Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance ()) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of . We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.
It is often not appreciated that different activity regimes can coexist with each other in a given neuron so that a transient stimulus can cause a persistent change of activity. Such multistability of the neuronal dynamics has in fact been shown in a variety of neurons and can play either a functional role or present a substrate for neurological diseases. We explored the propensity for multistability in a database of a leech heart interneuron model, testing each case (parameter set) in a database for multistability. We found a large proportion of multistable cases, especially the coexistence of silent and bursting regimes. This was a surprising result, since these cells pace the heartbeat of the leech, and the coexistence of silence and bursting could disrupt the functional pattern, threatening the viability of the leech. Analysis of networks of mutually inhibitory multistable neurons, however, showed robustness in maintaining functional activity, suggesting that the mutually inhibitory coupling can act as a protective mechanism against failures induced by multistability.