Journal of Computational Neuroscience

The development of many feedforward pathways in the brain, from sensory inputs to neocortex, have been studied and modeled extensively, but the development of feedback connections, which tend to occur after the development of feedforward pathways, have received less attention. The abundance of feedback connections within neocortex and between neocortex and thalamus suggests that understanding feedback connections is crucial to understanding connectivity and signal processing in the brain. It is well known that many neural layers are arranged topologically with respect to sensory input, and many neural models impose a symmetry of connections between layers, commonly referred to as reciprocal connectivity. Here, we are concerned with how such reciprocal, feedback connections develop so that the topology of the sensory input is preserved. We focus on feedback connections from layer 6 of visual area V1 to primary neurons in the Lateral Geniculate Nucleus (LGN). The proposed model is based on the hypothesis that feedback connections from V1-L6 to LGN use voltage-activated T-channels to appropriately establish and modify synapses in spite of unavoidable temporal delays. We also hypothesize that developmental spindling relates to synaptogenesis and memory consolidation.

Excitable cells exhibit different electrophysiological profiles while responding to current stimulation in current-clamp experiments. In theory, the differences could be explained by changes in the expression of proteins mediating transmembrane ion transport. Experimental verification by performing systematic, controlled variations in the expression of proteins of the same type (e.g. voltage-dependent, noninactivating Kv2.1 channels) is difficult to achieve in the absence of other changes. However, biophysical models enable this possibility and allows us to assess and characterise the electrophysiological phenotypes associated to different levels of expression of non-inactivating voltage-dependent K-channels of type Kv2.1. To do so, we use a 2-dimensional biophysical model of neuronal membrane potential and study the phase plane geometry and bifurcation structures associated with different levels of Kv2.1 expression with the input current as bifurcation parameter. We find that increasing the expression of Kv2.1 channels reduces the size of the region of the phase plane from which action potentials can be initiated. The changes in expression can also be related to different transitions between rest and repetitive firing in current clamp experiments. For instance, increasing the number of Kv2.1 channels shifts the rheobase current to higher levels, but also expands the dynamic range in which excitatory external current produces repetitive spiking. Our analysis shows that changes in the responses to increasing input currents can be associated to different sequences of fixed point bifurcations. In general, the fixed points are attracting, then repulsive, and later become attracting again as the input current increases, but the bifurcation sequences also include changes in fixed point type, and change qualitatively with the expression of Kv2.1 channels. In the non-repetitive spiking regime with low current stimulation, low expression of Kv2.1 channels yields bifurcation sequences that include transitions between 3 and 1 fixed points, and repetitive firing starts with delays that decrease with increasing current (aggregation). For higher expression of Kv2.1 channels there is only one fixed point that changes in type and attractivity as the input current increases, convergence to rest tends to be oscillatory (resonance), and repetitive spiking starts without noticeable delays. Our models explain how the same neuron is theoretically be capable of including both aggregating and resonant modes of integration for synaptic input, as shown in current clamp experiments.

Purkinje cells are the principal neurons of the cerebellar cortex. One of their distinguishing features is that they fire two distinct types of action potential, called simple and complex spikes, which interact with one another. Simple spikes are stereotypical action potentials that are elicited at high, but variable, rates (0 - 100 Hz) and have a consistent waveform. Complex spikes are composed of an initial action potential followed by a burst of lower amplitude spikelets. Complex spikes occur at comparatively low rates (~ 1 Hz) and have a variable waveform. Although they are critical to cerebellar operation a simple model that describes the complex spike waveform is lacking. Here, a novel single-compartment model of Purkinje cell electrodynamics is presented. The simpler version of this model, with two active conductances and a leak channel, can simulate the features typical of complex spikes recorded in vitro. If calcium dynamics are also included, the model can capture the pause in simple spike activity that occurs after complex spike events. Together, these models provide an insight into the mechanisms behind complex spike spikelet generation, waveform variability and their interactions with simple spike activity.

PurposeOscillations in the primary visual cortex of the mammalian brain have been demonstrated to arise from the balance between excitatory and inhibitory activity. Experimental studies suggest that different inhibitory neuron populations might make specific contributions to such oscillations, but the underlying mechanism has not yet been assessed. MethodsWe modified a standard excitatory-inhibitory spiking neuron model of layer 4 of the primary visual cortex and we investigated the effects on oscillations of the differentiation of inhibitory neurons in somatostatin and parvalbumin neurons. ResultsOur model reproduced the hypothesis that somatostatin and parvalbumin neurons are responsible for beta (15-25)Hz and gamma (40-70)Hz band oscillations, respectively. ConclusionTo date, this is the simplest model accounting for this phenomenon and could therefore be suited to study pathologies in which the two populations have specific roles, such as migraine.

AO_SCPLOWBSTRACTC_SCPLOWBoth subtractive and divisive inhibition has been recorded in cortical circuits and recent findings suggest that different interneuronal populations are responsible for the different types of inhibition. This calls for the formulation and description of these inhibitory mechanisms in computational models of cortical networks. Neural mass and neural field models typically only feature subtractive inhibition. Here, we introduce how divisive inhibition can be incorporated in such models, using the Wilson-Cowan modelling formalism as an example. In addition, we show how the subtractive and divisive modulations can be combined. Including divisive inhibition in neural mass models is a crucial step in understanding its role in shaping oscillatory phenomena in cortical networks.

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro. We examine the properties of these waves as inhibition varies in a cortical slice and then develop several computational models. We first show that in the slice, inhibition controls the velocity of propagation as well as the magnitude of the local field potential. We introduce a spiking model of sparsely connected excitatory and inhibitory theta neurons which are distributed on a one-dimensional domain and illustrate both evoked and spontaneous waves. The excitatory neurons have an additional spike-frequency adaptation current which limits their maximal activity. We show that increased inhibition slows the waves down and limits the participation of excitatory cells in this spiking network. Decreased inhibition leads to large amplitude faster moving waves similar to those seen in seizures. To gain further insight into the mechanism that control the waves, we then systematically reduce the model to a Wilson-Cowan type network using a mean-field approach. We simulate this network directly and by using numerical continuation to follow traveling waves in a moving coordinate system as we vary the strength and spread of inhibition and the strength of adaptation. We find several types of instability (bifurcations) that lead to the loss of waves and subsequent pattern formation. We approximate the smooth nonlinearity by a step function and obtain expressions for the velocity, wave-width, and stability. Author summaryStimuli and other aspects of neuronal activity are carried across areas in the brain through the concerted activity of recurrently connected neurons. The activity is controlled through negative feedback from both inhibitory neurons and intrinsic currents in the excitatory neurons. Evoked activity often appears in the form of a traveling pulse of activity. In this paper we study the speed, magnitude, and other properteis of these waves as various aspects of the negative feedback are altered. Inhibition enables information to be readily transmitted across distances without the neural activity blowing up into a seizure-like state.

The preBotzinger complex of the lower brainstem generates two breathing-related rhythms: one for inspiration on a timescale of seconds, and another that produces larger amplitude sighs on the order of minutes. We hypothesize that these two disparate rhythms emerge in tandem wherein recurrent excitation gives rise to the inspiratory rhythm while a calcium oscillator generates sighs; distinct neuronal populations are not required. We present several mathematical models that instantiate our working hypothesis including: (1) an activity (firing rate) model and (2) a minimal spiking network model. Both modeling frameworks corroborate the single-population rhythmogenic hypothesis.

Activity-dependent modifications of synaptic efficacies are a cellular substrate of learning and memory. Current theories propose that the long-term maintenance of synaptic efficacies and memory is accomplished via a positive-feedback loop at the level of production of a protein species or a protein state. Here we propose a qualitatively different theoretical framework based on negative feedback at the level of protein elimination. This theory is motivated by recent experimental findings regarding the binding of PKM{zeta} and KI-BRA, two synaptic proteins involved in maintenance of memory, and on how this binding downregulates the proteins degradation. We demonstrate this theoretical framework with two different models. First, a simple abstract model to explore generic features of the negative-feedback process. Second, a biophysical model based on PKM{zeta}-KIBRA dimers that cooperatively form larger complexes at active synapses. These larger complexes have slower degradation and diffusion, allowing for bistability of potentiated and unpotentiated synaptic states. The results of these models are qualitatively consistent with existing experiments showing reversal of long-term potentiation and erasure of long-term memory by inhibition of KIBRA-PKM{zeta} interactions. The theory generates novel predictions that could be experimentally tested to further validate or reject the negative-feedback theory.

Working memory is an essential human trait required for all cognitive activities. Our previous model from Mongillo et al. (1), Mi et al. (2) uses synaptic facilitation to store traces of working memory. Thus memories can be maintained without persistent neural activity. A critical component of this model is a central inhibition which prevents multiple item representations from being active at the same time. We know from experimental studies that multiple genetically-defined interneuron subtypes (e.g. PV, SOM) with different excitability and connectivity properties mediate inhibition in the cortex. The role of these sub-types in working memory however is not known. Here we develop a modified model with these interneuron subtypes, and propose their functional roles in working memory. We make concrete testable predictions about the roles of these groups.

In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an Action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. Interestingly, we find regimes for noise amplification that specifically occur when the inhibitory synapse has a low probability of release for synaptic vesicles. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.

We demonstrate how neuromodulation and spatially targetted inhibition can alter the integration of the two streams of excitatory input in a thick-tufted layer 5 pyramidal cell, using a computational reduced-compartmental cell models. Choosing suitable ranges of brief current stimulus amplitudes, applied basally to either the soma or basal dendrites (basal stimulation) and to the apical tuft (apical stimulation) results in burst firing due to either stimulus alone, if strong enough, or by a combination of the stimuli at lower amplitudes. Applying tonic inhibition to the apical tuft removes the ability of apical input alone to generate a burst over the chosen amplitude range. A similar effect is achieved by reducing the tuft calcium channel conductance as an outcome of neuromodulation. Similarly, tonic inhibition to the basal dendrites removes the ability of basal stimulation alone to generate a burst, without blocking bursts resulting from apical calcium spikes. HCN channels in the apical dendrites may amplify or reduce bursting probability, depending on other active and passive properties of dendrites. So neuromodulation that decreases the conductance of these channels may act to reduce or increase bursting probability across the across the ranges of basal and apical inputs, depending on cell properties. These effects mimic those found previously by simply limiting the range of stimulus amplitudes (Graham et al., 2025) but now show that such changes in two-stream signal integration can happen through network inhibition and neuromodulation with no change in the excitatory driving stimulus strengths. These changes in signal integration also lead to changes in information transmitted by the cells bursting probability about the two input streams, as shown in Graham et al. (2025). Changes in cell morphology are also investigated by reducing the apical trunk length and are revealed to alter this two-stream signal integration through differential effects on passive and active interaction between the soma and apical tuft.

Understanding the retina in health and disease is a key issue for neuroscience and neuroengineering applications such as retinal prostheses. During degeneration, the retinal network undergoes complex and multi-stage neuroanatomical alterations, which drastically impact the retinal ganglion cell (RGC) response and are of clinical importance. Here we present a biophysically detailed in silico model of retinal degeneration that simulates the network-level response to both light and electrical stimulation as a function of disease progression. The model is not only able to reproduce common findings about RGC activity in the degenerated retina, such as hyperactivity and increased electrical thresholds, but also offers testable predictions about the underlying neuroanatomical mechanisms. Overall, our findings demonstrate how biophysical changes associated with retinal degeneration affect retinal responses to both light and electrical stimulation, which may further our understanding of visual processing in the retina as well as inform the design and application of retinal prostheses.

Using simulation and a simple mathematical argument we argue that the refresh rate of overhead projectors, used in experiments on the visual system, may impact the perception of fast moving objects at the retinal and cortical level (V1), and thereby at the level of psychophysics.

Neurons form the fundamental unit of the central nervous system with the human brain containing close to 100 billion neurons. We present a systems-level model of a chemical synapse by which signals from a presynaptic neuron are transmitted to a postsynaptic neuron. In this model, neurotransmitter-filled synaptic vesicles (SVs) dock with a given rate at a fixed number of docking sites in the axon terminal of the presynaptic neuron. Upon the arrival of an action potential (AP), each docked SV has a certain probability to fuse with the presynaptic membrane and release neurotransmitters into the synaptic cleft. After the SV fusion event, the corresponding docking site undergoes repair before becoming available to be reoccupied by an SV. We develop a stochastic model of these coupled processes and derive exact analytical results quantifying the mean and the degree of random fluctuations (i.e., noise) in the levels of docked SVs and released neurotransmitters in response to a train of APs. Our results show that the repair of docking sites exacerbates synaptic depression, i.e., reduces the ability of the chemical synapse to release neurotransmitters in response to an AP. Moreover, repair amplifies statistical fluctuations in neurotransmission for fixed mean neurotransmitter levels. We next consider feedback regulation where the released neurotransmitters affect the rate of SV docking. Counterintuitively, our analysis reveals that for certain physiological parameter spaces, positive feedback loops can reduce noise levels in both the number of docked SVs and neurotransmitters in the cleft.

Epileptic seizures are characterized by abnormal synchronous bursting of neurons. This is commonly attributed to an imbalance between excitatory and inhibitory neurotransmission. We introduce compartmental models from epidemiology to study this interaction between excitatory and inhibitory populations of neurons in the context of epilepsy. Neurons could either be bursting or susceptible, and the propagation of action potentials within the brain through the bursting of neurons is considered as an infection spreading through a population. We model the recruitment of neurons into bursting and their subsequent decay to susceptibility to be influenced by the proportion of excitatory and inhibitory neurons bursting, resulting in a two population Susceptible - Infected - Susceptible (SIS) model. This approach provides a tractable framework to inspect the mechanisms behind seizure generation and termination. Considering the excitatory neurotransmission as an epidemic spreading through the neuronal population and the inhibitory neurotransmission as a competing epidemic that stops the spread of excitation, we establish the conditions for a seizure-like state to be stable. Subsequently, we show how an activity-dependent dysfunction of inhibitory mechanisms such as impaired GABAergic inhibition or inhibitory-inhibitory interactions could result in a seizure even when the above conditions are not satisfied.

We formulate a mechanistic model capturing the dynamics of neurotransmitter release in a chemical synapse. The proposed modeling framework captures key aspects such as the random arrival of action potentials (AP) in the presynaptic (input) neuron, probabilistic docking and release of neurotransmitter-filled vesicles, and clearance of the released neurotransmitter from the synaptic cleft. Feedback regulation is implemented by having the released neurotransmitter impact the vesicle docking rate that occurs biologically through "autoreceptors" on the presynaptic membrane. Our analytical results show that these feedbacks can amplify or buffer fluctuations in neurotransmitter levels depending on the relative interplay of neurotransmitter clearance rate with the AP arrival rate and the vesicle replenishment rate, with faster clearance rates leading to noise amplification. We next consider a postsynaptic (output) neuron that fires an AP based on integrating upstream neurotransmitter activity. Investigating the postsynaptic AP firing times, we identify scenarios that lead to band-pass filtering, i.e., the output neuron frequency is maximized at intermediate input neuron frequencies. We extend these results to consider feedforward regulation where in addition to a direct excitatory synapse, the input neuron also impacts the output indirectly via an inhibitory interneuron, and we identify parameter regimes where feedforward neuronal networks result in band-pass filtering.

Cortical spreading depression (CSD) is thought to precede migraine attacks with aura and is characterized by a slowly traveling wave of inactivity through cortical pyramidal cells. During CSD, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that propagates slowly across the cortex. While the identifying characteristic of CSD is the pyramidal cell hyperexcitation and subsequent spike block, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of CSD. We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block and CSD. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit.

GABA is generally known as the principal inhibitory neurotransmitter in the nervous system, usually acting by hyperpolarizing membrane potential. However, GABAergic currents sometimes exhibit non-inhibitory effects, depending on the brain region, developmental stage or pathological condition. Here, we investigate the diverse effects of GABA on the firing rate of several single neuron models, using both analytical calculations and numerical simulations. We find that GABAergic synaptic conductance and output firing rate exhibit three qualitatively different regimes as a function of GABA reversal potential, EGABA: monotonically decreasing for sufficiently low EGABA (inhibitory), monotonically increasing for EGABA above firing threshold (excitatory); and a non-monotonic region for intermediate values of EGABA. In the non-monotonic regime, small GABA conductances have an excitatory effect while large GABA conductances show an inhibitory effect. We provide a phase diagram of different GABAergic effects as a function of GABA reversal potential and glutamate conductance. We find that noisy inputs increase the range of EGABA for which the non-monotonic effect can be observed. We also construct a micro-circuit model of striatum to explain observed effects of GABAergic fast spiking interneurons on spiny projection neurons, including non-monotonicity, as well as the heterogeneity of the effects. Our work provides a mechanistic explanation of paradoxical effects of GABAergic synaptic inputs, with implications for understanding the effects of GABA in neural computation and development. Author summaryNeurons in nervous systems mainly communicate at chemical synapses by releasing neurotransmitters from the presynaptic side that bind to receptors on the post-synaptic side, triggering ion flow through ion channels on the cell membrane and changes in the membrane potential of the post-synaptic neuron. Gamma-aminobutyric acid (GABA) is the principal neurotransmitter expressed by inhibitory neurons. Its binding to GABAergic ionotropic receptors mainly causes a flow of chloride ions across the membrane, and typically hyperpolarizes the post-synaptic neuron, resulting in firing suppression. While GABA is canonically viewed as an inhibitory neurotransmitter, non-inhibitory effects have been observed in early stages of development, in stress-related disorders, and in specific parts of brain structures such as cortex, cerebellum and hippocampus [1-4]. Here, we employ analytical and computational approaches on spiking neuronal models to investigate the mechanisms of diverse effects of GABAergic synaptic inputs. We find that in addition to monotonically excitatory or monotonically inhibitory effects, GABAergic inputs show non-monotonic effects, for which the effect depends on the strength of the input. This effect is stronger in the presence of noise, and is observed in different models both at the single cell, and at the network level. Our findings provide a mechanistic explanation of several paradoxical experimental observations, with potential implications for neural network dynamics and computation.

Neuronal networks maintain robust patterns of activity despite a backdrop of noise from various sources. Mutually inhibiting neurons is a standard network motif implicated in rhythm generation. In an elementary network motif of two neurons capable of swapping from an active state to a quiescent state, we ask how different sources of stochasticity alter firing patterns. In this system, the alternating activity occurs via combined action of a calcium-dependent potassium current, sAHP (slow afterhyperpolarization), and a fast GABAergic synapse. We show that simulating extrinsic noise arising from background activity extends the dynamical range of neuronal firing. Extrinsic noise also has the effect of increasing the switching frequency via a faster build-up of sAHP current. We show that switching frequency as a function of input current has a non-monotonic behavior. Interestingly the noise tolerance of this system varies with the input current. It shows maximum robustness to noise at an input current that corresponds to the minimum switching frequency between the neurons. The slow decay time scale of sAHP conductance allows neurons to act as a low-pass filter, attenuate noise, and integrate over ion channel fluctuations. Additionally, we show that the slow inactivation time of the sAHP channel allows the neuron to act as an action potential counter. We propose that this intrinsic property of the current allows the network to maintain rhythmic activity critical for various functions, despite the noise, and operate as a temporal integrator.

1Traveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves evolution are synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model to investigate the propagation characteristics of traveling wave activity. We formulated a set of evolution equations based on the network connectivity parameters. We numerically investigated the stability of the traveling wave propagation with a series of perturbations with biological relevance.