Oscillations and other patterns of neuronal activity arise throughout the central nervous system. These activity patterns have been implicated in the generation of sleep rhythms, sensory processing, working memory and pathological rhythms that arise in diseased states such as schizophrenia and Parkinson's disease. While numerous mathematical models have been proposed for these systems, there has been very little mathematical analysis of these models. This is because the models are highly nonlinear, they exhibit an extremely complex structure of spatio-temporal dynamic behaviors and they depend in often unintuitive ways on the numerous parameters in the model. This research develops mathematical and computational tools for analyzing a general class of neuronal models. In particular, the research: (i) helps explain mechanisms underlying complex spatiotemporal patterns seen in recent experiments on early sensory processing in the insect antennal lobe; (ii) develops a novel model for working memory based on calcium dynamics and excitatory-inhibitory interactions within the prefrontal cortex; and (iii) develops new mathematical and computational tools for studying calcium and membrane potential wave propagation in spatial domains with complex geometries. The issues considered arise in many neuronal systems throughout the brain and the new mathematical tools will be very useful in the study of these other systems as well.
Everything that the brain does depends on the firing properties of neurons. This includes the control of movements, learning, memory, emotion and sensory processing. Changes in neuronal firing patterns are associated with memory and aging, and pathological patterns have been implicated in neurological diseases such as schizophrenia and Parkinson's disease. With the development of new sophisticated experimental techniques, neuroscientists are now beginning to better understand the functional roles of these firing patterns in normal brain processing, the biophysical mechanisms underlying these patterns and what is responsible for changes in these patterns during learning, aging and disease. However, it is becoming increasingly clear that mathematical modeling and computational methods are critically important in accounting for the massive amounts of new data, testing new hypotheses and understanding how complicated processes interact to generate complex brain rhythms. Novel mathematical tools are developed for analyzing detailed models that arise in numerous brain systems. In particular, models for working memory are constructed and analyzed; this corresponds to our ability to store and manipulate information for a short time in order to carry out complex tasks. Problems with working memory is associated with several neurological diseases including schizophrenia and the project explores how changes in neurotransmitters such as dopamine lead to pathological rhythms associated with these neurological diseases.
The neuroprotective role of stimulating glia mitochondria during stroke: Cerebral ischemic stroke is the number 3 cause of death, trailing only cancer and heart disease. Despite the urgent need, mechanisms underlying brain injuries during stroke remain largely unknown and current therapeutic strategies to combat stroke have been largely unsuccessful. We have developed a detailed mathematical model for many of the key processes associated with ischemic stroke. The model was constrained by recent experimental studies and is being used to compare, contrast and suggest mechanisms underlying observed behavior. Opposed to earlier studies that have targeted neuronal processes for treatment, we focused on astrocytes, which are inherently neuroprotective. Recent experiments by our collaborators have demonstrated that enhancing astrocyte mitochondrial ATP production significantly reduces neuronal and astrocyte damage after stroke, and also partially reverses this damage. Despite this success, the precise protective mechanisms that are enhanced by stimulation of astrocyte ATP production remained to be elucidated and this is a primary focus of the on-going research. [1] C. Diekman, C. Fall, J. Lechleiter and D. Terman (2013) Modeling the neuroprotective role of stimulating glial mitochondria during stroke. Biophysical Journal; 104, 1752–1763. Neuronal dynamics: The PI has published numerous papers related to analyzing mechanisms underlying activity patterns in neuronal systems. This work has been motivated by several applications, including sleep, olfaction, working memory and Parkinson’s disease. Rigorous mathematical analysis characterizes how neuronal processes interact to generate complex spiking patterns and how these patterns may change as parameters in the model are varied. Some of this work was motivated by experiments, which demonstrate that many brain states are characterized by irregular and uncorrelated spiking activity. For example, there is very little correlation among neurons within the basal ganglia of normal or healthy individuals. However, during Parkinson’s disease there is a sharp increase in correlated activity. It is unclear what mechanisms are responsible for the irregular spiking. Through detailed mathematical analysis, we characterized a class of neuronal networks that are capable of exhibiting this type of firing patterns. These results are potentially important in understanding experimentally observed firing patterns in other brain regions, including those implicated in working memory. [2] E. Lee and D. Terman (2013) Stable anti-phase oscillations in a network of electrically coupled model neurons. SIAM J. Applied Dynamical Systems; 12: 1-27. [3] D. Terman, J. Rubin, and C. Diekman (2013) Irregular activity arises as a natural consequence of synaptic inhibition. Chaos; 23. Broader impact: The PI has advised numerous undergraduate, graduate and postdoctoral students on research projects closely related to this grant. He is the Director of the Undergraduate Mathematics Major at Ohio State, serves on the curriculum committee for the undergraduate neuroscience major and lectures at the Cold Spring Harbor course on computational biology. Summary of outcomes of award: The PI has developed and analyzed models that arise in several areas of neuroscience and cell biology. These include models for olfaction, sleep, working memory, respiration, Parkinson’s disease and stroke. The published results demonstrate how the intrinsic properties of cells within a neuronal network may interact with synaptic and network properties to generate experimentally observed firing patterns. Issues addressed in these papers arise in other areas of neuroscience and cell biology besides those considered in the published papers. For example, calcium signaling and energy production plays a critical role in many cellular processes and has been implicated in a wide range of neurological diseases, including Parkinson’s, Alzheimer’s, Huntington’s and epilepsy. The insights that arise from the published research will have a bearing on the study of these other diseases, as well as phenomena as diverse as neuronal development, brain trauma, neurodegeneration and cardiac ischemia-reperfusion injury. The PI has advised numerous undergraduate, graduate and postdoctoral students on research projects closely related to this grant. He is the Director of the Undergraduate Mathematics Major at Ohio State, serves on the curriculum committee for the undergraduate neuroscience major and lectures at the Cold Spring Harbor course on computational biology.
