Excitatory Population Research Articles

Differential responses to ω-agatoxin IVA in murine frontal cortex and spinal cord derived neuronal networks

ω-Agatoxin-IVA is a well known P/Q-type Ca2+ channel blocker and has been shown to affect presynaptic Ca2+ currents as well postsynaptic potentials. P/Q-type voltage gated Ca2+ channels play a vital role in presynaptic neurotransmitter release and thus play a role in action potential generation. Monitoring spontaneous activity of neuronal networks on microelectrode arrays (MEAs) provides an important tool for examining this neurotoxin. Changes in extracellular action potentials are readily observed and are dependent on synaptic function. Given the efficacy of murine frontal cortex and spinal cord networks to detect neuroactive substances, we investigated the effects of ω-agatoxin on spontaneous action potential firing within these networks. We found that networks derived from spinal cord are more sensitive to the toxin than those from frontal cortex; a concentration of only 10nM produced statistically significant effects on activity from spinal cord networks whereas 50nM was required to alter activity in frontal cortex networks. Furthermore, the effects of the toxin on frontal cortex are more complex as unit specific responses were observed. These manifested as either a decrease or increase in action potential firing rate which could be statistically separated as unique clusters. Administration of bicuculline, a GABAA inhibitor, isolated a single response to ω-agatoxin, which was characterized by a reduction in network activity. These data support the notion that the two clusters detected with ω-agatoxin exposure represent differential responses from excitatory and inhibitory neuronal populations.

From lamprey to salamander: an exploratory modeling study on the architecture of the spinal locomotor networks in the salamander

The evolutionary transition from water to land required new locomotor modes and corresponding adjustments of the spinal "central pattern generators" for locomotion. Salamanders resemble the first terrestrial tetrapods and represent a key animal for the study of these changes. Based on recent physiological data from salamanders, and previous work on the swimming, limbless lamprey, we present a model of the basic oscillatory network in the salamander spinal cord, the spinal segment. Model neurons are of the Hodgkin-Huxley type. Spinal hemisegments contain sparsely connected excitatory and inhibitory neuron populations, and are coupled to a contralateral hemisegment. The model yields a large range of experimental findings, especially the NMDA-induced oscillations observed in isolated axial hemisegments and segments of the salamander Pleurodeles waltlii. The model reproduces most of the effects of the blockade of AMPA synapses, glycinergic synapses, calcium-activated potassium current, persistent sodium current, and [Formula: see text]-current. Driving segments with a population of brainstem neurons yields fast oscillations in the in vivo swimming frequency range. A minimal modification to the conductances involved in burst-termination yields the slower stepping frequency range. Slow oscillators can impose their frequency on fast oscillators, as is likely the case during gait transitions from swimming to stepping. Our study shows that a lamprey-like network can potentially serve as a building block of axial and limb oscillators for swimming and stepping in salamanders.

Loss of the Kv1.1 potassium channel promotes pathologic sharp waves and high frequency oscillations in in vitro hippocampal slices

In human disease, channelopathies involving functional reduction of the delayed rectifier potassium channel α-subunit Kv1.1 – either by mutation or autoimmune inhibition – result in temporal lobe epilepsy. Kv1.1 is prominently expressed in the axons of the hippocampal tri-synaptic pathway, suggesting its absence will result in widespread effects on normal network oscillatory activity. Here, we performed in vitro extracellular recordings using a multielectrode array to determine the effects of loss of Kv1.1 on spontaneous sharp waves (SPWs) and high frequency oscillations (HFOs). We found that Kcna1-null hippocampi generate SPWs and ripples (80–200Hz bandwidth) with a 50% increased rate of incidence and 50% longer duration, and that epilepsy-associated pathologic HFOs in the fast ripple bandwidth (200–600Hz) are also present. Furthermore, Kcna1-null CA3 has enhanced coupling of excitatory inputs and population spike generation and CA3 principal cells have reduced spike timing reliability. Removing the influence of mossy fiber and perforant path inputs by micro-dissecting the Kcna1-null CA3 region mostly rescued the oscillatory behavior and improved spike timing. We found that Kcna1-null mossy fibers and medial perforant path axons are hyperexcitable and produce greater pre- and post-synaptic responses with reduced paired-pulse ratios suggesting increased neurotransmitter release at these terminals. These findings were recapitulated in wild-type slices exposed to the Kv1.1 inhibitor dendrotoxin-κ. Collectively, these data indicate that loss of Kv1.1 enhances synaptic release in the CA3 region, which reduces spike timing precision of individual neurons leading to disorganization of network oscillatory activity and promotes the emergence of fast ripples.

Prepubertal castration causes the age‐dependent changes in hippocampal long‐term potentiation

The effects of prepubertal castration on hippocampal CA3-CA1 synaptic transmission and plasticity were studied at different ages in vitro. The field excitatory postsynaptic potentials (fEPSP) and population spikes (PS) were simultaneously recorded from stratum radiatum and stratum pylamidale of area CA1 following stimulation of Schaffer collaterals in slices taken from sham-castrated and castrated rats at postnatal days (PND) 28, 35, 45, and 60. Castration had no effect on baseline responses at different ages except at PND 60 that a decrease in the fEPSP slope was seen. Prepubertal castration caused age-specific changes in CA1-long term potentiation (LTP) induction. The castration did decrease both fEPSP-LTP and PS-LTP at PND 35 but a decrease was seen only in PS-LTP at PND 60. NMDA receptor antagonist AP5 (25 µM) completely blocked both fEPSP-LTP and PS-LTP at PND 60 and only PS-LTP at PND 35 in both sham-castrated and castrated groups. Although AP5 blocked fEPSP-LTP at PND 35 in sham-castrated group, it failed to inhibit fEPSP-LTP at PND 35 in castrated one. These findings suggest that prepubertal castration causes the age-dependent changes in CA1-LTP induction, which might arise from alterations in the NMDA receptors.

Structural-Functional Properties of Identified Excitatory and Inhibitory Interneurons within Pre-Bötzinger Complex Respiratory Microcircuits

We comparatively analyzed cellular and circuit properties of identified rhythmic excitatory and inhibitory interneurons within respiratory microcircuits of the neonatal rodent pre-Bötzinger complex (pre-BötC), the structure generating inspiratory rhythm in the brainstem. We combined high-resolution structural-functional imaging, molecular assays for neurotransmitter phenotype identification in conjunction with electrophysiological property phenotyping, and morphological reconstruction of interneurons in neonatal rat and mouse slices in vitro. This approach revealed previously undifferentiated structural-functional features that distinguish excitatory and inhibitory interneuronal populations. We identified distinct subpopulations of pre-BötC glutamatergic, glycinergic, GABAergic, and glycine-GABA coexpressing interneurons. Most commissural pre-BötC inspiratory interneurons were glutamatergic, with a substantial subset exhibiting intrinsic oscillatory bursting properties. Commissural excitatory interneurons projected with nearly planar trajectories to the contralateral pre-BötC, many also with axon collaterals to areas containing inspiratory hypoglossal (XII) premotoneurons and motoneurons. Inhibitory neurons as characterized in the present study did not exhibit intrinsic oscillatory bursting properties, but were electrophysiologically distinguished by more pronounced spike frequency adaptation properties. Axons of many inhibitory neurons projected ipsilaterally also to regions containing inspiratory XII premotoneurons and motoneurons, whereas a minority of inhibitory neurons had commissural axonal projections. Dendrites of both excitatory and inhibitory interneurons were arborized asymmetrically, primarily in the coronal plane. The dendritic fields of inhibitory neurons were more spatially compact than those of excitatory interneurons. Our results are consistent with the concepts of a compartmental circuit organization, a bilaterally coupled excitatory rhythmogenic kernel, and a role of pre-BötC inhibitory neurons in shaping inspiratory pattern as well as coordinating inspiratory and expiratory activity.

Intra-hippocampal injection of lipopolysaccharide inhibits kindled seizures and retards kindling rate in adult rats

Neuroinflammation facilitates seizure acquisition and epileptogenesis in developing brain. Yet, the studies on impact of neuroinflammation on mature brain epileptogenesis have led to inconsistent results. Hippocampus is particularly vulnerable to damage caused by ischemia, hypoxia and trauma, and the consequent neuroinflammation, which can lead in turn to epilepsy. Lipopolysaccharide (LPS) is extensively used in experimental studies to induce neuroinflammation. In this study, effect of acute and chronic intra-CA1 infusion of LPS on amygdala-kindled seizures and epileptogenesis was examined in mature rats. LPS (5μg/rat) inhibited evoked amygdala afterdischarges and behavioral seizures. Anticonvulsant effect of LPS was observed 0.5h after administration and continued up to 24h. This effect was accompanied by intra-hippocampal elevation of nitric oxide (NO), interleukin1-β, and tumor necrosis factor-α and was prevented by microglia inhibitor, naloxone, NO synthase inhibitor, Nω-nitro-L-arginine methyl ester, cyclooxygenase inhibitor, piroxicam, and interleukin1-β receptor antagonist, interleukin1-ra. Moreover, daily intra-hippocampal injection of LPS significantly retarded kindling rate. In order to further elucidate the effect of LPS on synaptic transmission and short-term plasticity, changes in field excitatory postsynaptic potentials and population spikes were measured in stratum radiatum and stratum pyramidale of LPS-treated kindled rats. LPS impaired baseline synaptic transmission in hippocampal Schaffer collateral-CA1 synapse and reduced the magnitude of paired-pulse facilitation. Our results suggest that direct suppression of presynaptic mechanisms in Schaffer collateral-CA1 synapses, as well as the inflammatory mediators released by LPS in the hippocampus, is involved in antiepileptic effect of LPS.

High serotonin levels during brain development alter the structural input-output connectivity of neural networks in the rat somatosensory layer IV

Homeostatic regulation of serotonin (5-HT) concentration is critical for “normal” topographical organization and development of thalamocortical (TC) afferent circuits. Down-regulation of the serotonin transporter (SERT) and the consequent impaired reuptake of 5-HT at the synapse, results in a reduced terminal branching of developing TC afferents within the primary somatosensory cortex (S1). Despite the presence of multiple genetic models, the effect of high extracellular 5-HT levels on the structure and function of developing intracortical neural networks is far from being understood. Here, using juvenile SERT knockout (SERT−/−) rats we investigated, in vitro, the effect of increased 5-HT levels on the structural organization of (i) the TC projections of the ventroposteromedial thalamic nucleus toward S1, (ii) the general barrel-field pattern, and (iii) the electrophysiological and morphological properties of the excitatory cell population in layer IV of S1 [spiny stellate (SpSt) and pyramidal cells]. Our results confirmed previous findings that high levels of 5-HT during development lead to a reduction of the topographical precision of TCA projections toward the barrel cortex. Also, the barrel pattern was altered but not abolished in SERT−/− rats. In layer IV, both excitatory SpSt and pyramidal cells showed a significantly reduced intracolumnar organization of their axonal projections. In addition, the layer IV SpSt cells gave rise to a prominent projection toward the infragranular layer Vb. Our findings point to a structural and functional reorganization of TCAs, as well as early stage intracortical microcircuitry, following the disruption of 5-HT reuptake during critical developmental periods. The increased projection pattern of the layer IV neurons suggests that the intracortical network changes are not limited to the main entry layer IV but may also affect the subsequent stages of the canonical circuits of the barrel cortex.

Neural circuits for peristaltic wave propagation in crawling Drosophila larvae: analysis and modeling.

Drosophila larvae crawl by peristaltic waves of muscle contractions, which propagate along the animal body and involve the simultaneous contraction of the left and right side of each segment. Coordinated propagation of contraction does not require sensory input, suggesting that movement is generated by a central pattern generator (CPG). We characterized crawling behavior of newly hatched Drosophila larvae by quantifying timing and duration of segmental boundary contractions. We developed a CPG network model that recapitulates these patterns based on segmentally repeated units of excitatory and inhibitory (EI) neuronal populations coupled with immediate neighboring segments. A single network with symmetric coupling between neighboring segments succeeded in generating both forward and backward propagation of activity. The CPG network was robust to changes in amplitude and variability of connectivity strength. Introducing sensory feedback via “stretch-sensitive” neurons improved wave propagation properties such as speed of propagation and segmental contraction duration as observed experimentally. Sensory feedback also restored propagating activity patterns when an inappropriately tuned CPG network failed to generate waves. Finally, in a two-sided CPG model we demonstrated that two types of connectivity could synchronize the activity of two independent networks: connections from excitatory neurons on one side to excitatory contralateral neurons (E to E), and connections from inhibitory neurons on one side to excitatory contralateral neurons (I to E). To our knowledge, such I to E connectivity has not yet been found in any experimental system; however, it provides the most robust mechanism to synchronize activity between contralateral CPGs in our model. Our model provides a general framework for studying the conditions under which a single locally coupled network generates bilaterally synchronized and longitudinally propagating waves in either direction.

Cortical information flow in Parkinson's disease: a composite network/field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main “input” layer of the cortex (layer 4) to the main “output” layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

Contrasting Existence and Robustness of REM/Non-REM Cycling in Physiologically Based Models of REM Sleep Regulatory Networks

Typical human sleep throughout the night consists of alternating periods of rapid eye movement (REM) sleep and non-REM (NREM) sleep. This ultradian rhythm of NREM/REM cycling is thought to be produced by the state-dependent activity of “REM-on” and “REM-off” brainstem and hypothalamic neuronal populations that, respectively, promote or suppress REM sleep. Synaptic interactions among these populations define REM sleep regulatory networks; however, the identity of the key neuronal populations in these networks and the dynamics of interactions among them are disputed and cannot be addressed comprehensively with current experimental techniques. The purpose of this study is to use physiologically based mathematical models to explore the dynamic implications associated with competing hypotheses for network-based REM sleep regulation. Generally, putative REM sleep regulatory networks fall into two categories: a reciprocal interaction network consisting of an excitatory REM-on population interacting with an inhibitory REM-off population, and a mutual inhibition network where both REM-on and REM-off populations are inhibitory. We focus on the generation of regular periodic cycling solutions, which would generate the NREM/REM ultradian rhythm, in these networks. By applying our understanding of network mechanisms, we develop efficient numerical criteria for the existence of stable cycling solutions in each network structure. To investigate the robustness of cycling, we systematically analyze the response of model dynamics to manipulation of the components governing network interactions. By establishing the implications of network structure for the mechanisms and dynamics of NREM/REM state transitions, this comparative analysis identifies key targets for future experimental work to distinguish the structure of the proposed physiological REM sleep regulatory network.

Hippocampal synaptic plasticity restoration and anti-apoptotic effect underlie berberine improvement of learning and memory in streptozotocin-diabetic rats

Chronic diabetes mellitus initiates apoptosis and negatively affects synaptic plasticity in the hippocampus with ensuing impairments of learning and memory. Berberine, an isoquinoline alkaloid, exhibits anti-diabetic, antioxidant and nootropic effects. This study was conducted to evaluate the effect of berberine on hippocampal CA1 neuronal apoptosis, synaptic plasticity and learning and memory of streptozotocin (STZ)-diabetic rats. Long-term potentiation (LTP) in perforant path-dentate gyrus synapses was recorded for assessment of synaptic plasticity and field excitatory post-synaptic potential (fEPSP) slope and population spike (PS) amplitude. PS amplitude and fEPSP significantly decreased in diabetic group versus control, and chronic berberine treatment (100mg/kg/day, p.o.) restored PS amplitude and fEPSP and ameliorated learning and memory impairment and attenuated apoptosis of pyramidal neurons in the CA1 area, as determined by the terminal deoxynucleotidyl transferase (TdT)-mediated dUTP nick end-labeling method. In summary, chronic berberine treatment of STZ-diabetic rats significantly ameliorates learning and memory impairment and part of its beneficial effect could be attributed to improvement of synaptic dysfunction and anti-apoptotic property.

Neural field theory of plasticity in the cerebral cortex

A generalized timing-dependent plasticity rule is incorporated into a recent neural field theory to explore synaptic plasticity in the cerebral cortex, with both excitatory and inhibitory populations included. Analysis in the time and frequency domains reveals that cortical network behavior gives rise to a saddle–node bifurcation and resonant frequencies, including a gamma-band resonance. These system resonances constrain cortical synaptic dynamics and divide it into four classes, which depend on the type of synaptic plasticity window. Depending on the dynamical class, synaptic strengths can either have a stable fixed point, or can diverge in the absence of a separate saturation mechanism. Parameter exploration shows that time-asymmetric plasticity windows, which are signatures of spike-timing dependent plasticity, enable the richest variety of synaptic dynamics to occur. In particular, we predict a zone in parameter space which may allow brains to attain the marginal stability phenomena observed experimentally, although additional regulatory mechanisms may be required to maintain these parameters.

Effect of Aggregated β-Amyloid (1-42) on Synaptic Plasticity of Hippocampal Dentate Gyrus Granule Cells in Vivo.

Alzheimer's disease (AD) is a common neurodegenerative disorder in elderly people with an impairment of cognitive decline and memory loss. β-amyloid (Aβ) as a potent neurotoxic peptide has a pivotal role in the pathogenesis of AD. This disease begins with impairment in synaptic functions before developing into later neuro¬degeneration and neuronal loss. The aim of this study was to evaluate the synaptic plasticity and electrophysiological function of granule cells in hippocampal dentate gyrus (DG) after intracerebroventricular (i.c.v.) administration of aggregated Aβ (1-42) peptide in vivo. Animals were divided to control and Aβ (1-42) groups. Long-term potentia¬tion (LTP) in perforant path-DG synapses was assessed in order to investigate the effect of aggregated Aβ (1-42) on synaptic plasticity. Field excitatory post-synaptic potential (fEPSP) slope and population spike (PS) amplitude were measured. Administration of Aβ (1-42) significantly decreased fEPSP slope and PS amplitude in Aβ (1-42) group comparing with the control group and had no effect on baseline activity of neurons. The present study indicates that administration of aggregated form of Aβ (1-42) into the lateral ventricle effectively inhibits LTP in granular cells of the DG in hippocampus in vivo.

Inhibitory interneurons enable sparse code formation in a spiking circuit model of V1

Sparse coding accounts for several physiological properties of primary visual cortex (V1), including the shapes of simple cell receptive fields and the highly kurtotic firing rates of V1 neurons [1]. Current spiking network models of pattern learning [2] and sparse coding [3] require direct inhibitory connections between the excitatory simple cells, in violation of Dale's Law which states that neurons can either excite or inhibit but not both. At the same time, the computational role of inhibitory neurons in cortical microcircuit function has yet to be fully explained. Here we show that adding a separate population of inhibitory neurons to a recently proposed model of V1 [3] not only brings spiking network models of sparse coding in line with Dale’s Law, but it also predicts excitatory-to-inhibitory neuron ratios and explains how inhibitory neurons may function computationally. When trained on natural images, this excitatory-inhibitory spiking circuit learns Gabor-like receptive fields as found in V1 using spiking neurons and synaptically local plasticity rules. The inhibitory cells enable sparse code formation using a novel learning rule by collaboratively discovering and suppressing correlations within the excitatory population (Figure ​(Figure1).1). The model predicts that only a small number of inhibitory cells is required relative to excitatory cells, matching physiological ratios observed in primary visual cortex. Figure 1 A. Circuit diagram of our spiking network with separate excitatory (E) and inhibitory (I) neural populations (top) compared to current single population models (bottom). This network was simulated with different numbers of excitatory and inhibitory cells. ...

Modeling the dynamics of neural codes in the olfaction of the Manduca-sexta moth

The Anntenal Lobe (AL) is the olfactory processing unit in insects, composed of projection neurons (PNs) and local neurons (LNs) [1]. It has been demonstrated that the AL reformats the sensory input information that it receives into spatiotemporal firing patterns exhibited by the PNs [2,3]. In many insects the LNs are mainly inhibitory which suggests that the inhibition is responsible for shaping the input into a robust pattern [4]. The robustness of the pattern is expressed as follows: over several applications of the same odor the projection of the data recorded from the PNs onto a few dominant firing patterns results in a robust low dimensional trajectory. This trajectory appears to be similar to a trajectory that converges to a stable unique fixed point [5]. In this work, we resolve several open questions raised by [5,6]. Specifically, we study how interactions between the LNs and PNs permit creation of robust and spatiotemporal codes. We further propose a simple model that mimics the dynamics of the AL and the dynamics of mixtures of odors. Our work is a combination of theoretical analysis and experimental studies. Theoretically we consider a network of excitatory-inhibitory firing units that has a similar structure to the AL. By proposing to project the dynamical equations of the network onto given orthogonal spatial patterns, we derive the conditions on the interactions between the inhibitory and excitatory population such that the network will support a unique stable fixed point. The analysis is based on requiring that the inhibitory neurons will suppress inputs that are not associated to specific odors (noise and unknown patterns) but being neutral to the given spatial patterns. These conditions allow us to prescribe the connections between PNs and LNs and do not require specific symmetries (in contrast to Hopfield networks). Experimentally we record the dynamics of PNs in the AL of the Manduca Sexta moth both for inputs that are single odor or mixtures of two odors. Extracting the spatial patterns (first PCA mode) obtained from experiments with single odor inputs we calibrate the network. We are able to establish similarity between the model dynamics and experimental projections and thus validate our theoretical construction. Once the model is calibrated we test it against experiments with inputs that are different ratios of two odors revealing similar dynamics. To test the importance of inhibition, conjectured to be responsible for existence of a stable fixed point, we repeat the experiments in which the inhibition is blocked by a drug. Results demonstrate that the robustness of the dynamics is destroyed.

Turing instabilities in a mean field model of electrocortical activity

The mean field model formulated by Liley et al. [1] describes the membrane potential and synaptic interaction of excitatory and inhibitory neuron populations in a two-dimensional slab of cortical tissue. When complemented with periodic boundary conditions, it yields a set of fourteen coupled partial differential equations that encompass both highly nonlinear local interaction and long-range interaction through cable equations. We consider these equations as an autonomous dynamical system and aim to parse it using bifurcation analysis. We focus in particular on Turing-type bifurcations from spatially homogeneous equilibria to time-periodic patterns. Such bifurcations have been considered in simplified models but, to the best of our knowledge, not in a physiologically realistic setting [2]. In this study, we fix the model parameters to values that have previously been shown to lead to physiologically interesting γ-range activity [3]. We locate the primary instability when varying the inhibitory-to-inhibitory connection density, known to strongly affect the power spectrum, and the system size. Although for small system size, spatially homogeneous periodic solutions appear, for system sizes of a few square centimeters we observe centimeter-scale, oscillating patterns, which appear in subcritical Hopf bifurcations and have a strong γ-band component in their power spectrum. An example is shown in Fig. ​Fig.1,1, for a domain of 12.8 by 12.8cm. The black curve denotes stable (solid) and unstable (dashed) equilibria, and the blue curve denotes spatially homogeneous periodic solutions. The latter can be stable to spatially homogeneous perturbations. The primary instability corresponds to a spatial wave number two in both directions. The inlay shows a snapshot of the excitatory membrane potential for the corresponding, mildly unstable, periodic solution near the Hopf bifurcation. Figure 1 Partial bifurcation diagram of the mean-field model. A periodic solution (blue) bifurcates from an equilibrium (black), both spatially homogeneous. The primary instability, however, is a Turing bifurcation to the pattern in the left inlay. The second ... We have implemented a time-stepper in the open-source PETSc environment [4]. It uses a finite difference approximation for the Laplacian and first order implicit time stepping, both for the field equations and for the tangent linear model. The distribution of the grid over CPUs is automated, allowing for efficient parallel computation. This code can be used for the computation of equilibria, traveling waves, periodic orbits, manifolds and other building blocks of dynamical systems analysis, leading to a greater insight in the model's behaviour than could previously be extracted from analysis of spatially homogeneous solutions alone.

Biologically realistic excitatory and inhibitory cell properties emerge from a sparse coding network

Neurons in the primary visual cortex exhibit a baffling array of tuning properties, often unaccountable by the classical linear feedforward model. Specifically, excitatory neurons display a number of nonlinear effects collectively known as non-classical receptive field (nCRF) effects [1], and inhibitory neurons have diverse orientation tuning properties [2]. Furthermore, excitatory cells outnumber inhibitory cells by a ratio of 9:1 [3], yet the excitatory and inhibitory drives are balanced. Efficient coding models of early vision have been shown to be able to explain key features of linear filtering properties [4] and some single cell nonlinear effects [5]. However, population statistics of nonlinear properties have not been studied in these models. In addition, inhibitory cells were not typically modeled. Here we demonstrate that many of the aforementioned excitatory cell and inhibitory cell properties emerge naturally from a network that implements sparse coding. To be specific, several nCRF effects including surround suppression, contrast invariant orientation tuning, and cross orientation suppression emerge in the excitatory cell population as a result of sparse coding strategy; the excitatory to inhibitory cell ratio could be understood largely as a result of the overcompletness of representation; moreover, a subpopulation of inhibitory interneurons exhibit orientation tuning due to sparse recurrent connections with the principal cells; another subpopulation displays untuned properties due to low rank connectivity patterns. We also demonstrate that the network exhibits balanced excitation and inhibition, as a result of the receptive field structure. We simulated a population of 2048 excitatory neurons with graded response described by the dynamics of locally competitive algorithm (LCA; [6]), which converges to the sparse coding representation at steady state. Inhibitory interneurons were described by linear units. The low rank and sparse recurrent connectivity pattern was a result of low rank plus sparse decomposition [7] of the LCA connectivity matrix. Non-classical receptive field effects were studied by presenting bar and drifting grating stimuli to the simulated network. Receptive fields of the inhibitory cells were mapped by sparse dots patterns.

Modeling Na+- and Ca2+-dependent mechanisms of rhythmic bursting in excitatory neural networks

The mechanisms generating neural oscillations in the mammalian brainstem, particularly in the pre-Botzinger complex (pre-BotC) involved in control of respiration, and the spinal cord (e.g. circuits controlling locomotion) that persist after blockade of synaptic inhibition, remain poorly understood. Experimental studies in medullary slices from neonatal rodents containing the pre-BotC identified two mechanisms that could potentially contribute to generation of rhythmic bursting in the pre-BotC: one based on the persistent sodium current (INaP) [1,2], and the other involving the voltage-gated calcium (ICa) [3] and/or the calcium-activated nonspecific cation current (ICAN), activated by intracellular Ca2+ accumulated from extra- and/or intracellular sources [4]. However, the involvement and relative roles of these mechanisms in rhythmic bursting are still under debate. In this theoretical/modeling study we investigated Na+- and Ca2+-dependent bursting generated in single cells and in a heterogeneous population of synaptically interconnected excitatory neurons with INaP, and ICa randomly distributed within the population. We analyzed the possible roles of network connections, ionotropic and metabotropic synaptic mechanisms, intracellular Ca2+ release, and the Na+/K+ pump in rhythmic bursting activity generated under different conditions. We show that the heterogeneous population of excitatory neurons can operate in different oscillatory regimes with bursting dependent on INaP and/or ICAN, or independent of both (Fig. ​(Fig.1).1). The oscillatory regime and operating bursting mechanism may depend on neuronal excitability, synaptic interactions and relative expression of particular ionic currents. Figure 1 A map of bursting activities derived from multiple simulations of the excitatory neuron population and presented in a 2D parameter space (gtonic, ), where gtonic is the external excitatory drive to all neurons, N is the number of neurons in the population, ... The existence of multiple oscillatory regimes and their state-dependency may provide explanations for different rhythmic activities observed in the brainstem and spinal cord under different experimental conditions.

Population density models of integrate-and-fire neurons with jumps: well-posedness

In this paper we study the well-posedness of different models of population of leaky integrate-and-fire neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the different behaviours of the model with jumps compared to its diffusion approximation.

Homeostatic Scaling of Excitability in Recurrent Neural Networks

Neurons adjust their intrinsic excitability when experiencing a persistent change in synaptic drive. This process can prevent neural activity from moving into either a quiescent state or a saturated state in the face of ongoing plasticity, and is thought to promote stability of the network in which neurons reside. However, most neurons are embedded in recurrent networks, which require a delicate balance between excitation and inhibition to maintain network stability. This balance could be disrupted when neurons independently adjust their intrinsic excitability. Here, we study the functioning of activity-dependent homeostatic scaling of intrinsic excitability (HSE) in a recurrent neural network. Using both simulations of a recurrent network consisting of excitatory and inhibitory neurons that implement HSE, and a mean-field description of adapting excitatory and inhibitory populations, we show that the stability of such adapting networks critically depends on the relationship between the adaptation time scales of both neuron populations. In a stable adapting network, HSE can keep all neurons functioning within their dynamic range, while the network is undergoing several (patho)physiologically relevant types of plasticity, such as persistent changes in external drive, changes in connection strengths, or the loss of inhibitory cells from the network. However, HSE cannot prevent the unstable network dynamics that result when, due to such plasticity, recurrent excitation in the network becomes too strong compared to feedback inhibition. This suggests that keeping a neural network in a stable and functional state requires the coordination of distinct homeostatic mechanisms that operate not only by adjusting neural excitability, but also by controlling network connectivity.