# 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.

Brooks Teaching Award. Duke University. December 2008

### Selected Grants

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

## Pages

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)

Suppiramaniam, V, Bloemer, J, Reed, M, and Bhattacharya, S. "Neurotransmitter Receptors." *Comprehensive Toxicology: Third Edition.* December 15, 2017. 174-201.
Full Text

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)

## Pages

Duncan, W, Best, J, Golubitsky, M, Nijhout, HF, and Reed, M. "Homeostasis despite instability." *Mathematical biosciences* 300 (March 26, 2018): 130-137.
Full Text

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.

## Pages

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.

Nijhout, HF, and Reed, MC. "Homeostasis and dynamic stability of the phenotype: Implications for understanding the nature and evolution of robustness and plasticity." 2014.

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.

## Pages

Only ten professors were named Distinguished Professors this year in the Trinity College of Arts and Sciences. This distinction is given to professors for their outstanding research and teaching accomplishments. We are proud to announce that three... read more »

Six graduate students participated in the May 15, 2016 graduation ceremonies to celebrate earning their PhDs in Mathematics. Their thesis topics were impressive and varied, and reflected the breadth of study in the department. Their advisors and... read more »

Mike Reed has been recognized by the graduated school for his excellence in mentoring. The Graduate School presents the Dean’s Awards for Excellence in Mentoring to recognize the considerable efforts and accomplishments of faculty and graduate... read more »

Mike Reed was named a 2016 SIAM Fellow for his contributions to analysis and mathematical biology. SIAM, the Society for Industrial and Applied Mathematics, only names 30 or so fellows each year. The honor represents sustained significant... read more »

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