# Michael C. Reed

- Professor of Mathematics
- Bass Fellow

**External address:**237 Physics Bldg., Duke University, Box 90320, Durham, NC 27708

**Internal office address:**Box 90320, Duke University 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2808

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 recent work on cell metabolism and public health, go to sites@duke.edu/metabolism.

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 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; this is collaborative work with Professor Nijhiout and with Janet Best, a mathematician at The Ohio State University. The biochemistry of these neurotransmitters affects the electrophysiology of the brain and the electrophysiology affects the biochemistry. Both affect gene expression, the endocrine system, 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. The models have shed new light on the mode of action of selective serotonin reuptake inhibitors (used for depression), the interactions between the serotonin and dopamine systems in Parkinson’s disease and levodopa therapy, and the interactions between histamine and serotonin.

Recent work on homeostatic mechanisms in cell biochemistry in health and disease have shown how difficult the task of precision medicine is. A gene polymorphism may make a protein such as an enzyme less effective but often the system compensates through a variety of homeostatic mechanisms. So even though an individual's genotype is different, his or her phenotype may not be different. The individuals with common polymorphisms tend tend to live on homeostatic plateaus and only those individuals near the edges of the plateau are at risk for disease processes. Interventions should try to enlarge the homeostatic plateau around the individual's genotype.

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

For general discussions of the connections between mathematics and biology, see his articles: ``Why is Mathematical Biology so Hard?,'' 2004, Notices of the AMS, 51, pp. 338-342, and ``Mathematical Biology is Good for Mathematics,'' 2015, Notices of the AMS, 62, pp., 1172-1176.

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.

Lawley, S. Reed, M., Mattingly, S. (2014), Sensitivity to switching rates in stochastically switched ODEs,'' Comm. Math. Sci. 12, 1343-1352.

Lawley, S., Mattingly, J, Reed, M. (2015), Stochastic switching in infinite dimensions with applications to parabolic PDE, SIAM J. Math. Anal. 47, 3035-3063.

### Selected Grants

(87-0536) Mathematical Sciences: Nonlinear Partial Differential Equations awarded by National Science Foundation (Principal Investigator). 1987 to 1990

(88-0233) Mathematical Sciences: Nonlinear Partial Differential Equations awarded by National Science Foundation (Principal Investigator). 1987 to 1989

(87-0200) Mathematical Simulations awarded by National Science Foundation (Principal Investigator). 1987 to 1988

(86-0115) Nonlinear Partial Differential Equations awarded by National Science Foundation (Principal Investigator). 1984 to 1987

## Pages

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Reed, MC. "Unsolved problems in the theory of non-linear wave equations." *Many Degrees of Freedom in Particle Physics and Field Theory.* Ed. L Streit. New York: Plenum Press. (Chapter)

## Pages

Reed, M, Nijhout, HF, and Best, J. "Projecting Biochemistry Over Long Distances." Ed. L Pujo-Menjouet. *Mathematical Modelling of Natural Phenomena* 9.1 (2014): 133-138.
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Lawley, SD, Mattingly, JC, and Reed, MC. "Sensitivity to switching rates in stochastically switched odes." *Communications in Mathematical Sciences* 12.7 (2014): 1343-1352.
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Wood, KM, Zeqja, A, Nijhout, HF, Reed, MC, Best, J, and Hashemi, P. "Voltammetric and mathematical evidence for dual transport mediation of serotonin clearance in vivo." *Journal of Neurochemistry* 130.3 (January 1, 2014): 351-359.
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Rios-Avila, L, Nijhout, HF, Reed, MC, Sitren, HS, and Gregory, JF. "A mathematical model of tryptophan metabolism via the kynurenine pathway provides insights into the effects of vitamin B-6 deficiency, tryptophan loading, and induction of tryptophan 2,3-dioxygenase on tryptophan metabolites." *J Nutr* 143.9 (September 2013): 1509-1519.
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Duncan, TM, Reed, MC, and Nijhout, HF. "A population model of folate-mediated one-carbon metabolism. (Published online)" *Nutrients* 5.7 (July 5, 2013): 2457-2474.
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Duncan, TM, Reed, MC, and Nijhout, HF. "The relationship between intracellular and plasma levels of folate and metabolites in the methionine cycle: a model." *Mol Nutr Food Res* 57.4 (April 2013): 628-636.
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Patel, M, and Reed, M. "Stimulus encoding within the barn owl optic tectum using gamma oscillations vs. spike rate: a modeling approach." *Network (Bristol, England)* 24.2 (January 2013): 52-74.
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Duncan, TM, Reed, MC, and Nijhout, HF. "The relationship between intracellular and plasma levels of folate and metabolites in the methionine cycle: A model." *Molecular Nutrition and Food Research* 57.4 (2013): 628-636.
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Best, J, Reed, MC, and Nijhout, HF. "Computational studies of the role of serotonin in the basal ganglia." *Frontiers in Integrative Neuroscience* MAY (2013).
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Ben-Shachar, R, Chen, Y, Luo, S, Hartman, C, Reed, M, and Nijhout, HF. "The biochemistry of acetaminophen hepatotoxicity and rescue: a mathematical model. (Published online)" *Theor Biol Med Model* 9 (December 19, 2012): 55-.
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