Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex

Spontaneous local gamma oscillation selectively enhances neural network responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.

In the nervous system, information is delivered and processed digitally via voltage spikes transmitted between cells. A neural system is characterized by its input/output spike signal patterns. Generally, a network of neurons shows a very different response pattern than that of a single neuron. In some cases, a neural network generates interesting population activities, such as synchronized oscillations, which are thought to modulate the response properties of the network. However, the exact role of these neural oscillations is unknown. We investigated the relationship between the oscillatory activity and the response modulation in neural networks using computational simulation modeling. We found that the response of the system is significantly modified by the oscillations in the network. In particular, the responsiveness to weak inputs is remarkably enhanced. This suggests that the oscillation can differentially amplify sensory information depending on the input signal conditions. We conclude that a neural network can dynamically modify its response properties by the selective amplification of sensory signals due to oscillation activity, which may explain some experimental observations and help us to better understand neural systems.

Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons

Spike generation in cortical neurons depends on the interplay between diverse intrinsic conductances. The phase response curve (PRC) is a measure of the spike time shift caused by perturbations of the membrane potential as a function of the phase of the spike cycle of a neuron. Near the rheobase, purely positive (type I) phase-response curves are associated with an onset of repetitive firing through a saddle-node bifurcation, whereas biphasic (type II) phase-response curves point towards a transition based on a Hopf-Andronov bifurcation. In recordings from layer 2/3 pyramidal neurons in cortical slices, cholinergic action, consistent with down-regulation of slow voltage-dependent potassium currents such as the M-current, switched the PRC from type II to type I. This is the first report showing that cholinergic neuromodulation may cause a qualitative switch in the PRCs type implying a change in the fundamental dynamical mechanism of spike generation.

Complex evolution of spike patterns during burst propagation through feed-forward networks

Stable signal transmission is crucial for information processing by the brain. Synfire-chains, defined as feed-forward networks of spiking neurons, are a well-studied class of circuit structure that can propagate a packet of single spikes while maintaining a fixed packet profile. Here, we studied the stable propagation of spike bursts, rather than single spike activities, in a feed-forward network of a general class of excitable bursting neurons. In contrast to single spikes, bursts can propagate stably without converging to any fixed profiles. Spike timings of bursts continue to change cyclically or irregularly during propagation depending on intrinsic properties of the neurons and the coupling strength of the network. To find the conditions under which bursts lose fixed profiles, we propose an analysis based on timing shifts of burst spikes similar to the phase response analysis of limit-cycle oscillators.

Reliability, synchrony and noise

The brain is noisy. Neurons receive tens of thousands of highly fluctuating inputs and generate spike trains that appear highly irregular. Much of this activity is spontaneous - uncoupled to overt stimuli or motor outputs - leading to questions about the functional impact of this noise. Although noise is most often thought of as disrupting patterned activity and interfering with the encoding of stimuli, recent theoretical and experimental work has shown that noise can play a constructive role - leading to increased reliability or regularity of neuronal firing in single neurons and across populations. These results raise fundamental questions about how noise can influence neural function and computation.

Synchronization engineering: theoretical framework and application to dynamical clustering

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.

Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering

A phase response curve (PRC) characterizes the signal transduction between oscillators such as neurons on a fixed network in a minimal manner, while spike-timing-dependent plasiticity (STDP) characterizes the way of rewiring networks in an activity-dependent manner. This paper demonstrates that these two key properties both related to the interaction times of oscillators work synergetically to carve functionally useful circuits. STDP working on neurons that prefer asynchrony converts the initial asynchronous firing to clustered firing with synchrony within a cluster. They get synchronized within a cluster despite their preference to asynchrony because STDP selectively disrupts intracluster connections, which we call wireless clustering. Our PRC analysis reveals a triad mechanism: the network structure affects how the PRC is read out to determine the synchrony tendency, the synchrony tendency affects how the STDP works, and STDP affects the network structure, closing the loop.

Class-II neurons display a higher degree of stochastic synchronization than class-I neurons

We describe the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs in addition to inputs from independent sources. We use perturbation methods to derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. We compute various measures of the degree of synchrony and cross correlation from the PDF's and use the same to compare and contrast differently shaped PRCs, with respect to their ability to undergo stochastic synchronization. Since the shape of the PRC depends on underlying dynamical details of the oscillator system, we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators. It is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the PRC (type I or type II). It is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation.

Balanced excitatory and inhibitory inputs to cortical neurons decouple firing irregularity from rate modulations

In vivo cortical neurons are known to exhibit highly irregular spike patterns. Because the intervals between successive spikes fluctuate greatly, irregular neuronal firing makes it difficult to estimate instantaneous firing rates accurately. If, however, the irregularity of spike timing is decoupled from rate modulations, the estimate of firing rate can be improved. Here, we introduce a novel coding scheme to make the firing irregularity orthogonal to the firing rate in information representation. The scheme is valid if an interspike interval distribution can be well fitted by the gamma distribution and the firing irregularity is constant over time. We investigated in a computational model whether fluctuating external inputs may generate gamma process-like spike outputs, and whether the two quantities are actually decoupled. Whole-cell patch-clamp recordings of cortical neurons were performed to confirm the predictions of the model. The output spikes were well fitted by the gamma distribution. The firing irregularity remained approximately constant regardless of the firing rate when we injected a balanced input, in which excitatory and inhibitory synapses are activated concurrently while keeping their conductance ratio fixed. The degree of irregular firing depended on the effective reversal potential set by the balance between excitation and inhibition. In contrast, when we modulated conductances out of balance, the irregularity varied with the firing rate. These results indicate that the balanced input may improve the efficiency of neural coding by clamping the firing irregularity of cortical neurons. We demonstrate how this novel coding scheme facilitates stimulus decoding.

Synchronization of excitatory neurons with strongly heterogeneous phase responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, the dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.

Optimal time scale for spike-time reliability: theory, simulations, and experiments

Use of spike timing to encode information requires that neurons respond with high temporal precision and with high reliability. Fast fluctuating stimuli are known to result in highly reproducible spike times across trials, whereas constant stimuli result in variable spike times. Here, we first studied mathematically how spike-time reliability depends on the rapidness of aperiodic stimuli. Then, we tested our theoretical predictions in computer simulations of neuron models (Hodgkin-Huxley and modified quadratic integrate-and-fire), as well as in patch-clamp experiments with real neurons (mitral cells in the olfactory bulb and pyramidal cells in the neocortex). As predicted by our theory, we found that for firing frequencies in the beta/gamma range, spike-time reliability is maximal when the time scale of the input fluctuations (autocorrelation time) is in the range of a few milliseconds (2-5 ms), coinciding with the time scale of fast synapses, and decreases substantially for faster and slower inputs. Finally, we comment how these findings relate to mechanisms causing neuronal synchronization.