Pacemaker Neuron and Network Oscillations Depend on a Neuromodulator-Regulated Linear Current

Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current IMI, which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of IMI for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs

The effects of varying the timing of inputs on a neural oscillator

The gastric mill network of the stomatogastric ganglion of the crab Cancer borealis is comprised of a set of neurons that require modulatory input from outside the stomatogastric ganglion and input from the pyloric network of the animal in order to oscillate. Here we study how the frequency of the gastric mill network is determined when it receives rhythmic input from two different sources but where the timing of these inputs may differ. We find that over a certain range of the time difference one of the two rhythmic inputs plays no role what so ever in determining the network frequency, while in another range, both inputs work together to determine the frequency. The existence and stability of periodic solutions to model sets of equations are obtained analytically using geometric singular perturbation theory. The results are validated through numerical simulations. Comparisons to experiments are also presented

On the role of theory and modeling in neuroscience

In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community