Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.     

Bilinearity in Spatiotemporal Integration of Synaptic Inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.     

Synaptic clustering by dendritic signalling mechanisms

Dendritic signal integration is one of the fundamental building blocks of information processing in the brain. Dendrites are endowed with mechanisms of nonlinear summation of synaptic inputs leading to regenerative dendritic events including local sodium, NMDA and calcium spikes. The generation of these events requires distinct spatio-temporal activation patterns of synaptic inputs. We hypothesise that the recent findings on dendritic spikes and local synaptic plasticity rules suggest clustering of common inputs along a subregion of a dendritic branch. These clusters may enable dendrites to separately threshold groups of functionally similar inputs, thus allowing single neurons to act as a superposition of many separate integrate and fire units. Ultimately, these properties expand our understanding about the computational power of neuronal networks.     

Synaptic integration gradients in single cortical pyramidal cell dendrites

Cortical pyramidal neurons receive thousands of synaptic inputs arriving at different dendritic locations with varying degrees of temporal synchrony. It is not known if different locations along single cortical dendrites integrate excitatory inputs in different ways. Here we have used two-photon glutamate uncaging and compartmental modeling to reveal a gradient of nonlinear synaptic integration in basal and apical oblique dendrites of cortical pyramidal neurons. Excitatory inputs to the proximal dendrite sum linearly and require precise temporal coincidence for effective summation, whereas distal inputs are amplified with high gain and integrated over broader time windows. This allows distal inputs to overcome their electrotonic disadvantage, and become surprisingly more effective than proximal inputs at influencing action potential output. Thus, single dendritic branches can already exhibit nonuniform synaptic integration, with the computational strategy shifting from temporal coding to rate coding along the dendrite.     

Input integration around the dendritic branches in hippocampal dentate granule cells

Recent studies have shown that the dendrites of several neurons are not simple translators but are crucial facilitators of excitatory postsynaptic potential (EPSP) propagation and summation of synaptic inputs to compensate for inherent voltage attenuation. Granule cells (GCs)are located at the gateway for valuable information arriving at the hippocampus from the entorhinal cortex. However, the underlying mechanisms of information integration along the dendrites of GCs in the hippocampus are still unclear. In this study, we investigated the input integration around dendritic branches of GCs in the rat hippocampus. We applied differential spatiotemporal stimulations to the dendrites using a high-speed glutamate-uncaging laser. Our results showed that when two sites close to and equidistant from a branching point were simultaneously stimulated, a nonlinear summation of EPSPs was observed at the soma. In addition, nonlinear summation (facilitation) depended on the stimulus location and was significantly blocked by the application of a voltage-dependent Ca²⁺ channel antagonist. These findings suggest that the nonlinear summation of EPSPs around the dendritic branches of hippocampal GCs is a result of voltage-dependent Ca²⁺ channel activation and may play a crucial role in the integration of input information.     

Bidirectional changes in spatial dendritic integration accompanying long-term synaptic modifications

Information processing in the neuron requires spatial summation of synaptic inputs at the dendrite. In CA1 pyramidal neurons of the hippocampus, a brief period of correlated pre- and postsynaptic activity, which induces long-term potentiation (LTP) or long-term depression (LTD), results in a persistent increase or decrease in the linearity of spatial summation, respectively. Such bidirectional modification of the summation property is specific to the modified input and reflects localized dendritic changes involving I(h) channels and NMDA receptors. Thus, correlated pre- and postsynaptic activity alters not only the strength of the activated input but also its dendritic integration with other inputs.     

Dendritic enlightenment: using patterned two-photon uncaging to reveal the secrets of the brain's smallest dendrites

It has been a longstanding challenge for experimentalists to manipulate precisely the spatial and temporal patterns of synaptic input to the dendritic tree in order to mimic activity occurring in the intact brain and determine their importance for synaptic integration. In this issue of Neuron, Losonczy and Magee have used rapid multisite two-photon uncaging of glutamate to define patterns of synaptic input on a submillisecond and micron scale to investigate the rules for summation of synaptic inputs in the fine oblique dendrites of pyramidal neurons.     

The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

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 both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated 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; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell

The rules of synaptic integration in pyramidal cells remain obscure, in part due to conflicting interpretations of existing experimental data. To clarify issues, we developed a CA1 pyramidal cell model calibrated with a broad spectrum of in vitro data. Using simultaneous dendritic and somatic recordings and combining results for two different response measures (peak versus mean EPSP), two different stimulus formats (single shock versus 50 Hz trains), and two different spatial integration conditions (within versus between-branch summation), we found that the cell's subthreshold responses to paired inputs are best described as a sum of nonlinear subunit responses, where the subunits correspond to different dendritic branches. In addition to suggesting a new type of experiment and providing testable predictions, our model shows how conclusions regarding synaptic arithmetic can be influenced by an array of seemingly innocuous experimental design choices.     

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.     

Changes in dendritic axial resistance alter synaptic integration in cerebellar Purkinje cells

The ability of neurons to process synaptic inputs depends critically on their passive electrical properties. The intracellular resistivity, R_i, is one of the parameters that determine passive properties, yet few experiments have explored how changes in R_i might affect synaptic integration. In this work, I addressed this issue by using targeted dendritic occlusion to locally increase R_i in cerebellar Purkinje cells and examining the consequences of this manipulation for the summation of synaptic inputs. To achieve dendritic occlusion, I used two glass micropipettes to gently pinch the dendritic trunk close to the soma. This pinching produced stereotypical changes in the responses to test pulses applied at the soma under voltage and current clamp. A simple model confirmed that these changes were due to increases in R_i in the dendritic trunk. These localized increases in R_i produced striking alterations in the shapes of postsynaptic potentials at the soma, increasing their amplitude and accelerating their decay kinetics. As a consequence, dendritic occlusion sharpened temporal precision during the summation of synaptic inputs. These findings highlight the importance of local changes in intracellular resistivity for the passive electrical properties of neurons, with implications for their ability to process synaptic information.     

Glutamate-Bound NMDARs Arising from In Vivo-like Network Activity Extend Spatio-temporal Integration in a L5 Cortical Pyramidal Cell Model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.     

Local control of AMPA receptor trafficking at the postsynaptic terminal by a small GTPase of the Rab family

The delivery of neurotransmitter receptors into the synaptic membrane is essential for synaptic function and plasticity. However, the molecular mechanisms of these specialized trafficking events and their integration with the intracellular membrane transport machinery are virtually unknown. Here, we have investigated the role of the Rab family of membrane sorting proteins in the late stages of receptor trafficking into the postsynaptic membrane. We have identified Rab8, a vesicular transport protein associated with trans-Golgi network membranes, as a critical component of the cellular machinery that delivers AMPA-type glutamatergic receptors (AMPARs) into synapses. Using electron microscopic techniques, we have found that Rab8 is localized in close proximity to the synaptic membrane, including the postsynaptic density. Electrophysiological studies indicated that Rab8 is necessary for the synaptic delivery of AMPARs during plasticity (long-term potentiation) and during constitutive receptor cycling. In addition, Rab8 is required for AMPAR delivery into the spine surface, but not for receptor transport from the dendritic shaft into the spine compartment or for delivery into the dendritic surface. Therefore, Rab8 specifically drives the local delivery of AMPARs into synapses. These results demonstrate a new role for the cellular secretory machinery in the control of synaptic function and plasticity directly at the postsynaptic membrane.     

Inhibitory Control of Linear and Supralinear Dendritic Excitation in CA1 Pyramidal Neurons

The transformation of dendritic excitatory synaptic inputs to axonal action potential output is the fundamental computation performed by all principal neurons. We show that in the hippocampus this transformation is potently controlled by recurrent inhibitory microcircuits. However, excitatory input on highly excitable dendritic branches could resist inhibitory?control by generating strong dendritic spikes and?trigger precisely timed action potential output. Furthermore, we show that inhibition-sensitive branches can be transformed into inhibition-resistant, strongly spiking branches by intrinsic plasticity of branch excitability. In addition, we demonstrate that the inhibitory control of spatially defined dendritic excitation is strongly regulated by network activity patterns. Our findings suggest that dendritic spikes may serve to transform correlated branch input into reliable and temporally precise output even in the presence of inhibition.     

Integration of subthreshold and suprathreshold excitatory barrages along the somatodendritic axis of pyramidal neurons

Neurons integrate inputs arriving in different cellular compartments to produce action potentials that are transmitted to other neurons. Because of the voltage- and time-dependent conductances in the dendrites and soma, summation of synaptic inputs is complex. To examine summation of membrane potentials and firing rates, we performed whole-cell recordings from layer 5 cortical pyramidal neurons in acute slices of the rat's somatosensory cortex. We delivered subthreshold and suprathreshold stimuli at the soma and several sites on the apical dendrite, and injected inputs that mimic synaptic barrages at individual or distributed sites. We found that summation of subthreshold potentials differed from that of firing rates. Subthreshold summation was linear when barrages were small but became supralinear as barrages increased. When neurons were discharging repetitively the rules were more diverse. At the soma and proximal apical dendrite summation of the evoked firing rates was predominantly sublinear whereas in the distal dendrite summation ranged from supralinear to sublinear. In addition, the integration of inputs delivered at a single location differed from that of distributed inputs only for suprathreshold responses. These results indicate that convergent inputs onto the apical dendrite and soma do not simply summate linearly, as suggested previously, and that distinct presynaptic afferents that target specific sites on the dendritic tree may perform unique sets of computations.     

Modeling activity-dependent synapse restructuring

The spread of electrical activity in a dendritic tree is shaped, in part, by its morphology. Conversely, experimental evidence is growing that electrical and chemical activity can slowly shape the morphology of the dendrite. In this theoretical study, the dendritic spines are dynamic elements, with biophysical properties that change in response to patterns of electrical activity. Recent experiments and diagrammatic models suggest that activity-dependent processes can regulate structural modifications in dendritic spines as well as their distribution along the dendrite. This study considers how local changes in spine structure (minutes to hours) can influence patterns of electrical activity along the dendrite; and how electrical activity due to synaptic events and excitable membrane dynamics can, over time, influence the morphology of the dendrite. The model presents a slow subsystem for structural synaptic plasticity associated with long-term potentiation. A perturbation problem evolves naturally when the spine stem shortens, since the ratio of spine stem resistance to input resistance is small. Hence, the difference between the spine head and dendritic potentials become negligible. This paper presents an asymptotic expansion of head potential in terms of dendritic potential. This leads to a reduced model for post-synaptic restructuring that captures the dynamics of the full model in a briefer computation period when the spines are well connected to the dendrite.     

Quantitative analysis of electrical properties of dendritic spines

Several sugestions have been made with regard to the functional significance of dendritic spines in connection with synaptic plasticity. We have shown that for a constant synaptic current, when the synaptic resistance is large compared to the spine-stem resistance, a morphological change in the spine does not produce a marked change in the postsynaptic potential (PSP). When the synaptic resistance is comparable to the spine-stem impedance a morphological change in the spine can induce changes in the synaptic current and the PSP due to the so-called nonlinear effect to the synapse (Kawato and Tsukahara, 1983, 1984). Consequently, in a study of the electrical properties of dendritic spines the input impedance of the parent dendrite, the spinestalk conductance and the conductance change associated with synaptic activity must be considered. We quantitatively estimated all three factors. By comparing electrophysiological data with morphological data, we estimated the synaptic conductance which causes corticorubral EPSP. Its maximum amplitude was 43 nS with a time-to-peak value of 0.3 ms. With this value, the effects of the spine were examined using an improved algorithm based on that of Butz and Cowan (1974). It uses a three-dimensional morphology of the rubrospinal (RS) neurons, which was reconstructed from serial sections containing HRP-filled RS cells. As the spine shortens, the amplitude of the EPSP becomes considerably larger, but its time-to-peak value does not markedly change. Moreover, if unitary EPSP in the RS cell is produced by the activation of several synaptic terminals a morphological change of the spine has a smaller effect on the EPSPs.     

The time window for generation of dendritic spikes by coincidence of action potentials and EPSPs is layer specific in somatosensory cortex

The precise timing of events in the brain has consequences for intracellular processes, synaptic plasticity, integration and network behaviour. Pyramidal neurons, the most widespread excitatory neuron of the neocortex have multiple spike initiation zones, which interact via dendritic and somatic spikes actively propagating in all directions within the dendritic tree. For these neurons, therefore, both the location and timing of synaptic inputs are critical. The time window for which the backpropagating action potential can influence dendritic spike generation has been extensively studied in layer 5 neocortical pyramidal neurons of rat somatosensory cortex. Here, we re-examine this coincidence detection window for pyramidal cell types across the rat somatosensory cortex in layers 2/3, 5 and 6. We find that the time-window for optimal interaction is widest and shifted in layer 5 pyramidal neurons relative to cells in layers 6 and 2/3. Inputs arriving at the same time and locations will therefore differentially affect spike-timing dependent processes in the different classes of pyramidal neurons.     

Active dendrites,potassium channels and synaptic plasticity

The dendrites of CA1 pyramidal neurons in the hippocampus express numerous types of voltage-gated ion channel, but the distributions or densities of many of these channels are very non-uniform. Sodium channels in the dendrites are responsible for action potential (AP) propagation from the axon into the dendrites (back-propagation); calcium channels are responsible for local changes in dendritic calcium concentrations following back-propagating APs and synaptic potentials; and potassium channels help regulate overall dendritic excitability. Several lines of evidence are presented here to suggest that back-propagating APs, when coincident with excitatory synaptic input, can lead to the induction of either long-term depression (LTD) or long-term potentiation (LTP). The induction of LTD or LTP is correlated with the magnitude of the rise in intracellular calcium. When brief bursts of synaptic potentials are paired with postsynaptic APs in a theta-burst pairing paradigm, the induction of LTP is dependent on the invasion of the AP into the dendritic tree. The amplitude of the AP in the dendrites is dependent, in part, on the activity of a transient, A-type potassium channel that is expressed at high density in the dendrites and correlates with the induction of the LTP. Furthermore, during the expression phase of the LTP, there are local changes in dendritic excitability that may result from modulation of the functioning of this transient potassium channel. The results support the view that the active properties of dendrites play important roles in synaptic integration and synaptic plasticity of these neurons.