Math @ Duke

Michael C. Reed, Arts & Sciences Distinguished Professor and Bass Fellow
 Contact Info:
Teaching (Fall 2023):
 MATH 431.01, INTRODUCTION TO REAL ANALYSIS
Synopsis
 Physics 119, MWF 10:20 AM11:10 AM
 MATH 431.02, INTRODUCTION TO REAL ANALYSIS
Synopsis
 Physics 235, MWF 01:40 PM02:30 PM
 MATH 731.01, INTRODUCTION TO REAL ANALYSIS
Synopsis
 Physics 119, MWF 10:20 AM11:10 AM
 MATH 731.02, INTRODUCTION TO REAL ANALYSIS
Synopsis
 Physics 235, MWF 01:40 PM02:30 PM
 Math 49S.01: Applications of Mathematics to
Physiology and Medicine [PDF]
 Office Hours:
 Friday, 12
 Education:
Ph.D.  Stanford University  1969 
Doctor of Philosophy  Stanford University  1969 
Master of Science  Stanford University  1966 
M.S.  Stanford University  1966 
Bachelor of Science  Yale  1963 
B.S.  Yale University  1963 
 Specialties:

Analysis
Applied Math Mathematical Biology
 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
 Postdocs Mentored
 Lydia Bilinsky (August 01, 2013  present)
 Badal Joshi (2009/082012/07)
 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)
 Kim, R; Nijhout, HF; Reed, MC, Mathematical insights into the role of dopamine signaling in circadian entrainment.,
Mathematical Biosciences, vol. 356
(February, 2023),
pp. 108956 [doi] [abs].
 Berger, SN; Baumberger, B; Samaranayake, S; Hersey, M; Mena, S; Bain, I; Duncan, W; Reed, MC; Nijhout, HF; Best, J; Hashemi, P, An In Vivo Definition of Brain Histamine Dynamics Reveals Critical Neuromodulatory Roles for This Elusive Messenger.,
International Journal of Molecular Sciences, vol. 23 no. 23
(November, 2022),
pp. 14862 [doi] [abs].
 Holmes, J; Lau, T; Saylor, R; FernándezNovel, N; Hersey, M; Keen, D; Hampel, L; Horschitz, S; Ladewig, J; Parke, B; Reed, MC; Nijhout, HF; Best, J; Koch, P; Hashemi, P, Voltammetric Approach for Characterizing the Biophysical and Chemical Functionality of Human Induced Pluripotent Stem CellDerived Serotonin Neurons.,
Analytical Chemistry, vol. 94 no. 25
(June, 2022),
pp. 88478856 [doi] [abs].
 Lawley, SD; Nijhout, HF; Reed, MC, Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.,
Journal of Mathematical Biology, vol. 84 no. 6
(April, 2022),
pp. 40 [doi] [abs].
 Hersey, M; Samaranayake, S; Berger, SN; Tavakoli, N; Mena, S; Nijhout, HF; Reed, MC; Best, J; Blakely, RD; Reagan, LP; Hashemi, P, InflammationInduced Histamine Impairs the Capacity of Escitalopram to Increase Hippocampal Extracellular Serotonin.,
The Journal of Neuroscience : the Official Journal of the Society for Neuroscience, vol. 41 no. 30
(July, 2021),
pp. 65646577 [doi] [abs].


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

