A computational study of the effects of serotonin on a molluscan burster neuron

Abstract

Abstract. A mathematical model of burster neuron R15from the abdominal ganglion of Aplysia is presented. This is an improvement over earlier models in that the bursting mechanism is more accurately represented. The improved model allows for simulated application of the neurotransmitter serotonin, which has been reported to have profound effects on the voltage waveform produced by Rl5. Computational analysis indicates that the serotonin-induced modulation of the waveform can be explained in terms of competition between stationary, bursting, and beating attractors. Analysis also indicates that, as a result of this competition, serotonin increases the sensitivity of the neuron to synaptic perturbations. This may have important consequences with regard to water balance in the Aplysia, particularly during egg laying.

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.…”

“…Plant and Kim, 1976;Canavier et al, 1991;Bertram, 1993;Smolen and Keizer, 1992;Guckenheimer et al, 1994;Rinzel and Troy, 1982;Traub et al, 1991;Wang et al, 1991) and a systematic mathematical analysis of one such model was first performed by Rinzel (1985). In this analysis the system variables were classified as either "fast", if the variable changed significantly over the duration of a single spike, or "slow", if significant change occurred only over the duration of the burst.…”

Computational Models of Neuromodulation

“…Numerous mathematical models have been developed to explain the cellular basis of single-cell oscillatory activity and bursting. Some models went further and studied the extrinsic modulation of oscillatory dynamics by substances such as DA and 5-HT (Bertram, 1993(Bertram, , 1994Butera et al, 1995), while others focused on the role of intrinsic modulation by calcium-dependent processes in conditioning (Gingrich & Byrne, 1987;Raymond et al, 1992).…”

“…A first series of studies used a simplified HH framework to model the effect of 5-HT as modifications in the conductance of a subthreshold K + current (Bertram, 1993(Bertram, , 1994. As for the models of the AB neuron, these models show that changes in maximal conductance can modify the firing properties of R15 from silent to bursting and beating and that the sensitivity of the cell to synaptic inputs is increased.…”

Making a Swim Central Pattern Generator Out of Latent Parabolic Bursters

“…The Plant model has been developed to accurately describe the voltage dynamics of the R15 neuron in a mollusk Aplysia Californica, which has turned out to be an endogenous burster [Levitan & Levitan, 1988]. Most dynamical properties of the R15 neuron have been modeled and studied in detail [Canavier et al, 1991;Bertran, 1993;Butera et al, 1995;Butera, 1998;Sieling & Butera, 2011;Ji et al, 2013].…”