Abstracts

Rationale: Seizures arise from a complex nonlinear interaction between specific excitatory and inhibitory cellular sub-types. The dynamics and excitability of such networks is further complicated by the fact that a variety of metabolic processes such as potassium gradients and local oxygen availability determine the excitability of those neuronal networks. We have recently shown that the interrelated dynamics of potassium and sodium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states [1, 2]. We found that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in the ion concentrations similar to what is seen physiologically in seizures. Our work emphasizes the critical role of ion concentration homeostasis in neuronal functions. We made several predictions about the effect of microenvironmental changes on the network behavior that needs to be tested in the experiment. However, the existing in vitro techniques are too limited to be able to test these predictions. Here we use the model based predictor-controller framework from modern control engineering to directly test these hypotheses. Methods: We use Unscented Kalman Filter (UKF) in conjunction with computer model for spontaneous seizure and noisy experimental data to estimate the entire dynamics of excitatory and inhibitory neurons during in vitro seizures. We model individual neurons using Hodgkin-Huxley type formulism. The reversal potentials for various ion currents and leak conductances are updated based on instantaneous ion concentrations inside and outside the cells. The K+/Na+ concentration in the interstitial volume surrounding each cell was continuously updated based on K+/Na+ currents across the neuronal membrane, K+/Na+ pumps, uptake by the glial network surrounding the neurons, and lateral diffusion of K+ within the extracellular space. Results: We assimilate noisy membrane potential measurements from hippocampal neurons to estimate the global dynamics of these cells and networks including their microenvironment during seizures. Using only membrane potential measurements in UKF, we estimate the gating variables and conductances of all ion channels, the microenvironment of individual neurons such as extracellular and intracellular potassium, sodium, and calcium concentrations, and the dynamics of the extracellular potassium buffering mechanism. Lastly, we introduce a strategy for dynamic clamping, and show the feasibility of controlling seizures using variety of control frameworks [3]. Conclusions: Here we put forward a framework that can estimate the entire dynamics of a neuronal system using noisy measurements of a single variable. Further, this framework can be utilized to generate control signals based on the estimated variables and parameters to control the system’s dynamics in situation such as seizures and Parkinson’s disease. Supported by: NIH Grants R01MH50006 (GU, SJS) and K02MH01493 (SJS). [1]. J. Comp. Neurosci. 26:159-170 (2009). [2]. J. Comp. Neurosci. 26:171-183 (2009). [3]. Phys. Rev. E 79, 040901(R) (2009)