The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus.

Spatiotemporal patterns of action potentials are considered to be closely related to information processing in the brain. Auto-generating neurons contributing to these processing tasks are known to cause multifractal behavior in the inter-spike intervals of the output action potentials. In this paper we define a novel relationship between this multifractality and the adaptive Nernst equilibrium in hippocampal neurons. Using this relationship we are able to differentiate between various drugs at varying dosages. Conventional methods limit their ability to account for cellular charge depletion by not including these adaptive Nernst equilibria. Our results provide a new theoretical approach for measuring the effects which drugs have on single-cell dynamics.

Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium.

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.