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While transitions between neuronal states are essential to cognitive and motor functions, they are less understood than the states themselves. Transitions often consist of irregular firing activity that computational models predict is chaotic, meaning that it is deterministic and sensitive to initial conditions. Previous work shows that neurons exhibit chaotic activity and that these levels of chaos can be reduced through network interactions, ultimately achieving stable network activity. This indicates that minimizing chaotic activity is desirable for neuronal network function. Therefore, we hypothesize that biological neurons possess mechanisms to reduce chaos during transitions.
To characterize the levels of chaos during transitions, we use a combined experimental and computational approach. In our experimental approach, we induce transitions in the well-characterized crustacean stomatogastric nervous system using the neuropeptide proctolin. In our model approach, we use the Huber-Braun single neuron model and implement the excitatory, depolarizing current that proctolin activates, IMI.
In agreement with previous studies, IMI in the model was sufficient to elicit transitions between stable activity states with chaos occurring between states. However, chaos was only observable when comparing individual models with distinct IMI values or when a time-dependent IMI was implemented for sufficiently long transition durations, i.e. time interval during which the transition takes place. Short transition durations did not exhibit chaos.
To test whether this was the case in the biological system, we synaptically isolated the lateral pyloric neuron (LP) and bath-applied proctolin. This increased firing rates and elicited rapid transitions from silent or arrhythmic spiking to bursting. We quantified the levels of chaos using Lyapunov exponents which measure how quickly a system becomes unpredictable. Although the system exhibited chaos throughout the transition, the levels of chaos did not change significantly during the transition itself. Taken together with the model results, this suggests that rapid neuronal transitions suppress increases in chaos.
To further explore how the history-dependence of neuromodulators affect chaotic transitions, we used dynamic clamp to inject discrete levels of IMI into LP, omitting the time-dependence of proctolin. Increasing IMI induced transitions from silent or arrhythmic to tonic. We found that the levels of chaos did not change significantly throughout this transition, possibly due to LP being unable to burst with IMI alone. To test this, we performed similar proctolin and dynamic clamp experiments with the inherently bursting pyloric dilator neuron (PD) of the pyloric circuit. We are currently analyzing the results of these experiments.
Gonzalez, Josselyn, "History-Dependence Of Neuromodulation Affects The Levels Of Chaos In Neuronal Transitions" (2021). Biology. 20.