Internal representation of hippocampal neuronal population spans a time-distance continuum.

The hippocampus plays a critical role in episodic memory: the sequential representation of visited places and experienced events. This function is mirrored by hippocampal activity that self organizes into sequences of neuronal activation that integrate spatiotemporal information. What are the underlying mechanisms of such integration is still unknown. Single cell activity was recently shown to combine time and distance information; however, it remains unknown whether a degree of tuning between space and time can be defined at the network level. Here, combining daily calcium imaging of CA1 sequence dynamics in running head-fixed mice and network modeling, we show that CA1 network activity tends to represent a specific combination of space and time at any given moment, and that the degree of tuning can shift within a continuum from 1 day to the next. Our computational model shows that this shift in tuning can happen under the control of the external drive power. We propose that extrinsic global inputs shape the nature of spatiotemporal integration in the hippocampus at the population level depending on the task at hand, a hypothesis which may guide future experimental studies.

Cell Assemblies in the Cortico-Hippocampal-Reuniens Network during Slow Oscillations.

The nucleus reuniens (NR) is an important anatomic and functional relay between the medial prefrontal cortex (mPFC) and the hippocampus (HPC). Whether the NR controls neuronal assemblies, a hallmark of information exchange between the HPC and mPFC for memory transfer/consolidation, is not known. Using simultaneous local field potential and unit recordings in NR, HPC, and mPFC in male rats during slow oscillations under anesthesia, we identified a reliable sequential activation of NR neurons at the beginning of UP states, which preceded mPFC ones. NR sequences were spatially organized, from dorsal to ventral NR. Chemical inactivation of the NR disrupted mPFC sequences at the onset of UP states as well as HPC sequences present during sharp-wave ripples. We conclude that the NR contributes to the coordination and stabilization of mPFC and HPC neuronal sequences during slow oscillations, possibly via the early activation of its own sequences.SIGNIFICANCE STATEMENT Neuronal assemblies are believed to be instrumental to code/encode/store information. They can be recorded in different brain regions, suggesting that widely distributed networks of networks are involved in such information processing. The medial prefrontal cortex, the hippocampus, and the thalamic nucleus reuniens constitute a typical example of a complex network involved in memory consolidation. In this study, we show that spatially organized cells assemblies are recruited in the nucleus reuniens at the UP state onset during slow oscillations. Nucleus reuniens activity appears to be necessary to the stability of medial prefrontal cortex and hippocampal cell assembly formation during slow oscillations. This result further highlights the role of the nucleus reuniens as a functional hub for exchanging and processing memories.

Cross frequency coupling in next generation inhibitory neural mass models.

Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study, we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory spiking network with exponential synapses, able to autonomously generate collective oscillations (COs). These oscillations emerge via a super-critical Hopf bifurcation, and their frequencies are controlled by the synaptic time scale, the synaptic coupling, and the excitability of the neural population. Furthermore, we show that two inhibitory populations in a master-slave configuration with different synaptic time scales can display various collective dynamical regimes: damped oscillations toward a stable focus, periodic and quasi-periodic oscillations, and chaos. Finally, when bidirectionally coupled, the two inhibitory populations can exhibit different types of θ-γ cross-frequency couplings (CFCs): phase-phase and phase-amplitude CFC. The coupling between θ and γ COs is enhanced in the presence of an external θ forcing, reminiscent of the type of modulation induced in hippocampal and cortex circuits via optogenetic drive.

Modeling driver cells in developing neuronal networks.

Spontaneous emergence of synchronized population activity is a characteristic feature of developing brain circuits. Recent experiments in the developing neo-cortex showed the existence of driver cells able to impact the synchronization dynamics when single-handedly stimulated. We have developed a spiking network model capable to reproduce the experimental results, thus identifying two classes of driver cells: functional hubs and low functionally connected (LC) neurons. The functional hubs arranged in a clique orchestrated the synchronization build-up, while the LC drivers were lately or not at all recruited in the synchronization process. Notwithstanding, they were able to alter the network state when stimulated by modifying the temporal activation of the functional clique or even its composition. LC drivers can lead either to higher population synchrony or even to the arrest of population dynamics, upon stimulation. Noticeably, some LC driver can display both effects depending on the received stimulus. We show that in the model the presence of inhibitory neurons together with the assumption that younger cells are more excitable and less connected is crucial for the emergence of LC drivers. These results provide a further understanding of the structural-functional mechanisms underlying synchronized firings in developing circuits possibly related to the coordinated activity of cell assemblies in the adult brain.

Cell Assembly Dynamics of Sparsely-Connected Inhibitory Networks: A Simple Model for the Collective Activity of Striatal Projection Neurons.

Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal population activity, as observed in brain slices. In particular we develop a new metric to determine the conditions under which sparse inhibitory networks form anti-correlated cell assemblies with time-varying activity of individual cells. We find that under these conditions the network displays an input-specific sequence of cell assembly switching, that effectively discriminates similar inputs. Our results support the proposal that GABAergic connections between striatal projection neurons allow stimulus-selective, temporally-extended sequential activation of cell assemblies. Furthermore, we help to show how altered intrastriatal GABAergic signaling may produce aberrant network-level information processing in disorders such as Parkinson's and Huntington's diseases.

Population spiking and bursting in next-generation neural masses with spike-frequency adaptation.

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the θ-γ range has revealed that a reduction of SFA leads to an increase of the θ frequency joined to a decrease of the γ one. This is analogous to what has been reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, which is known to reduce SFA.

Prominent in vivo influence of single interneurons in the developing barrel cortex.

Spontaneous synchronous activity is a hallmark of developing brain circuits and promotes their formation. Ex vivo, synchronous activity was shown to be orchestrated by a sparse population of highly connected GABAergic 'hub' neurons. The recent development of all-optical methods to record and manipulate neuronal activity in vivo now offers the unprecedented opportunity to probe the existence and function of hub cells in vivo. Using calcium imaging, connectivity analysis and holographic optical stimulation, we show that single GABAergic, but not glutamatergic, neurons influence population dynamics in the barrel cortex of non-anaesthetized mouse pups. Single GABAergic cells mainly exert an inhibitory influence on both spontaneous and sensory-evoked population bursts. Their network influence scales with their functional connectivity, with highly connected hub neurons displaying the strongest impact. We propose that hub neurons function in tailoring intrinsic cortical dynamics to external sensory inputs.

Greedy optimization for growing spatially embedded oscillatory networks.

The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper, we propose and explore a greedy algorithm to grow spatially embedded oscillator networks. The algorithm is constructed in such a way that nodes are sequentially added seeking to minimize the cost of the added links' length and optimize the linear stability of the growing network. We show that, for appropriate parameters, the stability of the resulting network, measured in terms of the dynamics of small perturbations and the correlation length of the disturbances, can be significantly improved with a minimal added length cost. In addition, we analyze numerically the topological properties of the resulting networks, and we find that, while being more stable, their degree distribution is approximately exponential and independent of the algorithm parameters. Moreover, we find that other topological parameters related with network resilience and efficiency are also affected by the proposed algorithm. Finally, we extend our findings to more general classes of networks with different sources of heterogeneity. Our results are a step in the development of algorithms for the directed growth of oscillatory networks with desirable stability, dynamical and topological properties.

Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control.

In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.

Hippocampal hub neurons maintain distinct connectivity throughout their lifetime.

The temporal embryonic origins of cortical GABA neurons are critical for their specialization. In the neonatal hippocampus, GABA cells born the earliest (ebGABAs) operate as 'hubs' by orchestrating population synchrony. However, their adult fate remains largely unknown. To fill this gap, we have examined CA1 ebGABAs using a combination of electrophysiology, neurochemical analysis, optogenetic connectivity mapping as well as ex vivo and in vivo calcium imaging. We show that CA1 ebGABAs not only operate as hubs during development, but also maintain distinct morpho-physiological and connectivity profiles, including a bias for long-range targets and local excitatory inputs. In vivo, ebGABAs are activated during locomotion, correlate with CA1 cell assemblies and display high functional connectivity. Hence, ebGABAs are specified from birth to ensure unique functions throughout their lifetime. In the adult brain, this may take the form of a long-range hub role through the coordination of cell assemblies across distant regions.

Neural activity of heterogeneous inhibitory spiking networks with delay.

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a winner-takes-all mechanism. For sufficiently large transmission delay we observe the emergence of collective oscillations in the system beyond a critical coupling value. Heterogeneity promotes neural inactivation and asynchronous dynamics and its effect can be counteracted by considering longer time delays. In sparse networks, inhibition has the counterintuitive effect of promoting neural reactivation of silent neurons for sufficiently large coupling. In this regime, current fluctuations are on one side responsible for neural firing of subthreshold neurons and on the other side for their desynchronization. Therefore, collective oscillations are present only in a limited range of coupling values, which remains finite in the thermodynamic limit. Out of this range the dynamics is asynchronous and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

Exact firing time statistics of neurons driven by discrete inhibitory noise.

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre- synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post- synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.