Energy optimisation predicts the capacity of ion buffering in the brain.

Neurons store energy in the ionic concentration gradients they build across their cell membrane. The amount of energy stored, and hence the work the ions can do by mixing, can be enhanced by the presence of ion buffers in extra- and intracellular space. Buffers act as sources and sinks of ions, however, and unless the buffering capacities for different ion species obey certain relationships, a complete mixing of the ions may be impeded by the physical conditions of charge neutrality and isotonicity. From these conditions, buffering capacities were calculated that enabled each ion species to mix completely. In all valid buffer distributions, the [Formula: see text] ions were buffered most, with a capacity exceeding that of [Formula: see text] and [Formula: see text] buffering by at least an order of magnitude. The similar magnitude of the (oppositely directed) [Formula: see text] and [Formula: see text] gradients made extracellular space behave as a [Formula: see text]-[Formula: see text] exchanger. Anions such as [Formula: see text] were buffered least. The great capacity of the extra- and intracellular [Formula: see text] buffers caused a large influx of [Formula: see text] ions as is typically observed during energy deprivation. These results explain many characteristics of the physiological buffer distributions but raise the question how the brain controls the capacity of its ion buffers. It is suggested that neurons and glial cells, by their great sensitivity to gradients of charge and osmolarity, respectively, sense deviations from electro-neutral and isotonic mixing, and use these signals to tune the chemical composition, and buffering capacity, of the extra- and intracellular matrices.

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials.

Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the computational study that follows, we show that a model circuit of interneurons, coupled via both GABAA receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/ f power scaling at low frequency (below 10 Hz), power accumulation in the γ-frequency band (30-100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/ f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplification of single-neuron spectral properties, owing to the refractory period, by parameters that favor neuronal synchrony, such as delayed inhibition. This study also confirms that both synaptic and voltage-gated membrane currents contribute substantially to the LFP and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.

Temporal integration and 1/f power scaling in a circuit model of cerebellar interneurons.

Inhibitory interneurons interconnected via electrical and chemical (GABAA receptor) synapses form extensive circuits in several brain regions. They are thought to be involved in timing and synchronization through fast feedforward control of principal neurons. Theoretical studies have shown, however, that whereas self-inhibition does indeed reduce response duration, lateral inhibition, in contrast, may generate slow response components through a process of gradual disinhibition. Here we simulated a circuit of interneurons (stellate and basket cells) of the molecular layer of the cerebellar cortex and observed circuit time constants that could rise, depending on parameter values, to >1 s. The integration time scaled both with the strength of inhibition, vanishing completely when inhibition was blocked, and with the average connection distance, which determined the balance between lateral and self-inhibition. Electrical synapses could further enhance the integration time by limiting heterogeneity among the interneurons and by introducing a slow capacitive current. The model can explain several observations, such as the slow time course of OFF-beam inhibition, the phase lag of interneurons during vestibular rotation, or the phase lead of Purkinje cells. Interestingly, the interneuron spike trains displayed power that scaled approximately as 1/f at low frequencies. In conclusion, stellate and basket cells in cerebellar cortex, and interneuron circuits in general, may not only provide fast inhibition to principal cells but also act as temporal integrators that build a very short-term memory.NEW & NOTEWORTHY The most common function attributed to inhibitory interneurons is feedforward control of principal neurons. In many brain regions, however, the interneurons are densely interconnected via both chemical and electrical synapses but the function of this coupling is largely unknown. Based on large-scale simulations of an interneuron circuit of cerebellar cortex, we propose that this coupling enhances the integration time constant, and hence the memory trace, of the circuit.

On the Nernst-Planck equation.

This review first discusses Nernst's and Planck's early papers on electro-diffusion, the brief priority conflict that followed, and the role these papers played in shaping the emerging concept of membrane excitability. The second part discusses in greater detail the constraints of the Nernst-Planck theory, and shows more recent examples of its applicability for neuronal modelling.

Dendritic morphology predicts pattern recognition performance in multi-compartmental model neurons with and without active conductances.

In this paper we examine how a neuron's dendritic morphology can affect its pattern recognition performance. We use two different algorithms to systematically explore the space of dendritic morphologies: an algorithm that generates all possible dendritic trees with 22 terminal points, and one that creates representative samples of trees with 128 terminal points. Based on these trees, we construct multi-compartmental models. To assess the performance of the resulting neuronal models, we quantify their ability to discriminate learnt and novel input patterns. We find that the dendritic morphology does have a considerable effect on pattern recognition performance and that the neuronal performance is inversely correlated with the mean depth of the dendritic tree. The results also reveal that the asymmetry index of the dendritic tree does not correlate with the performance for the full range of tree morphologies. The performance of neurons with dendritic tapering is best predicted by the mean and variance of the electrotonic distance of their synapses to the soma. All relationships found for passive neuron models also hold, even in more accentuated form, for neurons with active membranes.

Endogenous cholinergic inputs and local circuit mechanisms govern the phasic mesolimbic dopamine response to nicotine.

Nicotine exerts its reinforcing action by stimulating nicotinic acetylcholine receptors (nAChRs) and boosting dopamine (DA) output from the ventral tegmental area (VTA). Recent data have led to a debate about the principal pathway of nicotine action: direct stimulation of the DAergic cells through nAChR activation, or disinhibition mediated through desensitization of nAChRs on GABAergic interneurons. We use a computational model of the VTA circuitry and nAChR function to shed light on this issue. Our model illustrates that the α4ß2-containing nAChRs either on DA or GABA cells can mediate the acute effects of nicotine. We account for in vitro as well as in vivo data, and predict the conditions necessary for either direct stimulation or disinhibition to be at the origin of DA activity increases. We propose key experiments to disentangle the contribution of both mechanisms. We show that the rate of endogenous acetylcholine input crucially determines the evoked DA response for both mechanisms. Together our results delineate the mechanisms by which the VTA mediates the acute rewarding properties of nicotine and suggest an acetylcholine dependence hypothesis for nicotine reinforcement.

An integrator circuit in cerebellar cortex.

The brain builds dynamic models of the body and the outside world to predict the consequences of actions and stimuli. A well-known example is the oculomotor integrator, which anticipates the position-dependent elasticity forces acting on the eye ball by mathematically integrating over time oculomotor velocity commands. Many models of neural integration have been proposed, based on feedback excitation, lateral inhibition or intrinsic neuronal nonlinearities. We report here that a computational model of the cerebellar cortex, a structure thought to implement dynamic models, reveals a hitherto unrecognized integrator circuit. In this model, comprising Purkinje cells, molecular layer interneurons and parallel fibres, Purkinje cells were able to generate responses lasting more than 10 s, to which both neuronal and network mechanisms contributed. Activation of the somatic fast sodium current by subthreshold voltage fluctuations was able to maintain pulse-evoked graded persistent activity, whereas lateral inhibition among Purkinje cells via recurrent axon collaterals further prolonged the responses to step and sine wave stimulation. The responses of Purkinje cells decayed with a time-constant whose value depended on their baseline spike rate, with integration vanishing at low (< 1 per s) and high rates (> 30 per s). The model predicts that the apparently fast circuit of the cerebellar cortex may control the timing of slow processes without having to rely on sensory feedback. Thus, the cerebellar cortex may contain an adaptive temporal integrator, with the sensitivity of integration to the baseline spike rate offering a potential mechanism of plasticity of the response time-constant.

An Isotonic Model of Neuron Swelling Based on Co-Transport of Salt and Water.

Neurons spend most of their energy building ion gradients across the cell membrane. During energy deprivation the neurons swell, and the concomitant mixing of their ions is commonly assumed to lead toward a Donnan equilibrium, at which the concentration gradients of all permeant ion species have the same Nernst potential. This Donnan equilibrium, however, is not isotonic, as the total concentration of solute will be greater inside than outside the neurons. The present theoretical paper, in contrast, proposes that neurons follow a path along which they swell quasi-isotonically by co-transporting water and ions. The final neuronal volume on the path is taken that at which the concentration of impermeant anions in the shrinking extracellular space equals that inside the swelling neurons. At this final state, which is also a Donnan equilibrium, all permeant ions can mix completely, and their Nernst potentials vanish. This final state is isotonic and electro-neutral, as are all intermediate states along this path. The path is in principle reversible, and maximizes the work of mixing.

Current source density correlates of cerebellar Golgi and Purkinje cell responses to tactile input.

The overall circuitry of the cerebellar cortex has been known for over a century, but the function of many synaptic connections remains poorly characterized in vivo. We used a one-dimensional multielectrode probe to estimate the current source density (CSD) of Crus IIa in response to perioral tactile stimuli in anesthetized rats and to correlate current sinks and sources to changes in the spike rate of corecorded Golgi and Purkinje cells. The punctate stimuli evoked two distinct early waves of excitation (at <10 and ∼ 20 ms) associated with current sinks in the granular layer. The second wave was putatively of corticopontine origin, and its associated sink was located higher in the granular layer than the first trigeminal sink. The distinctive patterns of granular-layer sinks correlated with the spike responses of corecorded Golgi cells. In general, Golgi cell spike responses could be linearly reconstructed from the CSD profile. A dip in simple-spike activity of coregistered Purkinje cells correlated with a current source deep in the molecular layer, probably generated by basket cell synapses, interspersed between sparse early sinks presumably generated by synapses from granule cells. The late (>30 ms) enhancement of simple-spike activity in Purkinje cells was characterized by the absence of simultaneous sinks in the granular layer and by the suppression of corecorded Golgi cell activity, pointing at inhibition of Golgi cells by Purkinje axon collaterals as a likely mechanism of late Purkinje cell excitation.

STD-dependent and independent encoding of input irregularity as spike rate in a computational model of a cerebellar nucleus neuron.

Neurons in the cerebellar nuclei (CN) receive inhibitory inputs from Purkinje cells in the cerebellar cortex and provide the major output from the cerebellum, but their computational function is not well understood. It has recently been shown that the spike activity of Purkinje cells is more regular than previously assumed and that this regularity can affect motor behaviour. We use a conductance-based model of a CN neuron to study the effect of the regularity of Purkinje cell spiking on CN neuron activity. We find that increasing the irregularity of Purkinje cell activity accelerates the CN neuron spike rate and that the mechanism of this recoding of input irregularity as output spike rate depends on the number of Purkinje cells converging onto a CN neuron. For high convergence ratios, the irregularity induced spike rate acceleration depends on short-term depression (STD) at the Purkinje cell synapses. At low convergence ratios, or for synchronised Purkinje cell input, the firing rate increase is independent of STD. The transformation of input irregularity into output spike rate occurs in response to artificial input spike trains as well as to spike trains recorded from Purkinje cells in tottering mice, which show highly irregular spiking patterns. Our results suggest that STD may contribute to the accelerated CN spike rate in tottering mice and they raise the possibility that the deficits in motor control in these mutants partly result as a pathological consequence of this natural form of plasticity.

Effect of extracellular volume on the energy stored in transmembrane concentration gradients.

The amount of energy that can be retrieved from a concentration gradient across a membrane separating two compartments depends on the relative size of the compartments. Having a larger low-concentration compartment is in general beneficial. It is shown here analytically that the retrieved energy further increases when the high-concentration compartment shrinks during the mixing process, and a general formula is derived for the energy when the ratio of transported solvent to solute varies. These calculations are then applied to the interstitial compartment of the brain, which is rich in Na^{+} and Cl^{-} ions and poor in K^{+}. The reported shrinkage of this compartment, and swelling of the neurons, during oxygen deprivation is shown to enhance the energy recovered from NaCl entering the neurons. The slight loss of energy on the part of K^{+} can be compensated for by the uptake of K^{+} ions by glial cells. In conclusion, the present study proposes that the reported fluctuations in the size of the interstitial compartment of the brain (expansion during sleep and contraction during oxygen deprivation) optimize the amount of energy that neurons can store in, and retrieve from, their ionic concentration gradients.

Synaptic pathways in neural microcircuits.

The functions performed by different neural microcircuits depend on the anatomical and physiological properties of the various synaptic pathways connecting neurons. Neural microcircuits across various species and brain regions are similar in terms of their repertoire of neurotransmitters, their synaptic kinetics, their short-term and long-term plasticity, and the target-specificity of their synaptic connections. However, microcircuits can be fundamentally different in terms of the precise recurrent design used to achieve a specific functionality. In this review, which is part of the TINS Microcircuits Special Feature, we compare the connectivity designs in spinal, hippocampal, neocortical and cerebellar microcircuits, and discuss the different computational challenges that each microcircuit faces.

Nonspecific synaptic plasticity improves the recognition of sparse patterns degraded by local noise.

Many forms of synaptic plasticity require the local production of volatile or rapidly diffusing substances such as nitric oxide. The nonspecific plasticity these neuromodulators may induce at neighboring non-active synapses is thought to be detrimental for the specificity of memory storage. We show here that memory retrieval may benefit from this non-specific plasticity when the applied sparse binary input patterns are degraded by local noise. Simulations of a biophysically realistic model of a cerebellar Purkinje cell in a pattern recognition task show that, in the absence of noise, leakage of plasticity to adjacent synapses degrades the recognition of sparse static patterns. However, above a local noise level of 20%, the model with nonspecific plasticity outperforms the standard, specific model. The gain in performance is greatest when the spatial distribution of noise in the input matches the range of diffusion-induced plasticity. Hence non-specific plasticity may offer a benefit in noisy environments or when the pressure to generalize is strong.

Resonant synchronization in heterogeneous networks of inhibitory neurons.

Brain rhythms arise through the synchronization of neurons and their entrainment in a regular firing pattern. In this process, networks of reciprocally connected inhibitory neurons are often involved, but what mechanism determines the oscillation frequency is not completely understood. Analytical studies predict that the emerging frequency band is primarily constrained by the decay rate of the unitary IPSC. We observed a new phenomenon of resonant synchronization in computer-simulated networks of inhibitory neurons in which the synaptic current has a delayed onset, reflecting finite spike propagation and synaptic transmission times. At the resonant level of network excitation, all neurons fire synchronously and rhythmically with a period approximately four times the mean delay of the onset of the inhibitory synaptic current. The amplitude and decay time constant of the synaptic current have relatively minor effects on the emerging frequency band. By varying the axonal delay of the inhibitory connections, networks with a realistic synaptic kinetics can be tuned to frequencies from 40 to >200 Hz. This resonance phenomenon arises in heterogeneous networks with, on average, as few as five connections per neuron. We conclude that the delay of the synaptic current is the primary parameter controlling the oscillation frequency of inhibitory networks and propose that delay-induced synchronization is a mechanism for fast brain rhythms that depend on intact inhibitory synaptic transmission.

Inactivation of calcium-binding protein genes induces 160 Hz oscillations in the cerebellar cortex of alert mice.

Oscillations in neuronal populations may either be imposed by intrinsically oscillating pacemakers neurons or emerge from specific attributes of a distributed network of connected neurons. Calretinin and calbindin are two calcium-binding proteins involved in the shaping of intraneuronal Ca2+ fluxes. However, although their physiological function has been studied extensively at the level of a single neuron, little is known about their role at the network level. Here we found that null mutations of genes encoding calretinin or calbindin induce 160 Hz local field potential oscillations in the cerebellar cortex of alert mice. These oscillations reached maximum amplitude just beneath the Purkinje cell bodies and are reinforced in the cerebellum of mice deficient in both calretinin and calbindin. Purkinje cells fired simple spikes phase locked to the oscillations and synchronized along the parallel fiber axis. The oscillations reversibly disappeared when gap junctions or either GABA(A) or NMDA receptors were blocked. Cutaneous stimulation of the whisker region transiently suppressed the oscillations. However, the intrinsic somatic excitability of Purkinje cells recorded in slice preparation was not significantly altered in mutant mice. Functionally, these results suggest that 160 Hz oscillation emerges from a network mechanism combining synchronization of Purkinje cell assemblies through parallel fiber excitation and the network of coupled interneurons of the molecular layer. These findings demonstrate that subtle genetically induced modifications of Ca2+ homeostasis in specific neuron types can alter the observed dynamics of the global network.

Oscillations in the cerebellar cortex: a prediction of their frequency bands.

Local recurrent connections endow the cerebellar cortex with an intrinsic dynamics. We performed computer simulations to predict the frequency bands of the oscillations that will most likely emerge. Feedback inhibition from the Golgi to the granule cells induced 10-50 Hz oscillations, the period at resonance being approximately equal to four times the maximum conduction delay generated along the parallel-fiber connections from granule to Golgi cells. In the molecular layer, the interneurons tended to induce fast oscillations (100-250 Hz), having a period equal to about four times the delay over their reciprocal synaptic connections. Finally, although the presence of lateral inhibition among the Purkinje cells has not been firmly established, reciprocal Purkinje-cell synapses are predicted to transform the cerebellar cortex into a potential temporal integrator.

Understanding the role α7 nicotinic receptors play in dopamine efflux in nucleus accumbens.

Neuronal nicotinic acetylcholine receptors (NNRs) of the α7 subtype have been shown to contribute to the release of dopamine in the nucleus accumbens. The site of action and the underlying mechanism, however, are unclear. Here we applied a circuit modeling approach, supported by electrochemical in vivo recordings, to clarify this issue. Modeling revealed two potential mechanisms for the drop in accumbal dopamine efflux evoked by the selective α7 partial agonist TC-7020. TC-7020 could desensitize α7 NNRs located predominantly on dopamine neurons or glutamatergic afferents to them or, alternatively, activate α7 NNRs located on the glutamatergic afferents to GABAergic interneurons in the ventral tegmental area. Only the model based on desensitization, however, was able to explain the neutralizing effect of coapplied PNU-120596, a positive allosteric modulator. According to our results, the most likely sites of action are the preterminal α7 NNRs controlling glutamate release from cortical afferents to the nucleus accumbens. These findings offer a rationale for the further investigation of α7 NNR agonists as therapy for diseases associated with enhanced mesolimbic dopaminergic tone, such as schizophrenia and addiction.

Impaired facial emotion recognition in patients with ventromedial prefrontal hypoperfusion.

Empathy refers to our ability to recognize and share emotions by another human being. Impairment may underlie many of the emotional deficits commonly associated with a range of neuropsychiatric and neurological conditions. The prefrontal cortex (PFC) has long been implicated in these processes, but the specific contribution of subregions of the PFC remain unclear. Studies regarding the role of subregions of the prefrontal cortex such as the ventromedial prefrontal cortex (vmPFC)-in facial emotion recognition have yielded inconsistent results. The present study aimed to investigate the capacity to recognize nonverbal emotional facial expressions in a group of patients with the following: (a) perfusion deficits in the vmPFC (vmPFC group; N = 13), (b) hypoperfusions sparing the vmPFC (nonvmPFC group; N = 12), and in (c) a control group of healthy volunteers (control group; N = 17). Regions of hypoperfusion were identified by means of Single Photon Emission Computed Tomography (SPECT). Participants were asked to recognize facial expressions of the 7 basic emotions (happiness, fear, surprise, anger, disgust, sadness, or neutral). Detection of facial expressions of fear, disgust, and surprise was affected after functional disruption of the vmPFC. The present study confirms the role of the vmPFC in recognizing emotional facial expressions.

Enhancing the yield of high-density electrode arrays through automated electrode selection.

Recently developed CMOS-based microprobes contain hundreds of electrodes on a single shaft with inter-electrode distances as small as 30 µm. So far, neuroscientists needed to select electrodes manually from hundreds of electrodes. Here we present an electronic depth control algorithm that allows to select electrodes automatically, hereby allowing to reduce the amount of data and locating those electrodes that are close to neurons. The electrodes are selected according to a new penalized signal-to-noise ratio (PSNR) criterion that demotes electrodes from becoming selected if their signals are redundant with previously selected electrodes. It is shown that, using the PSNR, interneurons generating smaller spikes are also selected. We developed a model that aims to evaluate algorithms for electronic depth control, but also generates benchmark data for testing spike sorting and spike detection algorithms. The model comprises a realistic tufted pyramidal cell, non-tufted pyramidal cells and inhibitory interneurons. All neurons are synaptically activated by hundreds of fibers. This arrangement allows the algorithms to be tested in more realistic conditions, including backgrounds of synaptic potentials, varying spike rates with bursting and spike amplitude attenuation.