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.     

Preserved Excitatory-Inhibitory Balance of Cortical Synaptic Inputs following Deprived Eye Stimulation after a Saturating Period of Monocular Deprivation in Rats

Monocular deprivation (MD) during development leads to a dramatic loss of responsiveness through the deprived eye in primary visual cortical neurons, and to degraded spatial vision (amblyopia) in all species tested so far, including rodents. Such loss of responsiveness is accompanied since the beginning by a decreased excitatory drive from the thalamo-cortical inputs. However, in the thalamorecipient layer 4, inhibitory interneurons are initially unaffected by MD and their synapses onto pyramidal cells potentiate. It remains controversial whether ocular dominance plasticity similarly or differentially affects the excitatory and inhibitory synaptic conductances driven by visual stimulation of the deprived eye and impinging onto visual cortical pyramids, after a saturating period of MD. To address this issue, we isolated visually-driven excitatory and inhibitory conductances by in vivo whole-cell recordings from layer 4 regular-spiking neurons in the primary visual cortex (V1) of juvenile rats. We found that a saturating period of MD comparably reduced visually–driven excitatory and inhibitory conductances driven by visual stimulation of the deprived eye. Also, the excitatory and inhibitory conductances underlying the synaptic responses driven by the ipsilateral, left open eye were similarly potentiated compared to controls. Multiunit recordings in layer 4 followed by spike sorting indicated that the suprathreshold loss of responsiveness and the MD-driven ocular preference shifts were similar for narrow spiking, putative inhibitory neurons and broad spiking, putative excitatory neurons. Thus, by the time the plastic response has reached a plateau, inhibitory circuits adjust to preserve the normal balance between excitation and inhibition in the cortical network of the main thalamorecipient layer.     

States of high conductance in a large-scale model of the visual cortex

This paper reports on the consequences of large, activity dependent, synaptic conductances for neurons in a large-scale neuronal network model of the input layer 4C of the Macaque primary visual cortex (Area V1). This high conductance state accounts for experimental observations about orientation selectivity, dynamics, and response magnitude (D. McLaughlin et al. (2000) Proc. Natl. Acad. Sci. USA 97: 8087–8092), and the linear dependence of Simple cells on visual stimuli (J. Wielaard et al. (2001) J. Neuroscience 21: 5203–5211). The source of large conductances in the model can be traced to inhibitory corticocortical synapses, and the model's predictions of large conductance changes are consistent with recent intracellular measurements (L. Borg-Graham et al. (1998) Nature 393: 369–373; J. Hirsch et al. (1998) J. Neuroscience 15: 9517–9528; J.S. Anderson et al. (2000) J. Neurophysiol. 84: 909–926). During visual stimulation, these conductances are large enough that their associated time-scales become the shortest in the model cortex, even below that of synaptic interactions. One consequence of this activity driven separation of time-scales is that a neuron responds very quickly to temporal changes in its synaptic drive, with its intracellular membrane potential tracking closely an effective reversal potential composed of the instantaneous synaptic inputs. From the effective potential and large synaptic conductance, the spiking activity of a cell can be expressed in an interesting and simplified manner, with the result suggesting how accurate and smoothly graded responses are achieved in the model network. Further, since neurons in this high-conductance state respond quickly, they are also good candidates as coincidence detectors and burst transmitters.     

Gain modulation from background synaptic input

Gain modulation is a prominent feature of neuronal activity recorded in behaving animals, but the mechanism by which it occurs is unknown. By introducing a barrage of excitatory and inhibitory synaptic conductances that mimics conditions encountered in vivo into pyramidal neurons in slices of rat somatosensory cortex, we show that the gain of a neuronal response to excitatory drive can be modulated by varying the level of "background" synaptic input. Simultaneously increasing both excitatory and inhibitory background firing rates in a balanced manner results in a divisive gain modulation of the neuronal response without appreciable signal-independent increases in firing rate or spike-train variability. These results suggest that, within active cortical circuits, the overall level of synaptic input to a neuron acts as a gain control signal that modulates responsiveness to excitatory drive.     

A neuronal network model of primary visual cortex explains spatial frequency selectivity

We address how spatial frequency selectivity arises in Macaque primary visual cortex (V1) by simulating V1 with a large-scale network model consisting of O(10⁴) excitatory and inhibitory integrate-and-fire neurons with realistic synaptic conductances. The new model introduces variability of the widths of subregions in V1 neuron receptive fields. As a consequence different model V1 neurons prefer different spatial frequencies. The model cortex has distributions of spatial frequency selectivity and of preference that resemble experimental findings from the real V1. Two main sources of spatial frequency selectivity in the model are the spatial arrangement of feedforward excitation, and cortical nonlinear suppression, a result of cortical inhibition. Action Editor: Jonathan D. Victor     

Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks

Temporal precision in spike timing is important in cortical function, interactions, and plasticity. We found that, during periods of recurrent network activity (UP states), cortical pyramidal cells in vivo and in vitro receive strong barrages of both excitatory and inhibitory postsynaptic potentials, with the inhibitory potentials showing much higher power at all frequencies above approximately 10 Hz and more synchrony between nearby neurons. Fast-spiking inhibitory interneurons discharged strongly in relation to higher-frequency oscillations in the field potential in vivo and possess membrane, synaptic, and action potential properties that are advantageous for transmission of higher-frequency activity. Intracellular injection of synaptic conductances having the characteristics of the recorded EPSPs and IPSPs reveal that IPSPs are important in controlling the timing and probability of action potential generation in pyramidal cells. Our results support the hypothesis that inhibitory networks are largely responsible for the dissemination of higher-frequency activity in cortex.     

Activated cortical states: Experiments, analyses and models

In awake animals, the cerebral cortex displays an "activated" state, with distinct characteristics compared to other states like slow-wave sleep or anesthesia. These characteristics include a sustained depolarized membrane potential (V(m)) and irregular firing activity. In the present paper, we evaluate our understanding of cortical activated states from a computational neuroscience point of view. We start by reviewing the electrophysiological characteristics of activated cortical states based on recordings and analysis performed in awake cat association cortex. These analyses show that cortical activity is characterized by an apparent Poisson-distributed stochastic dynamics, both at the single-cell and population levels, and that single cells display a high-conductance state dominated by inhibition. We next overview computational models of the "awake" cortex, and perform the same analyses as in the experiments. Many properties identified experimentally are indeed reproduced by models, such as depolarized V(m), irregular firing with apparent Poisson statistics, and the determinant role of inhibitory fluctuations on spiking. However, other features are not well reproduced, such as firing statistics and the conductance state of the membrane, suggesting that the network state displayed by models is not entirely correct. We also show how networks can approach a correct conductance state, suggesting ways by which future models will generate activity fully consistent with experimental data.     

Control of computational dynamics of coupled integrate-and-fire neurons

 Generation and control of different dynamical modes of computational processes in a net of interconnected integrate-and-fire neurons are demonstrated. A net architecture resembling a generic cortical structure is formed from pairs of excitatory and inhibitory units with excitatory connections between and inhibitory connections within pairs. Integrate-and-fire model neurons derived from detailed conductance-based models of neocortical pyramidal cells and fast-spiking interneurons are employed for the excitatory and inhibitory units, respectively. Firing-rate adaptation is incorporated into the excitatory units based on the regulation of the slow afterhyperpolarization phase of action potentials by intracellular calcium ions. Saturation of synaptic conductances is implemented for the interconnections between units. It is shown that neuronal adaptation of the excitatory units can generate richer net dynamics than relaxation to fixed-point attractors in a pattern space. At strong adaptivity, i.e. when the neuronal excitability is strongly influenced by the preceding activity, complex dynamics of either aperiodic or limit-cycle character are generated in both the pattern space and the phase space of all dynamical variables. This regime corresponds to an exploratory mode of the system, in which the pattern space can be searched. At weak adaptivity, the dynamics are governed by fixed-point attractors in the pattern space, and this corresponds to a mode for retrieval of a particular pattern. In the brain, neuronal adaptivity can be regulated by various neuromodulators. The results are in accordance with those recently obtained by means of more abstract models formulated in terms of mean firing rates. The increased realism makes the present model reveal more detailed mechanisms and strengthens the relevance of the conclusions to biological systems. The simplicity and realism of the coupled integrate-and-fire neurons make the present model useful for studies of systems in which the temporal aspects of neural coding are important. Received: 8 December 1995 / Accepted in revised form: 23 January 1997     

A neural network model of reliably optimized spike transmission

We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.     

Population rate coding in recurrent neuronal networks with unreliable synapses

Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.     

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.     

State transitions through inhibitory interneurons in a cortical network model

Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.     

Extracting Information from the Power Spectrum of Synaptic Noise

In cortical neurons, synaptic "noise" is caused by the nearly random release of thousands of synapses. Few methods are presently available to analyze synaptic noise and deduce properties of the underlying synaptic inputs. We focus here on the power spectral density (PSD) of several models of synaptic noise. We examine different classes of analytically solvable kinetic models for synaptic currents, such as the "delta kinetic models," which use Dirac delta functions to represent the activation of the ion channel. We first show that, for this class of kinetic models, one can obtain an analytic expression for the PSD of the total synaptic conductance and derive equivalent stochastic models with only a few variables. This yields a method for constraining models of synaptic currents by analyzing voltage-clamp recordings of synaptic noise. Second, we show that a similar approach can be followed for the PSD of the the membrane potential (Vm) through an effective-leak approximation. Third, we show that this approach is also valid for inputs distributed in dendrites. In this case, the frequency scaling of the Vm PSD is preserved, suggesting that this approach may be applied to intracellular recordings of real neurons. In conclusion, using simple mathematical tools, we show that Vm recordings can be used to constrain kinetic models of synaptic currents, as well as to estimate equivalent stochastic models. This approach, therefore, provides a direct link between intracellular recordings in vivo and the design of models consistent with the dynamics and spectral structure of synaptic noise.     

Recurrent circuitry dynamically shapes the activation of piriform cortex

In the piriform cortex, individual odorants activate a unique ensemble of neurons that are distributed without discernable spatial order. Piriform neurons receive convergent excitatory inputs from random collections of olfactory bulb glomeruli. Pyramidal cells also make extensive recurrent connections with other excitatory and inhibitory neurons. We introduced channelrhodopsin into the piriform cortex to characterize these intrinsic circuits and to examine their contribution to activity driven by afferent bulbar inputs. We demonstrated that individual pyramidal cells are sparsely interconnected by thousands of excitatory synaptic connections that extend, largely undiminished, across the piriform cortex, forming a large excitatory network that can dominate the bulbar input. Pyramidal cells also activate inhibitory interneurons that mediate strong, local feedback inhibition that scales with excitation. This recurrent network can enhance or suppress bulbar input, depending on whether the input arrives before or after the cortex is activated. This circuitry may shape the ensembles of piriform cells that encode odorant identity.     

Chaos and synchrony in a model of a hypercolumn in visual cortex

Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This behavior is in marked contrast to the behavior of cortical neurons in vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show a significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a hypercolumn in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model of excitable voltage-clamped cells with several cellular and synaptic conductances. A slow potassium current is included in the dynamics of the excitatory population to reproduce the observed adaptation of the spike trains emitted by these neurons. The pattern of connectivity has a spatial structure which is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability of the neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. These results show that the cooperative dynamics of large neuronal networks are capable of generating variability and synchrony similar to those observed in cortex. Auto-correlation and cross-correlation functions of neuronal spike trains are computed, and their temporal and spatial features are analyzed. In other parameter regimes, the network exhibits two additional states: synchronized oscillations and an asynchronous state. We use our model to study cortical mechanisms for orientation selectivity. It is shown that in a suitable parameter regime, when the input is not oriented, the network has a continuum of states, each representing an inhomogeneous population activity which is peaked at one of the orientation columns. As a result, when a weakly oriented input stimulates the network, it yields a sharp orientation tuning. The properties of the network in this regime, including the appearance of virtual rotations and broad stimulus-dependent cross-correlations, are investigated. The results agree with the predictions of the mean field theory which was previously derived for a simplified model of stochastic, two-state neurons. The relation between the results of the model and experiments in visual cortex are discussed.     

A Dynamical Model of Fast Cortical Reorganization

In this work we study the connection between some dynamic effects at the synaptic level and fast reorganization of cortical sensory maps. By using a biologically plausible computational model of the primary somatosensory system we obtained simulation results that can be used to relate the dynamics of the interactions of excitatory and inhibitory neurons to the process of somatotopic map reorganization immediately after peripheral lesion. The model consists of three regions integrated into a single structure: tactile receptors representing the glabrous surface of the hand, ventral posterior lateral nucleus of the thalamus and area 3b of the primary somatosensory cortex, reproducing the main aspects of the connectivity of these regions. By applying informational measures to the simulation results of the dynamic behavior of AMPA, NMDA and GABA synaptic conductances we draw some conjectures about how the several neuronal synaptic elements are related to the initial stage of the digit-induced reorganization of the hand map in the somatosensory cortex.     

Cortically-Controlled Population Stochastic Facilitation as a Plausible Substrate for Guiding Sensory Transfer across the Thalamic Gateway

The thalamus is the primary gateway that relays sensory information to the cerebral cortex. While a single recipient cortical cell receives the convergence of many principal relay cells of the thalamus, each thalamic cell in turn integrates a dense and distributed synaptic feedback from the cortex. During sensory processing, the influence of this functional loop remains largely ignored. Using dynamic-clamp techniques in thalamic slices in vitro, we combined theoretical and experimental approaches to implement a realistic hybrid retino-thalamo-cortical pathway mixing biological cells and simulated circuits. The synaptic bombardment of cortical origin was mimicked through the injection of a stochastic mixture of excitatory and inhibitory conductances, resulting in a gradable correlation level of afferent activity shared by thalamic cells. The study of the impact of the simulated cortical input on the global retinocortical signal transfer efficiency revealed a novel control mechanism resulting from the collective resonance of all thalamic relay neurons. We show here that the transfer efficiency of sensory input transmission depends on three key features: i) the number of thalamocortical cells involved in the many-to-one convergence from thalamus to cortex, ii) the statistics of the corticothalamic synaptic bombardment and iii) the level of correlation imposed between converging thalamic relay cells. In particular, our results demonstrate counterintuitively that the retinocortical signal transfer efficiency increases when the level of correlation across thalamic cells decreases. This suggests that the transfer efficiency of relay cells could be selectively amplified when they become simultaneously desynchronized by the cortical feedback. When applied to the intact brain, this network regulation mechanism could direct an attentional focus to specific thalamic subassemblies and select the appropriate input lines to the cortex according to the descending influence of cortically-defined “priors”.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.     

Feedforward architectures driven by inhibitory interactions

Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward networks, activity is exclusively driven by excitatory neurons and the wiring patterns between them, while inhibitory neurons play only a stabilizing role for the network dynamics. Motivated by recent experimental discoveries of hippocampal circuitry, cortical circuitry, and the diversity of inhibitory neurons throughout the brain, here we illustrate that one can construct such networks even if the connectivity between the excitatory units in the system remains random. This is achieved by endowing inhibitory nodes with a more active role in the network. Our findings demonstrate that apparent feedforward activity can be caused by a much broader network-architectural basis than often assumed.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.