| Understanding how the brain works remains one of the toughest problems in science, despite the progress in scientific technology available for its study. The difficulty lies in the fact that the brain is a dynamic system, while the body of facts gathered from the experiments is static, a series of snapshots at one angle or magnification or time. Such an approach is adequate for capturing the brain's structure, but offers limited insight into its function. I present a series of mathematical models that allows one to restore the dynamic nature of the process by putting the experimental data into an organic whole and also to design experiments that capture information about the response of the brain to external stimuli or to internal changes due to a pathological process without losing its dynamic nature. These approaches are illustrated with two specific problems. The first centers on the ionic basis of CO 2 chemosensitivity in the brainstem. I developed several models that describe chemosensitivity as an aggregate property of multiple potassium ion channels whose contribution to changes in neuronal firing rate during hypercapnic acidosis is determined not only by the degree of their inhibition by pH but also by their location within the cell. The model predicts that intrinsic chemosensitivity is somatic in origin, while pH sensing in dendrites may enhance chemosensitivity at the network level. The second problem is the need to characterize the response of the basal ganglia to deep brain stimulation (DBS), a therapy for Parkinson's disease, in order to identify a feedback signal to control the stimulator's output based on brain function. Using a 6-hydroxydopamine hemi-Parkinsonian rat model, I measured glutamate release in the globus pallidus pars interna, while simultaneously subjecting the animal to a specifically designed stimulation sequence applied to the subthalamic nucleus. I found that the dopaminergic lesion altered the dynamics of neurotransmitter release in the globus pallidus, making it a candidate feedback signal for a closed-loop DBS device. The differences in the dynamics were described using a transfer function that predicts the glutamate concentration in response to any given stimulation sequence. |
