Inverse Stochastic Resonance in Cerebellar Purkinje Cells

Inverse stochastic resonance in a two-dimensional airfoil system with nonlinear pitching stiffness driven by Lévy noise

The aircraft can experience complex environments during the flight. For the random actions, the traditional Gaussian white noise assumption may not be sufficient to depict the realistic stochastic loads on the wing structures. Considering fluctuations with extreme conditions, Lévy noise is a better candidate describing the stochastic dynamical behaviors on the airfoil models. In this paper, we investigated a classical two-dimensional airfoil model with the nonlinear pitching stiffness subjected to the Lévy noise. For the deterministic case, the nonlinear stiffness coefficients reshape the bistable region, which influences the size of the large limit cycle oscillations before the flutter speed. The introduction of the additive Lévy noise can induce significant inverse stochastic resonance phenomena when the basin of attraction of the stable limit cycle is much smaller than that of the stable fixed point. The distribution parameters of the Lévy noise exhibit distinct impacts on the inverse stochastic resonance curves. Our results may shed some light on the design and control process of the airfoil models.

Inverse stochastic resonance in adaptive small-world neural networks

Inverse stochastic resonance (ISR) is a counterintuitive phenomenon where noise reduces the oscillation frequency of an oscillator to a minimum occurring at an intermediate noise intensity, and sometimes even to the complete absence of oscillations. In neuroscience, ISR was first experimentally verified with cerebellar Purkinje neurons [Buchin et al., PLOS Comput. Biol. 12, e1005000 (2016)]. These experiments showed that ISR enables a locally optimal information transfer between the input and output spike train of neurons. Subsequent studies have further demonstrated the efficiency of information processing and transfer in neural networks with small-world network topology. We have conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bi-metastable regime consisting of a metastable fixed point and a metastable limit cycle. Our results show that the degree of ISR is highly dependent on the value of the FHN model's timescale separation parameter ε. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter P or homeostatic structural plasticity (HSP) with rewiring frequency F. We demonstrate that both STDP and HSP amplify the effect of ISR when ε lies within the bi-stability region of FHN neurons. Specifically, at larger values of ε within the bi-stability regime, higher rewiring frequencies F are observed to enhance ISR at intermediate (weak) synaptic noise intensities, while values of P consistent with depression-domination (potentiation-domination) consistently enhance (deteriorate) ISR. Moreover, although STDP and HSP control parameters may jointly enhance ISR, P has a greater impact on improving ISR compared to F. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize local information transfer between input and output spike trains in neuromorphic systems and prompt venues for experiments in neural networks.

No effects of cerebellar transcranial random noise stimulation on cerebellar brain inhibition, visuomotor learning, and pupil diameter

Cerebellar brain inhibition (CBI) is an inhibitory output from the cerebellum to the primary motor cortex, which is decreased in early motor learning. Transcranial random noise stimulation (tRNS) is a noninvasive brain stimulation to induce brain plastic changes; however, the effects of cerebellar tRNS on CBI and motor learning have not been investigated yet to our knowledge. In this study, whether cerebellar tRNS decreases CBI and improves motor learning was examined, and pupil diameter was measured to examine physiological changes due to the effect of tRNS on motor learning. Thirty-four healthy subjects were assigned to either the cerebellar tRNS group or the Sham group. The subjects performed visuomotor tracking task with ten trials each in the early and late learning stages while receiving the stimulus intervention. CBI and motor evoked potentials were measured before the learning task, after the early learning stage, and after the late learning stage, and pupil diameter was measured during the task. There was no change in CBI in both groups. No group differences in motor learning rates were observed at any learning stages. Pupil diameter was smaller in the late learning stage than in the early learning stage in both groups. The cerebellar tRNS was suggested not to induce changes in CBI and improvement in motor learning, and it did not affect pupil diameter.

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

[The inverse stochastic resonance in a small-world neuronal network under electromagnetic stimulation]

Electromagnetic stimulation is an important neuromodulation technique that modulates the electrical activity of neurons and affects cortical excitability for the purpose of modulating the nervous system. The phenomenon of inverse stochastic resonance is a response mechanism of the biological nervous system to external signals and plays an important role in the signal processing of the nervous system. In this paper, a small-world neural network with electrical synaptic connections was constructed, and the inverse stochastic resonance of the small-world neural network under electromagnetic stimulation was investigated by analyzing the dynamics of the neural network. The results showed that: the Levy channel noise under electromagnetic stimulation could cause the occurrence of inverse stochastic resonance in small-world neural networks; the characteristic index and location parameter of the noise had significant effects on the intensity and duration of the inverse stochastic resonance in neural networks; the larger the probability of randomly adding edges and the number of nearest neighbor nodes in small-world networks, the more favorable the anti-stochastic resonance was; by adjusting the electromagnetic stimulation parameters, a dual regulation of the inverse stochastic resonance of the neural network can be achieved. The results of this study provide some theoretical support for exploring the regulation mechanism of electromagnetic nerve stimulation technology and the signal processing mechanism of nervous system.

Characterizing the information transmission of inverse stochastic resonance and noise-induced activity amplification in neuronal systems

Purkinje cells exhibit a reduction of the mean firing rate at intermediate-noise intensities, which is somewhat reminiscent of the response enhancement known as "stochastic resonance" (SR). Although the comparison with the stochastic resonance ends here, the current phenomenon has been given the name "inverse stochastic resonance" (ISR). Recent research has demonstrated that the ISR effect, like its close relative "nonstandard SR" [or, more correctly, noise-induced activity amplification (NIAA)], has been shown to stem from the weak-noise quenching of the initial distribution, in bistable regimes where the metastable state has a larger attraction basin than the global minimum. To understand the underlying mechanism of the ISR and NIAA phenomena, we study the probability distribution function of a one-dimensional system subjected to a bistable potential that has the property of symmetry, i.e., if we change the sign of one of its parameters, we can obtain both phenomena with the same properties in the depth of the wells and the width of their basins of attraction subjected to Gaussian white noise with variable intensity. Previous work has shown that one can theoretically determine the probability distribution function using the convex sum between the behavior at small and high noise intensities. To determine the probability distribution function more precisely, we resort to the "weighted ensemble Brownian dynamics simulation" model, which provides an accurate estimate of the probability distribution function for both low and high noise intensities and, most importantly, for the transition of both behaviors. In this way, on the one hand, we show that both phenomena emerge from a metastable system where, in the case of ISR, the global minimum of the system is in a state of lower activity, while in the case of NIAA, the global minimum is in a state of increased activity, the importance of which does not depend on the width of the basins of attraction. On the other hand, we see that quantifiers such as Fisher information, statistical complexity, and especially Shannon entropy fail to distinguish them, but they show the existence of the mentioned phenomena. Thus, noise management may well be a mechanism by which Purkinje cells find an efficient way to transmit information in the cerebral cortex.

Bistability at the onset of neuronal oscillations

The Hodgkin-Huxley (HH) model and squid axon (bathed in reduced Ca²⁺) fire repetitively for steady current injection. Moreover, for a current-range just suprathreshold, repetitive firing coexists with a stable steady state. Neuronal excitability, as such, shows bistability and hysteresis providing the opportunity for the system to perform as switchable between firing and non-firing states with transient input and providing the backbone as a dynamical mechanism for bursting oscillations. Some conditions for bistability can be derived by intricate analysis (bifurcation theory) and characterized by simulation, but conditions for emergence and robustness of such bistability do not typically follow from intuition. Here, we demonstrate with a semi-quantitative two-variable, V-w, reduction of the HH model features that promote/reduce bistability. Visualization of flow and trajectories in the V-w phase plane provides an intuitive grasp for bistability. The geometry of action potential recovery involves a late phase during which the dynamic negative feedback of [Formula: see text] inactivation and [Formula: see text] activation over/undershoot, respectively, their resting values, thereby leading to hyperexcitabilty and an intrinsically generated opportunity to by-pass the spiral-like stable rest state and initiate the next spike upstroke. We illustrate control of bistability and dependence of the degree of hysteresis on recovery timescales and gating properties. Our dynamical dissection reveals the strongly attracting depolarized phase of the spike, enabling approximations like the resetting feature of adapting integrate-and-fire models. We extend our insights and show that the Morris-Lecar model can also exhibit robust bistability.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Lobule-Related Action Potential Shape- and History-Dependent Current Integration in Purkinje Cells of Adult and Developing Mice

Purkinje cells (PCs) are the principal cells of the cerebellar cortex and form a central element in the modular organization of the cerebellum. Differentiation of PCs based on gene expression profiles revealed two subpopulations with distinct connectivity, action potential firing and learning-induced activity changes. However, which basal cell physiological features underlie the differences between these subpopulations and to what extent they integrate input differentially remains largely unclear. Here, we investigate the cellular electrophysiological properties of PC subpopulation in adult and juvenile mice. We found that multiple fundamental cell physiological properties, including membrane resistance and various aspects of the action potential shape, differ between PCs from anterior and nodular lobules. Moreover, the two PC subpopulations also differed in the integration of negative and positive current steps as well as in size of the hyperpolarization-activated current. A comparative analysis in juvenile mice confirmed that most of these lobule-specific differences are already present at pre-weaning ages. Finally, we found that current integration in PCs is input history-dependent for both positive and negative currents, but this is not a distinctive feature between anterior and nodular PCs. Our results support the concept of a fundamental differentiation of PCs subpopulations in terms of cell physiological properties and current integration, yet reveals that history-dependent input processing is consistent across PC subtypes.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

Dynamics and Information Import in Recurrent Neural Networks

Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by the statistics of the neural connection weights, such as the density d of non-zero connections, or the balance b between excitatory and inhibitory connections. However, for information processing purposes, RNNs need to receive external input signals, and it is not clear which of the dynamical regimes is optimal for this information import. We use both the average correlations C and the mutual information I between the momentary input vector and the next system state vector as quantitative measures of information import and analyze their dependence on the balance and density of the network. Remarkably, both resulting phase diagrams C(b, d) and I(b, d) are highly consistent, pointing to a link between the dynamical systems and the information-processing approach to complex systems. Information import is maximal not at the "edge of chaos," which is optimally suited for computation, but surprisingly in the low-density chaotic regime and at the border between the chaotic and fixed point regime. Moreover, we find a completely new type of resonance phenomenon, which we call "Import Resonance" (IR), where the information import shows a maximum, i.e., a peak-like dependence on the coupling strength between the RNN and its external input. IR complements previously found Recurrence Resonance (RR), where correlation and mutual information of successive system states peak for a certain amplitude of noise added to the system. Both IR and RR can be exploited to optimize information processing in artificial neural networks and might also play a crucial role in biological neural systems.

Unified mechanism of inverse stochastic resonance for monostability and bistability in Hindmarsh-Rose neuron

Noise is ubiquitous and has been verified to play constructive roles in various systems, among which the inverse stochastic resonance (ISR) has aroused much attention in contrast to positive effects such as stochastic resonance. The ISR has been observed in both bistable and monostable systems for which the mechanisms are revealed as noise-induced biased switching and noise-enhanced stability, respectively. In this paper, we investigate the ISR phenomenon in the monostable and bistable Hindmarsh-Rose neurons within a unified framework of large deviation theory. The critical noise strengths for both cases can be obtained by matching the timescales between noise-induced boundary crossing and the limit cycle. Furthermore, different stages of ISR are revealed by the bursting frequency distribution, where the gradual increase of the peak bursting frequency can also be explained within the same framework. The perspective and results in this paper may shed some light on the understanding of the noise-induced complex phenomena in stochastic dynamical systems.

Noise induced quiescence of epileptic spike generation in patients with epilepsy

Clinical scalp electroencephalographic recordings from patients with epilepsy are distinguished by the presence of epileptic discharges i.e. spikes or sharp waves. These often occur randomly on a background of fluctuating potentials. The spike rate varies between different brain states (sleep and awake) and patients. Epileptogenic tissue and regions near these often show increased spike rates in comparison to other cortical regions. Several studies have shown a relation between spike rate and background activity although the underlying reason for this is still poorly understood. Both these processes, spike occurrence and background activity show evidence of being at least partly stochastic processes. In this study we show that epileptic discharges seen on scalp electroencephalographic recordings and background activity are driven at least partly by a common biological noise. Furthermore, our results indicate noise induced quiescence of spike generation which, in analogy with computational models of spiking, indicate spikes to be generated by transitions between semi-stable states of the brain, similar to the generation of epileptic seizure activity. The deepened physiological understanding of spike generation in epilepsy that this study provides could be useful in the electrophysiological assessment of different therapies for epilepsy including the effect of different drugs or electrical stimulation.

Progressive alignment of inhibitory and excitatory delay may drive a rapid developmental switch in cortical network dynamics

Nervous system maturation occurs on multiple levels-synaptic, circuit, and network-at divergent timescales. For example, many synaptic properties mature gradually, whereas emergent network dynamics can change abruptly. Here we combine experimental and theoretical approaches to investigate a sudden transition in spontaneous and sensory evoked thalamocortical activity necessary for the development of vision. Inspired by in vivo measurements of timescales and amplitudes of synaptic currents, we extend the Wilson and Cowan model to take into account the relative onset timing and amplitudes of inhibitory and excitatory neural population responses. We study this system as these parameters are varied within amplitudes and timescales consistent with developmental observations to identify the bifurcations of the dynamics that might explain the network behaviors in vivo. Our findings indicate that the inhibitory timing is a critical determinant of thalamocortical activity maturation; a gradual decay of the ratio of inhibitory to excitatory onset time drives the system through a bifurcation that leads to a sudden switch of the network spontaneous activity from high-amplitude oscillations to a nonoscillatory active state. This switch also drives a change from a threshold bursting to linear response to transient stimuli, also consistent with in vivo observation. Thus we show that inhibitory timing is likely critical to the development of network dynamics and may underlie rapid changes in activity without similarly rapid changes in the underlying synaptic and cellular parameters.NEW & NOTEWORTHY Relying on a generalization of the Wilson-Cowan model, which allows a solid analytic foundation for the understanding of the link between maturation of inhibition and network dynamics, we propose a potential explanation for the role of developing excitatory/inhibitory synaptic delays in mediating a sudden switch in thalamocortical visual activity preceding vision onset.

Two paradigmatic scenarios for inverse stochastic resonance

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.

Proprioceptive Focal Stimulation (Equistasi®) May Improve the Quality of Gait in Middle-Moderate Parkinson's Disease Patients. Double-Blind, Double-Dummy, Randomized, Crossover, Italian Multicentric Study

Objective: The object of the study was to evaluate the efficacy of Proprioceptive Focal Stimulation on Gait in middle—advanced Parkinson (PD) patients by a crossover, randomized, double Blind double dummy study using Equistasi®, a nano-technological device of the dimension of a plaster which generates High Frequency Vibration (FV).

Background: The efficacy of Gait Analysis (GA) on evaluating gait modification on Parkinson's disease (PD) Patients is already well-known. Therefore, GA was recorded in a group of PD patients using Equistasi® device and its placebo.

Methods: Forty PD patients on optimal therapy were enrolled in the study. Patients were randomly assigned to receive active or sham stimulation for 8 weeks and, following a wash-out period, switched to an additional 8-week period with the reverse intervention. GA was performed at baseline and at the end of both 8-weeks treatment periods Clinical state was monitored by MDUPDRS part III.

Results: Active stimulation induced a significant improvement in Mean Velocity (Velocity), Stride Length (SL), Stance (STA), and Double Support (DST) percentage, both in left and right stride. The ANOVA analysis using H&Y stage as a factor, showed that DST and MDUPDRS III scores improved significantly more in the more severely affected subjects.

Conclusions: The findings obtained in this randomized controlled study show the efficacy of mechanical focal vibration, as stimulation of the proprioceptive system, in PD and encourage further investigation. The effect of the device on more severe patients may open a new possibility to identify the most appropriate candidate for the management of gait disturbances and postural instability with FV delivered with Equistasi®.

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks.

Weak-noise-induced transitions with inhibition and modulation of neural oscillations

We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh-Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of this bi-stability. In the parametric zone of bi-stability, weak-noise amplitudes may strongly inhibit the neuron's spiking activity. Surprisingly, increasing the noise strength leads to a minimum in the spiking activity, after which the activity starts to increase monotonically with an increase in noise strength. We investigate this inhibition and modulation of neural oscillations by weak-noise amplitudes by looking at the variation of the mean number of spikes per unit time with the noise intensity. We show that this phenomenon always occurs when the initial conditions lie in the basin of attraction of the stable limit cycle. For initial conditions in the basin of attraction of the stable fixed point, the phenomenon, however, disappears, unless the timescale separation parameter of the model is bounded within some interval. We provide a theoretical explanation of this phenomenon in terms of the stochastic sensitivity functions of the attractors and their minimum Mahalanobis distances from the separatrix isolating the basins of attraction.

Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure

Pharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state.

A circuit mechanism of time-to-space conversion for perception

Sensory information in a temporal sequence is processed as a collective unit by the nervous system. The cellular mechanisms underlying how sequential inputs are incorporated into the brain has emerged as an important subject in neuroscience. Here, we hypothesize that information-bearing (IB) signals can be entrained and amplified by a clock signal, allowing them to efficiently propagate along in a feedforward circuit. IB signals can remain latent on individual dendrites of the receiving neurons until they are read out by an oscillatory clock signal. In such a way, the IB signals pass through the next neurons along a linear chain. This hypothesis identifies a cellular process of time-to-space and sound-to-map conversion in primary auditory cortex, providing insight into a mechanistic principle underlying the representation and memory of temporal sequences of information.

Beta-gamma burst stimulations of the inferior olive induce high-frequency oscillations in the deep cerebellar nuclei

The cerebellum displays various sorts of rhythmic activities covering both low- and high-frequency oscillations. These cerebellar high-frequency oscillations were observed in the cerebellar cortex. Here, we hypothesised that not only is the cerebellar cortex a generator of high-frequency oscillations but also that the deep cerebellar nuclei may also play a similar role. Thus, we analysed local field potentials and single-unit activities in the deep cerebellar nuclei before, during and after electric stimulation in the inferior olive of awake mice. A high-frequency oscillation of 350 Hz triggered by the stimulation of the inferior olive, within the beta-gamma range, was observed in the deep cerebellar nuclei. The amplitude and frequency of the oscillation were independent of the frequency of stimulation. This oscillation emerged during the period of stimulation and persisted after the end of the stimulation. The oscillation coincided with the inhibition of deep cerebellar neurons. As the inhibition of the deep cerebellar nuclei is related to inhibitory inputs from Purkinje cells, we speculate that the oscillation represents the unmasking of the synchronous activation of another subtype of deep cerebellar neuronal subtype, devoid of GABA receptors and under the direct control of the climbing fibres from the inferior olive. Still, the mechanism sustaining this oscillation remains to be deciphered. Our study sheds new light on the role of the olivo-cerebellar loop as the final output control of the intercerebellar circuitry.

On the complex dynamics of savanna landscapes

Simple mathematical models can exhibit rich and complex behaviors. Prototypical examples of these drawn from biology and other disciplines have provided insights that extend well beyond the situations that inspired them. Here, we explore a set of simple, yet realistic, models for savanna-forest vegetation dynamics based on minimal ecological assumptions. These models are aimed at understanding how vegetation interacts with both climate (a primary global determinant of vegetation structure) and feedbacks with chronic disturbances from fire. The model includes three plant functional types-grasses, savanna trees, and forest trees. Grass and (when they allow grass to persist in their subcanopy) savanna trees promote the spread of fires, which in turn, demographically limit trees. The model exhibits a spectacular range of behaviors. In addition to bistability, analysis reveals (i) that diverse cyclic behaviors (including limit and homo- and heteroclinic cycles) occur for broad ranges of parameter space, (ii) that large shifts in landscape structure can result from endogenous dynamics and not just from external drivers or from noise, and (iii) that introducing noise into this system induces resonant and inverse resonant phenomena, some of which have never been previously observed in ecological models. Ecologically, these results raise questions about how to evaluate complicated dynamics with data. Mathematically, they lead to classes of behaviors that are likely to occur in other models with similar structure.

Inverse stochastic resonance in networks of spiking neurons

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

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.

Movement Rate Is Encoded and Influenced by Widespread, Coherent Activity of Cerebellar Molecular Layer Interneurons

Inhibition from molecular layer interneurons (MLIs) is thought to play an important role in cerebellar function by sharpening the precision of Purkinje cell spike output. Yet the coding features of MLIs during behavior are poorly understood. To study MLI activity, we used in vivo Ca²⁺ imaging in head-fixed mice during the performance of a rhythmic motor behavior, licking during water consumption. MLIs were robustly active during lick-related movement across a lobule-specific region of the cerebellum showing high temporal correspondence within their population. Average MLI Ca²⁺ activity strongly correlated with movement rate but not to the intentional, or unexpected, adjustment of lick position or to sensory feedback that varied with task condition. Chemogenetic suppression of MLI output reduced lick rate and altered tongue movements, indicating that activity of these interneurons not only encodes temporal aspects of movement kinematics but also influences motor outcome pointing to an integral role in online control of rhythmic behavior.SIGNIFICANCE STATEMENT The cerebellum helps fine-tune coordinated motor actions via signaling from projection neurons called Purkinje cells. Molecular layer interneurons (MLIs) provide powerful inhibition onto Purkinje cells, but little is understood about how this inhibitory circuit is engaged during behavior or what type of information is transmitted through these neurons. Our work establishes that MLIs in the lateral cerebellum are broadly activated during movement with calcium activity corresponding to movement rate. We also show that suppression of MLI output slows and disorganizes the precise movement pattern. Therefore, MLIs are an important circuit element in the cerebellum allowing for accurate motor control.

Double inverse stochastic resonance with dynamic synapses

We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.