Math @ Duke

Michael C Reed, Professor
 Contact Info:
Office Location:  237 Physics  Office Phone:  (919) 6602808, (919) 6602800  Email Address:  
Web Page:  http://www.math.duke.edu 
Teaching (Fall 2014):
 MATH 635.01, FUNCTIONAL ANALYSIS
Synopsis
 Physics 227, MWF 08:45 AM09:35 AM
 Math 49S.01: Applications of Mathematics to
Physiology and Medicine [PDF]
 Office Hours:
 Friday, 12
 Education:
 B.S., Yale University, 1963
Ph.D., Stanford University, 1969
 Specialties:

Analysis
Applied Math
 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. 338342.
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 maternalfetal 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, 115.
Mitchell, C., and M. Reed (2007) Neural Timing in Highly Convergent Systems, SIAM J. Appl. Math. 68, 720737.
Anderson,D., Mattingly, J., Nijhout, F., and M. Reed (2007) Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks, Bull. Math. Biol. 69, 17911813.
McKinley S, Popovic L, and M. Reed M. (2011) A Stochastic compartmental model for fast axonal transport, SIAM J. Appl. Math. 71, 15311556.
 Current Ph.D. Students
(Former Students)
 Shalla Hansen
 Ezgi Temamogullari
 Sean Lawley
 Postdocs Mentored
 Lydia Bilinsky (August 01, 2013  present)
 Mainak Patel (20112014)
 Badal Joshi (2009/082012/07)
 Mattias R Heymann (20072010)
 Garrett Mitchener (2004  2006)
 Paula Budu (2002/092005/08)
 Talitha Washington (2001/092004/08)
 Monica Romeo (2001/092004/08)
 Tracy Jackson (1999/082000/07)
 Patrick Nelson (1999/082000/07)
 Kirill Skouibine (1998/092000/08)
 Recent Publications
(More Publications)
 L. RiosAvila, H. F. Nijhout, M. C. Reed, H. S. Sitren, J. F. Gregory III, A mathematical model of tryptophan metabolism via the kynurenine pathway provides insights into the effects of vitamin B6 deficiency, tryptophan loading and induction of tryptophan 2,3dioxygenase on tryptophan metabolites,
J. Nutrition, vol. 143
(2013),
pp. 15091519 .
 M. Reed, H. F. Nijhout, J. Best, Computational studies of the role of serotonin in the basal ganglia,
Frontiers in Integrative Neuroscience, vol. 7
(2013),
pp. 18 .
 T. Duncan, M. Reed, H. F. Nijhout, A population model of folatemediated onecarbon metabolism,
Nutrients, vol. 5
(2013),
pp. 24572474 .
 M. Reed, H. F. Nijhout, J. Best, Projecting biochemistry over long distances,
Math. Models Natural Phenomena
(Accepted, 2013) .
 S. Lawley, J. Mattingly, M. Reed, Sensitivity to switching rates on stochastically switched ODEs
(Submitted, 2013) .


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

