Inhibitory Neural Populations Research Articles

Applications of information geometry to spiking neural network activity.

The space of possible behaviors that complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominent example of a biological system with complex behaviors. The number of possible patterns of spikes emitted by a local brain circuit is combinatorially large, although the brain may not make use of all of them. Understanding which of these possible patterns are actually used by the brain, and how those sets of patterns change as properties of neural circuitry change is a major goal in neuroscience. Recently, tools from information geometry have been used to study embeddings of probabilistic models onto a hierarchy of model manifolds that encode how model outputs change as a function of their parameters, giving a quantitative notion of "distances" between outputs. We apply this method to a network model of excitatory and inhibitory neural populations to understand how the competition between membrane and synaptic response timescales shapes the network's information geometry. The hyperbolic embedding allows us to identify the statistical parameters to which the model behavior is most sensitive, and demonstrate how the ranking of these coordinates changes with the balance of excitation and inhibition in the network.

Optimal control of a Wilson-Cowan model of neural population dynamics.

Nonlinear dynamical systems describe neural activity at various scales and are frequently used to study brain functions and the impact of external perturbations. Here, we explore methods from optimal control theory (OCT) to study efficient, stimulating "control" signals designed to make the neural activity match desired targets. Efficiency is quantified by a cost functional, which trades control strength against closeness to the target activity. Pontryagin's principle then enables to compute the cost-minimizing control signal. We then apply OCT to a Wilson-Cowan model of coupled excitatory and inhibitory neural populations. The model exhibits an oscillatory regime, low- and high-activity fixed points, and a bistable regime where low- and high-activity states coexist. We compute an optimal control for a state-switching (bistable regime) and a phase-shifting task (oscillatory regime) and allow for a finite transition period before penalizing the deviation from the target state. For the state-switching task, pulses of limited input strength push the activity minimally into the target basin of attraction. Pulse shapes do not change qualitatively when varying the duration of the transition period. For the phase-shifting task, periodic control signals cover the whole transition period. Amplitudes decrease when transition periods are extended, and their shapes are related to the phase sensitivity profile of the model to pulsed perturbations. Penalizing control strength via the integrated 1-norm yields control inputs targeting only one population for both tasks. Whether control inputs drive the excitatory or inhibitory population depends on the state-space location.

Dynamical Mechanism Analysis of Three Neuroregulatory Strategies on the Modulation of Seizures.

This paper attempts to explore and compare the regulatory mechanisms of optogenetic stimulation (OS), deep brain stimulation (DBS) and electromagnetic induction on epilepsy. Based on the Wilson-Cowan model, we first demonstrate that the external input received by excitatory and inhibitory neural populations can induce rich dynamic bifurcation behaviors such as Hopf bifurcation, and make the system exhibit epileptic and normal states. Then, both OS and DBS are shown to be effective in controlling the epileptic state to a normal low-level state, and the stimulus parameters have a broad effective range. However, electromagnetic induction cannot directly control epilepsy to this desired state, even if it can significantly reduce the oscillation frequency of neural populations. One main difference worth noting is that the high spatiotemporal specificity of OS allows it to target inhibitory neuronal populations, whereas DBS and electromagnetic induction can only stimulate excitatory as well as inhibitory neuronal populations together. Next, the propagation behavior of epilepsy is explored under a typical three-node feedback loop structure. An increase in coupling strength accelerates and exacerbates epileptic activity in other brain regions. Finally, OS and DBS applied to the epileptic focus play similar positive roles in controlling the behavior of the area of seizure propagation, while electromagnetic induction still only achieves unsatisfactory effects. It is hoped that these dynamical results can provide insights into the treatment of epilepsy as well as other neurological disorders.

Transition dynamics and optogenetic control of epileptiform activity in a modified mean filed model of human cortex

Physiological experiments have shown that inhibitory interneurons can induce and maintain epileptiform activities, and different interneuron subtypes may be responsible for different types of seizures. Here we aim to link these electrophysiological experimental phenomena with theoretical dynamic mechanisms based on an improved Liley mean field model. Fascinatingly, the number of synapses between inhibitory neural populations can induce a rich state transition. Typically, the system will experience normal rhythm discharges, multispike discharges, spike wave discharges (SWD), generalized periodic discharges (GPD), the beta band oscillation, and eventually return to the normal state. Interestingly, the transition process can also be reversed. Meanwhile, disinhibition circuits can cause more epileptiform activities after taking into account the delay of synaptic information transmission. Furthermore, we are committed to designing different control strategies for epileptiform activities. As we expected, both deep brain stimulation and optogenetic technology can destroy or even eliminate pathological waves. It is need to emphasis that the cell type specificity of optogenetic regulation allows it to precisely target inhibitory neural populations, which is agree with experiment. Particularly, three different optogenetic regulatory strategies targeting inhibitory neural populations are modeled and proposed, of which the intermittent is designed to save energy. These modeling results reproduce the experimental phenomena and more significantly, help understand the mechanism of epilepsy to guide the clinical practice.

Effect of visual input on syllable parsing in a computational model of a neural microcircuit for speech processing

Objective. Seeing a person talking can help us understand them, particularly in a noisy environment. However, how the brain integrates the visual information with the auditory signal to enhance speech comprehension remains poorly understood. Approach. Here we address this question in a computational model of a cortical microcircuit for speech processing. The model consists of an excitatory and an inhibitory neural population that together create oscillations in the theta frequency range. When stimulated with speech, the theta rhythm becomes entrained to the onsets of syllables, such that the onsets can be inferred from the network activity. We investigate how well the obtained syllable parsing performs when different types of visual stimuli are added. In particular, we consider currents related to the rate of syllables as well as currents related to the mouth-opening area of the talking faces. Main results. We find that currents that target the excitatory neuronal population can influence speech comprehension, both boosting it or impeding it, depending on the temporal delay and on whether the currents are excitatory or inhibitory. In contrast, currents that act on the inhibitory neurons do not impact speech comprehension significantly. Significance. Our results suggest neural mechanisms for the integration of visual information with the acoustic information in speech and make experimentally-testable predictions.

Coherence Resonance in Random Erdös-Rényi Neural Networks: Mean-Field Theory

Additive noise is known to tune the stability of nonlinear systems. Using a network of two randomly connected interacting excitatory and inhibitory neural populations driven by additive noise, we derive a closed mean-field representation that captures the global network dynamics. Building on the spectral properties of Erdös-Rényi networks, mean-field dynamics are obtained via a projection of the network dynamics onto the random network’s principal eigenmode. We consider Gaussian zero-mean and Poisson-like noise stimuli to excitatory neurons and show that these noise types induce coherence resonance. Specifically, the stochastic stimulation induces coherent stochastic oscillations in the γ-frequency range at intermediate noise intensity. We further show that this is valid for both global stimulation and partial stimulation, i.e. whenever a subset of excitatory neurons is stimulated only. The mean-field dynamics exposes the coherence resonance dynamics in the γ-range by a transition from a stable non-oscillatory equilibrium to an oscillatory equilibrium via a saddle-node bifurcation. We evaluate the transition between non-coherent and coherent state by various power spectra, Spike Field Coherence and information-theoretic measures.

Multiscale dynamic mean field (MDMF) model relates resting-state brain dynamics with local cortical excitatory-inhibitory neurotransmitter homeostasis.

Previous computational models have related spontaneous resting-state brain activity with local excitatory–inhibitory balance in neuronal populations. However, how underlying neurotransmitter kinetics associated with E–I balance govern resting-state spontaneous brain dynamics remains unknown. Understanding the mechanisms by virtue of which fluctuations in neurotransmitter concentrations, a hallmark of a variety of clinical conditions, relate to functional brain activity is of critical importance. We propose a multiscale dynamic mean field (MDMF) model—a system of coupled differential equations for capturing the synaptic gating dynamics in excitatory and inhibitory neural populations as a function of neurotransmitter kinetics. Individual brain regions are modeled as population of MDMF and are connected by realistic connection topologies estimated from diffusion tensor imaging data. First, MDMF successfully predicts resting-state functional connectivity. Second, our results show that optimal range of glutamate and GABA neurotransmitter concentrations subserve as the dynamic working point of the brain, that is, the state of heightened metastability observed in empirical blood-oxygen-level-dependent signals. Third, for predictive validity the network measures of segregation (modularity and clustering coefficient) and integration (global efficiency and characteristic path length) from existing healthy and pathological brain network studies could be captured by simulated functional connectivity from an MDMF model.

Analysis of the Hindriks and van Putten model for propofol anesthesia: Limitations and extensions

We present a detailed analysis of the Hindriks and van Putten thalamocortical mean-field model for propofol anesthesia [NeuroImage 60(23), 2012]. The Hindriks and van Putten (HvP) model predicts increases in delta and alpha power for moderate (up to 130%) prolongation of GABAA inhibitory response, corresponding to light anesthetic sedation. Our analysis reveals that, for deeper anesthetic effect, the model exhibits an unexpected abrupt jump in cortical activity from a low-firing state to an extremely high-firing stable state (∼250 spikes/s), and remains locked there even at GABAA prolongations as high as 300% which would be expected to induce full comatose suppression of all firing activity. We demonstrate that this unphysiological behavior can be completely suppressed with appropriate tuning of the parameters controlling the sigmoidal functions that map soma voltage to firing rate for the excitatory and inhibitory neural populations, coupled with elimination of the putative population-dependent anesthetic efficacies introduced in the HvP model. The modifications reported here constrain the anesthetized brain activity into a biologically plausible range in which the cortex now has access to a moderate-firing state (“awake”) and a low-firing (“anesthetized”) state such that the brain can transition from “awake” to “anesthetized” states at a critical level of drug concentration. The modified HvP model predicts a drug–effect hysteresis in which the drug concentration required for induction is larger than that at emergence. In addition, the revised model shows a decrease in the intensity and frequency of alpha-band fluctuations, transitioning to delta-band dominance, with deepening anesthesia. These predicted drug concentration-dependent changes in EEG dynamics are consistent with clinical reports.

Modeling motor-evoked potentials from neural field simulations of transcranial magnetic stimulation

ObjectiveTo develop a population-based biophysical model of motor-evoked potentials (MEPs) following transcranial magnetic stimulation (TMS). MethodsWe combined an existing MEP model with population-based cortical modeling. Layer 2/3 excitatory and inhibitory neural populations, modeled with neural-field theory, are stimulated with TMS and feed layer 5 corticospinal neurons, which also couple directly but weakly to the TMS pulse. The layer 5 output controls mean motoneuron responses, which generate a series of single motor-unit action potentials that are summed to estimate a MEP. ResultsA MEP waveform was generated comparable to those observed experimentally. The model captured TMS phenomena including a sigmoidal input–output curve, common paired pulse effects (short interval intracortical inhibition, intracortical facilitation, long interval intracortical inhibition) including responses to pharmacological interventions, and a cortical silent period. Changes in MEP amplitude following theta burst paradigms were observed including variability in outcome direction. ConclusionsThe model reproduces effects seen in common TMS paradigms. SignificanceThe model allows population-based modeling of changes in cortical dynamics due to TMS protocols to be assessed in terms of changes in MEPs, thus allowing a clear comparison between population-based modeling predictions and typical experimental outcome measures.

Disruption of Cholinergic Circuits as an Area for Targeted Drug Treatment of Alzheimer's Disease: In Vivo Assessment of Short-Term Plasticity in Rat Brain.

The search for new therapeutics for the treatment of Alzheimer’s disease (AD) is still in progress. Aberrant pathways of synaptic transmission in basal forebrain cholinergic neural circuits are thought to be associated with the progression of AD. However, the effect of amyloid-beta (Aβ) on short-term plasticity (STP) of cholinergic circuits in the nucleus basalis magnocellularis (NBM) is largely unknown. STP assessment in rat brain cholinergic circuitry may indicate a new target for AD cholinergic therapeutics. Thus, we aimed to study in vivo electrophysiological patterns of synaptic activity in NBM-hippocampus and NBM-basolateral amygdala circuits associated with AD-like neurodegeneration. The extracellular single-unit recordings of responses from the hippocampal and basolateral amygdala neurons to high-frequency stimulation (HFS) of the NBM were performed after intracerebroventricular injection of Aβ 25–35. We found that after Aβ 25–35 exposure the number of hippocampal neurons exhibiting inhibitory responses to HFS of NBM is decreased. The reverse tendency was seen in the basolateral amygdala inhibitory neural populations, whereas the number of amygdala neurons with excitatory responses decreased. The low intensity of inhibitory and excitatory responses during HFS and post-stimulus period is probably due to the anomalous basal synaptic transmission and excitability of hippocampal and amygdala neurons. These functional changes were accompanied by structural alteration of hippocampal, amygdala, and NBM neurons. We have thus demonstrated that Aβ 25–35 induces STP disruption in NBM-hippocampus and NBM-basolateral amygdala circuits as manifested by unbalanced excitatory/inhibitory responses and their frequency. The results of this study may contribute to a better understanding of synaptic integrity. We believe that advancing our understanding of in vivo mechanisms of synaptic plasticity disruption in specific neural circuits could lead to effective drug searches for AD treatment.

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution.

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

Divisive gain modulation enables flexible and rapid entrainment in a neocortical microcircuit model.

Neocortical circuits exhibit a rich dynamic repertoire, and their ability to achieve entrainment (adjustment of their frequency to match the input frequency) is thought to support many cognitive functions and indicate functional flexibility. Although previous studies have explored the influence of various circuit properties on this phenomenon, the role of divisive gain modulation (or divisive inhibition) is unknown. This gain control mechanism is thought to be delivered mainly by the soma-targeting interneurons in neocortical microcircuits. In this study, we use a neural mass model of the neocortical microcircuit (extended Wilson–Cowan model) featuring both soma-targeting and dendrite-targeting interneuronal subpopulations to investigate the role of divisive gain modulation in entrainment. Our results demonstrate that the presence of divisive inhibition in the microcircuit, as delivered by the soma-targeting interneurons, enables its entrainment to a wider range of input frequencies. Divisive inhibition also promotes a faster entrainment, with the microcircuit needing less time to converge to the fully entrained state. We suggest that divisive inhibition, working alongside subtractive inhibition, allows for more adaptive oscillatory responses in neocortical circuits and, thus, supports healthy brain functioning.NEW & NOTEWORTHY We introduce a computational neocortical microcircuit model that features two inhibitory neural populations, with one providing subtractive and the other divisive inhibition to the excitatory population. We demonstrate that divisive inhibition widens the range of input frequencies to which the microcircuit can become entrained and diminishes the time needed to reach full entrainment. We suggest that divisive inhibition enables more adaptive oscillatory activity, with important implications for both normal and pathological brain function.

Optogenetic stimulation of the pre‐Bötzinger Complex and the control of breathing in a mouse model of Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disorder well known for its progressive loss of dopaminergic neurons in the substantia nigra compacta (SNpc). Much less known, yet clinically very important, are the detrimental effects on breathing associated with this disease. Studies in the 6‐hydroxydopamine (6‐OHDA) rat model of PD revealed reductions of respiratory frequency (fR) and NK1r‐immunoreactivity in the pre‐Bötzinger complex (preBötC), a medullary region critical for generating inspiration. To unravel mechanisms that underlie breathing disturbances in PD, we used a transgenic approach to specifically label or stimulate different excitatory (Dbx1‐ERT2Cre, Vglut2‐Cre) and inhibitory (Vgat‐Cre) neural populations in the preBötC. Homozygous Cre mice were bred with homozygous Ai6 (ZsGreen) or Ai32 (ChR2) mice. Adult offspring then received bilateral injections of vehicle or 6‐OHDA (10 μg/μl) into the striatum (CPu) to induce PD; and Ai32 mice also received preBötC fiber optic cannulation. 10–12 days later, whole body plethysmography was used to measure ventilation at rest and during optogenetic photo‐stimulation of the preBötC in unanaesthetized and unrestrained mice. As expected, fR at rest was reduced by 24.9% in PD mice (154.6 ± 6.0 vs. vehicle: 205.9 ± 3.7 bpm, p<0.05). Dbx1 photo‐stimulation during the inspiratory phase did not affect the rhythm in control animals, but increased fR by 17% in PD animals. Similarly, Vglut2 photo‐stimulation in control animals did not change the rhythm, but increased fR by 30% in PD animals. No changes were elicited by photo‐stimulation during expiration. Photo‐stimulation of preBötC inhibitory Vgat neurons during inspiration increased fR by 21%, but only in vehicle‐injected mice; no changes were observed in PD mice. Histology confirmed that 6‐OHDA injections reduced the number of catecholaminergic neurons in the SNpc by 69% (150.4 ± 4.9 vs. vehicle: 494.7 ± 14.5 cells). Surprisingly, the number of Dbx1 and Vglut2 neurons in the preBötC and the adjacent ventral respiratory column (VRC) were also reduced by 47.6 and 17.3%, respectively (p<0.05), whereas the number of Vgat neurons did not change. In conclusion, our study reveals that the 6‐OHDA model of PD is associated with a specific reduction in the number of excitatory neurons within the preBötC, which includes rhythmogenic Dbx1 neurons. Photo‐stimulating specifically these neurons can restore breathing in this PD mouse model.Support or Funding InformationNIH and FAPESP.This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Chemosensory modulation of neural circuits for sodium appetite.

Sodium is the main cation in the extracellular fluid that regulates various physiological functions. Sodium-depletion in the body elevates the hedonic value of sodium taste, which drives animals toward sodium consumption 1,2. Conversely, oral sodium detection rapidly promotes satiation of sodium appetite 3,4, suggesting that chemosensory signals have a central role in sodium appetite and its satiety. Nevertheless, the neural basis of chemosensory-based appetite regulation remains poorly understood. Here, we dissect genetically-defined neural circuits in mice that control sodium intake by integrating sodium taste and internal depletion signals. We show that a subset of excitatory neurons in the pre-locus coeruleus (pre-LC) that express prodynorphin (PDYN) serve as a critical neural substrate for sodium intake behavior. Acute stimulation of this population triggered robust sodium ingestion even from rock salt by transmitting negative valence signals. Inhibition of the same neurons selectively reduced sodium consumption. We further demonstrate that peripheral chemosensory signals rapidly suppressed these sodium appetite neurons. Simultaneous in vivo optical recording and gastric infusion revealed that sensory detection of sodium, but not sodium ingestion per se, is required for the acute modulation of pre-LC PDYN neurons and satiety of sodium appetite. Moreover, retrograde virus tracing showed that sensory modulation is partly mediated by specific GABAergic neurons in the bed nucleus of the stria terminalis. This inhibitory neural population is activated upon sodium ingestion, and sends rapid inhibitory signals to sodium appetite neurons. Together, this study reveals a dynamic circuit diagram that integrates chemosensory signals and the internal need to maintain sodium balance.

Simulating laminar neuroimaging data for a visual delayed match-to-sample task

Invasive electrophysiological and neuroanatomical studies in nonhuman mammalian experimental preparations have helped elucidate the lamina (layer) dependence of neural computations and interregional connections. Noninvasive functional neuroimaging can, in principle, resolve cortical laminae (layers), and thus provide insight into human neural computations and interregional connections. However human neuroimaging data are noisy and difficult to interpret; biologically realistic simulations can aid experimental interpretation by relating the neuroimaging data to simulated neural activity. We illustrate the potential of laminar neuroimaging by upgrading an existing large-scale, multiregion neural model that simulates a visual delayed match-to-sample (DMS) task. The new laminar-based neural unit incorporates spiny stellate, pyramidal, and inhibitory neural populations which are divided among supragranular, granular, and infragranular laminae (layers). We simulated neural activity which is translated into local field potential-like data used to simulate conventional and laminar fMRI activity. We implemented the laminar connectivity schemes proposed by Felleman and Van Essen (Cerebral Cortex, 1991) for interregional connections. The hemodynamic model that we employ is a modified version of one due to Heinzle et al. (Neuroimage, 2016) that incorporates the effects of draining veins. We show that the laminar version of the model replicates the findings of the existing model. The laminar model shows the finer structure in fMRI activity and functional connectivity. Laminar differences in the magnitude of neural activities are a prominent finding; these are also visible in the simulated fMRI. We illustrate differences between task and control conditions in the fMRI signal, and demonstrate differences in interregional laminar functional connectivity that reflect the underlying connectivity scheme. These results indicate that multi-layer computational models can aid in interpreting layer-specific fMRI, and suggest that increased use of laminar fMRI could provide unique and fundamental insights to human neuroscience.

Average activity of excitatory and inhibitory neural populations.

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.

Closed-loop firing rate regulation of two interacting excitatory and inhibitory neural populations of the basal ganglia.

This paper develops a new closed-loop firing rate regulation strategy for a population of neurons in the subthalamic nucleus, derived using a model-based analysis of the basal ganglia. The system is described using a firing rate model, in order to analyse the generation of beta-band oscillations. On this system, a proportional regulation of the firing rate reduces the gain of the subthalamo-pallidal loop in the parkinsonian case, thus impeding pathological oscillation generation. A filter with a well-chosen frequency is added to this proportional scheme, in order to avoid a potential instability of the feedback loop due to actuation and measurement delays. Our main result is a set of conditions on the parameters of the stimulation strategy that guarantee both its stability and a prescribed delay margin. A discussion on the applicability of the proposed method and a complete set of mathematical proofs is included.

A canonical circuit for generating phase-amplitude coupling.

‘Phase amplitude coupling’ (PAC) in oscillatory neural activity describes a phenomenon whereby the amplitude of higher frequency activity is modulated by the phase of lower frequency activity. Such coupled oscillatory activity – also referred to as ‘cross-frequency coupling’ or ‘nested rhythms’ – has been shown to occur in a number of brain regions and at behaviorally relevant time points during cognitive tasks; this suggests functional relevance, but the circuit mechanisms of PAC generation remain unclear. In this paper we present a model of a canonical circuit for generating PAC activity, showing how interconnected excitatory and inhibitory neural populations can be periodically shifted in to and out of oscillatory firing patterns by afferent drive, hence generating higher frequency oscillations phase-locked to a lower frequency, oscillating input signal. Since many brain regions contain mutually connected excitatory-inhibitory populations receiving oscillatory input, the simplicity of the mechanism generating PAC in such networks may explain the ubiquity of PAC across diverse neural systems and behaviors. Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. Consequently, this model can inform attempts to associate distinct types of PAC with different network topologies and physiologies in real data.

Balanced cortical microcircuitry for spatial working memory based on corrective feedback control.

A hallmark of working memory is the ability to maintain graded representations of both the spatial location and amplitude of a memorized stimulus. Previous work has identified a neural correlate of spatial working memory in the persistent maintenance of spatially specific patterns of neural activity. How such activity is maintained by neocortical circuits remains unknown. Traditional models of working memory maintain analog representations of either the spatial location or the amplitude of a stimulus, but not both. Furthermore, although most previous models require local excitation and lateral inhibition to maintain spatially localized persistent activity stably, the substrate for lateral inhibitory feedback pathways is unclear. Here, we suggest an alternative model for spatial working memory that is capable of maintaining analog representations of both the spatial location and amplitude of a stimulus, and that does not rely on long-range feedback inhibition. The model consists of a functionally columnar network of recurrently connected excitatory and inhibitory neural populations. When excitation and inhibition are balanced in strength but offset in time, drifts in activity trigger spatially specific negative feedback that corrects memory decay. The resulting networks can temporally integrate inputs at any spatial location, are robust against many commonly considered perturbations in network parameters, and, when implemented in a spiking model, generate irregular neural firing characteristic of that observed experimentally during persistent activity. This work suggests balanced excitatory-inhibitory memory circuits implementing corrective negative feedback as a substrate for spatial working memory.

Some Joys and Trials of Mathematical Neuroscience

I describe the basic components of the nervous system—neurons and their connections via chemical synapses and electrical gap junctions—and review the model for the action potential produced by a single neuron, proposed by Hodgkin and Huxley (HH) over 60 years ago. I then review simplifications of the HH model and extensions that address bursting behavior typical of motoneurons, and describe some models of neural circuits found in pattern generators for locomotion. Such circuits can be studied and modeled in relative isolation from the central nervous system and brain, but the brain itself (and especially the human cortex) presents a much greater challenge due to the huge numbers of neurons and synapses involved. Nonetheless, simple stochastic accumulator models can reproduce both behavioral and electrophysiological data and offer explanations for human behavior in perceptual decisions. In the second part of the paper I introduce these models and describe their relation to an optimal strategy for identifying a signal obscured by noise, thus providing a norm against which behavior can be assessed and suggesting reasons for suboptimal performance. Accumulators describe average activities in brain areas associated with the stimuli and response modes used in the experiments, and they can be derived, albeit non-rigorously, from simplified HH models of excitatory and inhibitory neural populations. Finally, I note topics excluded due to space constraints and identify some open problems.