Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons

How neuronal morphology impacts the synchronisation state of neuronal networks

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Neuromodulatory effects on synchrony and network reorganization in networks of coupled Kuramoto oscillators

Neuromodulatory processes in the brain can critically change signal processing on a cellular level leading to dramatic changes in network level reorganization. Here, we use coupled non-identical Kuramoto oscillators to investigate how changes in the shape of phase response curves from Type 1 to Type 2, mediated by varying ACh levels, coupled with activity dependent plasticity may alter network reorganization. We first show that when plasticity is absent, the Type 1 networks, as expected, exhibit asynchronous dynamics with oscillators of the highest natural frequency robustly evolving faster in terms of their phase dynamics. At the same time, the Type 2 networks synchronize, with oscillators locked so that the ones with higher natural frequency have a constant phase lead as compared to the ones with lower natural frequency. This relationship establishes a robust mapping between the frequency and oscillators' phases in the network, leading to structure/frequency mapping when plasticity is present. Further we show that while connection plasticity can produce stable synchrony (so called splay states) in Type 1 networks, the structure/frequency reorganization observed in Type 2 networks is not present.

From dawn till dusk: Time-adaptive bayesian optimization for neurostimulation

Stimulation optimization has garnered considerable interest in recent years in order to efficiently parametrize neuromodulation-based therapies. To date, efforts focused on automatically identifying settings from parameter spaces that do not change over time. A limitation of these approaches, however, is that they lack consideration for time dependent factors that may influence therapy outcomes. Disease progression and biological rhythmicity are two sources of variation that may influence optimal stimulation settings over time. To account for this, we present a novel time-varying Bayesian optimization (TV-BayesOpt) for tracking the optimum parameter set for neuromodulation therapy. We evaluate the performance of TV-BayesOpt for tracking gradual and periodic slow variations over time. The algorithm was investigated within the context of a computational model of phase-locked deep brain stimulation for treating oscillopathies representative of common movement disorders such as Parkinson's disease and Essential Tremor. When the optimal stimulation settings changed due to gradual and periodic sources, TV-BayesOpt outperformed standard time-invariant techniques and was able to identify the appropriate stimulation setting. Through incorporation of both a gradual "forgetting" and periodic covariance functions, the algorithm maintained robust performance when a priori knowledge differed from observed variations. This algorithm presents a broad framework that can be leveraged for the treatment of a range of neurological and psychiatric conditions and can be used to track variations in optimal stimulation settings such as amplitude, pulse-width, frequency and phase for invasive and non-invasive neuromodulation strategies.

Acetylcholine facilitates localized synaptic potentiation and location specific feature binding

Forebrain acetylcholine (ACh) signaling has been shown to drive attention and learning. Recent experimental evidence of spatially and temporally constrained cholinergic signaling has sparked interest to investigate how it facilitates stimulus-induced learning. We use biophysical excitatory-inhibitory (E-I) multi-module neural network models to show that external stimuli and ACh signaling can mediate spatially constrained synaptic potentiation patterns. The effects of ACh on neural excitability are simulated by varying the conductance of a muscarinic receptor-regulated hyperpolarizing slow K+ current (m-current). Each network module consists of an E-I network with local excitatory connectivity and global inhibitory connectivity. The modules are interconnected with plastic excitatory synaptic connections, that change via a spike-timing-dependent plasticity (STDP) rule. Our results indicate that spatially constrained ACh release influences the information flow represented by network dynamics resulting in selective reorganization of inter-module interactions. Moreover the information flow depends on the level of synchrony in the network. For highly synchronous networks, the more excitable module leads firing in the less excitable one resulting in strengthening of the outgoing connections from the former and weakening of its incoming synapses. For networks with more noisy firing patterns, activity in high ACh regions is prone to induce feedback firing of synchronous volleys and thus strengthening of the incoming synapses to the more excitable region and weakening of outgoing synapses. Overall, these results suggest that spatially and directionally specific plasticity patterns, as are presumed necessary for feature binding, can be mediated by spatially constrained ACh release.

M-current modulation of cortical slow oscillations: Network dynamics and computational modeling

The slow oscillation is a synchronized network activity expressed by the cortical network in slow wave sleep and under anesthesia. Waking up requires a transition from this synchronized brain state to a desynchronized one. Cholinergic innervation is critical for the transition from slow-wave-sleep to wakefulness, and muscarinic action is largely exerted through the muscarinic-sensitive potassium current (M-current) block. We investigated the dynamical impact of blocking the M-current on slow oscillations, both in cortical slices and in a cortical network computational model. Blocking M-current resulted in an elongation of Up states (by four times) and in a significant firing rate increase, reflecting an increased network excitability, albeit no epileptiform discharges occurred. These effects were replicated in a biophysical cortical model, where a parametric reduction of the M-current resulted in a progressive elongation of Up states and firing rate. All neurons, and not only those modeled with M-current, increased their firing rates due to network recurrency. Further increases in excitability induced even longer Up states, approaching the microarousals described in the transition towards wakefulness. Our results bridge an ionic current with network modulation, providing a mechanistic insight into network dynamics of awakening.

A spiking computational model for striatal cholinergic interneurons

Cholinergic interneurons in the striatum, also known as tonically active interneurons or TANs, are thought to have a strong effect on corticostriatal plasticity and on striatal activity and outputs, which in turn play a critical role in modulating downstream basal ganglia activity and movement. Striatal TANs can exhibit a variety of firing patterns and responses to synaptic inputs; furthermore, they have been found to display various surges and pauses in activity associated with sensory cues and reward delivery in learning as well as with motor tic production. To help explain the factors that contribute to TAN activity patterns and to provide a resource for future studies, we present a novel conductance-based computational model of a striatal TAN. We show that this model produces the various characteristic firing patterns observed in recordings of TANs. With a single baseline tuning associated with tonic firing, the model also captures a wide range of TAN behaviors found in previous experiments involving a variety of manipulations. In addition to demonstrating these results, we explain how various ionic currents in the model contribute to them. Finally, we use this model to explore the contributions of the acetylcholine released by TANs to the production of surges and pauses in TAN activity in response to strong excitatory inputs. These results provide predictions for future experimental testing that may help with efforts to advance our understanding of the role of TANs in reinforcement learning and in motor disorders such as Tourette's syndrome.

Optimal phase-selective entrainment of heterogeneous oscillator ensembles

We develop a framework to design optimal entrainment signals that entrain an ensemble of heterogeneous nonlinear oscillators, described by phase models, at desired phases. We explicitly take into account heterogeneity in both oscillation frequency and the type of oscillators characterized by different Phase Response Curves. The central idea is to leverage the Fourier series representation of periodic functions to decode a phase-selective entrainment task into a quadratic program. We demonstrate our approach using a variety of phase models, where we entrain the oscillators into distinct phase patterns. Also, we show how the generalizability gained from our formulation enables us to meet a wide range of design objectives and constraints, such as minimum-power, fast entrainment, and charge-balanced controls.

Heterogeneous mechanisms for synchronization of networks of resonant neurons under different E/I balance regimes

Rhythmic synchronization of neuronal firing patterns is a widely present phenomenon in the brain-one that seems to be essential for many cognitive processes. A variety of mechanisms contribute to generation and synchronization of network oscillations, ranging from intrinsic cellular excitability to network mediated effects. However, it is unclear how these mechanisms interact together. Here, using computational modeling of excitatory-inhibitory neural networks, we show that different synchronization mechanisms dominate network dynamics at different levels of excitation and inhibition (i.e. E/I levels) as synaptic strength is systematically varied. Our results show that with low synaptic strength networks are sensitive to external oscillatory drive as a synchronizing mechanism-a hallmark of resonance. In contrast, in a strongly-connected regime, synchronization is driven by network effects via the direct interaction between excitation and inhibition, and spontaneous oscillations and cross-frequency coupling emerge. Unexpectedly, we find that while excitation dominates network synchrony at low excitatory coupling strengths, inhibition dominates at high excitatory coupling strengths. Together, our results provide novel insights into the oscillatory modulation of firing patterns in different excitation/inhibition regimes.

Tuning Neural Synchronization: The Role of Variable Oscillation Frequencies in Neural Circuits

Brain oscillations emerge during sensory and cognitive processes and have been classified into different frequency bands. Yet, even within the same frequency band and between nearby brain locations, the exact frequencies of brain oscillations can differ. These frequency differences (detuning) have been largely ignored and play little role in current functional theories of brain oscillations. This contrasts with the crucial role that detuning plays in synchronization theory, as originally derived in physical systems. Here, we propose that detuning is equally important to understand synchronization in biological systems. Detuning is a critical control parameter in synchronization, which is not only important in shaping phase-locking, but also in establishing preferred phase relations between oscillators. We review recent evidence that frequency differences between brain locations are ubiquitous and essential in shaping temporal neural coordination. With the rise of powerful experimental techniques to probe brain oscillations, the contributions of exact frequency and detuning across neural circuits will become increasingly clear and will play a key part in developing a new understanding of the role of oscillations in brain function.

Modeling cortical synaptic effects of anesthesia and their cholinergic reversal

General anesthetics work through a variety of molecular mechanisms while resulting in the common end point of sedation and loss of consciousness. Generally, the administration of common anesthetics induces reduction in synaptic excitation while promoting synaptic inhibition. Exogenous modulation of the anesthetics' synaptic effects can help determine the neuronal pathways involved in anesthesia. For example, both animal and human studies have shown that exogenously induced increases in acetylcholine in the brain can elicit wakeful-like behavior despite the continued presence of the anesthetic. However, the underlying mechanisms of anesthesia reversal at the cellular level have not been investigated. Here we apply a computational model of a network of excitatory and inhibitory neurons to simulate the network-wide effects of anesthesia, due to changes in synaptic inhibition and excitation, and their reversal by cholinergic activation through muscarinic receptors. We use a differential evolution algorithm to fit model parameters to match measures of spiking activity, neuronal connectivity, and network dynamics recorded in the visual cortex of rodents during anesthesia with desflurane in vivo. We find that facilitating muscarinic receptor effects of acetylcholine on top of anesthetic-induced synaptic changes predicts the reversal of anesthetic suppression of neurons' spiking activity, functional connectivity, as well as pairwise and population interactions. Thus, our model predicts a specific neuronal mechanism for the cholinergic reversal of anesthesia consistent with experimental behavioral observations.

A dynamic clamp protocol to artificially modify cell capacitance

Dynamics of excitable cells and networks depend on the membrane time constant, set by membrane resistance and capacitance. Whereas pharmacological and genetic manipulations of ionic conductances of excitable membranes are routine in electrophysiology, experimental control over capacitance remains a challenge. Here, we present capacitance clamp, an approach that allows electrophysiologists to mimic a modified capacitance in biological neurons via an unconventional application of the dynamic clamp technique. We first demonstrate the feasibility to quantitatively modulate capacitance in a mathematical neuron model and then confirm the functionality of capacitance clamp in in vitro experiments in granule cells of rodent dentate gyrus with up to threefold virtual capacitance changes. Clamping of capacitance thus constitutes a novel technique to probe and decipher mechanisms of neuronal signaling in ways that were so far inaccessible to experimental electrophysiology.

Dynamical Mechanism Underlying Scale-Free Network Reorganization in Low Acetylcholine States Corresponding to Slow Wave Sleep

Sleep is indispensable for most animals' cognitive functions, and is hypothesized to be a major factor in memory consolidation. Although we do not fully understand the mechanisms of network reorganisation driving memory consolidation, available data suggests that sleep-associated neurochemical changes may be important for such processes. In particular, global acetylcholine levels change across the sleep/wake cycle, with high cholinergic tone during wake and REM sleep and low cholinergic tone during slow wave sleep. Furthermore, experimental perturbation of cholinergic tone has been shown to impact memory storage. Through in silico modeling of neuronal networks, we show how spiking dynamics change in highly heterogenous networks under varying levels of cholinergic tone, with neuronal networks under high cholinergic modulation firing asynchronously and at high frequencies, while those under low cholinergic modulation exhibit synchronous patterns of activity. We further examined the network's dynamics and its reorganization mediated via changing levels of acetylcholine within the context of different scale-free topologies, comparing network activity within the hub cells, a small group of neurons having high degree connectivity, and with the rest of the network. We show a dramatic, state-dependent change in information flow throughout the network, with highly active hub cells integrating information in a high-acetylcholine state, and transferring it to rest of the network in a low-acetylcholine state. This result is experimentally corroborated by frequency-dependent frequency changes observed in vivo experiments. Together, these findings provide insight into how new neurons are recruited into memory traces during sleep, a mechanism which may underlie system memory consolidation.

Case Report: Embedding "Digital Chronotherapy" Into Medical Devices-A Canine Validation for Controlling Status Epilepticus Through Multi-Scale Rhythmic Brain Stimulation

Circadian and other physiological rhythms play a key role in both normal homeostasis and disease processes. Such is the case of circadian and infradian seizure patterns observed in epilepsy. However, these rhythms are not fully exploited in the design of active implantable medical devices. In this paper we explore a new implantable stimulator that implements chronotherapy as a feedforward input to supplement both open-loop and closed-loop methods. This integrated algorithm allows for stimulation to be adjusted to the ultradian, circadian and infradian patterns observed in patients through slowly-varying temporal adjustments of stimulation and algorithm sub-components, while also enabling adaption of stimulation based on immediate physiological needs such as a breakthrough seizure or change of posture. Embedded physiological sensors in the stimulator can be used to refine the baseline stimulation circadian pattern as a "digital zeitgeber," i.e., a source of stimulus that entrains or synchronizes the subject's natural rhythms. This algorithmic approach is tested on a canine with severe drug-resistant idiopathic generalized epilepsy exhibiting a characteristic diurnal pattern correlated with sleep-wake cycles. Prior to implantation, the canine's cluster seizures evolved to status epilepticus (SE) and required emergency pharmacological intervention. The cranially-mounted system was fully-implanted bilaterally into the centromedian nucleus of the thalamus. Using combinations of time-based modulation, thalamocortical rhythm-specific tuning of frequency parameters as well as fast-adaptive modes based on activity, the canine experienced no further SE events post-implant as of the time of writing (7 months). Importantly, no significant cluster seizures have been observed either, allowing the reduction of rescue medication. The use of digitally-enabled chronotherapy as a feedforward signal to augment adaptive neurostimulators could prove a useful algorithmic method in conditions where sensitivity to temporal patterns are characteristics of the disease state, providing a novel mechanism for tailoring a more patient-specific therapy approach.

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

Deciphering how interneuron specific 3 cells control oriens lacunosum-moleculare cells to contribute to circuit function

The wide diversity of inhibitory cells across the brain makes them suitable to contribute to network dynamics in specialized fashions. However, the contributions of a particular inhibitory cell type in a behaving animal are challenging to untangle as one needs to both record cellular activities and identify the cell type being recorded. Thus, using computational modeling and theory to predict and hypothesize cell-specific contributions is desirable. Here, we examine potential contributions of interneuron-specific 3 (I-S3) cells - an inhibitory interneuron found in CA1 hippocampus that only targets other inhibitory interneurons - during simulated theta rhythms. We use previously developed multi-compartment models of oriens lacunosum-moleculare (OLM) cells, the main target of I-S3 cells, and explore how I-S3 cell inputs during in vitro and in vivo scenarios contribute to theta. We find that I-S3 cells suppress OLM cell spiking, rather than engender its spiking via post-inhibitory rebound mechanisms, and contribute to theta frequency spike resonance during simulated in vivo scenarios. To elicit recruitment similar to in vitro experiments, inclusion of disinhibited pyramidal cell inputs is necessary, implying that I-S3 cell firing broadens the window for pyramidal cell disinhibition. Using in vivo virtual networks, we show that I-S3 cells contribute to a sharpening of OLM cell recruitment at theta frequencies. Further, shifting the timing of I-S3 cell spiking due to external modulation shifts the timing of the OLM cell firing and thus disinhibitory windows. We propose a specialized contribution of I-S3 cells to create temporally precise coordination of modulation pathways.

Optimal closed-loop deep brain stimulation using multiple independently controlled contacts

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson’s disease and essential tremor. The symptoms of these disorders are known to be associated with pathological synchronous neural activity in the basal ganglia and thalamus. It is hypothesised that DBS acts to desynchronise this activity, leading to an overall reduction in symptoms. Electrodes with multiple independently controllable contacts are a recent development in DBS technology which have the potential to target one or more pathological regions with greater precision, reducing side effects and potentially increasing both the efficacy and efficiency of the treatment. The increased complexity of these systems, however, motivates the need to understand the effects of DBS when applied to multiple regions or neural populations within the brain. On the basis of a theoretical model, our paper addresses the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Central to this are analytical expressions, which we derive, that predict how the symptom severity should change when stimulation is applied. Using these expressions, we construct a closed-loop DBS strategy describing how stimulation should be delivered to individual contacts using the phases and amplitudes of feedback signals. We simulate our method and compare it against two others found in the literature: coordinated reset and phase-locked stimulation. We also investigate the conditions for which our strategy is expected to yield the most benefit.

In this paper we use computer models of brain tissue to derive an optimal control algorithm for a recently developed new generation of deep brain stimulation (DBS) devices. DBS is a treatment for a variety of neurological disorders including Parkinson’s disease, essential tremor, depression and pain. There is a growing amount of evidence to suggest that delivering stimulation according to feedback from patients, or closed-loop, has the potential to improve the efficacy, efficiency and side effects of the treatment. An important recent development in DBS technology are electrodes with multiple independently controllable contacts and this paper is a theoretical study into the effects of using this new technology. On the basis of a theoretical model, we devise a closed-loop strategy and address the question of how to best apply DBS across multiple contacts to maximally desynchronise neural populations. We demonstrate using numerical simulation that, for the systems we consider, our methods are more effective than two well-known alternatives, namely phase-locked stimulation and coordinated reset. We also predict that the benefits of using multiple contacts should depend strongly on the intrinsic neuronal response. The insights from this work should lead to a better understanding of how to implement and optimise closed-loop multi-contact DBS systems which in turn should lead to more effective and efficient DBS treatments.

M-current induced Bogdanov-Takens bifurcation and switching of neuron excitability class

In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current [Formula: see text], the maximal conductance of the M-current [Formula: see text] and the conductance of the leak current [Formula: see text]. We give precise conditions for the model that ensure the existence of a Bogdanov-Takens (BT) point and show that such a point can occur by varying [Formula: see text] and [Formula: see text]. We discuss the case when the BT point becomes a Bogdanov-Takens-cusp (BTC) point and show that such a point can occur in the three-dimensional parameter space. The results of the bifurcation analysis are applied to different neuronal models and are verified and supplemented by numerical bifurcation diagrams generated using the package MATCONT. We conclude that there is a transition in the neuronal excitability type organised by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases.

Slowly activating outward membrane currents generate input-output sub-harmonic cross frequency coupling in neurons

A major challenge in understanding spike-time dependent information encoding in the neural system is the non-linear firing response to inputs of the individual neurons. Hence, quantitative exploration of the putative mechanisms of this non-linear behavior is fundamental to formulating the theory of information transfer in the neural system. The objective of this simulation study was to evaluate and quantify the effect of slowly activating outward membrane current, on the non-linearity in the output of a one-compartment Hodgkin-Huxley styled neuron. To evaluate this effect, the peak conductance of the slow potassium channel (g_K-slow) was varied from 0% to 200% of its normal value in steps of 33%. Both cross- and iso-frequency coupling between the input and the output of the simulated neuron was computed using a generalized coherence measure, i.e., n:m coherence. With increasing g_K-slow, the amount of sub-harmonic cross-frequency coupling, where the output frequencies (1-8 Hz) are lower than the input frequencies (15-35 Hz), increased progressively whereas no change in iso-frequency coupling was observed. Power spectral and phase-space analysis of the neuronal membrane voltage vs. slow potassium channel activation variable showed that the interaction of the slow channel dynamics with the fast membrane voltage dynamics generates the observed sub-harmonic coupling. This study provides quantitative insights into the role of an important membrane mechanism i.e. the slowly activating outward current in generating non-linearities in the output of a neuron.

Modelling and analysing biological oscillations in quorum sensing networks

Recent experiments have shown that the biological oscillation of quorum sensing (QS) system play a vital role not only in the process of bacterial synthesis but also in the treatment of cancer by releasing drugs. As known, these five substances TetR, CI, LacI, AiiA and AI are the core components of the QS system. However, the effects of AiiA and protein synthesis time delay on QS system are often ignored in the theoretical model, which is taken as a priority in the proposed research. Therefore, the authors developed a new mathematical model to explore the effects of AiiA and time delay on the dynamical behaviour of QS system theoretically and numerically. The results show that time delay can induce oscillation of QS system. Concretely, there exists a time delay threshold [inline-formula removed]. When time delay is less than [inline-formula removed], the system is stable. With the increasing of time delay and once it passes [inline-formula removed], oscillation behaviour occurs. Moreover, the length of time delay determines the amplitude and period of the QS oscillation. In addition, the value of [inline-formula removed] is sensitive to AiiA. These results may enhance the understanding of QS oscillations and provide new insights for bacterial release drugs to treat cancer.

Phasic cholinergic signaling promotes emergence of local gamma rhythms in excitatory-inhibitory networks

Recent experimental results have shown that the detection of cues in behavioral attention tasks relies on transient increases of acetylcholine (ACh) release in frontal cortex and cholinergically driven oscillatory activity in the gamma frequency band (Howe et al. Journal of Neuroscience, 2017, 37, 3215). The cue-induced gamma rhythmic activity requires stimulation of M1 muscarinic receptors. Using biophysical computational modeling, we show that a network of excitatory (E) and inhibitory (I) neurons that initially displays asynchronous firing can generate transient gamma oscillatory activity in response to simulated brief pulses of ACh. ACh effects are simulated as transient modulation of the conductance of an M-type K⁺ current which is blocked by activation of muscarinic receptors and has significant effects on neuronal excitability. The ACh-induced effects on the M current conductance, g_Ks , change network dynamics to promote the emergence of network gamma rhythmicity through a Pyramidal-Interneuronal Network Gamma mechanism. Depending on connectivity strengths between and among E and I cells, gamma activity decays with the simulated g_Ks transient modulation or is sustained in the network after the g_Ks transient has completely dissipated. We investigated the sensitivity of the emergent gamma activity to synaptic strengths, external noise and simulated levels of g_Ks modulation. To address recent experimental findings that cholinergic signaling is likely spatially focused and dynamic, we show that localized g_Ks modulation can induce transient changes of cellular excitability in local subnetworks, subsequently causing population-specific gamma oscillations. These results highlight dynamical mechanisms underlying localization of ACh-driven responses and suggest that spatially localized, cholinergically induced gamma may contribute to selectivity in the processing of competing external stimuli, as occurs in attentional tasks.

Emergence of global synchronization in directed excitatory networks of type I neurons

The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.

Delta phase reset predicts conflict-related changes in P3 amplitude and behavior

When multiple competing responses are activated, we respond more slowly than if only one response is activated (response conflict). Conflict-induced slowing is reduced for consecutive high-conflict stimuli, an effect known as conflict adaptation. Verguts and Notebaert's (2009) adaptation by binding theory suggests this is due to Hebbian learning of cognitive control, potentiated by the response of the locus coeruleus norepinephrine (NE) system. Phasic activity of the NE system can potentially be measured non-invasively in humans by recording the P3 component of the event-related potential (ERP), and the P3 is sensitive to conflict adaptation. Bouret and Sara's (2005) network reset theory suggests that phasic NE might functionally reset ongoing large-scale network activity, generating synchronous neural population activity like the P3. To examine the possibility that network reset contributes to conflict effects in the P3, we recorded high-density EEG data while subjects performed a flanker task. As expected, conflict and conflict adaptation modulated P3 amplitudes. Brain-behavior correlation analyses indicated that activity during the rise of the P3 was related to RT and predicted RT differences due to conflict. More importantly, phase of delta oscillations not only predicted reaction time differences between low-conflict and high-conflict conditions, but delta phase reset also predicted the amplitude of the P3. Delta oscillations exhibited dominant peaks both pre and post-stimulus, and delta at stimulus onset predicted the post-stimulus ERP, in particular the N2 and P3. This result bridges human EEG with basic mechanisms suggested by computational neural models and invasive patient recordings, namely that salient cognitive events might reset ongoing oscillations leading to the generation of the phase-locked evoked potential. We conclude that partial phase reset is a cortical mechanism involved in monitoring the environment for unexpected events, and this response contributes to conflict effects in the ERP. These results are in line with theories that phasic NE release might reset ongoing cortical activity, leading to the generation of ERP components like the P3.

Cholinergic Modulation Promotes Attentional Modulation in Primary Visual Cortex- A Modeling Study

Attention greatly influences sensory neural processing by enhancing firing rates of neurons that represent the attended stimuli and by modulating their tuning properties. The cholinergic system is believed to partly mediate the attention contingent improvement of cortical processing by influencing neuronal excitability, synaptic transmission and neural network characteristics. Here, we used a biophysically based model to investigate the mechanisms by which cholinergic system influences sensory information processing in the primary visual cortex (V1) layer 4C. The physiological properties and architectures of our model were inspired by experimental data and include feed-forward input from dorsal lateral geniculate nucleus that sets up orientation preference in V1 neural responses. When including a cholinergic drive, we found significant sharpening in orientation selectivity, desynchronization of LFP gamma power and spike-field coherence, decreased response variability and correlation reduction mostly by influencing intracortical interactions and by increasing inhibitory drive. Our results indicated that these effects emerged due to changes specific to the behavior of the inhibitory neurons. The behavior of our model closely resembles the effects of attention on neural activities in monkey V1. Our model suggests precise mechanisms through which cholinergic modulation may mediate the effects of attention in the visual cortex.

Acetylcholine Mediates Dynamic Switching Between Information Coding Schemes in Neuronal Networks

Rate coding and phase coding are the two major coding modes seen in the brain. For these two modes, network dynamics must either have a wide distribution of frequencies for rate coding, or a narrow one to achieve stability in phase dynamics for phase coding. Acetylcholine (ACh) is a potent regulator of neural excitability. Acting through the muscarinic receptor, ACh reduces the magnitude of the potassium M-current, a hyperpolarizing current that builds up as neurons fire. The M-current contributes to several excitability features of neurons, becoming a major player in facilitating the transition between Type 1 (integrator) and Type 2 (resonator) excitability. In this paper we argue that this transition enables a dynamic switch between rate coding and phase coding as levels of ACh release change. When a network is in a high ACh state variations in synaptic inputs will lead to a wider distribution of firing rates across the network and this distribution will reflect the network structure or pattern of external input to the network. When ACh is low, network frequencies become narrowly distributed and the structure of a network or pattern of external inputs will be represented through phase relationships between firing neurons. This work provides insights into how modulation of neuronal features influences network dynamics and information processing across brain states.

Predicting the effects of deep brain stimulation using a reduced coupled oscillator model

Deep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson's disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New 'closed-loop' approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude, provided a number of conditions are satisfied. For such patients, we predict that the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the closed-loop strategies found in the literature, namely phase-locked and adaptive DBS.

How rhythms of the sleeping brain tune memory and synaptic plasticity

Decades of neurobehavioral research has linked sleep-associated rhythms in various brain areas to improvements in cognitive performance. However, it remains unclear what synaptic changes might underlie sleep-dependent declarative memory consolidation and procedural task improvement, and why these same changes appear not to occur across a similar interval of wake. Here we describe recent research on how one specific feature of sleep-network rhythms characteristic of rapid eye movement and non-rapid eye movement-could drive synaptic strengthening or weakening in specific brain circuits. We provide an overview of how these rhythms could affect synaptic plasticity individually and in concert. We also present an overarching hypothesis for how all network rhythms occurring across the sleeping brain could aid in encoding new information in neural circuits.

Neuronal Dynamics Underlying Communication Signals in a Weakly Electric Fish: Implications for Connectivity in a Pacemaker Network

Neuronal networks can produce stable oscillations and synchrony that are under tight control yet flexible enough to rapidly switch between dynamical states. The pacemaker nucleus in the weakly electric fish comprises a network of electrically coupled neurons that fire synchronously at high frequency. This activity sets the timing for an oscillating electric organ discharge with the lowest cycle-to-cycle variability of all known biological oscillators. Despite this high temporal precision, pacemaker activity is behaviorally modulated on millisecond time-scales for the generation of electrocommunication signals. The network mechanisms that allow for this combination of stability and flexibility are not well understood. In this study, we use an in vitro pacemaker preparation from Apteronotus leptorhynchus to characterize the neural responses elicited by the synaptic inputs underlying electrocommunication. These responses involve a variable increase in firing frequency and a prominent desynchronization of neurons that recovers within 5 oscillation cycles. Using a previously developed computational model of the pacemaker network, we show that the frequency changes and rapid resynchronization observed experimentally are most easily explained when model neurons are interconnected more densely and with higher coupling strengths than suggested by published data. We suggest that the pacemaker network achieves both stability and flexibility by balancing coupling strength with interconnectivity and that variation in these network features may provide a substrate for species-specific evolution of electrocommunication signals.

Analyzing the competition of gamma rhythms with delayed pulse-coupled oscillators in phase representation

Networks of neurons can generate oscillatory activity as result of various types of coupling that lead to synchronization. A prominent type of oscillatory activity is gamma (30-80 Hz) rhythms, which may play an important role in neuronal information processing. Two mechanisms have mainly been proposed for their generation: (1) interneuron network gamma (ING) and (2) pyramidal-interneuron network gamma (PING). In vitro and in vivo experiments have shown that both mechanisms can exist in the same cortical circuits. This raises the questions: How do ING and PING interact when both can in principle occur? Are the network dynamics a superposition, or do ING and PING interact in a nonlinear way and if so, how? In this article, we first generalize the phase representation for nonlinear one-dimensional pulse coupled oscillators as introduced by Mirollo and Strogatz to type II oscillators whose phase response curve (PRC) has zero crossings. We then give a full theoretical analysis for the regular gamma-like oscillations of simple networks consisting of two neural oscillators, an "E neuron" mimicking a synchronized group of pyramidal cells, and an "I neuron" representing such a group of interneurons. Motivated by experimental findings, we choose the E neuron to have a type I PRC [leaky integrate-and-fire (LIF) neuron], while the I neuron has either a type I or type II PRC (LIF or "sine" neuron). The phase representation allows us to define in a simple manner scenarios of interaction between the two neurons, which are independent of the types and the details of the neuron models. The presence of delay in the couplings leads to an increased number of scenarios relevant for gamma-like oscillatory patterns. We analytically derive the set of such scenarios and describe their occurrence in terms of parameter values such as synaptic connectivity and drive to the E and I neurons. The networks can be tuned to oscillate in an ING or PING mode. We focus particularly on the transition region where both rhythms compete to govern the network dynamics and compare with oscillations in reduced networks, which can only generate either ING or PING. Our analytically derived oscillation frequency diagrams indicate that except for small coexistence regions, the networks generate ING if the oscillation frequency of the reduced ING network exceeds that of the reduced PING network, and vice versa. For networks with the LIF I neuron, the network oscillation frequency slightly exceeds the frequencies of corresponding reduced networks, while it lies between them for networks with the sine I neuron. In networks oscillating in ING (PING) mode, the oscillation frequency responds faster to changes in the drive to the I (E) neuron than to changes in the drive to the E (I) neuron. This finding suggests a method to analyze which mechanism governs an observed network oscillation. Notably, also when the network operates in ING mode, the E neuron can spike before the I neuron such that relative spike times of the pyramidal cells and the interneurons alone are not conclusive for distinguishing ING and PING.

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.

Understanding the Generation of Network Bursts by Adaptive Oscillatory Neurons

Experimental and numerical studies have revealed that isolated populations of oscillatory neurons can spontaneously synchronize and generate periodic bursts involving the whole network. Such a behavior has notably been observed for cultured neurons in rodent's cortex or hippocampus. We show here that a sufficient condition for this network bursting is the presence of an excitatory population of oscillatory neurons which displays spike-driven adaptation. We provide an analytic model to analyze network bursts generated by coupled adaptive exponential integrate-and-fire neurons. We show that, for strong synaptic coupling, intrinsically tonic spiking neurons evolve to reach a synchronized intermittent bursting state. The presence of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. Thanks to a simple self-consistent equation, our model gives an intuitive and semi-quantitative tool to understand the bursting behavior. Furthermore, it suggests that after-hyperpolarization currents are sufficient to explain bursting termination. Through a thorough mapping between the theoretical parameters and ion-channel properties, we discuss the biological mechanisms that could be involved and the relevance of the explored parameter-space. Such an insight enables us to propose experimentally-testable predictions regarding how blocking fast, medium or slow after-hyperpolarization channels would affect the firing rate and burst duration, as well as the interburst interval.

Dichotomous Dynamics in E-I Networks with Strongly and Weakly Intra-connected Inhibitory Neurons

The interconnectivity between excitatory and inhibitory neural networks informs mechanisms by which rhythmic bursts of excitatory activity can be produced in the brain. One such mechanism, Pyramidal Interneuron Network Gamma (PING), relies primarily upon reciprocal connectivity between the excitatory and inhibitory networks, while also including intra-connectivity of inhibitory cells. The causal relationship between excitatory activity and the subsequent burst of inhibitory activity is of paramount importance to the mechanism and has been well studied. However, the role of the intra-connectivity of the inhibitory network, while important for PING, has not been studied in detail, as most analyses of PING simply assume that inhibitory intra-connectivity is strong enough to suppress subsequent firing following the initial inhibitory burst. In this paper we investigate the role that the strength of inhibitory intra-connectivity plays in determining the dynamics of PING-style networks. We show that networks with weak inhibitory intra-connectivity exhibit variations in burst dynamics of both the excitatory and inhibitory cells that are not obtained with strong inhibitory intra-connectivity. Networks with weak inhibitory intra-connectivity exhibit excitatory rhythmic bursts with weak excitatory-to-inhibitory synapses for which classical PING networks would show no rhythmic activity. Additionally, variations in dynamics of these networks as the excitatory-to-inhibitory synaptic weight increases illustrates the important role that consistent pattern formation in the inhibitory cells serves in maintaining organized and periodic excitatory bursts. Finally, motivated by these results and the known diversity of interneurons, we show that a PING-style network with two inhibitory subnetworks, one strongly intra-connected and one weakly intra-connected, exhibits organized and periodic excitatory activity over a larger parameter regime than networks with a homogeneous inhibitory population. Taken together, these results serve to better articulate the role of inhibitory intra-connectivity in generating PING-like rhythms, while also revealing how heterogeneity amongst inhibitory synapses might make such rhythms more robust to a variety of network parameters.

Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation

Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.

Oscillatory expression in Escherichia coli mediated by microRNAs with transcriptional and translational time delays

The primary objective of this study is to study oscillatory expression of gene regulatory network in Escherichia coli mediated by microRNAs (sRNAs) with transcriptional and translational time delays. Motivated by the regulation of gene expression proposed by Shimoni et al. (Molecular Systems Biology, 2007), a general model of delayed gene regulatory network by sRNAs is formulated. This model can well describe many practical architectures of gene regulatory network by sRNAs, particularly when both transcriptional and translational time delays are introduced. Two functional issues on oscillatory expression of the gene regulatory network, i.e. stability and bifurcation, are investigated. Furthermore, an explicit algorithm determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions is presented. It turns out that both transcriptional and translational time delays can induce gene expression in E. coli to be oscillatory even when its deterministic counterpart exhibits no oscillations. Moreover, the obtained results are in consistence with the experimental observations found in the biological literatures (Elowitz MB et al.: Nature, 2000, 403, pp. 335-338; Lennart Hilbert et al.: Mol. BioSyst, 2011, 7, pp. 2599-2607), which demonstrates that both transcriptional and translational time delays play an important role in the gene regulatory process of E. coli.

Robustness of persistent spiking to partial synchronization in a minimal model of synaptically driven self-sustained activity

We study the behavior of a minimal model of synaptically sustained persistent activity that consists of two quadratic integrate-and-fire neurons mutually coupled via excitatory synapses. Importantly, each of the neurons is excitable, as opposed to an oscillator; hence when uncoupled it sits at a subthreshold rest state. When the constituent neurons are mutually coupled via sufficiently strong fast excitatory synapses, the system demonstrates bistability between a fixed point (quiescent background state) and a limit cycle (memory state with synaptically driven spiking activity). Previous work showed that this persistent activity can be stopped by an excitatory input that synchronizes the network. Here we analyzed how this persistent state reacts to partial synchronization. We considered three types of progressively more complex excitatory synaptic kernels: delta pulse, square, and exponential. The first two cases were treated analytically, and the latter case numerically. Using phase-plane methods, we characterized the shape of the region, such that all orbits starting within it correspond to infinite spike trains; this constitutes the persistent activity region. In the case of instant coupling, all such active orbits were neutrally stable; in the case of noninstant coupling, the activity region contained a unique stable limit cycle (so the activity region was the basin of attraction for the limit cycle). This limit cycle corresponded to purely antiphase spiking of two neurons. Increasing synchronization shifted the system toward the border of the activity region, eventually terminating spiking activity. We calculated three measures of robustness of the active state: width of the activity region in the phase plane, critical level of synchronization that can be tolerated by the persistent spiking activity, and speed of reconvergence to the limit cycle. Our analysis revealed that the self-sustained activity is more robust to synchronization when each individual neuron is closer to SNIC bifurcation (closer to being an intrinsic oscillator), the recurrent synaptic excitation is stronger, and the synaptic decay is slower, which is in agreement with the existing data on local circuits in the cortex that show sustained activity.

Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks

The plethora of inhibitory interneurons in the hippocampus and cortex play a pivotal role in generating rhythmic activity by clustering and synchronizing cell firing. Results of our simulations demonstrate that both the intrinsic cellular properties of neurons and the degree of network connectivity affect the characteristics of clustered dynamics exhibited in randomly connected, heterogeneous inhibitory networks. We quantify intrinsic cellular properties by the neuron's current-frequency relation (IF curve) and Phase Response Curve (PRC), a measure of how perturbations given at various phases of a neurons firing cycle affect subsequent spike timing. We analyze network bursting properties of networks of neurons with Type I or Type II properties in both excitability and PRC profile; Type I PRCs strictly show phase advances and IF curves that exhibit frequencies arbitrarily close to zero at firing threshold while Type II PRCs display both phase advances and delays and IF curves that have a non-zero frequency at threshold. Type II neurons whose properties arise with or without an M-type adaptation current are considered. We analyze network dynamics under different levels of cellular heterogeneity and as intrinsic cellular firing frequency and the time scale of decay of synaptic inhibition are varied. Many of the dynamics exhibited by these networks diverge from the predictions of the interneuron network gamma (ING) mechanism, as well as from results in all-to-all connected networks. Our results show that randomly connected networks of Type I neurons synchronize into a single cluster of active neurons while networks of Type II neurons organize into two mutually exclusive clusters segregated by the cells' intrinsic firing frequencies. Networks of Type II neurons containing the adaptation current behave similarly to networks of either Type I or Type II neurons depending on network parameters; however, the adaptation current creates differences in the cluster dynamics compared to those in networks of Type I or Type II neurons. To understand these results, we compute neuronal PRCs calculated with a perturbation matching the profile of the synaptic current in our networks. Differences in profiles of these PRCs across the different neuron types reveal mechanisms underlying the divergent network dynamics.

Interplay between excitability type and distributions of neuronal connectivity determines neuronal network synchronization

While the interplay between neuronal excitability properties and global properties of network topology is known to affect network propensity for synchronization, it is not clear how detailed characteristics of these properties affect spatiotemporal pattern formation. Here we study mixed networks, composed of neurons having type I and/or type II phase response curves, with varying distributions of local and random connections and show that not only average network properties, but also the connectivity distribution statistics, significantly affect network synchrony. Namely, we study networks with fixed networkwide properties, but vary the number of random connections that nodes project. We show that varying node excitability (type I vs type II) influences network synchrony most dramatically for systems with long-tailed distributions of the number of random connections per node. This indicates that a cluster of even a few highly rewired cells with a high propensity for synchronization can alter the degree of synchrony in the network as a whole. We show this effect generally on a network of coupled Kuramoto oscillators and investigate the impact of this effect more thoroughly in pulse-coupled networks of biophysical neurons.

Neurons as oscillators

Regularly spiking neurons can be described as oscillators. In this article we review some of the insights gained from this conceptualization and their relevance for systems neuroscience. First, we explain how a regularly spiking neuron can be viewed as an oscillator and how the phase-response curve (PRC) describes the response of the neuron's spike times to small perturbations. We then discuss the meaning of the PRC for a single neuron's spiking behavior and review the PRCs measured from a variety of neurons in a range of spiking regimes. Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram. We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior. Given the PRC, conduction delays, and the waveform and time course of the synaptic potentials, it is possible to predict neural population behavior such as synchronization. The PRC also allows us to quantify the robustness of the synchronization to heterogeneity and noise. We finally ask how to combine the measured PRCs and the predictions based on PRC to further the understanding of systems neuroscience. As an example, we discuss how the change of the PRC by the neuromodulator acetylcholine could lead to a destabilization of cortical network dynamics. Although all of these studies are grounded in mathematical abstractions that do not strictly hold in biology, they provide good estimates for the emergence of the brain's network activity from the properties of individual neurons. The study of neurons as oscillators can provide testable hypotheses and mechanistic explanations for systems neuroscience.

Phase-Dependent Modulation of Oscillatory Phase and Synchrony by Long-Lasting Depolarizing Inputs in Central Neurons

Oscillatory neural activities have been implicated in various types of information processing in the CNS. The procerebral (PC) lobe of the land mollusk Limax valentianus shows an ongoing oscillatory local field potential (LFP). Olfactory input increases both the frequency and spatial synchrony of the LFP oscillation by a nitric oxide (NO)-mediated mechanism, but how NO modulates the activity in a specific manner has been unclear. In the present study, we used electrical stimulation and NO uncaging to systematically analyze the response of the LFP oscillation and found phase-dependent effects on phase shifting and synchrony. The neurons that presumably release NO in the PC lobe preferentially fired at phases in which NO has a synchronizing effect, suggesting that the timing of NO release is regulated to induce a stereotyped response to natural sensory stimuli. The phase-response curve (PRC) describes the timing dependence of responses of an oscillatory system to external input. PRCs are usually constructed by recording the temporal shifts of the neural activity in response to brief electrical pulses. However, NO evokes a long-lasting depolarization persisting for several cycles of oscillation. The phase-response relationship obtained by NO stimulation was approximately the integral of the PRC. A similar relationship was also shown for regular firing of mouse cerebellar Purkinje cells receiving step depolarization, suggesting the generality of the results to oscillatory neural systems with highly distinct properties. These results indicate novel dynamic effects of long-lasting inputs on network oscillation and synchrony, which are based on simple and ubiquitous mechanisms.

Inverse Stochastic Resonance in Cerebellar Purkinje Cells

Purkinje neurons play an important role in cerebellar computation since their axons are the only projection from the cerebellar cortex to deeper cerebellar structures. They have complex internal dynamics, which allow them to fire spontaneously, display bistability, and also to be involved in network phenomena such as high frequency oscillations and travelling waves. Purkinje cells exhibit type II excitability, which can be revealed by a discontinuity in their f-I curves. We show that this excitability mechanism allows Purkinje cells to be efficiently inhibited by noise of a particular variance, a phenomenon known as inverse stochastic resonance (ISR). While ISR has been described in theoretical models of single neurons, here we provide the first experimental evidence for this effect. We find that an adaptive exponential integrate-and-fire model fitted to the basic Purkinje cell characteristics using a modified dynamic IV method displays ISR and bistability between the resting state and a repetitive activity limit cycle. ISR allows the Purkinje cell to operate in different functional regimes: the all-or-none toggle or the linear filter mode, depending on the variance of the synaptic input. We propose that synaptic noise allows Purkinje cells to quickly switch between these functional regimes. Using mutual information analysis, we demonstrate that ISR can lead to a locally optimal information transfer between the input and output spike train of the Purkinje cell. These results provide the first experimental evidence for ISR and suggest a functional role for ISR in cerebellar information processing.

How neurons generate output spikes in response to various combinations of inputs is a central issue in contemporary neuroscience. Due to their large dendritic tree and complex intrinsic properties, cerebellar Purkinje cells are an important model system to study this input-output transformation. Here we examine how noise can change the parameters of this transformation. In experiments we found that spike generation in Purkinje cells can be efficiently inhibited by noise of a particular amplitude. This effect is called inverse stochastic resonance (ISR) and has previously been described only in theoretical models of neurons. We explain the mechanism underlying ISR using a simple model matching the properties of experimentally characterized Purkinje cells. We found that ISR is present in Purkinje cells when the mean input current is near threshold for spike generation. ISR can be explained by the co-existence of resting and spiking solutions of the simple model. Changes of the input noise variance change the lifetime of these resting and spiking states, suggesting a mechanism for a tunable filter with long time constants implemented by a Purkinje cell population in the cerebellum. Finally, ISR leads to locally optimal information transfer from the input to the output of a Purkinje cell.

Network burst dynamics under heterogeneous cholinergic modulation of neural firing properties and heterogeneous synaptic connectivity

The characteristics of neural network activity depend on intrinsic neural properties and synaptic connectivity in the network. In brain networks, both of these properties are critically affected by the type and levels of neuromodulators present. The expression of many of the most powerful neuromodulators, including acetylcholine (ACh), varies tonically and phasically with behavioural state, leading to dynamic, heterogeneous changes in intrinsic neural properties and synaptic connectivity properties. Namely, ACh significantly alters neural firing properties as measured by the phase response curve in a manner that has been shown to alter the propensity for network synchronization. The aim of this simulation study was to build an understanding of how heterogeneity in cholinergic modulation of neural firing properties and heterogeneity in synaptic connectivity affect the initiation and maintenance of synchronous network bursting in excitatory networks. We show that cells that display different levels of ACh modulation have differential roles in generating network activity: weakly modulated cells are necessary for burst initiation and provide synchronizing drive to the rest of the network, whereas strongly modulated cells provide the overall activity level necessary to sustain burst firing. By applying several quantitative measures of network activity, we further show that the existence of network bursting and its characteristics, such as burst duration and intraburst synchrony, are dependent on the fraction of cell types providing the synaptic connections in the network. These results suggest mechanisms underlying ACh modulation of brain oscillations and the modulation of seizure activity during sleep states.

Formation and Dynamics of Waves in a Cortical Model of Cholinergic Modulation

Acetylcholine (ACh) is a regulator of neural excitability and one of the neurochemical substrates of sleep. Amongst the cellular effects induced by cholinergic modulation are a reduction in spike-frequency adaptation (SFA) and a shift in the phase response curve (PRC). We demonstrate in a biophysical model how changes in neural excitability and network structure interact to create three distinct functional regimes: localized asynchronous, traveling asynchronous, and traveling synchronous. Our results qualitatively match those observed experimentally. Cortical activity during slow wave sleep (SWS) differs from that during REM sleep or waking states. During SWS there are traveling patterns of activity in the cortex; in other states stationary patterns occur. Our model is a network composed of Hodgkin-Huxley type neurons with a M-current regulated by ACh. Regulation of ACh level can account for dynamical changes between functional regimes. Reduction of the magnitude of this current recreates the reduction in SFA the shift from a type 2 to a type 1 PRC observed in the presence of ACh. When SFA is minimal (in waking or REM sleep state, high ACh) patterns of activity are localized and easily pinned by network inhomogeneities. When SFA is present (decreasing ACh), traveling waves of activity naturally arise. A further decrease in ACh leads to a high degree of synchrony within traveling waves. We also show that the level of ACh determines how sensitive network activity is to synaptic heterogeneity. These regimes may have a profound functional significance as stationary patterns may play a role in the proper encoding of external input as memory and traveling waves could lead to synaptic regularization, giving unique insights into the role and significance of ACh in determining patterns of cortical activity and functional differences arising from the patterns.

Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.

Pattern segmentation with activity dependent natural frequency shift and sub-threshold resonance

Understanding the mechanisms underlying distributed pattern formation in brain networks and its content driven dynamical segmentation is an area of intense study. We investigate a theoretical mechanism for selective activation of diverse neural populations that is based on dynamically shifting cellular resonances in functionally or structurally coupled networks. We specifically show that sub-threshold neuronal depolarization from synaptic coupling or external input can shift neurons into and out of resonance with specific bands of existing extracellular oscillations, and this can act as a dynamic readout mechanism during information storage and retrieval. We find that this mechanism is robust and suggest it as a general coding strategy that can be applied to any network with oscillatory nodes.

Critical slowing down governs the transition to neuron spiking

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws.

Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.

Neurons efficiently convey information by being able to switch rapidly between two different states: quiescence and spiking. Such sudden shifts to a qualitatively different state are observed in many complex systems; the often dramatic consequences of these tipping points for diverse fields such as economics, ecology, and the brain have spurred interest to better understand their transition mechanisms and predict their sudden occurrences. By studying the transition from neuronal quiescence to spiking, we show that the quantitative scaling laws for critical slowing down, i.e., a system’s tendency to recover more slowly from perturbations upon approaching its transition point, inform about the underlying bifurcation mechanism and can be used to improve the prediction of a system’s tipping point.

Development and modulation of intrinsic membrane properties control the temporal precision of auditory brain stem neurons

Passive and active membrane properties determine the voltage responses of neurons. Within the auditory brain stem, refinements in these intrinsic properties during late postnatal development usually generate short integration times and precise action-potential generation. This developmentally acquired temporal precision is crucial for auditory signal processing. How the interactions of these intrinsic properties develop in concert to enable auditory neurons to transfer information with high temporal precision has not yet been elucidated in detail. Here, we show how the developmental interaction of intrinsic membrane parameters generates high firing precision. We performed in vitro recordings from neurons of postnatal days 9–28 in the ventral nucleus of the lateral lemniscus of Mongolian gerbils, an auditory brain stem structure that converts excitatory to inhibitory information with high temporal precision. During this developmental period, the input resistance and capacitance decrease, and action potentials acquire faster kinetics and enhanced precision. Depending on the stimulation time course, the input resistance and capacitance contribute differentially to action-potential thresholds. The decrease in input resistance, however, is sufficient to explain the enhanced action-potential precision. Alterations in passive membrane properties also interact with a developmental change in potassium currents to generate the emergence of the mature firing pattern, characteristic of coincidence-detector neurons. Cholinergic receptor-mediated depolarizations further modulate this intrinsic excitability profile by eliciting changes in the threshold and firing pattern, irrespective of the developmental stage. Thus our findings reveal how intrinsic membrane properties interact developmentally to promote temporally precise information processing.

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

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

Changes of Firing Rate Induced by Changes of Phase Response Curve in Bifurcation Transitions

We study dynamical mechanisms responsible for changes of the firing rate during four different bifurcation transitions in the two-dimensional Hindmarsh-Rose (2DHR) neuron model: the saddle node on an invariant circle (SNIC) bifurcation to the supercritical Andronov-Hopf (AH) one, the SNIC bifurcation to the saddle-separatrix loop (SSL) one, the AH bifurcation to the subcritical AH (SAH) one, and the SSL bifurcation to the AH one. For this purpose, we study slopes of the firing rate curve with respect to not only an external input current but also temperature that can be interpreted as a timescale in the 2DHR neuron model. These slopes are mathematically formulated with phase response curves (PRCs), expanding the firing rate with perturbations of the temperature and external input current on the one-dimensional space of the phase [Formula: see text] in the 2DHR oscillator. By analyzing the two different slopes of the firing rate curve with respect to the temperature and external input current, we find that during changes of the firing rate in all of the bifurcation transitions, the calculated slope with respect to the temperature also changes. This is largely dependent on changes in the PRC size that is also related to the slope with respect to the external input current. Furthermore, we find phase transition–like switches of the firing rate with a possible increase of the temperature during the SSL-to-AH bifurcation transition.

Origins and suppression of oscillations in a computational model of Parkinson's disease

Efficacy of deep brain stimulation (DBS) for motor signs of Parkinson's disease (PD) depends in part on post-operative programming of stimulus parameters. There is a need for a systematic approach to tuning parameters based on patient physiology. We used a physiologically realistic computational model of the basal ganglia network to investigate the emergence of a 34 Hz oscillation in the PD state and its optimal suppression with DBS. Discrete time transfer functions were fit to post-stimulus time histograms (PSTHs) collected in open-loop, by simulating the pharmacological block of synaptic connections, to describe the behavior of the basal ganglia nuclei. These functions were then connected to create a mean-field model of the closed-loop system, which was analyzed to determine the origin of the emergent 34 Hz pathological oscillation. This analysis determined that the oscillation could emerge from the coupling between the globus pallidus external (GPe) and subthalamic nucleus (STN). When coupled, the two resonate with each other in the PD state but not in the healthy state. By characterizing how this oscillation is affected by subthreshold DBS pulses, we hypothesize that it is possible to predict stimulus frequencies capable of suppressing this oscillation. To characterize the response to the stimulus, we developed a new method for estimating phase response curves (PRCs) from population data. Using the population PRC we were able to predict frequencies that enhance and suppress the 34 Hz pathological oscillation. This provides a systematic approach to tuning DBS frequencies and could enable closed-loop tuning of stimulation parameters.

Neuromodulation and aging: implications of aging neuronal gain control on cognition

The efficacy of various transmitter systems declines with advancing age. Of particular interest, various pre-synaptic and post-synaptic components of the dopaminergic system change across the human lifespan; impairments in these components play important roles in cognitive deficits commonly observed in the elderly. Here, we review evidence from recent multimodal neuroimaging, pharmacological and genetic studies that have provided new insights for the associations among dopamine functions, aging, functional brain activations and behavioral performance across key cognitive functions, ranging from working memory and episodic memory to goal-directed learning and decision making. Specifically, we discuss these empirical findings in the context of an established neurocomputational theory of aging neuronal gain control. We also highlight gaps in the current understanding of dopamine neuromodulation and aging brain functions and suggest avenues for future research.