Neural Bursting Research Articles

Synchronization Analysis of Multiple FitzHugh-Nagumo Noisy and Nonnoisy Neurobiological Networks

In the biological neural bursting and firing synchronization plays a vital role in all neuronal activities that are utilized for making decisions, executing commands, and sending information by neurons and their complex networks in the biological complexed brain. Understanding how the biological brain functionality comes out from different patterns of neuronal transmission between the large group of neural networks stands as one of the enduring challenges of modern neuroscience. This study investigated a methodology for synchronization of multiple single/dual state gap junctions FitzHugh-Nagumo (FHN) drive and slave networks under the condition of external noise. The theory of control was utilized to propose simple and diverse controllers to examine the synchronization problem of the different single and dual state gap junctions coupled nonnoisy and noisy FHN neurobiological drive and slave networks. Control laws are designed to stabilize the error dynamics without direct cancelation and synchronize all the states of both FHN neurobiological drive and slave networks. Sufficient conditions for achieving synchronization in the multiple single/dual state gap junction FHN noisy and nonnoisy neurobiological drive and slave networks were derived analytically using the theory of Lyapunov stability. Furthermore, the proposed controllers have been verified by using five noisy/nonnoisy FHN neurobiological drive and slave networks through numerical simulations.

Detection and Control of Epileptiform Regime in the Hodgkin–Huxley Artificial Neural Networks via Quantum Algorithms

The problem of detection and the following suppression of epileptiform dynamics in artificial neural networks (ANN) still is a hot topic in modern theoretical and applied neuroscience. For the purpose of such modeling, the Hodgkin–Huxley (HH) elements are important due to the variety of their behavior such as resting, singular spikes, and spike trains and bursts. This dynamical spectrum of individual HH neurons can cause an epileptiform regime originated in the hyper-synchronization of the cell outcomes. Our model covers the detection and suppression of ictal behavior in a small ANN consisting of HH cells. The model follows our approach [Borisenok et al., 2018] for the HH neurons as a classical dynamical system driving the collective neural bursting, but here we use a quantum paradigm-based algorithm emulated with the pair of HH neurons. Such emulation becomes possible due to the complexity of the individual 4d HH dynamics. The linear chain of two HH neurons is connected to the rest of ANN and works autonomously. The first neuron plays a role of the detecting element for the hyper-synchronization in the ANN and the quantum algorithm emulator; while the second one works as a measuring element (emulation of the quantum measurement converting the signals into the classical domain) and the trigger for the feedback suppressing the epileptiform regime. We use here the speed gradient algorithm for controling the emulating neuron and discuss its pros and cons to compare with our classical model of epileptiform suppression.

Beta-band bursting activity in computational model of heterogeneous external globus pallidus circuits

Exaggerated beta oscillations (13–35 Hz) in basal ganglia (BG) are the hallmark of dynamical properties in Parkinson’s disease (PD). Physiological experiments have shown that different subtypes of external globus pallidus (GPe) exhibit different changes in pathological conditions, which poses a challenge to the classic basal ganglia network modeling of PD, as the mechanism behind some novel phenomenon is almost impossible to reveal by classical models. We propose an extended striatum–GPe model including two subtypes of GPe, the calcium-binding protein parvalbumin GPe (PV GPe) and Lim homeobox 6 GPe (Lhx6 GPe). Based on this model, we illustrate the effect of inhibitory connections in GPe on neural bursting activities. The increase in self-inhibition of homogeneous GPe neurons can expand the spectral power of the beta-band, while mutual inhibition between heterogeneous GPe can regulate the burst of beta-band. Meanwhile, through the discussion about coupling parameters of GPe, we obtain a set of physiological parameters simulated healthy state. Furthermore, we find that both reducing M-current in striatal medium spine neuron (MSN) and degrading PV GPe to Lhx6 GPe could lead to bursting behaviors in PV GPe, and removing the connection from Lhx6 GPe to PV GPe can reduce the power of the beta-band. The role of heterogeneous GPe in Parkinsonian beta-band bursting is also revealed by simulating the specific optogenetic stimulation on GPe. These results demonstrate the facilitation and control function of heterogeneous GPe to abnormal oscillations and provide a novel insight into designing therapeutic interventions.

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.

Control for multifunctionality: bioinspired control based on feeding in Aplysia californica.

Animals exhibit remarkable feats of behavioral flexibility and multifunctional control that remain challenging for robotic systems. The neural and morphological basis of multifunctionality in animals can provide a source of bioinspiration for robotic controllers. However, many existing approaches to modeling biological neural networks rely on computationally expensive models and tend to focus solely on the nervous system, often neglecting the biomechanics of the periphery. As a consequence, while these models are excellent tools for neuroscience, they fail to predict functional behavior in real time, which is a critical capability for robotic control. To meet the need for real-time multifunctional control, we have developed a hybrid Boolean model framework capable of modeling neural bursting activity and simple biomechanics at speeds faster than real time. Using this approach, we present a multifunctional model of Aplysia californica feeding that qualitatively reproduces three key feeding behaviors (biting, swallowing, and rejection), demonstrates behavioral switching in response to external sensory cues, and incorporates both known neural connectivity and a simple bioinspired mechanical model of the feeding apparatus. We demonstrate that the model can be used for formulating testable hypotheses and discuss the implications of this approach for robotic control and neuroscience.

Lactate Attenuates Synaptic Transmission and Affects Brain Rhythms Featuring High Energy Expenditure.

SummaryLactate shuttled from blood, astrocytes, and/or oligodendrocytes may serve as the major glucose alternative in brain energy metabolism. However, its effectiveness in fueling neuronal information processing underlying complex cortex functions like perception and memory is unclear. We show that sole lactate disturbs electrical gamma and theta-gamma oscillations in hippocampal networks by either attenuation or neural bursts. Bursting is suppressed by elevating the glucose fraction in substrate supply. By contrast, lactate does not affect electrical sharp wave-ripple activity featuring lower energy use. Lactate increases the oxygen consumption during the network states, reflecting enhanced oxidative ATP synthesis in mitochondria. Finally, lactate attenuates synaptic transmission in excitatory pyramidal cells and fast-spiking, inhibitory interneurons by reduced neurotransmitter release from presynaptic terminals, whereas action potential generation in the axon is regular. In conclusion, sole lactate is less effective and potentially harmful during gamma-band rhythms by omitting obligatory ATP delivery through fast glycolysis at the synapse.

The Phenomenon of Neural Bursting and Spiking in Neurons: Morris-Lecar Model

In this study, we explore the interesting phenomenon of firing spikes and complex dynamics of Morris-Lecar model. We consider a set of parameters such that the model exhibits a wide range of phenomenons. We investigate the influences of injected current and temperature on the spiking dynamics of Morris-Lecar model. Moreover, we study bifurcations, and computational properties of this neuron model. Also, we define a bound (Max and Min voltage) for membrane potential and a certain voltage value or threshold for firing the spikes. Studying the two co-dimension bifurcations demonstrates much more complicated behaviors for this single neuron model. We also describe the phenomenon of neural bursting, and investigate the dynamics of Morris-Lecar model as a square-wave burster, elliptic burster and parabolic burster.

Characterization of in vitro neural functional connectivity on a neurofluidic device.

Understanding the mechanism of functional connectivity in neural system is of great benefit to lot of researches and applications. Microfluidics and microelectrode arrays (MEAs) have been frequently utilized for in vitro neural cultures study. However, there are few studies on the functional connectivity of neural cultures grown on a microfluidic chip. It is intriguing to unveil the influences of microfluidic structures on in vitro neuronal networks from the perspective of functional connectivity. Hence, in the present study, a device was established, which comprised a microfluidic chamber for cell growth and a MEA substrate for recording the electrophysiological response of the neuronal networks. The network topology, neural firing rate, neural bursting rate and network burst frequency were adopted as representative characteristics for neuronal networks analysis. Functional connectivity was estimated by means of cross-covariance analysis and graph theory. The results demonstrated that the functional connectivity of the in vitro neuronal networks formed in the microchannel has been apparently reinforced, corresponding to improve neuronal network density and increased small-worldness.

Inhibitory electromagnetic induction current induces enhancement instead of reduction of neural bursting activities

Nonlinear dynamics play an important role in identifying complex behaviors, dynamical mechanisms, and physiological functions of the neural firing activities. In contrast to the common viewpoint that the inhibitory effect should induce the reduction of neural firing activities, the present paper presents a novel example that inhibitory effect mediated by the electromagnetic induction current can induce the enhancement of bursting activities, which is characterized by the increase of firing frequency and period-adding bifurcations of bursting patterns, i.e. more spikes appearing within a burst. With the fast/slow variable dissection method and bifurcation analysis of the fold/homoclinic bursting pattern of the Hindmarsh–Rose model, the dynamical mechanism of the enhanced bursting activities induced by inhibitory effect is acquired and is different from the one induced by excitatory effect. With increasing the inhibitory effect of induction current, more spikes appear in a burst due to that the burst becomes wider, which is induced by the left shift of the initial phase of the burst, i.e. the fold/saddle-node bifurcation point of equilibrium of the fast subsystem. However, with increasing the excitatory effect of the stimulation, the period of limit cycle/spiking of the fast subsystem becomes short, which leads to that the interspike interval within a burst becomes short and then the burst contains more spikes. Furthermore, the enhancement of bursting activities induced by the inhibitory and excitatory effects is verified in a digital circuit which is designed in the Digital Signal Processor environment of MATLAB system. The result provides a novel example of nonlinear phenomenon contrast to the traditional viewpoint of the inhibitory effect and implies that the inhibitory induction current may be used as a possible measure to modulate the firing frequency and bursting patterns.

Bifurcation mechanism of not increase but decrease of spike number within a neural burst induced by excitatory effect

Nonlinear dynamics is identified to play very important roles in identifying the complex phenomenon, dynamical mechanism, and physiological functions of neural electronic activities. In the present paper, a novel viewpoint that the excitatory stimulus cannot enhance but reduce the number of the spikes within a burst, the novel viewpoint which is different from the traditional viewpoint, is proposed and is explained with the nonlinear dynamics. When the impulse current or the autaptic current with suitable strength is used in the suitable phase within the quiescent state of the bursting pattern of the Rulkov model, a novel firing pattern with reduced number of spikes within a burst is evoked. The earlier the application phase of the current within the quiescent state, the higher the threshold of the current strength to evoke the novel firing pattern is and the less the number of the spikes within a burst of the novel firing pattern. Moreover, such a novel phenomenon can be explained by the intrinsic nonlinear dynamics of the bursting combined with the characteristics of the current. The nonlinear behaviors of the fast subsystem of the Rulkov model are acquired by the fast and slow variable dissection method, respectively. For the fast subsystem, there exist a stable node with lower membrane potential, a stable limit cycle with higher membrane potential, a saddle serving as the border between the stable node and limit cycle, a saddle-node bifurcation, and a homoclinic orbit bifurcation. When external simulation is not received, the bursting pattern of the Rulkov model exhibits behavior alternating between the spikes corresponding to the limit cycle of the fast subsystem and quiescent state of the fast subsystem, which is located within the parameter region between the saddle-node bifurcation point and the homoclinic orbit bifurcation point of the fast subsystem. The spikes begin with the saddle-node bifurcation and end with the homoclinic orbit bifurcation. As the bifurcation parameter turns close to the homoclinic orbit bifurcation, the disturbation or stimulus that can induce the transition from the quiescent state to the spikes becomes strong. Therefore, as the application phase of the current within the quiescent state becomes earlier, the strength threshold of the current that can induce the transition from the quiescent state to the spikes becomes stronger, and the initial phase of the spikes becomes closer to the homoclinic orbit bifurcation, which leads the parameter region of the spikes to become shorter and then leads the number of spikes within a burst to turn less. It is the dynamical mechanism of the decrease of the spike number induced by the excitatory currents. The results enrich the nonlinear phenomenon and dynamical mechanism, present a novel viewpoint for the excitatory effect, and provide a new approach to modulating the neural bursting patterns.

Neural field model of seizure-like activity in isolated cortex.

Epileptiform discharges on an isolated cortex are explored using neural field theory. A neural field model of the isolated cortex is used that consists of three neural populations, excitatory, inhibitory, and excitatory bursting. Mechanisms by which an isolated cortex gives rise to seizure-like waveforms thought to underly pathological EEG waveforms on the deafferented cortex are explored. It is shown that the model reproduces similar time series and oscillatory frequencies for paroxysmal discharges when compared with physiological recordings both during acute and chronic deafferentation states. Furthermore, within our model ictal activity arises from perturbations to steady-states very close to the dynamical system's instability boundary; hence, these are distinct from corticothalamic seizures observed in the model for the intact brain which involved limit-cycle dynamics. The results are applied to experiments in deafferented cats.

Phase analysis method for burst onset prediction.

The response of bursting neurons to fluctuating inputs is usually hard to predict, due to their strong nonlinearity. For the same reason, decoding the injected stimulus from the activity of a bursting neuron is generally difficult. In this paper we propose a method describing (for neuron models) a mechanism of phase coding relating the burst onsets with the phase profile of the input current. This relation suggests that burst onset may provide a way for postsynaptic neurons to track the input phase. Moreover, we define a method of phase decoding to solve the inverse problem and estimate the likelihood of burst onset given the input state. Both methods are presented here in a unified framework, describing a complete coding-decoding procedure. This procedure is tested by using different neuron models, stimulated with different inputs (stochastic, sinusoidal, up, and down states). The results obtained show the efficacy and broad range of application of the proposed methods. Possible applications range from the study of sensory information processing, in which phase-of-firing codes are known to play a crucial role, to clinical applications such as deep brain stimulation, helping to design stimuli in order to trigger or prevent neural bursting.

The distinct stochastic and deterministic dynamics between period-adding and period-doubling bifurcations of neural bursting patterns

Period-adding bifurcations and period-doubling bifurcations of neural firing patterns, which were both observed in the biological experiment on a neural pacemaker and simulated in a theoretical model (Chay model), manifested different stochastic dynamics near the bifurcation points. For period-adding bifurcations, a noise-induced stochastic bursting, whose behavior is stochastic transition between period-k and period-( $$k+1$$ ) bursts, lying between period-k and period-( $$k+1$$ ) burstings ( $$k=1,2,3$$ ). For period-doubling bifurcations, period-1 bursting is changed to period-2 bursting firstly and then to period-4 bursting. No stochastic firing patterns similar to those lying in the period-adding bifurcation were detected. Using the method of the fast–slow variables dissection, the deterministic burstings in both period-adding bifurcation and period-doubling bifurcation are classified into “fold/homoclinic” bursting with a saddle-node point and a saddle-homoclinic point, which behaves as a critical phase sensitive to noisy disturbance. For the bursting pattern near the period-doubling bifurcation point, the trajectory of burstings is far from the saddle-homoclinic point. Near the period-adding bifurcation points from period-k to period-( $$k+1$$ ) burstings, the trajectories of the bursting patterns pass through the neighborhood of the saddle-homoclinic point and exhibit a platform. The platform appears after the k-th spike for the period-k bursting and between the k-th spike and the ( $$k+1$$ )-th spike for the period-( $$k+1$$ ) bursting. For some bursts of period-k bursting, noise can induce a novel spike near the platform to form a burst with $$k+1$$ spikes, and for some bursts of period-( $$k+1$$ ) bursting, the last spike can be terminated by noise to form a burst with k spikes. It is the cause that the stochastic bursting whose behavior is stochastic transition between period-k burst and period-( $$k+1$$ ) burst is induced by noise, and the stochastic transition happens within or near the platform, i.e., the neighborhood of the saddle-homoclinic point. More detailed transition dynamics can be explained by the stable/unstable manifold of the saddle point. The underlying deterministic dynamics between period-adding and period-doubling bifurcation points that can lead to distinct stochastic dynamics are identified, which are helpful for understanding the roles of noise and provide critical phase to apply control strategy to modulate the firing patterns.

Commentary: Burst Firing in a Motion-Sensitive Neural Pathway Correlates with Expansion Properties of Looming Objects That Evoke Avoidance Behaviors.

Commentary: Burst Firing in a Motion-Sensitive Neural Pathway Correlates with Expansion Properties of Looming Objects That Evoke Avoidance Behaviors.

Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-plateau Bursting

Pseudo-plateau bursting is a type of oscillatory waveform associated with mixed mode dynamics in slow/fast systems and commonly found in neural bursting models. In a recent model for the electrical activity and calcium signaling in a pituitary lactotroph, two types of pseudo-plateau bursts were discovered: one in which the calcium drives the bursts and another in which the calcium simply follows them. Multiple methods from dynamical systems theory have been used to understand the bursting. The classic 2-timescale approach treats the calcium concentration as a slowly varying parameter and considers a parametrized family of fast subsystems. A more novel and successful 2-timescale approach divides the system so that there is only one fast variable and shows that the bursting arises from canard dynamics. Both methods can be effective analytic tools, but there has been little justification for one approach over the other. In this work, we use the lactotroph model to demonstrate that the two analysis techniques are different unfoldings of a 3-timescale system. We show that elementary applications of geometric singular perturbation theory in the 2-timescale and 3-timescale methods provide us with substantial predictive power. We use that predictive power to explain the transient and long-term dynamics of the pituitary lactotroph model.

Erratum to: Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation

This paper illustrates an informatic technique for inferring and quantifying the dynamic role of a single intrinsic current in a mechanism of neural bursting activity. We analyze the patterns of the most dominant currents in a model of half-center oscillation in the leech heartbeat central pattern generator. We find that the patterns of dominance change substantially over a cycle, allowing different local reductions to be applied to the model. The result is a hybrid dynamical systems model, which is a piecewise representation of the mechanism combining multiple vector fields and discrete state changes. The simulation of such a model tests explicit hypotheses about the mechanism and is a novel way to retain both mathematical clarity and scientific detail in answering mechanistic questions about a complex model. Several insights into the central mechanism of “escape-release” in the model are elucidated by this analysis and compared with previous studies. The broader application and extension of this technique is also discussed.

Canards of mixed type in a neural burster

Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilibria, and torus canards, which spend long times near attracting and repelling branches of periodic orbits. The canards of mixed type arise in a model of neural bursting activity of fold-fold cycle type, and, as other canard phenomena, separate different dynamic states.

Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation

This paper illustrates an informatic technique for inferring and quantifying the dynamic role of a single intrinsic current in a mechanism of neural bursting activity. We analyze the patterns of the most dominant currents in a model of half-center oscillation in the leech heartbeat central pattern generator. We find that the patterns of dominance change substantially over a cycle, allowing different local reductions to be applied to the model. The result is a hybrid dynamical systems model, which is a piecewise representation of the mechanism combining multiple vector fields and discrete state changes. The simulation of such a model tests explicit hypotheses about the mechanism and is a novel way to retain both mathematical clarity and scientific detail in answering mechanistic questions about a complex model. Several insights into the central mechanism of "escape-release" in the model are elucidated by this analysis and compared with previous studies. The broader application and extension of this technique is also discussed.

Mapping Functional Connectivity between Neuronal Ensembles with Larval Zebrafish Transgenic for a Ratiometric Calcium Indicator

The ability to map functional connectivity is necessary for the study of the flow of activity in neuronal circuits. Optical imaging of calcium indicators, including FRET-based genetically encoded indicators and extrinsic dyes, is an important adjunct to electrophysiology and is widely used to visualize neuronal activity. However, techniques for mapping functional connectivities with calcium imaging data have been lacking. We present a procedure to compute reduced functional couplings between neuronal ensembles undergoing seizure activity from ratiometric calcium imaging data in three steps: (1) calculation of calcium concentrations and neuronal firing rates from ratiometric data; (2) identification of putative neuronal populations from spatio-temporal time-series of neural bursting activity; and then, (3) derivation of reduced connectivity matrices that represent neuronal population interactions. We apply our method to the larval zebrafish central nervous system undergoing chemoconvulsant-induced seizures. These seizures generate propagating, central nervous system-wide neural activity from which population connectivities may be calculated. This automatic functional connectivity mapping procedure provides a practical and user-independent means for summarizing the flow of activity between neuronal ensembles.

Regulation of the Ca2+ Sensitivity of the Nonselective Cation Channel TRPM4

TRPM4, a Ca(2+)-activated cation channel of the transient receptor potential superfamily, undergoes a fast desensitization to Ca(2+). The mechanisms underlying the alterations in Ca(2+) sensitivity are unknown. Here we show that cytoplasmic ATP reversed Ca(2+) sensitivity after desensitization, whereas mutations to putative ATP binding sites resulted in faster and more complete desensitization. Phorbol ester-induced activation of protein kinase C (PKC) increased the Ca(2+) sensitivity of wild-type TRPM4 but not of two mutants mutated at putative PKC phosphorylation sites. Overexpression of a calmodulin mutant unable to bind Ca(2+) dramatically reduced TRPM4 activation. We identified five Ca(2+)-calmodulin binding sites in TRPM4 and showed that deletion of any of the three C-terminal sites strongly impaired current activation by reducing Ca(2+) sensitivity and shifting the voltage dependence of activation to very positive potentials. Thus, the Ca(2+) sensitivity of TRPM4 is regulated by ATP, PKC-dependent phosphorylation, and calmodulin binding at the C terminus.