Gamma oscillations organize top-down signalling to hypothalamus and enable food seeking.

Both humans and animals seek primary rewards in the environment, even when such rewards do not correspond to current physiological needs. An example of this is a dissociation between food-seeking behaviour and metabolic needs, a notoriously difficult-to-treat symptom of eating disorders. Feeding relies on distinct cell groups in the hypothalamus, the activity of which also changes in anticipation of feeding onset. The hypothalamus receives strong descending inputs from the lateral septum, which is connected, in turn, with cortical networks, but cognitive regulation of feeding-related behaviours is not yet understood. Cortical cognitive processing involves gamma oscillations, which support memory, attention, cognitive flexibility and sensory responses. These functions contribute crucially to feeding behaviour by unknown neural mechanisms. Here we show that coordinated gamma (30-90 Hz) oscillations in the lateral hypothalamus and upstream brain regions organize food-seeking behaviour in mice. Gamma-rhythmic input to the lateral hypothalamus from somatostatin-positive lateral septum cells evokes food approach without affecting food intake. Inhibitory inputs from the lateral septum enable separate signalling by lateral hypothalamus neurons according to their feeding-related activity, making them fire at distinct phases of the gamma oscillation. Upstream, medial prefrontal cortical projections provide gamma-rhythmic inputs to the lateral septum; these inputs are causally associated with improved performance in a food-rewarded learning task. Overall, our work identifies a top-down pathway that uses gamma synchronization to guide the activity of subcortical networks and to regulate feeding behaviour by dynamic reorganization of functional cell groups in the hypothalamus.

On Rhythms in Neuronal Networks with Recurrent Excitation.

We investigate rhythms in networks of neurons with recurrent excitation, that is, with excitatory cells exciting each other. Recurrent excitation can sustain activity even when the cells in the network are driven below threshold, too weak to fire on their own. This sort of "reverberating" activity is often thought to be the basis of working memory. Recurrent excitation can also lead to "runaway" transitions, sudden transitions to high-frequency firing; this may be related to epileptic seizures. Not all fundamental questions about these phenomena have been answered with clarity in the literature. We focus on three questions here: (1) How much recurrent excitation is needed to sustain reverberating activity? How does the answer depend on parameters? (2) Is there a positive minimum frequency of reverberating activity, a positive "onset frequency"? How does it depend on parameters? (3) When do runaway transitions occur? For reduced models, we give mathematical answers to these questions. We also examine computationally to which extent our findings are reflected in the behavior of biophysically more realistic model networks. Our main results can be summarized as follows. (1) Reverberating activity can be fueled by extremely weak slow recurrent excitation, but only by sufficiently strong fast recurrent excitation. (2) The onset of reverberating activity, as recurrent excitation is strengthened or external drive is raised, occurs at a positive frequency. It is faster when the external drive is weaker (and the recurrent excitation stronger). It is slower when the recurrent excitation has a longer decay time constant. (3) Runaway transitions occur only with fast, not with slow, recurrent excitation. We also demonstrate that the relation between reverberating activity fueled by recurrent excitation and runaway transitions can be visualized in an instructive way by a (generalized) cusp catastrophe surface.

Mesoscale-duration activated states gate spiking in response to fast rises in membrane voltage in the awake brain.

Seconds-scale network states, affecting many neurons within a network, modulate neural activity by complementing fast integration of neuron-specific inputs that arrive in the milliseconds before spiking. Nonrhythmic subthreshold dynamics at intermediate timescales, however, are less well characterized. We found, using automated whole cell patch clamping in vivo, that spikes recorded in CA1 and barrel cortex in awake mice are often preceded not only by monotonic voltage rises lasting milliseconds but also by more gradual (lasting tens to hundreds of milliseconds) depolarizations. The latter exert a gating function on spiking, in a fashion that depends on the gradual rise duration: the probability of spiking was higher for longer gradual rises, even when controlled for the amplitude of the gradual rises. Barrel cortex double-autopatch recordings show that gradual rises are shared across some, but not all, neurons. The gradual rises may represent a new kind of state, intermediate both in timescale and in proportion of neurons participating, which gates a neuron's ability to respond to subsequent inputs.NEW & NOTEWORTHY We analyzed subthreshold activity preceding spikes in hippocampus and barrel cortex of awake mice. Aperiodic voltage ramps extending over tens to hundreds of milliseconds consistently precede and facilitate spikes, in a manner dependent on both their amplitude and their duration. These voltage ramps represent a "mesoscale" activated state that gates spike production in vivo.

GABA(B) autoreceptor-mediated cell type-specific reduction of inhibition in epileptic mice.

GABA(B) receptors (GABA(B)Rs) mediate slow inhibitory effects on neuronal excitability and synaptic transmission in the brain. However, the GABA(B)R agonist baclofen can also promote excitability and seizure generation in human patients and animals models. Here we show that baclofen has concentration-dependent effects on the hippocampal network in a mouse model of mesial temporal lobe epilepsy. Application of baclofen at a high dose (10 mg/kg i.p.) reduced the power of γ oscillations and the frequency of pathological discharges in the Cornu Ammonis area 3 (CA3) area of freely moving epileptic mice. Unexpectedly, at a lower dose (1 mg/kg), baclofen markedly increased γ activity accompanied by a higher incidence of pathological discharges. Intracellular recordings from CA3 pyramidal cells in vitro further revealed that, although at a high concentration (10 µM), baclofen invariably resulted in hyperpolarization, at low concentrations (0.5 µM), the drug had divergent effects, producing depolarization and an increase in firing frequency in epileptic but not control mice. These excitatory effects were mediated by the selective muting of inhibitory cholecystokinin-positive basket cells (CCK(+) BCs), through enhanced inhibition of GABA release via presynaptic GABA(B)Rs. We conclude that cell type-specific up-regulation of GABA(B)R-mediated autoinhibition in CCK(+) BCs promotes aberrant high frequency oscillations and hyperexcitability in hippocampal networks of chronic epileptic mice.

Neurosystems: brain rhythms and cognitive processing.

Neuronal rhythms are ubiquitous features of brain dynamics, and are highly correlated with cognitive processing. However, the relationship between the physiological mechanisms producing these rhythms and the functions associated with the rhythms remains mysterious. This article investigates the contributions of rhythms to basic cognitive computations (such as filtering signals by coherence and/or frequency) and to major cognitive functions (such as attention and multi-modal coordination). We offer support to the premise that the physiology underlying brain rhythms plays an essential role in how these rhythms facilitate some cognitive operations.

Minimal size of cell assemblies coordinated by gamma oscillations.

In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25-100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.

Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model.

Simultaneous presentation of multiple stimuli can reduce the firing rates of neurons in extrastriate visual cortex below the rate elicited by a single preferred stimulus. We describe computational results suggesting how this remarkable effect may arise from strong excitatory drive to a substantial local population of fast-spiking inhibitory interneurons, which can lead to a loss of coherence in that population and thereby raise the effectiveness of inhibition. We propose that in attentional states fast-spiking interneurons may be subject to a bath of inhibition resulting from cholinergic activation of a second class of inhibitory interneurons, restoring conditions needed for gamma rhythmicity. Oscillations and coherence are emergent features, not assumptions, in our model. The gamma oscillations in turn support stimulus competition. The mechanism is a form of "oscillatory selection," in which neural interactions change phase relationships that regulate firing rates, and attention shapes those neural interactions.

Mechanisms of very fast oscillations in networks of axons coupled by gap junctions.

Because electrical coupling among the neurons of the brain is much faster than chemical synaptic coupling, it is natural to hypothesize that gap junctions may play a crucial role in mechanisms underlying very fast oscillations (VFOs), i.e., oscillations at more than 80 Hz. There is now a substantial body of experimental and modeling literature supporting this hypothesis. A series of modeling papers, starting with work by Roger Traub and collaborators, have suggested that VFOs may arise from expanding waves propagating through an "axonal plexus", a large random network of electrically coupled axons. Traub et al. also proposed a cellular automaton (CA) model to study the mechanisms of VFOs in the axonal plexus. In this model, the expanding waves take the appearance of topologically circular "target patterns". Random external stimuli initiate each wave. We therefore call this kind of VFO "externally driven". Using a computational model, we show that an axonal plexus can also exhibit a second, distinctly different kind of VFO in a wide parameter range. These VFOs arise from activity propagating around cycles in the network. Once triggered, they persist without any source of excitation. With idealized, regular connectivity, they take the appearance of spiral waves. We call these VFOs "re-entrant". The behavior of the axonal plexus depends on the reliability with which action potentials propagate from one axon to the next, which, in turn, depends on the somatic membrane potential V (s) and the gap junction conductance g (gj). To study these dependencies, we impose a fixed value of V (s), then study the effects of varying V (s) and g (gj). Not surprisingly, propagation becomes more reliable with rising V (s) and g (gj). Externally driven VFOs occur when V (s) and g (gj) are so high that propagation never fails. For lower V (s) or g (gj), propagation is nearly reliable, but fails in rare circumstances. Surprisingly, the parameter regime where this occurs is fairly large. Even a single propagation failure can trigger re-entrant VFOs in this regime. Lowering V (s) and g (gj) further, one finds a third parameter regime in which propagation is unreliable, and no VFOs arise. We analyze these three parameter regimes by means of computations using model networks adapted from Traub et al., as well as much smaller model networks.

The response of a classical Hodgkin-Huxley neuron to an inhibitory input pulse.

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30-80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin-Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.

Approximate, not Perfect Synchrony Maximizes the Downstream Effectiveness of Excitatory Neuronal Ensembles.

The most basic functional role commonly ascribed to synchrony in the brain is that of amplifying excitatory neuronal signals. The reasoning is straightforward: When positive charge is injected into a leaky target neuron over a time window of positive duration, some of it will have time to leak back out before an action potential is triggered in the target, and it will in that sense be wasted. If the goal is to elicit a firing response in the target using as little charge as possible, it seems best to deliver the charge all at once, i.e., in perfect synchrony. In this article, we show that this reasoning is correct only if one assumes that the input ceases when the target crosses the firing threshold, but before it actually fires. If the input ceases later-for instance, in response to a feedback signal triggered by the firing of the target-the "most economical" way of delivering input (the way that requires the least total amount of input) is no longer precisely synchronous, but merely approximately so. If the target is a heterogeneous network, as it always is in the brain, then ceasing the input "when the target crosses the firing threshold" is not an option, because there is no single moment when the firing threshold is crossed. In this sense, precise synchrony is never optimal in the brain.

Toggling between gamma-frequency activity and suppression of cell assemblies.

Gamma (30-80 Hz) rhythms in hippocampus and neocortex resulting from the interaction of excitatory and inhibitory cells (E- and I-cells), called Pyramidal-Interneuronal Network Gamma (PING), require that the I-cells respond to the E-cells, but don't fire on their own. In idealized models, there is a sharp boundary between a parameter regime where the I-cells have weak-enough drive for PING, and one where they have so much drive that they fire without being prompted by the E-cells. In the latter regime, they often de-synchronize and suppress the E-cells; the boundary was therefore called the "suppression boundary" by Börgers and Kopell (2005). The model I-cells used in the earlier work by Börgers and Kopell have a "type 1" phase response, i.e., excitatory input always advances them. However, fast-spiking inhibitory basket cells often have a "type 2" phase response: Excitatory input arriving soon after they fire delays them. We study the effect of the phase response type on the suppression transition, under the additional assumption that the I-cells are kept synchronous by gap junctions. When many E-cells participate on a given cycle, the resulting excitation advances the I-cells on the next cycle if their phase response is of type 1, and this can result in suppression of more E-cells on the next cycle. Therefore, strong E-cell spike volleys tend to be followed by weaker ones, and vice versa. This often results in erratic fluctuations in the strengths of the E-cell spike volleys. When the phase response of the I-cells is of type 2, the opposite happens: strong E-cell spike volleys delay the inhibition on the next cycle, therefore tend to be followed by yet stronger ones. The strengths of the E-cell spike volleys don't oscillate, and there is a nearly abrupt transition from PING to ING (a rhythm involving I-cells only).

EXPONENTIAL TIME DIFFERENCING FOR HODGKIN-HUXLEY-LIKE ODES.

Several authors have proposed the use of exponential time differencing (ETD) for Hodgkin-Huxley-like partial and ordinary differential equations (PDEs and ODEs). For Hodgkin-Huxley-like PDEs, ETD is attractive because it can deal effectively with the stiffness issues that diffusion gives rise to. However, large neuronal networks are often simulated assuming "space-clamped" neurons, i.e., using the Hodgkin-Huxley ODEs, in which there are no diffusion terms. Our goal is to clarify whether ETD is a good idea even in that case. We present a numerical comparison of first- and second-order ETD with standard explicit time-stepping schemes (Euler's method, the midpoint method, and the classical fourth-order Runge-Kutta method). We find that in the standard schemes, the stable computation of the very rapid rising phase of the action potential often forces time steps of a small fraction of a millisecond. This can result in an expensive calculation yielding greater overall accuracy than needed. Although it is tempting at first to try to address this issue with adaptive or fully implicit time-stepping, we argue that neither is effective here. The main advantage of ETD for Hodgkin-Huxley-like systems of ODEs is that it allows underresolution of the rising phase of the action potential without causing instability, using time steps on the order of one millisecond. When high quantitative accuracy is not necessary and perhaps, because of modeling inaccuracies, not even useful, ETD allows much faster simulations than standard explicit time-stepping schemes. The second-order ETD scheme is found to be substantially more accurate than the first-order one even for large values of Δt.

Gamma oscillations and stimulus selection.

More coherent excitatory stimuli are known to have a competitive advantage over less coherent ones. We show here that this advantage is amplified greatly when the target includes inhibitory interneurons acting via GABA(A)-receptor-mediated synapses and the coherent input oscillates at gamma frequency. We hypothesize that therein lies, at least in part, the functional significance of the experimentally observed link between attentional biasing of stimulus competition and gamma frequency rhythmicity.

Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons.

Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and Icells (excitatory and inhibitory cells). The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as PING (pyramidal-interneuronal gamma) rhythms. The PING mechanism requires that the drive I(I) to the I-cells be sufficiently low; the rhythm is lost when I(I) gets too large. This can happen in at least two ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism does not work far above the gamma range in the presence of heterogeneity, this justifies the "G" in "PING."

Background gamma rhythmicity and attention in cortical local circuits: a computational study.

We describe a simple computational model, based on generic features of cortical local circuits, that links cholinergic neuromodulation, gamma rhythmicity, and attentional selection. We propose that cholinergic modulation, by reducing adaptation currents in principal cells, induces a transition from asynchronous spontaneous activity to a "background" gamma rhythm (resembling the persistent gamma rhythms evoked in vitro by cholinergic agonists) in which individual principal cells participate infrequently and irregularly. We suggest that such rhythms accompany states of preparatory attention or vigilance and report simulations demonstrating that their presence can amplify stimulus-specific responses and enhance stimulus competition within a local circuit.

Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity.

In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions-homogeneity in relevant network parameters and all-to-all connectivity, for instance-this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E --> I synapses. More surprising, it cannot be reduced by strengthening the I --> E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.