Spike frequency adaptation and neocortical rhythms

Spiking attractor model of motor cortex explains modulation of neural and behavioral variability by prior target information

When preparing a movement, we often rely on partial or incomplete information, which can decrement task performance. In behaving monkeys we show that the degree of cued target information is reflected in both, neural variability in motor cortex and behavioral reaction times. We study the underlying mechanisms in a spiking motor-cortical attractor model. By introducing a biologically realistic network topology where excitatory neuron clusters are locally balanced with inhibitory neuron clusters we robustly achieve metastable network activity across a wide range of network parameters. In application to the monkey task, the model performs target-specific action selection and accurately reproduces the task-epoch dependent reduction of trial-to-trial variability in vivo where the degree of reduction directly reflects the amount of processed target information, while spiking irregularity remained constant throughout the task. In the context of incomplete cue information, the increased target selection time of the model can explain increased behavioral reaction times. We conclude that context-dependent neural and behavioral variability is a signum of attractor computation in the motor cortex.

Firing rate adaptation affords place cell theta sweeps, phase precession, and procession

Hippocampal place cells in freely moving rodents display both theta phase precession and procession, which is thought to play important roles in cognition, but the neural mechanism for producing theta phase shift remains largely unknown. Here, we show that firing rate adaptation within a continuous attractor neural network causes the neural activity bump to oscillate around the external input, resembling theta sweeps of decoded position during locomotion. These forward and backward sweeps naturally account for theta phase precession and procession of individual neurons, respectively. By tuning the adaptation strength, our model explains the difference between 'bimodal cells' showing interleaved phase precession and procession, and 'unimodal cells' in which phase precession predominates. Our model also explains the constant cycling of theta sweeps along different arms in a T-maze environment, the speed modulation of place cells' firing frequency, and the continued phase shift after transient silencing of the hippocampus. We hope that this study will aid an understanding of the neural mechanism supporting theta phase coding in the brain.

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Theta-gamma phase amplitude coupling in a hippocampal CA1 microcircuit

Phase amplitude coupling (PAC) between slow and fast oscillations is found throughout the brain and plays important functional roles. Its neural origin remains unclear. Experimental findings are often puzzling and sometimes contradictory. Most computational models rely on pairs of pacemaker neurons or neural populations tuned at different frequencies to produce PAC. Here, using a data-driven model of a hippocampal microcircuit, we demonstrate that PAC can naturally emerge from a single feedback mechanism involving an inhibitory and excitatory neuron population, which interplay to generate theta frequency periodic bursts of higher frequency gamma. The model suggests the conditions under which a CA1 microcircuit can operate to elicit theta-gamma PAC, and highlights the modulatory role of OLM and PVBC cells, recurrent connectivity, and short term synaptic plasticity. Surprisingly, the results suggest the experimentally testable prediction that the generation of the slow population oscillation requires the fast one and cannot occur without it.

Macroscopic dynamics of neural networks with heterogeneous spiking thresholds

Mean-field theory links the physiological properties of individual neurons to the emergent dynamics of neural population activity. These models provide an essential tool for studying brain function at different scales; however, for their application to neural populations on large scale, they need to account for differences between distinct neuron types. The Izhikevich single neuron model can account for a broad range of different neuron types and spiking patterns, thus rendering it an optimal candidate for a mean-field theoretic treatment of brain dynamics in heterogeneous networks. Here we derive the mean-field equations for networks of all-to-all coupled Izhikevich neurons with heterogeneous spiking thresholds. Using methods from bifurcation theory, we examine the conditions under which the mean-field theory accurately predicts the dynamics of the Izhikevich neuron network. To this end, we focus on three important features of the Izhikevich model that are subject here to simplifying assumptions: (i) spike-frequency adaptation, (ii) the spike reset conditions, and (iii) the distribution of single-cell spike thresholds across neurons. Our results indicate that, while the mean-field model is not an exact model of the Izhikevich network dynamics, it faithfully captures its different dynamic regimes and phase transitions. We thus present a mean-field model that can represent different neuron types and spiking dynamics. The model comprises biophysical state variables and parameters, incorporates realistic spike resetting conditions, and accounts for heterogeneity in neural spiking thresholds. These features allow for a broad applicability of the model as well as for a direct comparison to experimental data.

Network resonance can be generated independently at distinct levels of neuronal organization

Resonance is defined as maximal response of a system to periodic inputs in a limited frequency band. Resonance may serve to optimize inter-neuronal communication, and has been observed at multiple levels of neuronal organization. However, it is unknown how neuronal resonance observed at the network level is generated and how network resonance depends on the properties of the network building blocks. Here, we first develop a metric for quantifying spike timing resonance in the presence of background noise, extending the notion of spiking resonance for in vivo experiments. Using conductance-based models, we find that network resonance can be inherited from resonances at other levels of organization, or be intrinsically generated by combining mechanisms across distinct levels. Resonance of membrane potential fluctuations, postsynaptic potentials, and single neuron spiking can each be generated independently of resonance at any other level and be propagated to the network level. At all levels of organization, interactions between processes that give rise to low- and high-pass filters generate the observed resonance. Intrinsic network resonance can be generated by the combination of filters belonging to different levels of organization. Inhibition-induced network resonance can emerge by inheritance from resonance of membrane potential fluctuations, and be sharpened by presynaptic high-pass filtering. Our results demonstrate a multiplicity of qualitatively different mechanisms that can generate resonance in neuronal systems, and provide analysis tools and a conceptual framework for the mechanistic investigation of network resonance in terms of circuit components, across levels of neuronal organization.

How one part of the brain responds to periodic input from another part depends on resonant circuit properties. Resonance is a basic property of physical systems, and has been experimentally observed at various levels of neuronal organization both in vitro and in vivo. Yet how resonance is generated in neuronal networks is largely unknown. In particular, whether resonance can be generated directly at the level of a network of spiking neurons remains to be determined. Using detailed biophysical modeling, we develop a conceptual framework according to which resonance at a given level of organization is generated by the interplay of low- and high-pass filters, implemented at either the same or across levels of neuronal organization. We tease apart representative, biophysically-plausible generative mechanisms of resonance at four different levels of organization: membrane potential fluctuations, single neuron spiking, synaptic transmission, and neuronal networks. We identify conditions under which resonance at one level can be inherited to another level of organization, provide conclusive evidence that resonance at each level can be generated without resonance at any other level, and describe a number of representative routes to network resonance. The proposed framework facilitates the investigation of resonance in neuronal systems.

Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.

Kv2.1 Potassium Channels Regulate Repetitive Burst Firing in Extratelencephalic Neocortical Pyramidal Neurons

Coincidence detection and cortical rhythmicity are both greatly influenced by neurons' propensity to fire bursts of action potentials. In the neocortex, repetitive burst firing can also initiate abnormal neocortical rhythmicity (including epilepsy). Bursts are generated by inward currents that underlie a fast afterdepolarization (fADP) but less is known about outward currents that regulate bursting. We tested whether Kv2 channels regulate the fADP and burst firing in labeled layer 5 PNs from motor cortex of the Thy1-h mouse. Kv2 block with guangxitoxin-1E (GTx) converted single spike responses evoked by dendritic stimulation into multispike bursts riding on an enhanced fADP. Immunohistochemistry revealed that Thy1-h PNs expressed Kv2.1 (not Kv2.2) channels perisomatically (not in the dendrites). In somatic macropatches, GTx-sensitive current was the largest component of outward current with biophysical properties well-suited for regulating bursting. GTx drove ~40% of Thy1 PNs stimulated with noisy somatic current steps to repetitive burst firing and shifted the maximal frequency-dependent gain. A network model showed that reduction of Kv2-like conductance in a small subset of neurons resulted in repetitive bursting and entrainment of the circuit to seizure-like rhythmic activity. Kv2 channels play a dominant role in regulating onset bursts and preventing repetitive bursting in Thy1 PNs.

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Hyperexcitable Neurons Enable Precise and Persistent Information Encoding in the Superficial Retrosplenial Cortex

The retrosplenial cortex (RSC) is essential for memory and navigation, but the neural codes underlying these functions remain largely unknown. Here, we show that the most prominent cell type in layers 2/3 (L2/3) of the mouse granular RSC is a hyperexcitable, small pyramidal cell. These cells have a low rheobase (LR), high input resistance, lack of spike frequency adaptation, and spike widths intermediate to those of neighboring fast-spiking (FS) inhibitory neurons and regular-spiking (RS) excitatory neurons. LR cells are excitatory but rarely synapse onto neighboring neurons. Instead, L2/3 is a feedforward, not feedback, inhibition-dominated network with dense connectivity between FS cells and from FS to LR neurons. Biophysical models of LR but not RS cells precisely and continuously encode sustained input from afferent postsubicular head-direction cells. Thus, the distinct intrinsic properties of LR neurons can support both the precision and persistence necessary to encode information over multiple timescales in the RSC.

Neuronal spike-rate adaptation supports working memory in language processing

Language processing involves the ability to store and integrate pieces of information in working memory over short periods of time. According to the dominant view, information is maintained through sustained, elevated neural activity. Other work has argued that short-term synaptic facilitation can serve as a substrate of memory. Here we propose an account where memory is supported by intrinsic plasticity that downregulates neuronal firing rates. Single neuron responses are dependent on experience, and we show through simulations that these adaptive changes in excitability provide memory on timescales ranging from milliseconds to seconds. On this account, spiking activity writes information into coupled dynamic variables that control adaptation and move at slower timescales than the membrane potential. From these variables, information is continuously read back into the active membrane state for processing. This neuronal memory mechanism does not rely on persistent activity, excitatory feedback, or synaptic plasticity for storage. Instead, information is maintained in adaptive conductances that reduce firing rates and can be accessed directly without cued retrieval. Memory span is systematically related to both the time constant of adaptation and baseline levels of neuronal excitability. Interference effects within memory arise when adaptation is long lasting. We demonstrate that this mechanism is sensitive to context and serial order which makes it suitable for temporal integration in sequence processing within the language domain. We also show that it enables the binding of linguistic features over time within dynamic memory registers. This work provides a step toward a computational neurobiology of language.

A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

Cortical reliability amid noise and chaos

Typical responses of cortical neurons to identical sensory stimuli appear highly variable. It has thus been proposed that the cortex primarily uses a rate code. However, other studies have argued for spike-time coding under certain conditions. The potential role of spike-time coding is directly limited by the internally generated variability of cortical circuits, which remains largely unexplored. Here, we quantify this internally generated variability using a biophysical model of rat neocortical microcircuitry with biologically realistic noise sources. We find that stochastic neurotransmitter release is a critical component of internally generated variability, causing rapidly diverging, chaotic recurrent network dynamics. Surprisingly, the same nonlinear recurrent network dynamics can transiently overcome the chaos in response to weak feed-forward thalamocortical inputs, and support reliable spike times with millisecond precision. Our model shows that the noisy and chaotic network dynamics of recurrent cortical microcircuitry are compatible with stimulus-evoked, millisecond spike-time reliability, resolving a long-standing debate.

Mechanisms underlying sharpening of visual response dynamics with familiarity

Experience-dependent modifications of synaptic connections are thought to change patterns of network activities and stimulus tuning with learning. However, only a few studies explored how synaptic plasticity shapes the response dynamics of cortical circuits. Here, we investigated the mechanism underlying sharpening of both stimulus selectivity and response dynamics with familiarity observed in monkey inferotemporal cortex. Broadening the distribution of activities and stronger oscillations in the response dynamics after learning provide evidence for synaptic plasticity in recurrent connections modifying the strength of positive feedback. Its interplay with slow negative feedback via firing rate adaptation is critical in sharpening response dynamics. Analysis of changes in temporal patterns also enables us to disentangle recurrent and feedforward synaptic plasticity and provides a measure for the strengths of recurrent synaptic plasticity. Overall, this work highlights the importance of analyzing changes in dynamics as well as network patterns to further reveal the mechanisms of visual learning.

Frequency-dependent entrainment of striatal fast-spiking interneurons

Striatal fast-spiking interneurons (FSIs) fire in variable-length runs of action potentials at 20-200 spikes/s separated by pauses. In vivo, or with fluctuating applied current, both runs and pauses become briefer and more variable. During runs, spikes are entrained specifically to gamma-frequency components of the input fluctuations. We stimulated parvalbumin-expressing striatal FSIs in mouse brain slices with broadband noise currents added to direct current steps and measured spike entrainment across all frequencies. As the constant current level was increased, FSIs produced longer runs and showed sharper frequency tuning, with best entrainment at the stimulus frequency matching their intrarun firing rate. We separated the contributions of previous spikes from that of the fluctuating stimulus, revealing a strong contribution of previous action potentials to gamma-frequency entrainment. In contrast, after subtraction of the effect inherited from the previous spike, the remaining stimulus contribution to spike generation was less sharply tuned, showing a larger contribution of lower frequencies. The frequency specificity of entrainment within a run was reproduced with a phase resetting model based on experimentally measured phase resetting curves of the same FSIs. In the model, broadly tuned phase entrainment for the first spike in a run evolved into sharply tuned gamma entrainment over the next few spikes. The data and modeling results indicate that for FSIs firing in brief runs and pauses firing within runs is entrained by gamma-frequency components of the input, whereas the onset timing of runs may be sensitive to a wider range of stimulus frequency components.NEW & NOTEWORTHY Specific types of neurons entrain their spikes to particular oscillation frequencies in their synaptic input. This entrainment is commonly understood in terms of the subthreshold voltage response, but how this translates to spiking is not clear. We show that in striatal fast-spiking interneurons, entrainment to gamma-frequency input depends on rhythmic spike runs and is explained by the phase resetting curve, whereas run initiation can be triggered by a broad range of input frequencies.

Oscillations and Spike Entrainment

Oscillatory input to networks, as indicated by field potentials, must entrain neuronal firing to be a causal agent in brain activity. Even when the oscillatory input is prominent, entrainment of firing is not a foregone conclusion but depends on the intrinsic dynamics of the postsynaptic neurons, including cell type-specific resonances, and background firing rates. Within any local network of neurons, only a subset of neurons may have their firing entrained by an oscillating synaptic input, and oscillations of different frequency may engage separate subsets of neurons.

Tune it in: mechanisms and computational significance of neuron-autonomous plasticity

The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.

Nanodiamonds-induced effects on neuronal firing of mouse hippocampal microcircuits

Fluorescent nanodiamonds (FND) are carbon-based nanomaterials that can efficiently incorporate optically active photoluminescent centers such as the nitrogen-vacancy complex, thus making them promising candidates as optical biolabels and drug-delivery agents. FNDs exhibit bright fluorescence without photobleaching combined with high uptake rate and low cytotoxicity. Focusing on FNDs interference with neuronal function, here we examined their effect on cultured hippocampal neurons, monitoring the whole network development as well as the electrophysiological properties of single neurons. We observed that FNDs drastically decreased the frequency of inhibitory (from 1.81 Hz to 0.86 Hz) and excitatory (from 1.61 to 0.68 Hz) miniature postsynaptic currents, and consistently reduced action potential (AP) firing frequency (by 36%), as measured by microelectrode arrays. On the contrary, bursts synchronization was preserved, as well as the amplitude of spontaneous inhibitory and excitatory events. Current-clamp recordings revealed that the ratio of neurons responding with AP trains of high-frequency (fast-spiking) versus neurons responding with trains of low-frequency (slow-spiking) was unaltered, suggesting that FNDs exerted a comparable action on neuronal subpopulations. At the single cell level, rapid onset of the somatic AP (“kink”) was drastically reduced in FND-treated neurons, suggesting a reduced contribution of axonal and dendritic components while preserving neuronal excitability.

Dynamical response properties of neocortical neurons to conductance-driven time-varying inputs

Ensembles of cortical neurons can track fast-varying inputs and relay them in their spike trains, far beyond the cut-off imposed by membrane passive electrical properties and mean firing rates. Initially explored in silico and later demonstrated experimentally, investigating how neurons respond to sinusoidally modulated stimuli provides a deeper insight into spike initiation mechanisms and information processing than conventional F-I curve methodologies. Besides net membrane currents, physiological synaptic inputs can also induce a stimulus-dependent modulation of the total membrane conductance, which is not reproduced by standard current-clamp protocols. Here, we investigated whether rat cortical neurons can track fast temporal modulations over a noisy conductance background. We also determined input-output transfer properties over a range of conditions, including: distinct presynaptic activation rates, postsynaptic firing rates and variability and type of temporal modulations. We found a very broad signal transfer bandwidth across all conditions, similar large cut-off frequencies and power-law attenuations of fast-varying inputs. At slow and intermediate input modulations, the response gain decreased for increasing output mean firing rates. The gain also decreased significantly for increasing intensities of background synaptic activity, thus generalising earlier studies on F-I curves. We also found a direct correlation between the action potentials' onset rapidness and the neuronal bandwidth. Our novel results extend previous investigations of dynamical response properties to non-stationary and conductance-driven conditions, and provide computational neuroscientists with a novel set of observations that models must capture when aiming to replicate cortical cellular excitability.

Computations in the deep vs superficial layers of the cerebral cortex

A fundamental question is how the cerebral neocortex operates functionally, computationally. The cerebral neocortex with its superficial and deep layers and highly developed recurrent collateral systems that provide a basis for memory-related processing might perform somewhat different computations in the superficial and deep layers. Here we take into account the quantitative connectivity within and between laminae. Using integrate-and-fire neuronal network simulations that incorporate this connectivity, we first show that attractor networks implemented in the deep layers that are activated by the superficial layers could be partly independent in that the deep layers might have a different time course, which might because of adaptation be more transient and useful for outputs from the neocortex. In contrast the superficial layers could implement more prolonged firing, useful for slow learning and for short-term memory. Second, we show that a different type of computation could in principle be performed in the superficial and deep layers, by showing that the superficial layers could operate as a discrete attractor network useful for categorisation and feeding information forward up a cortical hierarchy, whereas the deep layers could operate as a continuous attractor network useful for providing a spatially and temporally smooth output to output systems in the brain. A key advance is that we draw attention to the functions of the recurrent collateral connections between cortical pyramidal cells, often omitted in canonical models of the neocortex, and address principles of operation of the neocortex by which the superficial and deep layers might be specialized for different types of attractor-related memory functions implemented by the recurrent collaterals.

Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons

Electrophysiological recordings in cortex in vivo have revealed a rich variety of dynamical regimes ranging from irregular asynchronous states to a diversity of synchronized states, depending on species, anesthesia, and external stimulation. The average population firing rate in these states is typically low. We study analytically and numerically a network of sparsely connected excitatory and inhibitory integrate-and-fire neurons in the inhibition-dominated, low firing rate regime. For sufficiently high values of the external input, the network exhibits an asynchronous low firing frequency state (L). Depending on synaptic time constants, we show that two scenarios may occur when external inputs are decreased: (1) the L state can destabilize through a Hopf bifucation as the external input is decreased, leading to synchronized oscillations spanning d δ to β frequencies; (2) the network can reach a bistable region, between the low firing frequency network state (L) and a quiescent one (Q). Adding an adaptation current to excitatory neurons leads to spontaneous alternations between L and Q states, similar to experimental observations on UP and DOWN states alternations.

Inhibition of Metabotropic Glutamate Receptor Subtype 1 Alters the Excitability of the Commissural Pyramidal Neuron in the Rat Anterior Cingulate Cortex after Chronic Constriction Injury to the Sciatic Nerve

Background

Inhibition of the metabotropic glutamate receptor subtype 1 in the anterior cingulate cortex has an analgesic effect during sustained nociceptive hypersensitivity. However, the specific changes in different subtypes of anterior cingulate cortex layer 5 pyramidal neurons, as well as the distinct effect of metabotropic glutamate receptor subtype 1 inhibition on different neuronal subtypes, have not been well studied.

Methods

Retrograde labeling combined with immunofluorescence, whole cell clamp recording, and behavioral tests combined with RNA interference were performed in a rat model of chronic constriction injury to the sciatic nerve.

Results

Commissural layer 5 pyramidal neurons (projecting to the contralateral cortex) existed in the anterior cingulate cortex. The voltage-gated potassium channel subunit 2–mediated current in these neurons were substantially reduced after chronic constriction injury (current densities at +30 mV for the sham, and chronic constriction injury neurons were [mean ± SD] 10.22 ± 3.42 pA/pF vs. 5.58 ± 2.71 pA/pF, respectively; n = 11; P < 0.01), which increased the spike width and fast afterhyperpolarization potential, resulting in hyperexcitability. Inhibition of metabotropic glutamate receptor subtype 1 alleviated the down-regulation of voltage-gated potassium channel subunit 2 currents (current density increased by 8.11 ± 3.22 pA/pF; n = 7; P < 0.01). Furthermore, knockdown of voltage-gated potassium channel subunit 2 current in the commissural neurons attenuated the analgesic effect of metabotropic glutamate receptor subtype 1 inhibition (n = 6 rats; P < 0.05).

Conclusions

The effect of metabotropic glutamate receptor subtype 1 inhibition on commissural anterior cingulate cortex layer 5 pyramidal neurons is likely different with the modification of previously studied hyperpolarization-activated/cyclic nucleotide-gated channel-dependent neurons but relies on the alteration of voltage-gated potassium channel subunit 2 currents. These results will contribute to a better understanding of the therapeutic role of metabotropic glutamate receptor subtype 1 in chronic pain.

An integrative model of the intrinsic hippocampal theta rhythm

Hippocampal theta oscillations (4–12 Hz) are consistently recorded during memory tasks and spatial navigation. Despite several known circuits and structures that generate hippocampal theta locally in vitro, none of them were found to be critical in vivo, and the hippocampal theta rhythm is severely attenuated by disruption of external input from medial septum or entorhinal cortex. We investigated these discrepancies that question the sufficiency and robustness of hippocampal theta generation using a biophysical spiking network model of the CA3 region of the hippocampus that included an interconnected network of pyramidal cells, inhibitory basket cells (BC) and oriens-lacunosum moleculare (OLM) cells. The model was developed by matching biological data characterizing neuronal firing patterns, synaptic dynamics, short-term synaptic plasticity, neuromodulatory inputs, and the three-dimensional organization of the hippocampus. The model generated theta power robustly through five cooperating generators: spiking oscillations of pyramidal cells, recurrent connections between them, slow-firing interneurons and pyramidal cells subnetwork, the fast-spiking interneurons and pyramidal cells subnetwork, and non-rhythmic structured external input from entorhinal cortex to CA3. We used the modeling framework to quantify the relative contributions of each of these generators to theta power, across different cholinergic states. The largest contribution to theta power was that of the divergent input from the entorhinal cortex to CA3, despite being constrained to random Poisson activity. We found that the low cholinergic states engaged the recurrent connections in generating theta activity, whereas high cholinergic states utilized the OLM-pyramidal subnetwork. These findings revealed that theta might be generated differently across cholinergic states, and demonstrated a direct link between specific theta generators and neuromodulatory states.

Modulation of neuronal dynamic range using two different adaptation mechanisms

The capability of neurons to discriminate between intensity of external stimulus is measured by its dynamic range. A larger dynamic range indicates a greater probability of neuronal survival. In this study, the potential roles of adaptation mechanisms (ion currents) in modulating neuronal dynamic range were numerically investigated. Based on the adaptive exponential integrate-and-fire model, which includes two different adaptation mechanisms, i.e. subthreshold and suprathreshold (spike-triggered) adaptation, our results reveal that the two adaptation mechanisms exhibit rather different roles in regulating neuronal dynamic range. Specifically, subthreshold adaptation acts as a negative factor that observably decreases the neuronal dynamic range, while suprathreshold adaptation has little influence on the neuronal dynamic range. Moreover, when stochastic noise was introduced into the adaptation mechanisms, the dynamic range was apparently enhanced, regardless of what state the neuron was in, e.g. adaptive or non-adaptive. Our model results suggested that the neuronal dynamic range can be differentially modulated by different adaptation mechanisms. Additionally, noise was a non-ignorable factor, which could effectively modulate the neuronal dynamic range.

Spatial separation of two different pathways accounting for the generation of calcium signals in astrocytes

Astrocytes integrate and process synaptic information and exhibit calcium (Ca2+) signals in response to incoming information from neighboring synapses. The generation of Ca2+ signals is mostly attributed to Ca2+ release from internal Ca2+ stores evoked by an elevated metabotropic glutamate receptor (mGluR) activity. Different experimental results associated the generation of Ca2+ signals to the activity of the glutamate transporter (GluT). The GluT itself does not influence the intracellular Ca2+ concentration, but it indirectly activates Ca2+ entry over the membrane. A closer look into Ca2+ signaling in different astrocytic compartments revealed a spatial separation of those two pathways. Ca2+ signals in the soma are mainly generated by Ca2+ release from internal Ca2+ stores (mGluR-dependent pathway). In astrocytic compartments close to the synapse most Ca2+ signals are evoked by Ca2+ entry over the plasma membrane (GluT-dependent pathway). This assumption is supported by the finding, that the volume ratio between the internal Ca2+ store and the intracellular space decreases from the soma towards the synapse. We extended a model for mGluR-dependent Ca2+ signals in astrocytes with the GluT-dependent pathway. Additionally, we included the volume ratio between the internal Ca2+ store and the intracellular compartment into the model in order to analyze Ca2+ signals either in the soma or close to the synapse. Our model results confirm the spatial separation of the mGluR- and GluT-dependent pathways along the astrocytic process. The model allows to study the binary Ca2+ response during a block of either of both pathways. Moreover, the model contributes to a better understanding of the impact of channel densities on the interaction of both pathways and on the Ca2+ signal.

A leaky integrate-and-fire model with adaptation for the generation of a spike train

A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.

Incorporating spike-rate adaptation into a rate code in mathematical and biological neurons

For a slowly varying stimulus, the simplest relationship between a neuron's input and output is a rate code, in which the spike rate is a unique function of the stimulus at that instant. In the case of spike-rate adaptation, there is no unique relationship between input and output, because the spike rate at any time depends both on the instantaneous stimulus and on prior spiking (the "history"). To improve the decoding of spike trains produced by neurons that show spike-rate adaptation, we developed a simple scheme that incorporates "history" into a rate code. We utilized this rate-history code successfully to decode spike trains produced by 1) mathematical models of a neuron in which the mechanism for adaptation (IAHP) is specified, and 2) the gastropyloric receptor (GPR2), a stretch-sensitive neuron in the stomatogastric nervous system of the crab Cancer borealis, that exhibits long-lasting adaptation of unknown origin. Moreover, when we modified the spike rate either mathematically in a model system or by applying neuromodulatory agents to the experimental system, we found that changes in the rate-history code could be related to the biophysical mechanisms responsible for altering the spiking.

Non-monotonic Temporal-Weighting Indicates a Dynamically Modulated Evidence-Integration Mechanism

Perceptual decisions are thought to be mediated by a mechanism of sequential sampling and integration of noisy evidence whose temporal weighting profile affects the decision quality. To examine temporal weighting, participants were presented with two brightness-fluctuating disks for 1, 2 or 3 seconds and were requested to choose the overall brighter disk at the end of each trial. By employing a signal-perturbation method, which deploys across trials a set of systematically controlled temporal dispersions of the same overall signal, we were able to quantify the participants' temporal weighting profile. Results indicate that, for intervals of 1 or 2 sec, participants exhibit a primacy-bias. However, for longer stimuli (3-sec) the temporal weighting profile is non-monotonic, with concurrent primacy and recency, which is inconsistent with the predictions of previously suggested computational models of perceptual decision-making (drift-diffusion and Ornstein-Uhlenbeck processes). We propose a novel, dynamic variant of the leaky-competing accumulator model as a potential account for this finding, and we discuss potential neural mechanisms.

A memristive spiking neuron with firing rate coding

Perception, decisions, and sensations are all encoded into trains of action potentials in the brain. The relation between stimulus strength and all-or-nothing spiking of neurons is widely believed to be the basis of this coding. This initiated the development of spiking neuron models; one of today's most powerful conceptual tool for the analysis and emulation of neural dynamics. The success of electronic circuit models and their physical realization within silicon field-effect transistor circuits lead to elegant technical approaches. Recently, the spectrum of electronic devices for neural computing has been extended by memristive devices, mainly used to emulate static synaptic functionality. Their capabilities for emulations of neural activity were recently demonstrated using a memristive neuristor circuit, while a memristive neuron circuit has so far been elusive. Here, a spiking neuron model is experimentally realized in a compact circuit comprising memristive and memcapacitive devices based on the strongly correlated electron material vanadium dioxide (VO₂) and on the chemical electromigration cell Ag/TiO_2−x/Al. The circuit can emulate dynamical spiking patterns in response to an external stimulus including adaptation, which is at the heart of firing rate coding as first observed by E.D. Adrian in 1926.

Bud extracts from Tilia tomentosa Moench inhibit hippocampal neuronal firing through GABAA and benzodiazepine receptors activation

ETHNOPHARMACOLOGICAL RELEVANCE

Tilia tomentosa Moench bud extracts (TTBEs) is used in traditional medicine for centuries as sedative compound. Different plants belonging to the Tilia genus have shown their efficacy in the treatment of anxiety but still little is known about the mechanism of action of their bud extracts.

AIM OF THE STUDY

To evaluate the action of TTBEs as anxiolytic and sedative compound on in vitro hippocampal neurons.

MATERIAL AND METHODS

The anxiolytic effect of TTBEs was assayed by testing the effects of these compounds on GABAA receptor-activated chloride current of hippocampal neurons by means of the patch-clamp technique and microelectrode-arrays (MEAs).

RESULTS

TTBEs acutely administered on mouse hippocampal neurons, activated a chloride current comparable to that measured in the presence of GABA (100 µM). Bicuculline (100 µM) and picrotoxin (100 µM) blocked about 90% of this current, while the remaining 10% was blocked by adding the benzodiazepine (BDZ) antagonist flumazenil (30 µM). Flumazenil alone blocked nearly 60% of the TTBEs activated current, suggesting that TTBEs binds to both GABAA and BDZ receptor sites. Application of high-doses of TTBEs on spontaneous active hippocampal neurons grown for 3 weeks on MEAs blocked the synchronous activity of these neurons. The effects were mimicked by GABA and prevented by picrotoxin (100µM) and flumazenil (30 µM). At minimal doses, TTBEs reduced the frequency of synchronized bursts and increased the cross-correlation index of synchronized neuronal firing.

CONCLUSIONS

Our data suggest that TTBEs mimics GABA and BDZ agonists by targeting hippocampal GABAergic synapses and inhibiting network excitability by increasing the strength of inhibitory synaptic outputs. Our results contribute toward the validation of TTBEs as effective sedative and anxiolytic compound.

Neuronal morphology generates high-frequency firing resonance

The attenuation of neuronal voltage responses to high-frequency current inputs by the membrane capacitance is believed to limit single-cell bandwidth. However, neuronal populations subject to stochastic fluctuations can follow inputs beyond this limit. We investigated this apparent paradox theoretically and experimentally using Purkinje cells in the cerebellum, a motor structure that benefits from rapid information transfer. We analyzed the modulation of firing in response to the somatic injection of sinusoidal currents. Computational modeling suggested that, instead of decreasing with frequency, modulation amplitude can increase up to high frequencies because of cellular morphology. Electrophysiological measurements in adult rat slices confirmed this prediction and displayed a marked resonance at 200 Hz. We elucidated the underlying mechanism, showing that the two-compartment morphology of the Purkinje cell, interacting with a simple spiking mechanism and dendritic fluctuations, is sufficient to create high-frequency signal amplification. This mechanism, which we term morphology-induced resonance, is selective for somatic inputs, which in the Purkinje cell are exclusively inhibitory. The resonance sensitizes Purkinje cells in the frequency range of population oscillations observed in vivo.

Influence of developmental nicotine exposure on spike-timing precision and reliability in hypoglossal motoneurons

Smoothly graded muscle contractions depend in part on the precision and reliability of motoneuron action potential generation. Whether or not a motoneuron generates spikes precisely and reliably depends on both its intrinsic membrane properties and the nature of the synaptic input that it receives. Factors that perturb neuronal intrinsic properties and/or synaptic drive may compromise the temporal precision and the reliability of action potential generation. We have previously shown that developmental nicotine exposure (DNE) alters intrinsic properties and synaptic transmission in hypoglossal motoneurons (XIIMNs). Here we show that the effects of DNE also include alterations in spike-timing precision and reliability, and spike-frequency adaptation, in response to sinusoidal current injection. Current-clamp experiments in brainstem slices from neonatal rats show that DNE lowers the threshold for spike generation but increases the variability of spike-timing mechanisms. DNE is also associated with an increase in spike-frequency adaptation and reductions in both peak and steady-state firing rate in response to brief, square wave current injections. Taken together, our data indicate that DNE causes significant alterations in the input-output efficiency of XIIMNs. These alterations may play a role in the increased frequency of obstructive apneas and altered suckling strength and coordination observed in nicotine-exposed neonatal humans.

Stochastic cortical neurodynamics underlying the memory and cognitive changes in aging

The relatively random spiking times of individual neurons provide a source of noise in the brain. We show how this noise interacting with altered depth in the basins of attraction of networks involved in short-term memory, attention, and episodic memory provide an approach to understanding some of the cognitive changes in normal aging. The effects of the neurobiological changes in aging that are considered include reduced synaptic modification and maintenance during learning produced in part through reduced acetylcholine in normal aging, reduced dopamine which reduces NMDA-receptor mediated effects, reduced noradrenaline which increases cAMP and thus shunts excitatory synaptic inputs, and the effects of a reduction in acetylcholine in increasing spike frequency adaptation. Using integrate-and-fire simulations of an attractor network implementing memory recall and short-term memory, it is shown that all these changes associated with aging reduce the firing rates of the excitatory neurons, which in turn reduce the depth of the basins of attraction, resulting in a much decreased probability in maintaining in short-term memory what has been recalled from the attractor network. This stochastic dynamics approach opens up new ways to understand and potentially treat the effects of normal aging on memory and cognitive functions.

ADAPTATION-DEPENDENT SYNCHRONIZATION TRANSITIONS AND BURST GENERATIONS IN ELECTRICALLY COUPLED NEURAL NETWORKS

A typical feature of neurons is their ability to encode neural information dynamically through spike frequency adaptation (SFA). Previous studies of SFA on neuronal synchronization were mainly concentrated on the correlated firing between neuron pairs, while the synchronization of neuron populations in the presence of SFA is still unclear. In this study, the influence of SFA on the population synchronization of neurons was numerically explored in electrically coupled networks, with regular, small-world, and random connectivity, respectively. The simulation results indicate that cross-correlation indices decrease significantly when the neurons have adaptation compared with those of nonadapting neurons, similar to previous experimental observations. However, the synchronous activity of population neurons exhibits a rather complex adaptation-dependent manner. Specifically, synchronization strength of neuron populations changes nonmonotonically, depending on the degree of adaptation. In addition, single neurons in the networks can switch from regular spiking to bursting with the increase of adaptation degree. Furthermore, the connection probability among neurons exhibits significant influence on the population synchronous activity, but has little effect on the burst generation of single neurons. Accordingly, the results may suggest that synchronous activity and burst firing of population neurons are both adaptation-dependent.

Image familiarization sharpens response dynamics of neurons in inferotemporal cortex

Repeated viewing of an image over days and weeks induces a marked reduction in the strength with which neurons in monkey inferotemporal cortex respond to it. The processing advantage that attaches to this reduction is unknown. One possibility is that truncation of the response to a familiar image leaves neurons in a state of readiness to respond to ensuing images and thereby enhances their ability to track rapidly changing displays. We explored this possibility by assessing neuronal responses to familiar and novel images in rapid serial visual displays. Inferotemporal neurons responded more strongly to familiar than to novel images in such displays. The effect was stronger among putative inhibitory neurons than among putative excitatory neurons. A comparable effect occurred at the level of the scalp potential in humans. We conclude that long-term familiarization sharpens the response dynamics of neurons in both monkey and human extrastriate visual cortex.

Networks for memory, perception, and decision-making, and beyond to how the syntax for language might be implemented in the brain

Neural principles that provide a foundation for memory, perception, and decision-making include place coding with sparse distributed representations, associative synaptic modification, and attractor networks in which the storage capacity is in the order of the number of associatively modifiable recurrent synapses on any one neuron. Based on those and further principles of cortical computation, hypotheses are explored in which syntax is encoded in the cortex using sparse distributed place coding. Each cortical module 2-3 mm in diameter is proposed to be formed of a local attractor neuronal network with a capacity in the order of 10,000 words (e.g. subjects, verbs or objects depending on the module). Such a system may form a deep language-of-thought layer. For the information to be communicated to other people, the modules in which the neurons are firing which encode the syntactic role, as well as which neurons are firing to specify the words, must be communicated. It is proposed that one solution to this (used in English) is temporal order encoding, for example subject-verb-object. It is shown with integrate-and-fire simulations that this order encoding could be implemented by weakly forward-coupled subject-verb-object modules. A related system can decode a temporal sequence. This approach based on known principles of cortical computation needs to be extended to investigate further whether it could form a biological foundation for the implementation of language in the brain. This article is part of a Special Issue entitled SI: Brain and Memory.

Analytical approximations of the firing rate of an adaptive exponential integrate-and-fire neuron in the presence of synaptic noise

Computational models offer a unique tool for understanding the network-dynamical mechanisms which mediate between physiological and biophysical properties, and behavioral function. A traditional challenge in computational neuroscience is, however, that simple neuronal models which can be studied analytically fail to reproduce the diversity of electrophysiological behaviors seen in real neurons, while detailed neuronal models which do reproduce such diversity are intractable analytically and computationally expensive. A number of intermediate models have been proposed whose aim is to capture the diversity of firing behaviors and spike times of real neurons while entailing the simplest possible mathematical description. One such model is the exponential integrate-and-fire neuron with spike rate adaptation (aEIF) which consists of two differential equations for the membrane potential (V) and an adaptation current (w). Despite its simplicity, it can reproduce a wide variety of physiologically observed spiking patterns, can be fit to physiological recordings quantitatively, and, once done so, is able to predict spike times on traces not used for model fitting. Here we compute the steady-state firing rate of aEIF in the presence of Gaussian synaptic noise, using two approaches. The first approach is based on the 2-dimensional Fokker-Planck equation that describes the (V,w)-probability distribution, which is solved using an expansion in the ratio between the time constants of the two variables. The second is based on the firing rate of the EIF model, which is averaged over the distribution of the w variable. These analytically derived closed-form expressions were tested on simulations from a large variety of model cells quantitatively fitted to in vitro electrophysiological recordings from pyramidal cells and interneurons. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise.

Muscarinic acetylcholine receptors are expressed by most parvalbumin-immunoreactive neurons in area MT of the macaque

BACKGROUND

In the mammalian neocortex, cells that express parvalbumin (PV neurons) comprise a dominant class of inhibitory neuron that substantially overlaps with the fast/narrow-spiking physiological phenotype. Attention has pronounced effects on narrow-spiking neurons in the extrastriate cortex of macaques, and more consistently so than on their broad-spiking neighbors. Cortical neuromodulation by acetylcholine (ACh) is a candidate mechanism for aspects of attention and in the primary visual cortex (V1) of the macaque, receptors for ACh (AChRs) are strongly expressed by inhibitory neurons. In particular, most PV neurons in macaque V1 express m1 muscarinic AChRs and exogenously applied ACh can cause the release of γ-aminobutyric acid. In contrast, few PV neurons in rat V1 express m1 AChRs. While this could be a species difference, it has also been argued that macaque V1 is anatomically unique when compared with other cortical areas in macaques.

AIMS

The aim of this study was to better understand the extent to which V1 offers a suitable model circuit for cholinergic anatomy in the macaque occipital lobe, and to explore cholinergic modulation as a biological basis for the changes in circuit behavior seen with attention.

MATERIALS AND METHODS

We compared expression of m1 AChRs by PV neurons between area V1 and the middle temporal visual area (MT) in macaque monkeys using dual-immunofluorescence confocal microscopy.

RESULTS AND CONCLUSION

We find that, as in V1, most PV neurons in MT express m1 AChRs but, unlike in V1, it appears that so do most excitatory neurons. This provides support for V1 as a model of cholinergic modulation of inhibition in macaque visual cortex, but not of cholinergic modulation of visual cortical circuits in general. We also propose that ACh acting via m1 AChRs is a candidate underlying mechanism for the strong effects of attention on narrow-spiking neurons observed in behaving animals.

A computational paradigm for dynamic logic-gates in neuronal activity

In 1943 McCulloch and Pitts suggested that the brain is composed of reliable logic-gates similar to the logic at the core of today's computers. This framework had a limited impact on neuroscience, since neurons exhibit far richer dynamics. Here we propose a new experimentally corroborated paradigm in which the truth tables of the brain's logic-gates are time dependent, i.e., dynamic logic-gates (DLGs). The truth tables of the DLGs depend on the history of their activity and the stimulation frequencies of their input neurons. Our experimental results are based on a procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. We demonstrate that the underlying biological mechanism is the unavoidable increase of neuronal response latencies to ongoing stimulations, which imposes a non-uniform gradual stretching of network delays. The limited experimental results are confirmed and extended by simulations and theoretical arguments based on identical neurons with a fixed increase of the neuronal response latency per evoked spike. We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra.

Sleep and synaptic homeostasis

In the last decades a substantial knowledge about sleep mechanisms has been accumulated. However, the function of sleep still remains elusive. The difficulty with unraveling sleep's function may arise from the lack of understanding of how the multitude of processes associated with waking and sleep-from gene expression and single neuron activity to the whole brain dynamics and behavior-functionally and mechanistically relate to each other. Therefore, novel conceptual frameworks, which integrate and take into account the variety of phenomena occurring during waking and sleep at different levels, will likely lead to advances in our understanding of the function of sleep, above and beyond what merely descriptive or correlative approaches can provide. One such framework, the synaptic homeostasis hypothesis, focuses on wake- and sleep-dependent changes in synaptic strength. The core claim of this hypothesis is that learning and experience during wakefulness are associated with a net increase in synaptic strength. In turn, the proposed function of sleep is to provide synaptic renormalization, which has important implications with respect to energy needs, intracranial space, metabolic supplies, and, importantly, enables further plastic changes. In this article we review the empirical evidence for this hypothesis, which was obtained at several levels-from gene expression and cellular excitability to structural synaptic modifications and behavioral outcomes. We conclude that although the mechanisms behind the proposed role of sleep in synaptic homeostasis are undoubtedly complex, this conceptual framework offers a unique opportunity to provide mechanistic and functional explanation for many previously disparate observations, and define future research strategies.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.

How delays matter in an oscillatory whole-brain spiking-neuron network model for MEG alpha-rhythms at rest

In recent years the study of the intrinsic brain dynamics in a relaxed awake state in the absence of any specific task has gained increasing attention, as spontaneous neural activity has been found to be highly structured at a large scale. This so called resting-state activity has been found to be comprised by nonrandom spatiotemporal patterns and fluctuations, and several Resting-State Networks (RSN) have been found in BOLD-fMRI as well as in MEG signal power envelope correlations. The underlying anatomical connectivity structure between areas of the brain has been identified as being a key to the observed functional network connectivity, but the mechanisms behind this are still underdetermined. Theoretical large-scale brain models for fMRI data have corroborated the importance of the connectome in shaping network dynamics, while the importance of delays and noise differ between studies and depend on the models' specific dynamics. In the current study, we present a spiking neuron network model that is able to produce noisy, distributed alpha-oscillations, matching the power peak in the spectrum of group resting-state MEG recordings. We studied how well the model captured the inter-node correlation structure of the alpha-band power envelopes for different delays between brain areas, and found that the model performs best for propagation delays inside the physiological range (5-10 m/s). Delays also shift the transition from noisy to bursting oscillations to higher global coupling values in the model. Thus, in contrast to the asynchronous fMRI state, delays are important to consider in the presence of oscillation.

How adaptation currents change threshold, gain, and variability of neuronal spiking

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow K(+) currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in vivo like fluctuating synaptic input, spike rate output, and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current that primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold, and decreases its slope (response gain) for low spike rates. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of an adaptation current naturally increase the mean interspike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow K(+) conductances contribute to the two different types of an adaptation current and find that Ca(2+)-activated K(+) currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or Na(+)-activated K(+) currents show a dominant subthreshold component.

Firing properties of entorhinal cortex neurons and early alterations in an Alzheimer's disease transgenic model

The entorhinal cortex (EC) is divided into medial (MEC) and lateral (LEC) anatomical areas, and layer II neurons of these two regions project to granule cells of the dentate gyrus through the medial and lateral perforant pathways (MPP and LPP), respectively. Stellate cells (SCs) represent the main neurons constituting the MPP inputs, while fan cells (FCs) represent the main LPP inputs. Here, we first characterized the excitability properties of SCs and FCs in adult wild-type (WT) mouse brain. Our data indicate that, during sustained depolarization, action potentials (APs) generated by SCs exhibit increased fast afterhyperpolarization and overshoot, making them able to fire at higher frequencies and to exhibit higher spike frequency adaptation (SFA) than FCs. Since the EC is one of the earliest brain regions affected during Alzheimer's disease (AD) progression, we compared SCs and FCs firing in 4-month-old WT and transgenic Tg2576 mice, a well-established AD mouse model. Tg2576-SCs displayed a slight increase in firing frequency during mild depolarization but otherwise normal excitability properties during higher stimulations. On the contrary, Tg2576-FCs exhibited a decreased firing frequency during mild and higher depolarizations, as well as an increased SFA. Our data identify the FCs as a neuronal population particularly sensitive to early pathological effects of chronic accumulation of APP-derived peptides, as it occurs in Tg2576 mice. As FCs represent the major input of sensory information to the hippocampus during memory acquisition, early alterations in their excitability profile could significantly contribute to the onset of cognitive decline in AD.

Alterations in membrane and firing properties of layer 2/3 pyramidal neurons following focal laser lesions in rat visual cortex

Focal cortical injuries are well known to cause changes in function and excitability of the surviving cortical areas but the cellular correlates of these physiological alterations are not fully understood. In the present study we employed a well established ex vivo-in vitro model of focal laser lesions in the rat visual cortex and we studied membrane and firing properties of the surviving layer 2/3 pyramidal neurons. Patch-clamp recordings, performed in the first week post-injury, revealed an increased input resistance, a depolarized spike threshold as well as alterations in the firing pattern of neurons in the cortex ipsilateral to the lesion. Notably, the reported lesion-induced alterations emerged or became more evident when an exciting perfusing solution, known as modified artificial cerebrospinal fluid, was used to increase the ongoing synaptic activity in cortical slices. Conversely, application of glutamatergic or GABAA receptor blockers reduced the observed alterations and GABAB receptor blockers abolished the differences completely. All together the present findings suggest that changes in synaptic receptors function, following focal cortical injuries, can modulate membrane and firing properties of layer 2/3 pyramidal neurons. This previously unknown functional interplay between synaptic and membrane properties may constitute a novel cellular mechanism to explain alterations in neuronal network function and excitability following focal cortical injuries.

How adaptation shapes spike rate oscillations in recurrent neuronal networks

Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network-based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance-based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network-based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

Programming time-multiplexed reconfigurable hardware using a scalable neuromorphic compiler

Scalability and connectivity are two key challenges in designing neuromorphic hardware that can match biological levels. In this paper, we describe a neuromorphic system architecture design that addresses an approach to meet these challenges using traditional complementary metal-oxide-semiconductor (CMOS) hardware. A key requirement in realizing such neural architectures in hardware is the ability to automatically configure the hardware to emulate any neural architecture or model. The focus for this paper is to describe the details of such a programmable front-end. This programmable front-end is composed of a neuromorphic compiler and a digital memory, and is designed based on the concept of synaptic time-multiplexing (STM). The neuromorphic compiler automatically translates any given neural architecture to hardware switch states and these states are stored in digital memory to enable desired neural architectures. STM enables our proposed architecture to address scalability and connectivity using traditional CMOS hardware. We describe the details of the proposed design and the programmable front-end, and provide examples to illustrate its capabilities. We also provide perspectives for future extensions and potential applications.

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.

Nonlinear-dynamics theory of up-down transitions in neocortical neural networks

The neurons of the neocortex show ~1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.