Nonlinear dynamics in a model neuron provide a novel mechanism for transient synaptic inputs to produce long-term alterations of postsynaptic activity

Abstract

1. A mathematical model of a bursting molluscan neuron has been found to possess multiple modes of electrical activity, such as periodic beating (tonic firing), periodic bursting (bursts of action potentials separated by quiescent periods), and potentially chaotic bursting, all at a single set of parameters. The multiple modes correspond to multiple stable attractors, whose existence is an emergent property of the nonlinear dynamics of the system. 2. Transient synaptic inputs can switch the activity of the neuron between different modes. These mode transitions, which do not require any changes in the biochemical or biophysical parameters of the neuron, provide an enduring response to a transient input, as well as a mechanism for phasic sensitivity (i.e., temporal specificity). 3. These results provide new insights into the role of nonlinear dynamics in information processing and storage at the level of the single neuron.

Topological and phenomenological classification of bursting oscillations

“…Examples exist of models generating type II bursting in which instantaneous perturbations can reset the oscillation. These include the model of bursting in R 15 by Bertram (1993Bertram ( , 1994, where one of the slow variables is sufficiently fast at some voltages to respond quickly to the perturbation (although this model does not fit precisely into the present framework since it has a quintic, rather than cubic, slow manifold), and the R15 model by Canavier et al (1991) in which several bursting, beating, and chaotic attractors coexist (Canavier et al, 1993). Phase resetting, then, provides only a limited experimental tool in the classification of a bursting oscillation.…”

Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

“…͑1͒ and ͑2͒, respectively. The slow subsystem can act independently, 21 be affected synaptically, 17 or interact locally with the spiking fast subsystem 5,[15][16][17] to produce alternating periods of spiking and silence in time. To examine the dynamical mechanism implicit to a bursting behavior, y is treated as a bifurcation parameter of the fast subsystem.…”

“…͑2͒ degenerates into an algebraic equation, but the assumption is reasonable when there is a large time separation between fast and slow dynamics. Using this technique, all autonomously bursting single neuron models displaying multirhythmic bursting in literature 15,16 are topologically classified as the circle/circle type; 22,23 that is, their fast subsystem is driven back and forth across a saddle node on invariant circle ͑SNIC͒ bifurcation to produce alternating spiking and silent states. These models can be reduced to a form that supports a topological normal SNIC to and from the active phase.…”

“…This can be seen in the biophysical models that support multirhythmic bursting. 15,16 UPOs in these systems correspond to the unstable fixed points of P which separate contraction mappings.…”

“…The feasibility of multistability as an information storage and processing mechanism in neural systems has been widely discussed in terms of neural recurrent loops and delayed feedback mechanisms. [12][13][14] Theoretical studies have shown multirhythmic bursting behavior in a number of single neuron models 15,16 as well as in a model two-cell inhibitory ͑half-center oscillator͒ network. 17 In biological neurons, it is possible that these dynamics are employed as a short term memory.…”