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Michael C. Reed, Arts & Sciences Professor of Mathematics and Bass Fellow of Mathematics


Michael C. Reed

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

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.

Contact Info:
Office Location:  237 Physics Bldg., Duke University, Box 90320, Durham, NC 27708
Office Phone:  (919) 660-2810, (919) 660-2808
Email Address: send me a message
Web Page:

Teaching (Fall 2018):

  • MATH 431.01, ADVANCED CALCULUS I Synopsis
    Physics 119, MWF 08:45 AM-09:35 AM
  • MATH 431.02, ADVANCED CALCULUS I Synopsis
    Physics 119, MWF 10:20 AM-11:10 AM
  • MATH 731.01, ADVANCED CALCULUS I Synopsis
    Physics 119, MWF 08:45 AM-09:35 AM
  • MATH 731.02, ADVANCED CALCULUS I Synopsis
    Physics 119, MWF 10:20 AM-11:10 AM


Doctor of PhilosophyStanford University1969
Ph.D.Stanford University1969
Master of ScienceStanford University1966
M.S.Stanford University1966
Bachelor of ScienceYale1963
B.S.Yale University1963


Applied Math

Research Interests: Analysis, Applications of Mathematics to Physiology and Medicine

Professor Reed is engaged in several research projects involving both applications of mathematics to physiology and medicine and questions in analysis that arise naturally in this context. 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. 338-342.

A new research area involves the applications of mathematics to the study of various aspects of cell metabolism, in particular, folate and methionine metabolism. The folic acid cycle plays a central role in cell metabolism. Among the important functions of the folate cycle are the synthesis of pyrimidines and purines and the delivery of one carbon units to the methionine cycle for use in methylation reactions. Dietary folate deficiencies as well as mutations in enzymes of the folate cycle are associated with megaloblastic anemia, cancers of the colon, breast and cervix, affective disorders, cleft palate, neural tube defects, Alzheimers disease, Down's syndrome, preeclampsia and early pregnancy loss and several enzymes in the cycle are the targets of anti-cancer drugs. The methionine cycle is important for the regulation of homocysteine, an important risk factor for heart disease, and for the control of DNA methylation. Both hyper- and hypomethylation have been proposed as crucial steps in chains of events that turn normal cells into cancerous cells. The purpose of the project is to use mathematics to understand normal folate and methionine metabolism, DNA methylation, and purine and pyrimidine synthesis and then to understand how they are affected by alterations in diet and gene abnormalities. This is a joint project with Fred Nijhout of the Duke Department of Biology and Cornelia Ulrich of the Fred Hutchinson Cancer Research Center. See: M.C. Reed, H. F. Nijhout, R. Sparks, C. M. Ulrich, A Mathematical Model of the Methionine Cycle, Journal of Theoretical Biology , 226 (2004), pp. 33-43, and Nijhout, F., Reed, M., Budu, P. and N. Ulrich, A Mathematical Model of the Folate Cycle - New Insights into Folate Homeostasis, J. Biological Chemistry , 279 , 55008-55016.

A continuing research area is the study of information processing in the mammalian auditory brainstem by the use of mathematical and computational models. The purpose is to understand what the nuclei in the brainstem (and midbrain) are computing and how they do it. This is done by creating mathematical and computational models, based on known (partial) information about physiology and anatomy, which incorporate hypotheses about the details of the anatomy and physiology of the nuclei and the ways in which the nuclei communicate with each other. By investigating these models and comparing the results to experimental findings one can (one hopes) confirm or reject the hypotheses and thus contribute to understanding of the brainstem. Recent work has utilized probabilistic methods and has focused on hyperacuity and the mechanism of sharpening timing as information progresses from the auditory periphery up the brainstem. This is joint work with Colleen Mitchell. See, for example: M.Reed, J. Blum, and C. Mitchell, Precision of Neural Timing: Effects of Convergence and Time-windowing, J.Computational Neuroscience , 13 (2002), 35-47.

A recent research project studies the biochemical cascade by which pituitary cells produce luteinizing hormone in response to pulses of GnRH released by the hypothalmus (with J. Blum, Talitha Washington, and Michael Conn of the Oregon Health Sciences Center). See, for example: M. Reed, J. Blum, Jo Ann Janovick and M. Conn, A Mathematical Model Quantifying GnRH--induced LH Secretion from Gonadotropes, Amer. J. Physiol. Endocrinol. Metab. 278 (2000), 263-272, and T. Washington, J. Blum, M. Reed, and M. Conn, A Mathematical Model for LH Release in Response to Continuous and Pulsatile Exposure of Gonadotrophs to GnRH, Theoretical Biology and Medical Modelling , 1 (2004), 1-17.

A current research project involves the study of large systems of ordinary differential equations that arise from chemical reactions, for example in cell metabolism and cell signalling processes. What properties of the system depend only on the geometry and topology of the reaction diagram? What classes of reaction diagrams guarantee certain kinds of system behavior? How can large systems be simplified and yet keep their essential behavior? How do stochastic variations of one component of the system affect the other components? This is joint work with David Anderson (Ph.D., 2005) and Jonathon Mattingly.

A current research project involves the study of time-delayed partial hyperbolic differential equations. The goals are to prove global theorems about existence, propagation of singularities, and asymptotic behavior in time. See, for example, T. Laurent, B. Rider, and M. Reed, Parabolic Behavior of a Hyberbolic Delay Equation, SIAM J. Analysis , 38, 1-15, 2006.


Acetaminophen • Acetylcholinesterase • Acoustic Stimulation • Actins • Action Potentials • Adaptor Proteins, Signal Transducing • Adenosine • Adolescent • Adult • Algorithms • Alleles • Allosteric Regulation • Allosteric Site • Animals • Anti-Inflammatory Agents, Non-Steroidal • Antidepressive Agents • Antigenic Variation • Antioxidants • Arsenic • Auditory Pathways • Auditory Perception • Auditory Threshold • Autistic Disorder • Autoreceptors • Axonal Transport • Axons • Bangladesh • Betaine • Biochemistry • Biological Markers • Biological Transport • Brain • Brain Mapping • Brain Stem • Calcium • Carbon • Case-Control Studies • Cats • cdc42 GTP-Binding Protein, Saccharomyces cerevisiae • Cells • Child • Child, Preschool • Cholesterol • Choline • Cochlear Nerve • Cochlear Nucleus • Computational Biology • Computational neuroscience • Computer Simulation • Contraceptives, Oral • Cystathionine • Cystathionine beta-Synthase • Cysteine • Cytoskeletal Proteins • Cytoskeleton • Cytosol • Data Interpretation, Statistical • Diet • Dietary Supplements • Diffusion • Dimerization • DNA Damage • DNA Methylation • DNA Modification Methylases • DNA Repair • DNA, Neoplasm • Dominance, Cerebral • Dopamine • Dose-Response Relationship, Drug • Down Syndrome • Ear • Electric Stimulation • Electrophysiology • Endoplasmic Reticulum • Enzymes • Epigenesis, Genetic • Evaluation Studies as Topic • Extracellular Space • Feedback • Feedback, Physiological • Female • Flavins • Fluoxetine • Folic Acid • Folic Acid Deficiency • Food • Formate-Tetrahydrofolate Ligase • Functional Laterality • Ganglia, Spinal • Gene Expression Regulation • Gene Expression Regulation, Bacterial • Gene Knockdown Techniques • Gene Silencing • Gene Targeting • Genetic Predisposition to Disease • Genetic Variation • Genome, Bacterial • Genotype • Glucuronides • Glutathione • Glycine • Glycine Hydroxymethyltransferase • Gonadotropin-Releasing Hormone • GTP-Binding Proteins • Guanine • Half-Life • Hearing • Hepatocytes • Homeostasis • Homocysteine • Humans • Hydrolases • Immune Evasion • Immunity, Innate • Infant • Inferior Colliculi • Inflammation • Influenza A Virus, H3N2 Subtype • Influenza, Human • Inositol 1,4,5-Trisphosphate • Insects • Intermediate Filaments • Intestines • Juvenile Hormones • Kinetics • Kynurenic Acid • Kynurenine • Levodopa • Linear Models • Lipid Metabolism • Liver • Luteinizing Hormone • Male • Mathematics • Medial Forebrain Bundle • Metabolic Detoxication, Drug • Metabolic Networks and Pathways • Metabolome • Methionine • Methotrexate • Methylation • Methylenetetrahydrofolate Reductase (NADPH2) • Methyltransferases • Mice • Mice, Knockout • Mitochondria, Liver • Models, Biological • Models, Chemical • Models, Genetic • Models, Immunological • Models, Neurological • Models, Statistical • Models, Structural • Models, Theoretical • Molecular Biology • Molecular Epidemiology • Muscles • Neoplasms • Nerve Degeneration • Nerve Fibers • Nerve Net • Nervous System Diseases • Nervous System Physiological Phenomena • Neural Inhibition • Neural Networks (Computer) • Neural Pathways • Neural Tube Defects • Neurons • Noise • Nonlinear Dynamics • Nutrition Surveys • Nutritional Physiological Phenomena • Nutritional Status • Oligopeptides • Olivary Nucleus • One-Carbon Group Transferases • Organ Specificity • ortho-Aminobenzoates • Osmolar Concentration • Oxidative Stress • Phosphatidylcholines • Phosphatidylethanolamines • Phosphatidylglycerols • Phosphofructokinases • Phosphoribosylaminoimidazolecarboxamide Formyltransferase • Pituitary Gland, Anterior • Polymorphism, Genetic • Polymorphism, Single Nucleotide • Population Dynamics • Presynaptic Terminals • Probability • Promoter Regions, Genetic • Protein Binding • Proteins • Pyrrolidonecarboxylic Acid • Raphe Nuclei • Rats • Reaction Time • Receptor, Serotonin, 5-HT1A • Receptor, Serotonin, 5-HT1B • Receptors, LHRH • Reproducibility of Results • Rhodobacter capsulatus • S-Adenosylhomocysteine • S-Adenosylmethionine • Saccharomyces cerevisiae • Saccharomyces cerevisiae Proteins • Sarcosine • Sciatic Nerve • Serine • Serotonin • Serotonin Plasma Membrane Transport Proteins • Serotonin Receptor Agonists • Serotonin Uptake Inhibitors • Signal Transduction • Sound Localization • Species Specificity • Stochastic Processes • Strigiformes • Substrate Specificity • Superior Colliculi • Synapses • Synaptic Transmission • Systems Biology • Tetrahydrofolate Dehydrogenase • Tetrahydrofolates • Thymidine Monophosphate • Thymidylate Synthase • Time Factors • Transaminases • Tryptophan • Tryptophan Hydroxylase • Tryptophan Oxygenase • Tumor Markers, Biological • Tyrosine • Tyrosine 3-Monooxygenase • Up-Regulation • Vestibulocochlear Nerve • Viral Load • Vitamin B 12 Deficiency • Vitamin B 6 Deficiency • Vitamin B Complex • Vitamins • Young Adult

Current Ph.D. Students   (Former Students)
  • Shalla Hansen  
  • Ezgi Temamogullari  

Postdocs Mentored
  • Lydia Bilinsky (August 01, 2013 - present)  
  • Badal Joshi (2009/08-2012/07)  
  • Garrett Mitchener (2004 - 2006)  
  • Paula Budu (2002/09-2005/08)  
  • Talitha Washington (2001/09-2004/08)  
  • Monica Romeo (2001/09-2004/08)  
  • Tracy Jackson (1999/08-2000/07)  
  • Patrick Nelson (1999/08-2000/07)  
  • Kirill Skouibine (1998/09-2000/08)  

Undergraduate Researches Supervised
  • Lindsey Brown (May 15, 2014 - present)
    Thesis: Applications of abstract algebra to neuroscience 

Recent Publications   (More Publications)

  1. West, A; Best, J; Abdalla, A; Nijhout, F; Reed, M; Hashemi, P, Voltammetric evidence for discrete serotonin circuits, linked to specific reuptake domains, in the mouse medial prefrontal cortex., Neurochemistry International (July, 2018) [doi]  [abs]
  2. Duncan, W; Best, J; Golubitsky, M; Nijhout, HF; Reed, M, Homeostasis despite instability., Mathematical Biosciences, vol. 300 (March, 2018), pp. 130-137 [doi]  [abs]
  3. Suppiramaniam, V; Bloemer, J; Reed, M; Bhattacharya, S, Neurotransmitter Receptors, in Comprehensive Toxicology: Third Edition, vol. 6-15 (December, 2017), pp. 174-201, ISBN 9780081006122 [doi]  [abs]
  4. Best, J; Nijhout, HF; Samaranayake, S; Hashemi, P; Reed, M, A mathematical model for histamine synthesis, release, and control in varicosities., Theoretical Biology & Medical Modelling, vol. 14 no. 1 (December, 2017), pp. 24 [doi]  [abs]
  5. Reed, M; Best, J; Golubitsky, M; Stewart, I; Nijhout, HF, Analysis of Homeostatic Mechanisms in Biochemical Networks., Bulletin of Mathematical Biology, vol. 79 no. 11 (November, 2017), pp. 2534-2557 [doi]  [abs]