Complex bursting dynamics in an embryonic respiratory neuron model

A novel mechanism for ramping bursts based on slow negative feedback in model respiratory neurons

Recordings from pre-Bötzinger complex neurons responsible for the inspiratory phase of the respiratory rhythm reveal a ramping burst pattern, starting around the time that the transition from expiration to inspiration begins, in which the spike rate gradually rises until a transition into a high-frequency burst occurs. The spike rate increase along the burst is accompanied by a gradual depolarization of the plateau potential that underlies the spikes. These effects may be functionally important for inducing the onset of inspiration and hence maintaining effective respiration; however, most mathematical models for inspiratory bursting do not capture this activity pattern. Here, we study how the modulation of spike height and afterhyperpolarization via the slow inactivation of an inward current can support various activity patterns including ramping bursts. We use dynamical systems methods designed for multiple timescale systems, such as bifurcation analysis based on timescale decomposition and averaging over fast oscillations, to generate an understanding of and predictions about the specific dynamic effects that lead to ramping bursts. We also analyze how transitions between ramping and other activity patterns may occur with parameter changes, which could be associated with experimental manipulations, environmental conditions, and/or development.

Mixed-mode oscillations in a three-timescale coupled Morris-Lecar system

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris-Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

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.

Putting the theory into 'burstlet theory' with a biophysical model of burstlets and bursts in the respiratory preBötzinger complex

Inspiratory breathing rhythms arise from synchronized neuronal activity in a bilaterally distributed brainstem structure known as the preBötzinger complex (preBötC). In in vitro slice preparations containing the preBötC, extracellular potassium must be elevated above physiological levels (to 7-9 mM) to observe regular rhythmic respiratory motor output in the hypoglossal nerve to which the preBötC projects. Reexamination of how extracellular K+ affects preBötC neuronal activity has revealed that low-amplitude oscillations persist at physiological levels. These oscillatory events are subthreshold from the standpoint of transmission to motor output and are dubbed burstlets. Burstlets arise from synchronized neural activity in a rhythmogenic neuronal subpopulation within the preBötC that in some instances may fail to recruit the larger network events, or bursts, required to generate motor output. The fraction of subthreshold preBötC oscillatory events (burstlet fraction) decreases sigmoidally with increasing extracellular potassium. These observations underlie the burstlet theory of respiratory rhythm generation. Experimental and computational studies have suggested that recruitment of the non-rhythmogenic component of the preBötC population requires intracellular Ca2+ dynamics and activation of a calcium-activated nonselective cationic current. In this computational study, we show how intracellular calcium dynamics driven by synaptically triggered Ca2+ influx as well as Ca2+ release/uptake by the endoplasmic reticulum in conjunction with a calcium-activated nonselective cationic current can reproduce and offer an explanation for many of the key properties associated with the burstlet theory of respiratory rhythm generation. Altogether, our modeling work provides a mechanistic basis that can unify a wide range of experimental findings on rhythm generation and motor output recruitment in the preBötC.

Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.

Synchronization of the neurons coupled with sequential developing electrical and chemical synapses

There is some evidence representing the sequential formation and elimination of electrical and chemical synapses in particular brain regions. Relying on this feature, this paper presents a purely mathematical modeling study on the synchronization among neurons connected by transient electrical synapses transformed to chemical synapses over time. This deletion and development of synapses are considered consecutive. The results represent that the transient synapses lead to burst synchronization of the neurons while the neurons are resting when both synapses exist constantly. The period of the transitions and also the time of presence of electrical synapses to chemical ones are effective on the synchronization. The larger synchronization error is obtained by increasing the transition period and the time of chemical synapses' existence.

Dynamics of ramping bursts in a respiratory neuron model

Intensive computational and theoretical work has led to the development of multiple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full-blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-BötC neuron bursting, along with some parameter adjustments, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature.

Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding

Cerebellar stellate cells (CSCs) are spontaneously active, tonically firing (5-30 Hz), inhibitory interneurons that synapse onto Purkinje cells. We previously analyzed the excitability properties of CSCs, focusing on four key features: type I excitability, non-monotonic first-spike latency, switching in responsiveness and runup (i.e., temporal increase in excitability during whole-cell configuration). In this study, we extend this analysis by using whole-cell configuration to show that these neurons can also burst when treated with certain pharmacological agents separately or jointly. Indeed, treatment with 4-Aminopyridine (4-AP), a partial blocker of delayed rectifier and A-type K⁺ channels, at low doses induces a bursting profile in CSCs significantly different than that produced at high doses or when it is applied at low doses but with cadmium (Cd²⁺), a blocker of high voltage-activated (HVA) Ca²⁺ channels. By expanding a previously revised Hodgkin–Huxley type model, through the inclusion of Ca²⁺-activated K⁺ (K(Ca)) and HVA currents, we explain how these bursts are generated and what their underlying dynamics are. Specifically, we demonstrate that the expanded model preserves the four excitability features of CSCs, as well as captures their bursting patterns induced by 4-AP and Cd²⁺. Model investigation reveals that 4-AP is potentiating HVA, inducing square-wave bursting at low doses and pseudo-plateau bursting at high doses, whereas Cd²⁺ is potentiating K(Ca), inducing pseudo-plateau bursting when applied in combination with low doses of 4-AP. Using bifurcation analysis, we show that spike adding in square-wave bursts is non-sequential when gradually changing HVA and K(Ca) maximum conductances, delayed Hopf is responsible for generating the plateau segment within the active phase of pseudo-plateau bursts, and bursting can become “chaotic” when HVA and K(Ca) maximum conductances are made low and high, respectively. These results highlight the secondary effects of the drugs applied and suggest that CSCs have all the ingredients needed for bursting.

Excitable cells, including neurons, fire action potentials (APs) in their membrane voltage that allow them to communicate with each other and to serve certain physiological purposes. They do so either tonically by firing APs periodically, or episodically by repeatedly firing clusters of APs (called bursts) separated by quiescent periods. Each one of those firing patterns can be neuron-specific and dependent on synaptic inputs and/or their physiological environment. Cerebellar stellate cells (CSCs) that synapse onto Purkinje cells, the sole output of the cerebellum responsible for motor control, are spontaneously active inhibitory interneurons that fire APs tonically. We previously studied the excitability properties of these neurons and showed that they possess several important key features, including type I excitability, runup, non-monotonic first spike latency and switching in responsiveness. In this study, we show that CSCs can also exhibit two modes of burst firing, called square-wave and pseudo-plateau, when treated with certain pharmacological agents. Using bifurcation theory, we demonstrate that spike adding in the square-wave burst is non-sequential, changing by several spikes when certain conductances are altered gradually. This study thus sheds lights onto the overall effects of the pharmacological agents and highlights the ability of CSCs to burst in certain biological conditions.