Impulse pattern in bi-directionally coupled model neurons of different dynamics

Computational and experimental modulation of a noisy chaotic neuronal system

In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.

Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks' activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing-all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.

Effects of reciprocal inhibitory coupling in model neurons

Central pattern generators are neuron networks that produce vital rhythmic motor outputs such as those observed in mastication, walking and breathing. Their activity patterns depend on the tuning of their intrinsic ionic conductances, their synaptic interconnectivity and entrainment by extrinsic neurons. The influence of two commonly found synaptic connectivities--reciprocal inhibition and electrical coupling--are investigated here using a neuron model with subthreshold oscillation capability, in different firing and entrainment regimes. We study the dynamics displayed by a network of a pair of neurons with various firing regimes, coupled by either (i) only reciprocal inhibition or by (ii) electrical coupling first and then reciprocal inhibition. In both scenarios a range of coupling strengths for the reciprocal inhibition is tested, and in general the neuron with the lower firing rate stops spiking for strong enough inhibitory coupling, while the faster neuron remains active. However, in scenario (ii) the originally slower neuron stops spiking at weaker inhibitory coupling strength, suggesting that the electrical coupling introduces an element of instability to the two-neuron network.

An analog circuit implementation of a Huber-Braun cold receptor neuron model

We present the design and implementation of an electronic device that, using off the shelf discrete analog components, implements the mathematical model of a cold receptor neuron called Huber-Braun. This model describes the electrical behavior of certain kinds of receptors when interacting with their environment, and it consists of a set of differential equations that has only been solved by numeric simulations. By these means a chaotic behavior has been found. An analog computer can be relevant for further analysis and validation of the model. The results obtained by means of numeric simulations and through our analog circuit simulator are consistent. In particular, temperature and external current bifurcation diagrams were successfully built. Finally, the electronic device allows the observation of all relevant variables and most of the expected behavior (tonic firing, chaotic, burst discharge, subthreshold oscillation and steady state).

Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.

On the role of subthreshold currents in the Huber-Braun cold receptor model

We study the role of the strength of subthreshold currents in a four-dimensional Hodgkin-Huxley-type model of mammalian cold receptors. Since a total diminution of subthreshold activity corresponds to a decomposition of the model into a slow, subthreshold, and a fast, spiking subsystem, we first elucidate their respective dynamics separately and draw conclusions about their role for the generation of different spiking patterns. These results motivate a numerical bifurcation analysis of the effect of varying the strength of subthreshold currents, which is done by varying a suitable control parameter. We work out the key mechanisms which can be attributed to subthreshold activity and furthermore elucidate the dynamical backbone of different activity patterns generated by this model.

A computational study of the interdependencies between neuronal impulse pattern, noise effects and synchronization

Alterations of individual neurons dynamics and associated changes of the activity pattern, especially the transition from tonic firing (single-spikes) to bursts discharges (impulse groups), play an important role for neuronal information processing and synchronization in many physiological processes (sensory encoding, information binding, hormone release, sleep-wake cycles) as well as in disease (Parkinson, epilepsy). We have used Hodgkin-Huxley-type model neurons with subthreshold oscillations to examine the impact of noise on neuronal encoding and thereby have seen significant differences depending on noise implementation as well as on the neuron's dynamic state. The importance of the individual neurons' dynamics is further elucidated by simulation studies with electrotonically coupled model neurons which revealed mutual interdependencies between the alterations of the network's coupling strength and neurons' activity patterns with regard to synchronization. Remarkably, a pacemaker-like activity pattern which revealed to be much more noise sensitive than the bursting patterns also requires much higher coupling strengths for synchronization. This seemingly simple pattern is obviously governed by more complex dynamics than expected from a conventional pacemaker which may explain why neurons more easily synchronize in the bursting than in the tonic firing mode.

Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations

We have examined the effects of current and conductance noise in a single-neuron model which can generate a variety of physiologically important impulse patterns. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Additive Gaussian white noise which is implemented as conductance noise appears in the voltage equations as an additive and a multiplicative term. Moreover, the originally white noise is turned into colored noise. The noise correlation time is a function of the system's control parameters which may explain the different effects of current and conductance noise in different dynamic states. We have found the most significant, qualitative differences between different noise implementations in a pacemaker-like, tonic firing regime at the transition to chaotic burst discharges. This reflects a dynamic state of high physiological relevance.