau potential in striatal spiny projection neurons

Lindroos

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…Furthermore, an interesting consequence of minimizing wiring to target synapses is that synapses that are close together are more likely to be linked by the same stretch of dendrite and therefore involved in a local computation (31)(32)(33), such that geometry is a key determinant of information processing. There is increasing evidence that such sophisticated local processing may be carried out within the dendritic tree (34,35), with nonlinear interactions between synaptic inputs shaping the output of the neuron (36)(37)(38)(39). We therefore predict it will be fruitful to study how the scaling laws of wiring and branching place constraints on the overall computational power of single neurons.…”

Section: Discussionmentioning

confidence: 99%

A scaling law derived from optimal dendritic wiring

Cuntz

Mathy

Häusser

2012

Proc. Natl. Acad. Sci. U.S.A.

111

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The wide diversity of dendritic trees is one of the most striking features of neural circuits. Here we develop a general quantitative theory relating the total length of dendritic wiring to the number of branch points and synapses. We show that optimal wiring predicts a 2/3 power law between these measures. We demonstrate that the theory is consistent with data from a wide variety of neurons across many different species and helps define the computational compartments in dendritic trees. Our results imply fundamentally distinct design principles for dendritic arbors compared with vascular, bronchial, and botanical trees.computational neuroscience | branching | dendrite | morphology | minimum spanning tree O ne of the main roles of dendrites is to connect a neuron to its synaptic inputs. To interpret neural connectivity from morphological data, it is important to understand the relationship between dendrite shape and synaptic input distribution (1-4). As early as the end of the 19th century (5), it was suggested that dendrites optimize connectivity in terms of cable length and conduction time costs, and a number of recent studies have supported the idea that optimal wiring explains dendritic branching patterns using simulations (6-8) or by reasoning from first principles (1, 2, 9, 10). However, although dendrite length is the most common measure for molecular studies of dendritic growth (11), its relationship to dendritic branching and the number of synaptic contacts has not been elucidated. Understanding this relationship should provide crucial constraints for circuit structure and function. Here we directly test the hypothesis that neurons wire up a space in an optimal way by studying the consequences for dendrite length and branching complexity. We derive a simple equation that directly relates dendrite length with the number of branch points, dendrite spanning volume, and number of synapses. ResultsRelating Total Dendritic Length to Optimal Wiring. We assume that a dendritic tree of total length L connects n target points distributed over a volume V (Fig. 1A). Each target point occupies an average volume V =n. A tree that optimizes wiring will tend to connect points to their nearest neighbors, which are on average located at distances proportional to ðV =nÞ 1=3 . We need at least n such dendritic sections to make up the tree. The total length L of these sections sums up toThis result shows that a 2/3 power law relationship between L and n (12) provides a lower bound for the total dendritic length, where c is a proportionality constant. Approximating the volume around each target point by a sphere, then c ¼ ð3=4πÞ 1=3 , and each dendritic section corresponds to the radius of a sphere, giving(SI Text and Fig. S1). Importantly, assuming a constant ratio between the number of branch points, bp and the number of target points (which is addressed later), this assumption also results in a 2/3 power law between wiring length and the number of branch points. Supporting these intuitive derivations of power laws, there ...

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“…A postsynaptic mechanism reliant on shunting inhibition requires that the synapses be electrotonically remote from the soma for direction selectivity to be generated locally within the dendritic tree (Torre and Poggio, 1978;Koch et al, 1983). The linearity of the I-V relations and the clear reversal potentials observed at positive potentials seem inconsistent with an electrotonically extensive dendritic arbor.…”

Section: Locus Of Direction Selectivitymentioning

confidence: 99%

Diverse Synaptic Mechanisms Generate Direction Selectivity in the Rabbit Retina

2002

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The synaptic conductance of the On-Off direction-selective ganglion cells was measured during visual stimulation to determine whether the direction selectivity is a property of the circuitry presynaptic to the ganglion cells or is generated by postsynaptic interaction of excitatory and inhibitory inputs. Three synaptic asymmetries were identified that contribute to the generation of direction-selective responses: (1) a presynaptic mechanism producing stronger excitation in the preferred direction, (2) a presynaptic mechanism producing stronger inhibition in the opposite direction, and (3) postsynaptic interaction of excitation with spatially offset inhibition. Although the on-and off-responses showed the same directional tuning, the off-response was generated by all three mechanisms, whereas the on-response was generated primarily by the two presynaptic mechanisms. The results indicate that, within a single neuron, different strategies are used within distinct dendritic arbors to accomplish the same neural computation.Key words: direction selectivity; ganglion cells; synaptic conductance; inhibition; excitation; dendritic integration; on-and off-pathways; rabbit retinaThe direction-selective ganglion cells (DSGCs) in the rabbit retina are a model system for investigating neural computation (Vaney et al., 2001). These cells respond strongly to an image moving in a preferred direction but only weakly to an image moving in the opposite "null" direction. The foundation for understanding the cellular mechanisms of direction selectivity in vertebrates was laid by Barlow and Levick (1965), whose extracellular recordings from DSGCs indicated that direction selectivity was mediated primarily by inhibition activated by nulldirection image motion. Strong support for the inhibitory model was provided by subsequent pharmacological experiments, which showed that GABA A -receptor antagonists abolish direction selectivity (Wyatt and Daw, 1976;Ariel and Daw, 1982;Kittila and Massey, 1997). However, these extracellular recording experiments provided no information about whether the inhibition acted directly on the DSGC or presynaptically on the excitatory interneurons.Torre and Poggio (1978) proposed a postsynaptic model in which DSGCs receive an inhibitory input that is spatially offset relative to the excitatory input; moreover, the inhibition is nondirectional, being activated equally well by image motion in the preferred and null directions. During null-direction motion, the spatial offset means that delayed inhibitory synapses at locations ahead of the stimulus are activated and veto the excitation as the stimulus sweeps across the receptive field. For preferreddirection motion, the inhibition trails behind the stimulus and thus arrives too late to veto the excitation. For this model to work, the inhibition must act locally within the dendritic arbor of the DSGC. This occurs when the inhibitory reversal potential is at, or close to, the resting potential of the cell, and therefore the inhibitory input does not polarize the c...

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Nonlinear interactions in a dendritic tree: localization, timing, and role in information processing.

Cited by 455 publications

References 18 publications

Cell-type–specific inhibition of the dendritic plateau potential in striatal spiny projection neurons

Cell-type–specific inhibition of the dendritic plateau potential in striatal spiny projection neurons

A scaling law derived from optimal dendritic wiring

Diverse Synaptic Mechanisms Generate Direction Selectivity in the Rabbit Retina

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