Cellularly-driven differences in network synchronization propensity are differentially modulated by firing frequency

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.     

Membrane Resonance and Stochastic Resonance Modulate Firing Patterns of Thalamocortical Neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.     

Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics

We review and extend recent results on the instantaneous firing rate dynamics of simplified models of spiking neurons in response to noisy current inputs. It has been shown recently that the response of the instantaneous firing rate to small amplitude oscillations in the mean inputs depends in the large frequency limit f on the spike initiation dynamics. A particular simplified model, the exponential integrate-and-fire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductance-based models with a Hodgkin-Huxley type fast sodium current. Here, we show that the response of the EIF instantaneous firing rate also decays as 1/f in the case of an oscillation in the variance of the inputs for both white and colored noise. We then compute the initial transient response of the firing rate of the EIF model to a step change in its mean inputs and/or in the variance of its inputs. We show that in both cases the response speed is proportional to the neuron stationary firing rate and inversely proportional to a spike slope factor _T that controls the sharpness of spike initiation: as 1/_T for a step change in mean inputs, and as 1/_T² for a step change in the variance in the inputs.     

Beyond Two-Cell Networks: Experimental Measurement of Neuronal Responses to Multiple Synaptic Inputs

Oscillations of large populations of neurons are thought to be important in the normal functioning of the brain. We have used phase response curve (PRC) methods to characterize the dynamics of single neurons and predict population dynamics. Our past experimental work was limited to special circumstances (e.g., 2-cell networks of periodically firing neurons). Here, we explore the feasibility of extending our methods to predict the synchronization properties of stellate cells (SCs) in the rat entorhinal cortex under broader conditions. In particular, we test the hypothesis that PRCs in SCs scale linearly with changes in synaptic amplitude, and measure how well responses to Poisson process-driven inputs can be predicted in terms of PRCs. Although we see nonlinear responses to excitatory and inhibitory inputs, we find that models based on weak coupling account for scaling and Poisson process-driven inputs reasonably accurately.     

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.     

Identifying and Tracking Simulated Synaptic Inputs from Neuronal Firing: Insights from In Vitro Experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.     

Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.     

Random perturbations of spiking activity in a pair of coupled neurons

We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin–Huxley model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from      

Slope-Based Stochastic Resonance: How Noise Enables Phasic Neurons to Encode Slow Signals

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal''s rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.     

Analytical and Simulation Results for Stochastic Fitzhugh-Nagumo Neurons and Neural Networks

An analytical approach is presented for determining the response of a neuron or of the activity in a network of connected neurons, represented by systems of nonlinear ordinary stochastic differential equations—the Fitzhugh-Nagumo system with Gaussian white noise current. For a single neuron, five equations hold for the first- and second-order central moments of the voltage and recovery variables. From this system we obtain, under certain assumptions, five differential equations for the means, variances, and covariance of the two components. One may use these quantities to estimate the probability that a neuron is emitting an action potential at any given time. The differential equations are solved by numerical methods. We also perform simulations on the stochastic Fitzugh-Nagumo system and compare the results with those obtained from the differential equations for both sustained and intermittent deterministic current inputs withsuperimposed noise. For intermittent currents, which mimic synaptic input, the agreement between the analytical and simulation results for the moments is excellent. For sustained input, the analytical approximations perform well for small noise as there is excellent agreement for the moments. In addition, the probability that a neuron is spiking as obtained from the empirical distribution of the potential in the simulations gives a result almost identical to that obtained using the analytical approach. However, when there is sustained large-amplitude noise, the analytical method is only accurate for short time intervals. Using the simulation method, we study the distribution of the interspike interval directly from simulated sample paths. We confirm that noise extends the range of input currents over which (nonperiodic) spike trains may exist and investigate the dependence of such firing on the magnitude of the mean input current and the noise amplitude. For networks we find the differential equations for the means, variances, and covariances of the voltage and recovery variables and show how solving them leads to an expression for the probability that a given neuron, or given set of neurons, is firing at time t. Using such expressions one may implement dynamical rules for changing synaptic strengths directly without sampling. The present analytical method applies equally well to temporally nonhomogeneous input currents and is expected to be useful for computational studies of information processing in various nervous system centers.     

Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocorrelation

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation of the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.     

Frequency-independent synaptic transmission supports a linear vestibular behavior

The vestibular system is responsible for transforming head motion into precise eye, head, and body movements that rapidly stabilize gaze and posture. How do central excitatory synapses mediate behavioral outputs accurately matched to sensory inputs over a wide dynamic range? Here we demonstrate that vestibular afferent synapses in vitro express frequency-independent transmission that spans their in vivo dynamic range (5-150 spikes/s). As a result, the synaptic charge transfer per unit time is linearly related to vestibular afferent activity in both projection and intrinsic neurons of the vestibular nuclei. Neither postsynaptic glutamate receptor desensitization nor saturation affect the relative amplitude or frequency-independence of steady-state transmission. Finally, we show that vestibular nucleus neurons can transduce synaptic inputs into linear changes in firing rate output without relying on one-to-one calyceal transmission. These data provide a physiological basis for the remarkable linearity of vestibular reflexes.     

Signal propagation in feedforward neuronal networks with unreliable synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.     

Synaptic integration in spinal motoneurones.

Spinal motoneurones receive thousands of presynaptic excitatory and inhibitory synaptic contacts distributed throughout their dendritic trees. Despite this extensive convergence, there have been very few studies of how synaptic inputs interact in mammalian motoneurones when they are activated concurrently. In the experiments reported here, we measured the effective synaptic currents and the changes in firing rate evoked in cat spinal motoneurones by concurrent repetitive activation of two separate sets of presynaptic neurons. We compared these effects to those predicted by a linear sum of the effects produced by activating each set of presynaptic neurons separately. We generally found that when two inputs were activated concurrently, both the effective synaptic currents and the synaptically-evoked changes in firing rate they produced in motoneurones were generally linear, or slightly less than the linear sum of the effects produced by activating each input alone. The results suggest that the spatial distribution synaptic terminals on the dendritic trees of motoneurones may help isolate synapses from one another, minimizing non-linear interactions.     

Consistency and Diversity of Spike Dynamics in the Neurons of Bed Nucleus of Stria Terminalis of the Rat: A Dynamic Clamp Study

Neurons display a high degree of variability and diversity in the expression and regulation of their voltage-dependent ionic channels. Under low level of synaptic background a number of physiologically distinct cell types can be identified in most brain areas that display different responses to standard forms of intracellular current stimulation. Nevertheless, it is not well understood how biophysically different neurons process synaptic inputs in natural conditions, i.e., when experiencing intense synaptic bombardment in vivo. While distinct cell types might process synaptic inputs into different patterns of action potentials representing specific “motifs” of network activity, standard methods of electrophysiology are not well suited to resolve such questions. In the current paper we performed dynamic clamp experiments with simulated synaptic inputs that were presented to three types of neurons in the juxtacapsular bed nucleus of stria terminalis (jcBNST) of the rat. Our analysis on the temporal structure of firing showed that the three types of jcBNST neurons did not produce qualitatively different spike responses under identical patterns of input. However, we observed consistent, cell type dependent variations in the fine structure of firing, at the level of single spikes. At the millisecond resolution structure of firing we found high degree of diversity across the entire spectrum of neurons irrespective of their type. Additionally, we identified a new cell type with intrinsic oscillatory properties that produced a rhythmic and regular firing under synaptic stimulation that distinguishes it from the previously described jcBNST cell types. Our findings suggest a sophisticated, cell type dependent regulation of spike dynamics of neurons when experiencing a complex synaptic background. The high degree of their dynamical diversity has implications to their cooperative dynamics and synchronization.     

Influence of sound pressure level on the processing of amplitude modulations by auditory neurons of the locust

Typical features of natural sounds are amplitude changes at different time scales. In many species, amplitude modulations constitute decisive cues to recognize communication signals. Since these signals should be recognizable over a broad intensity range, we investigated how the encoding of amplitude modulations by auditory neurons depends on sound pressure level. Identified neurons that represent different processing stages in the locusts’ auditory pathway were stimulated with sinusoidal modulations of a broad band noise carrier, at different intensities, and characteristic parameters of modulation transfer functions (MTFs) were determined. The corner frequencies of temporal MTFs turned out to be independent of intensity for all neurons except one. Furthermore, for none of the neurons investigated corner frequencies were significantly correlated with spike rate, indicating a remarkable intensity invariance of the upper limits of temporal resolution. The shape of the tMTFs changed with increasing intensity from a low-pass to a band-pass for receptors and local neurons, while no consistent change was observed for ascending neurons. The best modulation frequency depended on intensity and spike rate, especially for receptors and local neurons. Remarkably, the adaptation state of some neurons turned out to be independent of the spike rate during the modulation part of the stimulus.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

From stimulus estimation to combination sensitivity: encoding and processing of amplitude and timing information in parallel,convergent sensory pathways

Information theoretical approaches to sensory processing in electric fish have focused on the encoding of amplitude modulations in a single sensory pathway in the South American gymnotiforms. To assess the generality of these studies, we investigated the encoding of amplitude and phase modulations in the distantly related African fish Gymnarchus. In both the amplitude- and time-coding pathways, primary afferents accurately estimated the time course of random modulations whereas hindbrain neurons extracted information about specific stimulus features. Despite exhibiting a clear preference for encoding amplitude or phase, afferents and hindbrain neurons could encode significant amounts of modulation of their nonpreferred attribute. Although no increase in feature extraction performance occurred where the two pathways converge in the midbrain, neurons there were increasingly sensitive to simultaneous modulation of both attributes. A shift from accurate stimulus estimation in the periphery to increasingly sparse representations of specific features appears to be a general strategy in electrosensory processing.     

Inhibitory synchrony as a mechanism for attentional gain modulation

Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron's firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f-I) curves. For a large number of inhibitory inputs (approximately 50), the f-I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity-the model neuron responded to weaker inputs I. For a small number (approximately 10), the f-I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response-the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.