Michael C. Reed
- Professor of Mathematics
- Bass Fellow
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 email@example.com/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.
Brooks Teaching Award. Duke University. December 2008
The Physiological Basis of Allometry awarded by National Science Foundation (Co-Principal Investigator). 2016 to 2020
Voltametric determination of serotonin and histamine co-regulation awarded by University of South Carolina (Principal Investigator). 2016 to 2018
An in vivo voltammetric serotonin biomarker for antidepressant efficacy awarded by University of South Carolina (Principal Investigator). 2016 to 2018
EMSW21-RTG: awarded by National Science Foundation (Principal Investigator). 2010 to 2017
Theoretical Principles of Genotype-Phenotype Mapping awarded by National Science Foundation (Co-Principal Investigator). 2010 to 2016
Methods for Pathway Modeling with Application to Folate awarded by University of Southern California (Co-Principal Investigator). 2010 to 2016
Analysis of Mechanisms of Biochemical Homeostasis awarded by National Science Foundation (Principal Investigator). 2006 to 2010
Hyperacuity in the Auditory System awarded by National Science Foundation (Principal Investigator). 2001 to 2006
(98-0372) Mathematical Investigation of Neural Processing in the Auditory Brainstem awarded by National Science Foundation (Principal Investigator). 1998 to 2001
Mathematical Sciences/GIG: Applications of Mathematics to Physiology awarded by National Science Foundation (Principal Investigator). 1997 to 2001
Reed, MC. Fundamental Ideas of Analysis. New York: John Wiley & Sons, 1998. (Textbook)
Reed, MC, and Simon, B. Methods of Modern Mathematical Physics III: Scattering Theory. New York: Academic Press, 1979.
Reed, MC, and Simon, B. Methods of Modern Mathematical Physics IV: Analysis of Operators. New York: Academic Press, 1978.
Reed, MC. Abstract Non-linear Wave Equations. New York: Springer, 1976.
Reed, MC, and Simon, B. Methods of Modern Mathematical Physics II: Fourier Analysis, Self-adjointness. Academic Press, 1975.
Reed, MC, and Simon, B. Methods of Modern Mathematical Physics I: Functional Analysis. New York: Academic press, 1972. (Textbook)
Reed, MC, Best, J, and Nijhout, HF. "Mathematical models of neuromodulation and implications for neurology and psychiatry (Accepted)." Computational Neurology and Psychiatry. Ed. P Erdi, B Bhattacharya, and A Cochran. New York: Springer, 2017. (Chapter)
Reed, MC, Nijhout, HF, and Kurtz, T. "Mathematical modeling of cell metabolism." Encyclopedia of Applied and Computational Mathematics. Ed. B Engquist. New York: Springer, 2016. (Chapter)
Reed, MC, Best, J, Nijhout, HF, and Oakley, G. "Mathematical models: Interactions between serotonion and dopamine in Parkinson's disease." Etiology and Pathophysiology of Parkinson's Disease. Ed. AQ Rana. InTech Pub., 2011. (Chapter)
Reed, MC. "Mathematical biology." The Princeton Companion to Mathematics. July 18, 2010. 837-848.
Reed, MC, Nijhout, HF, and Ulrich, C. "Mathematical Models of One-Carbon Metabolism." Vitamins and Hormones, Volume 79. Ed. G Litvack. Amsterdam NE: Elsevier, 2008. 42-85. (Chapter)
Reed, MC, and Blum, J. "Envelope coding in the Auditory Brainstem." Proc. Conference on Biomedical Simulation. Ed. P Cellier. 1997. (Chapter)
Reed, MC, and Blum, J. "Models of Axonal Transport: Applications to Understanding Certain Neuropathies." Handbook of Neurotoxicology I: Basic Principles and Current Concepts. New York: Dekker, 1994. (Chapter)
Reed, MC, and Blum, J. "Mathematical Questions in Axonal Transport." American Mathematical Society, 1994. (Chapter)
Reed, MC, and Blum, J. "Information Processing in the Auditory Brainstem." Engineering Principles of Physiologic Function. Ed. D Schneck. New York: New York U. press, 1990. (Chapter)
Best, J, Nijhout, HF, Samaranayake, S, Hashemi, P, and Reed, M. "A mathematical model for histamine synthesis, release, and control in varicosities." Theoretical biology & medical modelling 14.1 (December 12, 2017): 24-. Full Text Open Access Copy
Reed, M, Best, J, Golubitsky, M, Stewart, I, and Nijhout, HF. "Analysis of Homeostatic Mechanisms in Biochemical Networks." Bulletin of mathematical biology 79.11 (November 2017): 2534-2557. Full Text
Nijhout, HF, Sadre-Marandi, F, Best, J, and Reed, MC. "Systems Biology of Phenotypic Robustness and Plasticity." Integrative and comparative biology 57.2 (August 2017): 171-184. Full Text Open Access Copy
Reed, MC, Lawley, S, and Nijhout, HF. "Spiracular fluttering increases oxygen uptake (Submitted)." (2017).
Reed, MC, Best, J, and Nijhout, HF. "Mathematical models of neuromodulation and implications for neurology and psychiatry (Accepted)." Ed. P Erdi, B Battacharya, and A Cochran. (2017).
Samaranayake, S, Abdalla, A, Robke, R, Nijhout, HF, Reed, MC, Best, J, and Hashemi, P. "A voltammetric and mathematical analysis of histaminergic modulation of serotonin in the mouse hypothalamus." Journal of neurochemistry 138.3 (August 2016): 374-383. Full Text
Lawley, SD, Best, JA, and Reed, MC. "Neurotransmitter concentrations in the presence of neural switching in one dimension." Discrete and Continuous Dynamical Systems - Series B 21.7 (August 2016): 2255-2273. Full Text
Temamogullari, NE, Nijhout, HF, and C Reed, M. "Mathematical modeling of perifusion cell culture experiments on GnRH signaling." Mathematical biosciences 276 (June 2016): 121-132. Full Text
Thanacoody, HKR, Nijhout, FH, Reed, MC, and Thomas, SHL. "Mathematical modelling of the effect of a high dose acetylcysteine regimen based on the SNAP trial on hepatic glutathione regeneration and hepatocyte death." CLINICAL TOXICOLOGY 54.4 (2016): 494-494.
Thanacoody, HKR, Nijhout, HF, Reed, MC, and Thomas, S. "Mathematical modeling of the effect of different intravenous acetylcysteine regimens on hepatic glutathione regeneration and hepatocyte death following simulated acetaminophen overdose." 2017.
Thanacoody, HKR, Nijhout, HF, Reed, MC, and Thomas, S. "Mathematical modeling of the effect of late administration of a novel acetylcysteine regimen based on the SNAP trial on hepatic glutathione regeneration and hepatocyte death following simulated acetaminophen overdose." 2017.
Rios-Avila, L, Nijhout, HF, Reed, MC, Sitren, HS, and Gregory, JF. "Mathematical model gives insights into vitamin B6 and kynurenine metabolism." April 2012.
Reed, MC, and Blum, JJ. "Envelope coding in the auditory brainstem." 1997.
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