Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Linear summation of excitatory inputs by CA1 pyramidal neurons

A fundamental problem in neurobiology is understanding the arithmetic that dendrites use to integrate inputs. The impact of dendritic morphology and active conductances on input summation is still unknown. To study this, we use glutamate iontophoresis and synaptic stimulation to position pairs of excitatory inputs throughout the apical, oblique, and basal dendrites of CA1 pyramidal neurons in rat hippocampal slices. Under a variety of stimulation regimes, we find a linear summation of most input combinations that is implemented by a surprising balance of boosting and shunting mechanisms. Active conductances in dendrites paradoxically serve to make summation linear. This "active linearity" can reconcile predictions from cable theory with the observed linear summation in vivo and suggests that a simple arithmetic is used by apparently complex dendritic trees.     

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.     

A model of binocular brightness and binaural loudness perception in humans with general applications to nonlinear summation of sensory inputs

A single neural model is proposed to account for how responses of the two eyes and two ears combine to form the perception of binocular brightness and binaural loudness respectively. It involves nonlinear reciprocal feedback inhibition between left and right channels, followed by linear summation between the channels. Local circuit synaptic interactions are an important source of nonlinearity. The model combines inputs in a manner that approximates vector magnitude models in general. This suggests that the model can be applied to a variety of circumstances beyond the visual and auditory data discussed here.     

Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels

Computer simulations of a dendrite possessing voltage-sensitive potassium conductances were used to determine the effects of these conductances on synaptic transmission and on the propagation of synaptic signals within the dendritic tree. Potassium conductances had two principal effects on voltage transients generated by current injections or synaptic conductances. Locally (near the source of the transient), voltage-gated potassium channels produced a potassium shunt current that reduced the amplitude of voltage transients generated by depolarizing currents. This shunt current increased as the amplitude of the depolarizing transient increased and so acted to prevent large synaptic transients from reaching levels that would saturate due to a reduction in driving force. In the presence of rapidly activating potassium currents, excitatory synapses produced larger synaptic currents that were more linearly related to synaptic conductance, but these produced smaller voltage transients. The maximum amplitudes of the voltage transients were limited by the voltage sensitivity of the K⁺ conductance and the rate at which it could activate. Sufficiently rapid synaptic currents could outrun the K⁺ conductance and thus achieve high local peak amplitudes. These effects of K⁺ conductances were unrelated to whether they were located on dendrites or not, being related only to their proximity to the source of synaptic current. The second class of effects of K⁺ conductances depended on their alteration of the electrotonic structure of the postsynaptic cell and so were observed only when they were located on postsynaptic dendrites. Voltage-gated K⁺ conductances produced voltage-dependent electrotonic expansion of depolarized dendrites, which had the effect of isolating synaptic inputs on depolarized dendrites from events on the rest of the neuron. Thus, synapses on the same dendrite interacted destructively to a degree much greater than that expected from the classical driving force nonlinearity. Synapses located proximally to a depolarized dendritic region were less effected than those located distally, and the range of the nonlinear interaction between synapses was dependent on the kinetics of activation and deactivation of the conductance. When present in conjunction with rapidly activating dendritic sodium conductance, the potassium conductance sharpened the requirement for spatial and temporal coincidence to produce synaptic boosting by inward currents, and suppressed out-of-synchrony synaptic inputs.     

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.     

Computer simulation of the segmental neural network generating locomotion in lamprey by using populations of network interneurons

Realistic computer simulations of the experimentally established local spinal cord neural network generating swimming in the lamprey have been performed. Populations of network interneurons were used in which cellular properties, like cell size and membrane conductance including voltage dependent ion channels were randomly distributed around experimentally obtained mean values, as were synaptic conductances (kainate/AMPA, NMDA, glycine) and delays. This population model displayed more robust burst activity over a wider frequency range than the more simple subsample model used previously, and the pattern of interneuronal activity was appropriate. The strength of the reciprocal inhibition played a very important role in the regulation of burst frequency, and just by changing the inhibitory bias the entire physiological range could be covered. At the lower frequency range of bursting the segmental excitatory interneurons provide stability as does the activation of voltage dependent NMDA receptors. Spike frequency adaptation by means of summation of afterhyperpolarization (AHP) serves as a major burst terminating factor, and at lower rates the membrane properties conferred by the NMDA receptor activation. The lateral interneurons were not of critical importance for the burst termination. They may, however, be of particular importance for inducing a rapid burst termination during for instance steering and righting reactions. Several cellular factors combine to provide a secure and stable motor pattern in the entire frequency range.     

Integrative properties of radial oblique dendrites in hippocampal CA1 pyramidal neurons

Although radial oblique dendrites are a major synaptic input site in CA1 pyramidal neurons, little is known about their integrative properties. We have used multisite two-photon glutamate uncaging to deliver different spatiotemporal input patterns to single branches while simultaneously recording the uncaging-evoked excitatory postsynaptic potentials and local Ca2+ signals. Asynchronous input patterns sum linearly in spite of the spatial clustering and produce Ca2+ signals that are mediated by NMDA receptors (NMDARs). Appropriately timed and sized input patterns ( approximately 20 inputs within approximately 6 ms) produce a supralinear summation due to the initiation of a dendritic spike. The Ca2+ signals associated with synchronous input were larger and mediated by influx through both NMDARs and voltage-gated Ca2+ channels (VGCCs). The oblique spike is a fast Na+ spike whose duration is shaped by the coincident activation of NMDAR, VGCCs, and transient K+ currents. Our results suggest that individual branches can function as single integrative compartments.     

Dendrites: bug or feature?

The integrative properties of dendrites are determined by a complex mixture of factors, including their morphology, the spatio-temporal patterning of synaptic inputs, the balance of excitation and inhibition, and neuromodulatory influences, all of which interact with the many voltage-gated conductances present in the dendritic membrane. Recent efforts to grapple with this complexity have focused on identifying functional compartments in the dendritic tree, the number and size of which depend on the aspect of dendritic function being considered. We discuss how dendritic compartments and the interactions between them help to enhance the computational power of the neuron and define the rules for the induction of synaptic plasticity.     

Spike propagation synchronized by temporally asymmetric Hebbian learning

 Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue. Received: 28 May 2002 / Accepted: 3 June 2002 RID="*" ID="*" Correspondence to: R. E. Suri Intelligent Optical Systems (IOS), 2520 W 237th St, Torrance, CA 90505-5217, USA (e-mail: rsuri@intopsys.com, Tel.: +1-310-5307130 ext. 108, Fax: +1-210-5307417)     

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.     

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.     

Dynamics of action potential initiation in the GABAergic thalamic reticular nucleus in vivo

Understanding the neural mechanisms of action potential generation is critical to establish the way neural circuits generate and coordinate activity. Accordingly, we investigated the dynamics of action potential initiation in the GABAergic thalamic reticular nucleus (TRN) using in vivo intracellular recordings in cats in order to preserve anatomically-intact axo-dendritic distributions and naturally-occurring spatiotemporal patterns of synaptic activity in this structure that regulates the thalamic relay to neocortex. We found a wide operational range of voltage thresholds for action potentials, mostly due to intrinsic voltage-gated conductances and not synaptic activity driven by network oscillations. Varying levels of synchronous synaptic inputs produced fast rates of membrane potential depolarization preceding the action potential onset that were associated with lower thresholds and increased excitability, consistent with TRN neurons performing as coincidence detectors. On the other hand the presence of action potentials preceding any given spike was associated with more depolarized thresholds. The phase-plane trajectory of the action potential showed somato-dendritic propagation, but no obvious axon initial segment component, prominent in other neuronal classes and allegedly responsible for the high onset speed. Overall, our results suggest that TRN neurons could flexibly integrate synaptic inputs to discharge action potentials over wide voltage ranges, and perform as coincidence detectors and temporal integrators, supported by a dynamic action potential threshold.     

The role of retinal bipolar cell in early vision: an implication with analogue networks and regularization theory

A linear analogue network model is proposed to describe the neuronal circuit of the outer retina consisting of cones, horizontal cells, and bipolar cells. The model reflects previous physiological findings on the spatial response properties of these neurons to dim illumination and is expressed by physiological mechanisms, i.e., membrane conductances, gap-junctional conductances, and strengths of chemical synaptic interactions. Using the model, we characterized the spatial filtering properties of the bipolar cell receptive field with the standard regularization theory, in which the early vision problems are attributed to minimization of a cost function. The cost function accompanying the present characterization is derived from the linear analogue network model, and one can gain intuitive insights on how physiological mechanisms contribute to the spatial filtering properties of the bipolar cell receptive field. We also elucidated a quantitative relation between the Laplacian of Gaussian operator and the bipolar cell receptive field. From the computational point of view, the dopaminergic modulation of the gap-junctional conductance between horizontal cells is inferred to be a suitable neural adaptation mechanism for transition between photopic and mesopic vision. Received: 20 December 1996 / Accepted in revised form: 16 May 1997     

Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells

Significant inroads have been made to understand cerebellar cortical processing but neural coding at the output stage of the cerebellum in the deep cerebellar nuclei (DCN) remains poorly understood. The DCN are unlikely to just present a relay nucleus because Purkinje cell inhibition has to be turned into an excitatory output signal, and DCN neurons exhibit complex intrinsic properties. In particular, DCN neurons exhibit a range of rebound spiking properties following hyperpolarizing current injection, raising the question how this could contribute to signal processing in behaving animals. Computer modeling presents an ideal tool to investigate how intrinsic voltage-gated conductances in DCN neurons could generate the heterogeneous firing behavior observed, and what input conditions could result in rebound responses. To enable such an investigation we built a compartmental DCN neuron model with a full dendritic morphology and appropriate active conductances. We generated a good match of our simulations with DCN current clamp data we recorded in acute slices, including the heterogeneity in the rebound responses. We then examined how inhibitory and excitatory synaptic input interacted with these intrinsic conductances to control DCN firing. We found that the output spiking of the model reflected the ongoing balance of excitatory and inhibitory input rates and that changing the level of inhibition performed an additive operation. Rebound firing following strong Purkinje cell input bursts was also possible, but only if the chloride reversal potential was more negative than −70 mV to allow de-inactivation of rebound currents. Fast rebound bursts due to T-type calcium current and slow rebounds due to persistent sodium current could be differentially regulated by synaptic input, and the pattern of these rebounds was further influenced by HCN current. Our findings suggest that active properties of DCN neurons could play a crucial role for signal processing in the cerebellum.     

The Autapse: A Simple Illustration of Short-Term Analog Memory Storage by Tuned Synaptic Feedback

According to a popular hypothesis, short-term memories are stored as persistent neural activity maintained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averaging to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear and if its feedforward bias and autapse strength are precisely tuned.     

Neuromodulation to the Rescue: Compensation of Temperature-Induced Breakdown of Rhythmic Motor Patterns via Extrinsic Neuromodulatory Input

Stable rhythmic neural activity depends on the well-coordinated interplay of synaptic and cell-intrinsic conductances. Since all biophysical processes are temperature dependent, this interplay is challenged during temperature fluctuations. How the nervous system remains functional during temperature perturbations remains mostly unknown. We present a hitherto unknown mechanism of how temperature-induced changes in neural networks are compensated by changing their neuromodulatory state: activation of neuromodulatory pathways establishes a dynamic coregulation of synaptic and intrinsic conductances with opposing effects on neuronal activity when temperature changes, hence rescuing neuronal activity. Using the well-studied gastric mill pattern generator of the crab, we show that modest temperature increase can abolish rhythmic activity in isolated neural circuits due to increased leak currents in rhythm-generating neurons. Dynamic clamp-mediated addition of leak currents was sufficient to stop neuronal oscillations at low temperatures, and subtraction of additional leak currents at elevated temperatures was sufficient to rescue the rhythm. Despite the apparent sensitivity of the isolated nervous system to temperature fluctuations, the rhythm could be stabilized by activating extrinsic neuromodulatory inputs from descending projection neurons, a strategy that we indeed found to be implemented in intact animals. In the isolated nervous system, temperature compensation was achieved by stronger extrinsic neuromodulatory input from projection neurons or by augmenting projection neuron influence via bath application of the peptide cotransmitter Cancer borealis tachykinin-related peptide Ia (CabTRP Ia). CabTRP Ia activates the modulator-induced current I_MI (a nonlinear voltage-gated inward current) that effectively acted as a negative leak current and counterbalanced the temperature-induced leak to rescue neuronal oscillations. Computational modelling revealed the ability of I_MI to reduce detrimental leak-current influences on neuronal networks over a broad conductance range and indicated that leak and I_MI are closely coregulated in the biological system to enable stable motor patterns. In conclusion, these results show that temperature compensation does not need to be implemented within the network itself but can be conditionally provided by extrinsic neuromodulatory input that counterbalances temperature-induced modifications of circuit-intrinsic properties.     

Modeling the leech heartbeat elemental oscillator I. Interactions of intrinsic and synaptic currents

We have developed a biophysical model of a pair of reciprocally inhibitory interneurons comprising an elemental heartbeat oscillator of the leech. We incorporate various intrinsic and synaptic ionic currents based on voltage-clamp data. Synaptic transmission between the interneurons consists of both a graded and a spike-mediated component. By using maximal conductances as parameters, we have constructed a canonical model whose activity appears close to the real neurons. Oscillations in the model arise from interactions between synaptic and intrinsic currents. The inhibitory synaptic currents hyperpolarize the cell, resulting in activation of a hyperpolarization-activated inward currentI _h and the removal of inactivation from regenerative inward currents. These inward currents depolarize the cell to produce spiking and inhibit the opposite cell. Spike-mediated IPSPs in the inhibited neuron cause inactivation of low-threshold Ca⁺⁺ currents that are responsible for generating the graded synaptic inhibition in the opposite cell. Thus, although the model cells can potentially generate large graded IPSPs, synaptic inhibition during canonical oscillations is dominated by the spike-mediated component.