Neurons generate the activity that drives behaviors thanks to electrical currents that flow across their membranes through several different but highly specific channels. These channels are formed by specialized proteins synthesized by each cell and embedded in their membranes. The activity that one can record from these cells (such as rhythmic oscillations) is expected to vary if the number of these channel-proteins varies. Yet, neurons of the same type have been observed to express extremely variable numbers of each channel-protein type, and thus extremely variable electrical currents flowing across their membranes, with relatively minimal effects on their activity (e.g., their oscillation frequency). Whether their existence ensures that the activity of these cells will be similar, and what the consequences for network function are, remains largely unclear. The general goal of this project is to examine what features of neuronal activity are regulated by electrical current correlations, whether these features of activity are propagated to the networks they form part of, and what universal principles or mechanisms these relationships obey. The results of this project are expected to have impact in various areas of mathematical biology, and the project will promote interdisciplinary training of undergraduate and graduate students through involvement in the research.
High variability in the levels of ionic conductance expressed by identical neurons have been observed in a number of preparations. In some of the same preparations, a tendency of some of the ionic conductances to co-vary has been identified. This co-variation appears as correlations of these currents in populations of neurons, which are thought to lead to the generation of very similar types of activity despite the variability of individual currents, in a sort of homeostatic scaling of these currents. This project will test the hypothesis that the existence of correlations among subsets of ionic currents determines a stable and robust neuronal activity, and that this effect propagates to the level of the networks. The features of activity affected by these correlations are expected to lie close to so-called level sets of activity for the oscillation attributes (e.g., frequency, amplitude, duty cycle). The mathematical concept of level sets has been applied to dynamical neuronal systems to a limited degree and only at the level of single neurons. The project team will investigate the mechanisms of generation of level sets, particularly related to the existence of ionic current correlations, in single neurons of a well-known neuronal network (the crustacean pyloric network). This project will (i) extend this to determine the consequences of their existence for network dynamics, (ii) determine if there are universal mechanisms, understandable in terms of classes of ionic current properties rather than individual current properties, that determine the emergence of level sets, and (iii) investigate what other factors determine the existence of level sets besides the amplitude of the conductances. Graduate and undergraduate students will be trained in a multidisciplinary investigation of the properties of neuronal systems, including computations, dynamical systems theory, and experiments.
