Effects of reciprocal inhibitory coupling in model neurons

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.

Temperature effects on neuronal firing rates and tonic-to-bursting transitions

Temperature fluctuations can affect neurological processes at a variety of levels, with the overall output that higher temperatures in general increase neuronal activity. While variations in firing rates can happen with the neuronal system maintaining its homeostatic firing pattern of tonic firing, or bursting, changes in firing rates can also be associated with transitions between the two patterns of firing. Our computer simulations suggest a possible mechanism directly related to the shortening of the duration of the action potential for higher firing rates with temperature increase. Increased temperatures also shorten the period doubling cascade and chaos transition between tonic and burting regimes.

Synchronous tonic-to-bursting transitions in a neuronal hub motif

We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.

Bifurcation transitions in gap-junction-coupled neurons

Here we investigate transitions occurring in the dynamical states of pairs of distinct neurons electrically coupled, with one neuron tonic and the other bursting. Depending on the dynamics of the individual neurons, and for strong enough coupling, they synchronize either in a tonic or a bursting regime, or initially tonic transitioning to bursting via a period doubling cascade. Certain intrinsic properties of the individual neurons such as minimum firing rates are carried over into the dynamics of the coupled neurons affecting their ultimate synchronous state.

Microcircuits in respiratory rhythm generation: commonalities with other rhythm generating networks and evolutionary perspectives

Rhythmicity is critical for the generation of rhythmic behaviors and higher brain functions. This review discusses common mechanisms of rhythm generation, including the role of synaptic inhibition and excitation, with a focus on the mammalian respiratory network. This network generates three phases of breathing and is highly integrated with brain regions associated with numerous non-ventilatory behaviors. We hypothesize that during evolution multiple rhythmogenic microcircuits were recruited to accommodate the generation of each breathing phase. While these microcircuits relied primarily on excitatory mechanisms, synaptic inhibition became increasingly important to coordinate the different microcircuits and to integrate breathing into a rich behavioral repertoire that links breathing to sensory processing, arousal, and emotions as well as learning and memory.

Dynamics of signal propagation and collision in axons

Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. While typically thought of as being unidirectional, it is not uncommon for axonal propagation of action potentials to happen in both directions. This is the case because action potentials can be initiated at multiple "ectopic" positions along the axon. Two ectopic action potentials generated at distinct sites, and traveling toward each other, will collide. As neuronal information is encoded in the frequency of action potentials, action potential collision and annihilation may affect the way in which neuronal information is received, processed, and transmitted. We investigate action potential propagation and collision using an axonal multicompartment model based on the Hodgkin-Huxley equations. We characterize propagation speed, refractory period, excitability, and action potential collision for slow (type I) and fast (type II) axons. In addition, our studies include experimental measurements of action potential propagation in axons of two biological systems. Both computational and experimental results unequivocally indicate that colliding action potentials do not pass each other; they are reciprocally annihilated.