Current Research Projects
Neuronal control of sleep-wake regulation
In a joint project with Cecilia Diniz Behn (Colorado School of Mines, Department of Mathematics), we are constructing neurophysiologically based models of the neuronal networks and neurotransmitter interactions in the brainstem and hypothalamus that regulate wake and sleep states. While individual neuronal populations and neurotransmitter actions have been identified that participate in the wake-sleep cycle and the generation of rapid-eye-movement (REM) sleep, the specific interactions responsible for the transitions between wake, non-REM sleep and REM sleep states are not completely understood. We have developed a novel mathematical modeling framework that is uniquely suited to investigating the structure and dynamics of the sleep-wake regulatory network in the brainstem and hypothalamus. It is based on a population firing rate model formalism that is expanded to explicitly include concentration levels of neurotransmitters released to postsynaptic populations. Using this framework, we model interactions among primary brainstem and hypothalamic neuronal nuclei involved in rat sleep-wake regulation. Experimental results that we are investigating with the model include effects on sleep states of microinjections of neurotransmitter agonists and antagonists into specific neuronal populations, and the circadian modulation of sleep-wake patterning induced by the interaction of the sleep-wake nuclei with the suprachiasmatic nucleus, the circadian pacemaker in mammals. We collaborate on this project with Danny Forger (UM, Department of Mathematics), George Mashour and Dinesh Pal (UM, Department of Anesthesiology).
Interaction of neuronal properties and network structure on network dynamics
With Michal Zochowski (UM, Physics and Biophysics), we are working on projects addressing the general question of the influence of intrinsic neuron properties and network topology on the generation of spatio-temporal activity patterns in large-scale neuronal networks. We are motivated by experimental observations of changes in neuronal properties induced by key neuromodulators in the brain as well as changes in network connectivity structure as a result of learning and synaptic plasticity. We are developing large scale networks consisting of biophysical model neurons to investigate the interactions of neuronal excitability properties and network structure in the determination of spatio-temporal patterning of network activity.