Mathematical Biology Seminar Alexander Ginsburg, UU Math Wednesday, September 27, 2023 1:45pm in LCB 323 Firing-rate models and chronic pain Abstract: Neurons make the nervous system tick. By communicating via electrical impulses, neurons form concentrated networks in localized regions of the brain to carry out the complex tasks required of the nervous system, ranging from moving the limbs to coordinating circadian rhythms. Despite their complexity, these networks encode much information in their rates of electrical impulse production?their firing rates. Hence, researchers have sought to model these networks via firing-rate models, and we begin with a brief review thereof. Namely, we highlight several models that spearheaded the development of the field, and we augment our review with an analysis of the corresponding network of citations. In doing so, we quantify how key papers contribute to the literature. We then highlight an application of firing-rate models to the study of chronic pain. Specifically, we employ coupled firing-rate models to understand two biophysically motivated circuit structures that represent common motifs within the dorsal horn of the spinal cord. The circuit motifs, respectively, regulate the production of static and dynamic allodynia, wherein gentle pressure (static) and gentle brushing sensations (dynamic) cause pain. To understand how dysregulation of these circuits can lead to allodynia, we provide a new sensitivity analysis methodology. The methodology involves first identifying the sets of coupling strengths that produce experimentally observed behaviors. To identify how the corresponding ?properly behaving? circuits are most vulnerable towards producing allodynia, we compute the minimal alteration in coupling strengths needed to induce the circuits to produce allodynia. We cluster the properly behaving circuits accordingly. Results indicate that in each circuit motif, allodynia is caused by unbalancing excitation and inhibition. Results further clarify how differences in coupling strengths or circuit structure lead to different vulnerabilities towards producing allodynia.