High Prevalence of Multistability of Rest States and Bursting in a Database of a Model Neuron

Abstract

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.

Temperature compensation in a small rhythmic circuit

“…Hysteresis and multistability are often observed in conductance based models of neuronal activity (Malashchenko et al, 2011;Marin et al, 2013), and the network studied here also exhibits such features. We explored hysteretic behavior in the models by increasing temperature linearly from 10°C to 35°C in 30 minutes and then decreasing it back to 10°C at the same pace.…”

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

“…For example, among 99,066 total realistic HCOs, only 1,055 (1.06%) were composed of bursters (263 instances) (including 990 realistic HCOs that were composed of realistic bursters (238 instances)) as stated above, but 94,487 (95.37%) were composed of spiking isolated neurons (12,443 instances) and 3,524 (3.56%) were composed of neurons classified as either bistable isolated neurons (3,096 HCOs from 820 isolated neuron instances), as irregular isolated neurons (368 HCOs from isolated neuron 55 instances), as silent isolated neurons (58 HCOs from 28 isolated neuron instances) or as plateau neurons (2 HCOs from 2 isolated neuron instances).Thus realistic HCOs could also consist of irregular (irregular bursters or irregular tonic firers), silent, or even bistable neurons. Previous work from our group shows that our burster instances have a high propensity for multistability and that mutual inhibition makes multistability much less prevalent [33]. Although we have not tested this idea systematically, we suspect that such multistability is present in the other classes of isolated neuron instances.…”

Computational models in the age of large datasets

“…First, the models are typically nonlinear, so the relation between the parameters and the output can be complicated and many-valued. Averages of measured parameters can give rise to non-observed behavior [26] and models can be exquisitely sensitive to measured parameters [27,28,29,30]. The value of averaging as a means of combating experimental noise might thus be obviated by the possibility that the average values are not valid parameter combinations themselves.…”