Michael Reed

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  The Auditory System for Mathematicians
  Michael Reed
  This will be an introductory lecture on the auditory system for mathematicians. I'll start with sound waves, discuss the outer, middle, and inner ears, the VIIIth nerve, and up into the brain stem. Then I'll outline work on sound localization, stochasticity, hyperacuity, and the ocular-vestibular reflex. The emphasis will be on mathematical issues and the need for new conceptual constructs.
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  Mathematical models of serotonin metabolism: What is the mechanism of action of SSRIs?
  Michael Reed

  Despite more than 50 years of research, the etiology of depressive illness remains unknown. A hypothesis that has been central to much work in pharmacology and electrophysiology is that depression is caused by dysfunction in the serotonergic signaling system. In recent work, with Janet Best (OSU) and H. Frederik Nijhout (Duke), a mathematical model of a serotonergic synapse was created to study regulatory mechanisms in the serotonin system. After an introduction to the serotonin system, the model will be described as well as comparisons to experimental results. We will discuss why it is so difficult to understand the mechanism of efficacy of selective serotonin reuptake inhibitors (SSRIs). We will present predictions of the model as well as a new hypothesis for the mechanism of action of the SSRIs.

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  Serotonin and the mysteries of depression and SSRI action
  Michael Reed

  Despite decades of research, the biochemical and neurophysiological causes of depression remain unknown. Furthermore, although selective serotonin reuptake inhibitors (SSRIs) block the reuptake of serotonin and alleviate depression in some patients, it is not clear how or why they work. Mathematical models of serotonin synthesis, release, and reuptake can shed light on the control mechanisms of the serotonin system and suggest hypotheses about the action of SSRIs. We will discuss two of the standard hypotheses and propose a new hypothesis.

  Parkinson?s disease has been traditionally thought of as a dopaminergic disease in which cells of the substantia nigra pars compacta (SNc) die. However, accumulating evidence implies an important role for the serotonergic system in Parkinson?s disease in general and in physiological responses to levodopa therapy, the first line of treatment. We use a mathematical model to investigate the consequences of levodopa therapy on the serotonergic system and on the pulsatile release of dopamine (DA) from dopaminergic and serotonergic terminals in the striatum.

  We will also ask, and propose an answer to, the question of what serotonin is doing in the striatum anyway?

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  Liver Metabolism and Public Health
  Michael Reed

  I will discuss mathematical models of parts of liver metabolism that relate to public health including folate metabolism, neural tube defects, cancer chemotherapy, DNA methylation, colon cancer and folate supplementation, arsenic detoxification, and the toxicity of acetaminophen. What makes a model good? How do you determine parameters?  How do you conduct biological experiments with models? As a mathematician, how do you figure out what problems to work on and what people to talk to? These hard questions are the subtext of the lecture.

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  Cell Metabolism and Neuroscience
  Michael Reed

  Mathematical and computational neuroscience have contributed to the brain sciences by the study of the dynamics of individual neurons and more recently the study of the dynamics of electrophysiological networks. Often these studies treat individual neurons as points or the nodes in networks and the biochemistry of the brain appears, if at all, as some intermediate variables by which the neurons communicate with each other. In fact, many neurons change brain function not by communicating in one-to-one fashion with other neurons, but instead by projecting changes in biochemistry over long distances. This biochemical network is of crucial importance for brain function and it influences and is influenced by the more traditional electrophysiological networks. Understanding how biochemical networks interact with electrophysiological networks to produce brain function both in health and disease poses new challenges for mathematical neuroscience.

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  How Mathematicians can Contribute to Genomic Medicine
  Michael Reed

  Mathematical models of physiological processes allow one to study the homeostatic mechanisms that keep important phenotypic variables within certain normal ranges. When these variables leave the homeostatic range often disease processes ensue. From the models one can derive surfaces that show the relationship between genetic polymorphisms and particularly important phenotypic variables. Known gene polymorphisms correspond to particular points on the surface, some of which are located near the edge of the homeostatic region. The purpose of medical advice tailored to the patient’s genotype is to suggest dietary changes or exercise changes that move the patient back towards the middle of the homeostatic region.

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  Stochastics in Biological Networks
  Michael Reed
  Most biological questions are network questions because biological systems are large and complicated. Stochastic processes arise naturally (1) as external forcing to which the system must adapt; (2) as an external probe of system dynamics; (3) as a representation of underlying biological diversity; (4) as a fundamental mechanism for a biological object to achieve a specific purpose. Examples will be given. Biological networks have myriad control mechanisms that ensure that some variables remain stable while other fluctuate wildly. How can one tell from the network (and the dynamics) which variables are the stable ones? Many examples of (4) will be given including gene expression and volume transmission in the brain. To find exciting and new mathematical questions, one should focus on how specific biological systems work.