Jarrett L. Lancaster

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.

Modeling excitable systems: Reentrant tachycardia

Excitable membranes are an important type of nonlinear dynamical system, and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and neural tissues. One model is based on the Fitzhugh–Nagumo equations, and the other is based on a three-transistor excitable circuit. We construct a circuit that simulates reentrant tachycardia and its treatment by surgical ablation. This project is appropriate for advanced undergraduates as a laboratory capstone project or as a senior thesis or honors project and can also be a collaborative project, with one student responsible for the computational predictions and another for the circuit construction and measurements.

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.

Non-invasive evaluation of cardiac repolarization in mice exposed to single-wall carbon nanotubes and ceria nanoparticles via intratracheal instillation

We present results obtained from electrocardiogram (ECG) measurements performed on mice exposed to single-walled carbon nanotubes and ceria nanoparticles through instillation. From these non-invasive ECG measurements, QT and RR intervals were obtained at various times after exposure and used to compute a novel metric for evaluating cardiac signal propagation stability, the reserve of refractoriness (RoR). It is demonstrated that while the isolated QT and RR intervals are essentially uncorrelated with histological data from hematoxylin and eosin stains of control and exposed tissue samples, the RoR is sensitive to cardiovascular effects from the exposure to nanoparticles.

Modeling order-disorder transition in Low-Density Lipoprotein

Low Density Lipoproteins (LDL) undergo a reversible order-disorder thermal transition close to biological temperature due to cooperative melting of the cholesteryl esters (CE) in the core of the LDL particle. We have noticed that chain-chain interactions between CE molecules are responsible for the stability of the ordered smectic phase; thus, we formulated a simple “coarse-grained” two-state model to describe the melting process. In this model only nearest neighbor interactions are allowed. On the basis of these assumptions we performed Metropolis Monte Carlo (MC) simulation in order to obtain the heat capacity curve. The resulting profile reveals well-known features of the systems with a finite size.