Math @ Duke
Michael C. Reed, Arts & Sciences Professor and Bass Fellow
- Contact Info:
Teaching (Fall 2019):
- MATH 431.01, INTRODUCTION TO REAL ANALYSIS
- Physics 119, MWF 08:45 AM-09:35 AM
- MATH 431.02, INTRODUCTION TO REAL ANALYSIS
- Physics 119, MWF 10:20 AM-11:10 AM
- Math 49S.01: Applications of Mathematics to
Physiology and Medicine [PDF]
- Office Hours:
- Friday, 1-2
|Doctor of Philosophy||Stanford University||1969|
|Master of Science||Stanford University||1966|
|Bachelor of Science||Yale||1963|
- 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
``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
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.
- Current Ph.D. Students
- Shalla Hansen
- Ezgi Temamogullari
- Postdocs Mentored
- Lydia Bilinsky (August 01, 2013 - present)
- Badal Joshi (2009/08-2012/07)
- Garrett Mitchener (2004 - 2006)
- Paula Budu (2002/09-2005/08)
- Talitha Washington (2001/09-2004/08)
- Monica Romeo (2001/09-2004/08)
- Tracy Jackson (1999/08-2000/07)
- Patrick Nelson (1999/08-2000/07)
- Kirill Skouibine (1998/09-2000/08)
- Recent Publications
- Abdalla, A; West, A; Jin, Y; Saylor, R; Qiang, B; Peña, E; Linden, DJ; Nijhout, HF; Reed, MC; Best, J; Hashemi, P, Fast Serotonin Voltammetry as a Versatile Tool for Mapping Dynamic Tissue Architecture: I. Responses at Carbon Fibers Describe Local Tissue Physiology.,
Journal of Neurochemistry
(August, 2019) [doi] [abs].
- Nijhout, HF; Best, JA; Reed, MC, Systems biology of robustness and homeostatic mechanisms.,
Wiley Interdisciplinary Reviews. Systems Biology and Medicine, vol. 11 no. 3
pp. e1440 [doi] [abs].
- West, A; Best, J; Abdalla, A; Nijhout, HF; Reed, M; Hashemi, P, Voltammetric evidence for discrete serotonin circuits, linked to specific reuptake domains, in the mouse medial prefrontal cortex.,
Neurochemistry International, vol. 123
pp. 50-58 [doi] [abs].
- Saylor, RA; Hersey, M; West, A; Buchanan, AM; Berger, SN; Nijhout, HF; Reed, MC; Best, J; Hashemi, P, In vivo Hippocampal Serotonin Dynamics in Male and Female Mice: Determining Effects of Acute Escitalopram Using Fast Scan Cyclic Voltammetry.,
Frontiers in Neuroscience, vol. 13
pp. 362 [doi] [abs].
- Saylor, RA; Hersey, M; West, A; Buchanan, AM; Berger, SN; Nijhout, HF; Reed, MC; Best, J; Hashemi, P, Corrigendum: In vivo Hippocampal Serotonin Dynamics in Male and Female Mice: Determining Effects of Acute Escitalopram Using Fast Scan Cyclic Voltammetry.,
Frontiers in Neuroscience, vol. 13
pp. 726 [doi] [abs].
Duke University, Box 90320
Durham, NC 27708-0320