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Research Interests for Michael C. Reed

Research Interests: Analysis, Applications of Mathematics to Physiology and Medicine

Professor Reed is engaged in a large number of research projects that involve the application of mathematics to questions in physiology and medicine. He also works on questions in analysis that are stimulated by biological questions. For a general discussion of the applications of mathematics to problems in biology, see his article, ``Why is Mathematical Biology so Hard?'' in the March, 2004, Notices of the American Mathematical Society, pp. 338-342.

Since 2003, Professor Reed has worked with Professor Fred Nijhout (Duke Biology) to use mathematical methods to understand regulatory mechanisms in cell metabolism. Most of the questions studied are directly related to public health questions. A list of publications in this area and the corresponding pdfs are available at the website metabolism.math.duke.edu (no www).

A primary topic of interest has been liver cell metabolism where Reed and Nijhout have created mathematical models for the methionine cycle, the folate cycle, and glutathione metabolism. The goal is to understand the system behavior of these parts of cell metabolism. The models have enabled them to answer biological questions in the literature and to give insight into a variety of disease processes and syndromes including: neural tube defects, Down’s syndrome, autism, vitamin B6 deficiency, acetaminophen toxicity, and arsenic poisoning.

A second major topic has been the investigation of dopamine and serotonin metabolism in the brain. The biochemistry of these neurotransmitters affects the electrophysiology of the brain and the electrophysiology affects the biochemistry. Both affect gene expression and behavior. In this complicated situation, especially because of the difficulty of experimentation, mathematical models are an essential investigative tool that can shed like on questions that are difficult to get at experimentally or clinically. This work has been done by Reed and Nijhout jointly with Janet Best, a mathematician at Ohio State. The models have shed new light on the mode of action of selective serotonin reuptake inhibitors (used for depression) and the interactions between the serotonin and dopamine systems in Parkinson’s disease.

Other areas in which Reed uses mathematical models to understand physiological questions include: models of pituitary cells that make luteinizing hormone and follicle stimulating hormone, models of the mammalian auditory brainstem, models of maternal-fetal competition, models of the owl’s optic tectum, and models of insect metabolism.

Often, problems in biology give rise to new questions in pure mathematics. Examples of work with collaborators on such questions follow:

Laurent, T, Rider, B., and M. Reed (2006) Parabolic Behavior of a Hyberbolic Delay Equation, SIAM J. Analysis, 38, 1-15.

Mitchell, C., and M. Reed (2007) Neural Timing in Highly Convergent Systems, SIAM J. Appl. Math. 68, 720-737.

Anderson,D., Mattingly, J., Nijhout, F., and M. Reed (2007) Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks, Bull. Math. Biol. 69, 1791-1813.

McKinley S, Popovic L, and M. Reed M. (2011) A Stochastic compartmental model for fast axonal transport, SIAM J. Appl. Math. 71, 1531-1556.

Keywords:
Acetaminophen, Acetylcholinesterase, Acoustic Stimulation, Actins, Action Potentials, Adaptor Proteins, Signal Transducing, Adenosine, Adolescent, Adult, Algorithms, Alleles, Allosteric Regulation, Allosteric Site, Animals, Anti-Inflammatory Agents, Non-Steroidal, Antidepressive Agents, Antigenic Variation, Antioxidants, Arsenic, Auditory Pathways, Auditory Perception, Auditory Threshold, Autistic Disorder, Autoreceptors, Axonal Transport, Axons, Bangladesh, Betaine, Biochemistry, Biological Markers, Biological Transport, Brain, Brain Mapping, Brain Stem, Calcium, Carbon, Case-Control Studies, Cats, cdc42 GTP-Binding Protein, Saccharomyces cerevisiae, Cells, Child, Child, Preschool, Cholesterol, Choline, Cochlear Nerve, Cochlear Nucleus, Computational Biology, Computational neuroscience, Computer Simulation, Contraceptives, Oral, Cystathionine, Cystathionine beta-Synthase, Cysteine, Cytoskeletal Proteins, Cytoskeleton, Cytosol, Data Interpretation, Statistical, Diet, Dietary Supplements, Diffusion, Dimerization, DNA Damage, DNA Methylation, DNA Modification Methylases, DNA Repair, DNA, Neoplasm, Dominance, Cerebral, Dopamine, Dose-Response Relationship, Drug, Down Syndrome, Ear, Electric Stimulation, Electrophysiology, Endoplasmic Reticulum, Enzymes, Epigenesis, Genetic, Evaluation Studies as Topic, Extracellular Space, Feedback, Feedback, Physiological, Female, Flavins, Fluoxetine, Folic Acid, Folic Acid Deficiency, Food, Formate-Tetrahydrofolate Ligase, Functional Laterality, Ganglia, Spinal, Gene Expression Regulation, Gene Expression Regulation, Bacterial, Gene Knockdown Techniques, Gene Silencing, Gene Targeting, Genetic Predisposition to Disease, Genetic Variation, Genome, Bacterial, Genotype, Glucuronides, Glutathione, Glycine, Glycine Hydroxymethyltransferase, Gonadotropin-Releasing Hormone, GTP-Binding Proteins, Guanine, Half-Life, Hearing, Hepatocytes, Homeostasis, Homocysteine, Humans, Hydrolases, Immune Evasion, Immunity, Innate, Infant, Inferior Colliculi, Inflammation, Influenza A Virus, H3N2 Subtype, Influenza, Human, Inositol 1,4,5-Trisphosphate, Insects, Intermediate Filaments, Intestines, Juvenile Hormones, Kinetics, Kynurenic Acid, Kynurenine, Levodopa, Linear Models, Lipid Metabolism, Liver, Luteinizing Hormone, Male, Mathematics, Medial Forebrain Bundle, Metabolic Detoxication, Drug, Metabolic Networks and Pathways, Metabolome, Methionine, Methotrexate, Methylation, Methylenetetrahydrofolate Reductase (NADPH2), Methyltransferases, Mice, Mice, Knockout, Mitochondria, Liver, Models, Biological, Models, Chemical, Models, Genetic, Models, Immunological, Models, Neurological, Models, Statistical, Models, Structural, Models, Theoretical, Molecular Biology, Molecular Epidemiology, Muscles, Neoplasms, Nerve Degeneration, Nerve Fibers, Nerve Net, Nervous System Diseases, Nervous System Physiological Phenomena, Neural Inhibition, Neural Networks (Computer), Neural Pathways, Neural Tube Defects, Neurons, Noise, Nonlinear Dynamics, Nutrition Surveys, Nutritional Physiological Phenomena, Nutritional Status, Oligopeptides, Olivary Nucleus, One-Carbon Group Transferases, Organ Specificity, ortho-Aminobenzoates, Osmolar Concentration, Oxidative Stress, Phosphatidylcholines, Phosphatidylethanolamines, Phosphatidylglycerols, Phosphofructokinases, Phosphoribosylaminoimidazolecarboxamide Formyltransferase, Pituitary Gland, Anterior, Polymorphism, Genetic, Polymorphism, Single Nucleotide, Population Dynamics, Presynaptic Terminals, Probability, Promoter Regions, Genetic, Protein Binding, Proteins, Pyrrolidonecarboxylic Acid, Raphe Nuclei, Rats, Reaction Time, Receptor, Serotonin, 5-HT1A, Receptor, Serotonin, 5-HT1B, Receptors, LHRH, Reproducibility of Results, Rhodobacter capsulatus, S-Adenosylhomocysteine, S-Adenosylmethionine, Saccharomyces cerevisiae, Saccharomyces cerevisiae Proteins, Sarcosine, Sciatic Nerve, Serine, Serotonin, Serotonin Plasma Membrane Transport Proteins, Serotonin Receptor Agonists, Serotonin Uptake Inhibitors, Signal Transduction, Sound Localization, Species Specificity, Stochastic Processes, Strigiformes, Substrate Specificity, Superior Colliculi, Synapses, Synaptic Transmission, Systems Biology, Tetrahydrofolate Dehydrogenase, Tetrahydrofolates, Thymidine Monophosphate, Thymidylate Synthase, Time Factors, Transaminases, Tryptophan, Tryptophan Hydroxylase, Tryptophan Oxygenase, Tumor Markers, Biological, Tyrosine, Tyrosine 3-Monooxygenase, Up-Regulation, Vestibulocochlear Nerve, Viral Load, Vitamin B 12 Deficiency, Vitamin B 6 Deficiency, Vitamin B Complex, Vitamins, Young Adult
Recent Publications
  1. Reed, M; Best, J; Golubitsky, M; Stewart, I; Nijhout, HF, Analysis of Homeostatic Mechanisms in Biochemical Networks., Bulletin of Mathematical Biology, vol. 79 no. 11 (November, 2017), pp. 2534-2557 [doi[abs]
  2. Reed, MC; Best, J; Nijhout, HF, Mathematical models of neuromodulation and implications for neurology and psychiatry, edited by Erdi, P; Battacharya, B; Cochran, A (2017)
  3. Reed, MC; Lawley, S; Nijhout, HF, Spiracular fluttering increases oxygen uptake (2017)
  4. Reed, MC; Best, J; Nijhout, HF, Mathematical models of neuromodulation and implications for neurology and psychiatry, in Computational Neurology and Psychiatry, edited by Erdi, P; Bhattacharya, B; Cochran, A (2017), Springer
  5. Samaranayake, S; Abdalla, A; Robke, R; Nijhout, HF; Reed, MC; Best, J; Hashemi, P, A voltammetric and mathematical analysis of histaminergic modulation of serotonin in the mouse hypothalamus., Journal of Neurochemistry, vol. 138 no. 3 (August, 2016), pp. 374-383 [doi[abs]

 

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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320