Michael C. Reed
Professor of Mathematics
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 maternalfetal 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. 338342, and ``Mathematical Biology is Good for Mathematics,'' 2015, Notices of the AMS, 62, pp., 11721176.
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.
Lawley, S. Reed, M., Mattingly, S. (2014), Sensitivity to switching rates in stochastically switched ODEs,'' Comm. Math. Sci. 12, 13431352.
Lawley, S., Mattingly, J, Reed, M. (2015), Stochastic switching in infinite dimensions with applications to parabolic PDE, SIAM J. Math. Anal. 47, 30353063.
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1974
 Arts & Sciences Professor, Mathematics, Trinity College of Arts & Sciences 2018
 Bass Fellow, Mathematics, Trinity College of Arts & Sciences 2008
Contact Information
 237 Physics Bldg., Duke University, Box 90320, Durham, NC 27708
 Box 90320, Duke University 90320, Durham, NC 277080320
 reed@math.duke.edu (919) 6602808
 For recent research on cell metabolism and public health, see this link
 Background

Education, Training, & Certifications
 Ph.D., Stanford University 1969
 M.S., Stanford University 1966
 B.S., Yale University 1963

Duke Appointment History
 Associate Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2001  2003
 Chairman, Mathematics, Trinity College of Arts & Sciences 1986  1989
 Recognition

In the News

Awards & Honors
 Dean's Award for Excellence in Mentoring. Duke Graduate School. March 2016
 Voltametric determination of Serotonin and Histamine Coregulation. NIH. February 2016
 Fellow of the Society for Industrial and Applied Mathematics, 2016. The Society for Industrial and Applied Mathematics. 2016
 Fellow of the American Mathematical Society, 2014. American Mathematical Society. 2014
 Fellow. American Mathematical Society. 2013
 Brooks Teaching Award. Duke University. December 2008
 Bass Fellow, 2008. Duke University. 2008
 BishopMacDermott Professor of Mathematics, 20032008. Duke University. 2003
 Research

Selected Grants
 Bioinformatics and Computational Biology Training Program awarded by National Institutes of Health 2005  2021
 An in vivo voltammetric serotonin biomarker for antidepressant efficacy awarded by University of South Carolina 2016  2021
 The Physiological Basis of Allometry awarded by National Science Foundation 2016  2020
 Voltametric determination of serotonin and histamine coregulation awarded by University of South Carolina 2016  2019
 EMSW21RTG: awarded by National Science Foundation 2010  2017
 Theoretical Principles of GenotypePhenotype Mapping awarded by National Science Foundation 2010  2016
 Methods for Pathway Modeling with Application to Folate awarded by University of Southern California 2010  2016
 Analysis of Mechanisms of Biochemical Homeostasis awarded by National Science Foundation 2006  2010
 Hyperacuity in the Auditory System awarded by National Science Foundation 2001  2006
 (980372) Mathematical Investigation of Neural Processing in the Auditory Brainstem awarded by National Science Foundation 1998  2001
 Mathematical Sciences/GIG: Applications of Mathematics to Physiology awarded by National Science Foundation 1997  2001
 (970521) Applications of Mathematics to Physiology awarded by National Science Foundation 1997  1999
 (950205) Application of Mathematics in Neurobiology awarded by National Science Foundation 1995  1997
 (960881) Applications of Mathematics in Neurobiology awarded by National Science Foundation 1995  1997
 (940062) Mathematical Models of Neural Processing in the Auditory Brainstem awarded by National Science Foundation 1992  1995
 (950033) Mathematical Models of Neural Processing in the Auditory Brainstem awarded by National Science Foundation 1992  1995
 (920227) Mathematical Models of Neural Processing in the Auditory Brainstem awarded by National Science Foundation 1992  1994
 (920043) Mathematical Sciences: Applications of Mathematics to Physiology awarded by National Science Foundation 1989  1992
 (900657) Mathematical Sciences: Applications of Mathematics to Physiology awarded by National Science Foundation 1989  1991
 (890115) Applications of Mathematics to Physiology awarded by National Science Foundation 1989  1990
 (890396) NonLinear Partial Differential Equations awarded by National Science Foundation 1987  1990
 (870536) Mathematical Sciences: Nonlinear Partial Differential Equations awarded by National Science Foundation 1987  1990
 (880233) Mathematical Sciences: Nonlinear Partial Differential Equations awarded by National Science Foundation 1987  1989
 (870200) Mathematical Simulations awarded by National Science Foundation 1987  1988
 (860115) Nonlinear Partial Differential Equations awarded by National Science Foundation 1984  1987
 Publications & Artistic Works

Selected Publications

Books
 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 Nonlinear Wave Equations. New York: Springer, 1976.
 Reed, MC, and Simon, B. Methods of Modern Mathematical Physics II: Fourier Analysis, Selfadjointness. Academic Press, 1975.
 Reed, MC, and Simon, B. Methods of Modern Mathematical Physics I: Functional Analysis. New York: Academic press, 1972. (Textbook)

Book Sections
 Suppiramaniam, V, Bloemer, J, Reed, M, and Bhattacharya, S. "Neurotransmitter Receptors." In Comprehensive Toxicology: Third Edition, 174201. December 15, 2017. Full Text
 Reed, MC, Best, J, and Nijhout, HF. "Mathematical models of neuromodulation and implications for neurology and psychiatry (Accepted)." In Computational Neurology and Psychiatry, edited by P Erdi, B Bhattacharya, and A Cochran. New York: Springer, 2017. (Chapter)
 Reed, MC, Nijhout, HF, and Kurtz, T. "Mathematical modeling of cell metabolism." In Encyclopedia of Applied and Computational Mathematics, edited by 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." In Etiology and Pathophysiology of Parkinson's Disease, edited by AQ Rana. InTech Pub., 2011. (Chapter)
 Reed, MC. "Mathematical biology." In The Princeton Companion to Mathematics, 837848. July 18, 2010.
 Reed, MC, Nijhout, HF, and Ulrich, C. "Mathematical Models of OneCarbon Metabolism." In Vitamins and Hormones, Volume 79, edited by G Litvack, 4285. Amsterdam NE: Elsevier, 2008. (Chapter)
 Reed, MC, and Blum, J. "Envelope coding in the Auditory Brainstem." In Proc. Conference on Biomedical Simulation, edited by P Cellier. 1997. (Chapter)
 Reed, MC, and Blum, J. "Models of Axonal Transport: Applications to Understanding Certain Neuropathies." In 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." In Engineering Principles of Physiologic Function, edited by D Schneck. New York: New York U. press, 1990. (Chapter)
 Reed, MC, and Rauch, J. "Bounded, stratified, and striated solutions of hyperbolic equations." In Nonlinear Partial Differential Equations and their Applications, Volume IX, edited by H Brezis and J Lions. New York: John Wiley & Sons, 1988. (Chapter)
 Reed, MC, and Blum, J. "A reactionhyperbolic system in Physiology." In Nonlinear Semigroups, Partial Differential Equations, and Attractors, edited by T Gill and W Zachary, 127133. New York: Springer, 1987. (Chapter)
 Reed, MC, and Rauch, J. "On the absorption of singularities in dissipative nonlinear equations." In Differential Equations and Mathematical Physics, edited by I Knowles and Y Saito, 403407. New York: Springer, 1987. (Chapter)
 Reed, MC, and Rauch, J. "Ultrasingularities in nonlinear waves." In Nonlinear Semigroups, Partial Differential Equations, and Attractors, edited by T Gill and W Zachary, 134141. New York: Springer, 1985. (Chapter)
 Reed, MC, and Rauch, J. "Geometric structures in the singularity theory of hyperbolic equations." In Advances in Nonlinear Waves, I, edited by E Debnath, 273280. Cambridge UK: Cambridge University Press, 1984. (Chapter)
 Reed, MC. "Geometry and discrete velocity approximations to the Boltzmann equation." In Differential Equations, edited by I Knowles and R Lewis. Amsterdam, NE: NorthHolland, 1984. (Chapter)
 Reed, MC. "Propagation of singularities." In Many Degrees of Freedom in Particle Physics and Field Theory, edited by L Streit. New York: Plenum Press, 1978. (Chapter)
 Reed, MC. "Propagation of singularities in wave equations of KleinGordon type." In Nonlinear Partial Differential Equations and Applications, edited by J Chadam. 1978. (Chapter)
 Reed, MC. "The GNS Constructiona pedagogical example." In Lectures on Elementary Particles and Quantum Field Theory, 415438. Cambridge, MA: MIT Press, 1970. (Chapter)
 Reed, MC. "Functional analysis and probability theory." In Constructive Quantum Field Theory, edited by A Wightman.. (Chapter)
 Reed, MC. "Unsolved problems in the theory of nonlinear wave equations." In Many Degrees of Freedom in Particle Physics and Field Theory, edited by L Streit. New York: Plenum Press. (Chapter)

Conference Papers
 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. Link to Item
 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. Link to Item
 Nijhout, HF, and Reed, MC. "Homeostasis and dynamic stability of the phenotype: Implications for understanding the nature and evolution of robustness and plasticity." 2014. Link to Item
 RiosAvila, L, Nijhout, HF, Reed, MC, Sitren, HS, and Gregory, JF. "Mathematical model gives insights into vitamin B6 and kynurenine metabolism." April 2012. Link to Item
 Reed, MC, and Blum, JJ. "Envelope coding in the auditory brainstem." 1997. Link to Item

Journal Articles
 West, A, Best, J, Abdalla, A, Nijhout, F, Reed, M, and Hashemi, P. "Voltammetric evidence for discrete serotonin circuits, linked to specific reuptake domains, in the mouse medial prefrontal cortex." Neurochemistry International (July 19, 2018). Full Text
 Duncan, W, Best, J, Golubitsky, M, Nijhout, HF, and Reed, M. "Homeostasis despite instability." Mathematical biosciences 300 (March 26, 2018): 130137. 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, no. 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, no. 11 (November 2017): 25342557. Full Text
 Nijhout, HF, SadreMarandi, F, Best, J, and Reed, MC. "Systems Biology of Phenotypic Robustness and Plasticity." Integrative and comparative biology 57, no. 2 (August 2017): 171184. Full Text Open Access Copy
 Reed, MC, Best, J, and Nijhout, HF. "Mathematical models of neuromodulation and implications for neurology and psychiatry (Accepted)." Edited by P Erdi, B Battacharya, and A Cochran. (2017).
 Reed, MC, Lawley, S, and Nijhout, HF. "Spiracular fluttering increases oxygen uptake (Submitted)." (2017).
 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, no. 7 (August 2016): 22552273. Full Text
 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, no. 3 (August 2016): 374383. 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): 121132. 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, no. 4 (2016): 494494. Link to Item
 Reed, MC. "Mathematical Biology is Good for Mathematics." Notices of the American Mathematical Society 62, no. 10 (November 1, 2015): 11721176. Full Text
 Reed, MC, Gamble, MV, Hall, MN, and Nijhout, HF. "Mathematical analysis of the regulation of competing methyltransferases." BMC systems biology 9 (October 14, 2015): 69. Full Text
 Bilinsky, LM, Reed, MC, and Nijhout, HF. "The role of skeletal muscle in liver glutathione metabolism during acetaminophen overdose." Journal of theoretical biology 376 (July 2015): 118133. Full Text
 Lawley, SD, Mattingly, JC, and Reed, MC. "Stochastic Switching in Infinite Dimensions with Applications to Random Parabolic PDE." Siam Journal on Mathematical Analysis 47, no. 4 (January 2015): 30353063. Full Text Open Access Copy
 Nijhout, HF, Best, JA, and Reed, MC. "Using mathematical models to understand metabolism, genes, and disease." BMC biology 13 (January 2015): 79. Full Text
 Nijhout, HF, Best, J, and Reed, MC. "Escape from homeostasis." Mathematical biosciences 257 (November 2014): 104110. Full Text
 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, no. 3 (August 2014): 351359. Full Text
 Nijhout, HF, and Reed, MC. "Homeostasis and dynamic stability of the phenotype link robustness and plasticity." Integrative and comparative biology 54, no. 2 (July 2014): 264275. Full Text
 da Silva, VR, Ralat, MA, Quinlivan, EP, DeRatt, BN, Garrett, TJ, Chi, YY, Frederik Nijhout, H, Reed, MC, and Gregory, JF. "Targeted metabolomics and mathematical modeling demonstrate that vitamin B6 restriction alters onecarbon metabolism in cultured HepG2 cells." American Journal of Physiology. Endocrinology and Metabolism 307, no. 1 (July 2014): E93101. Full Text
 Lawley, SD, Yun, J, Gamble, MV, Hall, MN, Reed, MC, and Nijhout, HF. "Mathematical modeling of the effects of glutathione on arsenic methylation." Theoretical Biology & Medical Modelling 11 (May 16, 2014): 20null. Full Text
 Lawley, SD, Mattingly, JC, and Reed, MC. "Sensitivity to switching rates in stochastically switched odes." Communications in Mathematical Sciences 12, no. 7 (2014): 13431352. Full Text Open Access Copy
 Reed, M, Nijhout, HF, and Best, J. "Projecting Biochemistry Over Long Distances." Edited by L PujoMenjouet. Mathematical Modelling of Natural Phenomena 9, no. 1 (2014): 133138. Full Text
 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, no. 3 (January 1, 2014): 351359. Full Text
 RiosAvila, 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 B6 deficiency, tryptophan loading, and induction of tryptophan 2,3dioxygenase on tryptophan metabolites." The Journal of Nutrition 143, no. 9 (September 2013): 15091519. Full Text
 Duncan, TM, Reed, MC, and Nijhout, HF. "A population model of folatemediated onecarbon metabolism. (Published online)" Nutrients 5, no. 7 (July 5, 2013): 24572474. Full Text Open Access Copy Link to Item
 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, no. 4 (April 2013): 628636. Full Text Link to Item
 Best, J, Reed, MC, and Nijhout, HF. "Computational studies of the role of serotonin in the basal ganglia." Frontiers in Integrative Neuroscience , no. MAY (2013). Full Text
 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, no. 4 (2013): 628636. Full Text
 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, no. 2 (January 2013): 5274. Full Text
 BenShachar, 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. Full Text Link to Item
 Luo, S, Reed, M, Mattingly, JC, and Koelle, K. "The impact of host immune status on the withinhost and population dynamics of antigenic immune escape." J R Soc Interface 9, no. 75 (October 7, 2012): 26032613. Full Text Open Access Copy Link to Item
 Obeid, R, Hartmuth, K, Herrmann, W, Gortner, L, Rohrer, TR, Geisel, J, Reed, MC, and Nijhout, HF. "Blood biomarkers of methylation in Down syndrome and metabolic simulations using a mathematical model." Mol Nutr Food Res 56, no. 10 (October 2012): 15821589. Full Text Link to Item
 Geenen, S, du Preez, FB, Reed, M, Nijhout, HF, Kenna, JG, Wilson, ID, Westerhoff, HV, and Snoep, JL. "A mathematical modelling approach to assessing the reliability of biomarkers of glutathione metabolism." European Journal of Pharmaceutical Sciences : Official Journal of the European Federation for Pharmaceutical Sciences 46, no. 4 (July 2012): 233243. Full Text
 Luo, S, Reed, M, Mattingly, J, and Koelle, K. "population dynamics of antigenic immune escape The impact of host immune status on the withinhost and." J. Royal Soc. Interface (doi: 10.1098/rsif.2012.0180) (2012). (Academic Article)
 Mitchell, C, and Reed, MC. "Do Real Neurons Have Time Windows? (Submitted)." Journal of Computational Neuroscience (2012). (Academic Article)
 Reed, MC, Nijhout, HF, and Best, JA. "Mathematical insights into the effects of levodopa. (Published online)" Front Integr Neurosci 6 (2012): 21. Full Text Link to Item
 Neuhouser, ML, Nijhout, HF, Gregory, JF, Reed, MC, James, SJ, Liu, A, Shane, B, and Ulrich, CM. "Mathematical modeling predicts the effect of folate deficiency and excess on cancerrelated biomarkers." Cancer Epidemiology, Biomarkers & Prevention : a Publication of the American Association for Cancer Research, Cosponsored by the American Society of Preventive Oncology 20, no. 9 (September 2011): 19121917. Full Text
 Lawley, SD, Cinderella, M, Hall, MN, Gamble, MV, Nijhout, HF, and Reed, MC. "Mathematical model insights into arsenic detoxification." Theoretical Biology & Medical Modelling 8 (August 26, 2011): 31null. Full Text
 Best, J, Nijhout, HF, and Reed, M. "Bursts and the efficacy of selective serotonin reuptake inhibitors." Pharmacopsychiatry 44 Suppl 1 (May 2011): S76S83. Full Text Link to Item
 Lawley, SD, Cinderella, M, Hall, MN, Gamble, MV, Nijhout, HF, and Reed, MC. "Mathematical model insights into arsenic detoxification." Theoretical biology & medical modelling 8 (2011): 31. Full Text
 Popovic, L, McKinley, SA, and Reed, MC. "A stochastic compartmental model for fast axonal transport." SIAM Journal on Applied Mathematics 71, no. 4 (2011): 15311556. Full Text
 Best, J, Nijhout, HF, and Reed, M. "Serotonin synthesis, release and reuptake in terminals: a mathematical model. (Published online)" Theor Biol Med Model 7 (August 19, 2010): 34. Full Text Open Access Copy Link to Item
 Best, J, Reed, M, and Nijhout, HF. "Models of dopaminergic and serotonergic signaling." Pharmacopsychiatry 43 Suppl 1 (May 2010): S61S66. Full Text Link to Item
 Reed, MC, Lieb, A, and Nijhout, HF. "The biological significance of substrate inhibition: a mechanism with diverse functions." Bioessays : News and Reviews in Molecular, Cellular and Developmental Biology 32, no. 5 (May 2010): 422429. (Review) Full Text
 RiosAvila, L, Nijhout, HF, Reed, MC, Sitren, HS, and Gregory, JF. "Mathematical model gives insights into vitamin B6 and kynurenine metabolism." FASEB JOURNAL 24 (April 2010). Link to Item
 Reed, M, Lieb, A, and Nijhout, HF. "Biological Signiﬁcance of Substrate Inhibition." BioEssays 32 (2010): 422429. (Academic Article)
 Howell, AS, Savage, NS, Johnson, SA, Bose, I, Wagner, AW, Zyla, TR, Nijhout, HF, Reed, MC, Goryachev, AB, and Lew, DJ. "Singularity in polarization: rewiring yeast cells to make two buds." Cell 139, no. 4 (November 2009): 731743. Full Text
 Thomas, DC, Conti, DV, Baurley, J, Nijhout, F, Reed, M, and Ulrich, CM. "Use of pathway information in molecular epidemiology." Human genomics 4, no. 1 (October 2009): 2142. (Review) Full Text
 Best, JA, Nijhout, HF, and Reed, MC. "Homeostatic mechanisms in dopamine synthesis and release: a mathematical model. (Published online)" Theor Biol Med Model 6 (September 10, 2009): 21. Full Text Link to Item
 Nijhout, HF, Gregory, JF, Fitzpatrick, C, Cho, E, Lamers, KY, Ulrich, CM, and Reed, MC. "A mathematical model gives insights into the effects of vitamin B6 deficiency on 1carbon and glutathione metabolism." The Journal of Nutrition 139, no. 4 (April 2009): 784791. Full Text
 Reed, MC, Best, J, and Nijhout, HF. "Passive and active stabilization of dopamine in the striatum." Bioscience Hypotheses 2, no. 4 (2009): 240244. Full Text
 Thomas, DC, Conti, DV, Baurley, J, Nijhout, F, Reed, M, and Ulrich, CM. "Use of pathway information in molecular epidemiology." Human genomics 4, no. 1 (2009): 2142. Full Text
 Thomas, DC, Conti, DV, Ulrich, CM, Nijhout, HF, Reed, MC, and Baurly, J. "Use of pathway information in molecular epidemiology. Human Genomics." Human Genomics 4 (2009): 2142. (Academic Article)
 Ulrich, CM, Reed, MC, and Nijhout, HF. "Modeling folate, onecarbon metabolism, and DNA methylation." Nutr Rev 66 Suppl 1 (August 2008): S27S30. (Review) Full Text Link to Item
 Ulrich, CM, Neuhouser, M, Liu, AY, Boynton, A, Gregory, JF, Shane, B, James, SJ, Reed, MC, and Nijhout, HF. "Mathematical modeling of folate metabolism: predicted effects of genetic polymorphisms on mechanisms and biomarkers relevant to carcinogenesis." Cancer Epidemiology, Biomarkers & Prevention : a Publication of the American Association for Cancer Research, Cosponsored by the American Society of Preventive Oncology 17, no. 7 (July 2008): 18221831. Full Text
 Reed, MC, Thomas, RL, Pavisic, J, James, SJ, Ulrich, CM, and Nijhout, HF. "A mathematical model of glutathione metabolism." Theoretical Biology & Medical Modelling 5 (April 28, 2008): 8null. Full Text
 Nijhout, HF, Reed, MC, and Ulrich, CM. "Mathematical models of folatemediated onecarbon metabolism." Vitamins and Hormones 79 (January 2008): 4582. Full Text
 Nijhout, HF, and Reed, MC. "A Mathematical Model for Juvenile Hormone Titers." Journal of Insect Physiology 54, no. 255264 (2008). (Academic Article)
 Nijhout, HF, and Reed, MC. "A mathematical model for the regulation of juvenile hormone titers." J Insect Physiol 54, no. 1 (January 2008): 255264. Full Text Link to Item
 Leduc, D, Escartin, F, Nijhout, HF, Reed, MC, Liebl, U, Skouloubris, S, and Myllykallio, H. "Flavindependent thymidylate synthase ThyX activity: implications for the folate cycle in bacteria." Journal of Bacteriology 189, no. 23 (December 2007): 85378545. Full Text
 Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: linear SSC networks." Bulletin of Mathematical Biology 69, no. 6 (August 2007): 17911813. Full Text Open Access Copy
 Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: Linear SSC networks." BULLETIN OF MATHEMATICAL BIOLOGY 69, no. 6 (August 2007): 17911813. Full Text Link to Item
 Mitchell, C, and Reed, M. "Neural timing in highly convergent systems." SIAM Journal on Applied Mathematics 68, no. 3 (2007): 720737. Full Text
 Nijhout, HF, Reed, MC, and Ulrich, CM. "A day in the life of cell metabolism." Biological Theory (in press) (2007). (Academic Article)
 Nijhout, HF, Reed, MC, Lam, SL, Shane, B, Gregory, JF, and Ulrich, CM. "In silico experimentation with a model of hepatic mitochondrial folate metabolism. (Published online)" Theor Biol Med Model 3 (December 6, 2006): 40. Full Text Link to Item
 Boyles, AL, Billups, AV, Deak, KL, Siegel, DG, Mehltretter, L, Slifer, SH, Bassuk, AG, Kessler, JA, Reed, MC, Nijhout, HF, George, TM, Enterline, DS, Gilbert, JR, Speer, MC, and NTD Collaborative Group, . "Neural tube defects and folate pathway genes: familybased association tests of genegene and geneenvironment interactions." Environmental Health Perspectives 114, no. 10 (October 2006): 15471552. Full Text
 Reed, MC, Nijhout, HF, Neuhouser, ML, Gregory, JF, Shane, B, James, SJ, Boynton, A, and Ulrich, CM. "A mathematical model gives insights into nutritional and genetic aspects of folatemediated onecarbon metabolism." The Journal of Nutrition 136, no. 10 (October 2006): 26532661. Full Text
 Ulrich, CM, Nijhout, HF, and Reed, MC. "Mathematical modeling: epidemiology meets systems biology." Cancer Epidemiol Biomarkers Prev 15, no. 5 (May 2006): 827829. Full Text Link to Item
 Nijhout, HF, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "Longrange allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate." Epigenetics 1, no. 2 (April 2006): 8187. Link to Item
 Laurent, T, Rider, B, and Reed, M. "Parabolic behavior of a hyperbolic delay equation." SIAM Journal on Mathematical Analysis 38, no. 1 (2006): 115. Full Text
 Nijhout, HF, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "LongRange Allosteric Interactions between the Folate and Methionine Cycles Stabilize DNA Methylation Reaction Rate (vol 2, pg 81, 2006)." EPIGENETICS 1, no. 3 (2006): 115115. Full Text Link to Item
 Nijhout, HF, Reed, MC, Budu, P, and Ulrich, CM. "A mathematical model of the folate cycle: new insights into folate homeostasis." The Journal of Biological Chemistry 279, no. 53 (December 2004): 5500855016. Full Text
 Reed, MC, Nijhout, HF, Sparks, R, and Ulrich, CM. "A mathematical model of the methionine cycle." J Theor Biol 226, no. 1 (January 7, 2004): 3343. Link to Item
 Reed, MC. "Why is mathematical biology so hard?." Notices of the American Mathematical Society 51, no. 3 (2004): 338.
 Washington, TM, Blum, JJ, Reed, MC, and Conn, PM. "A mathematical model for LH release in response to continuous and pulsatile exposure of gonadotrophs to GnRH." Theoretical Biology and Medical Modelling 1 (2004). Full Text
 Reed, MC, Blum, JJ, and Mitchell, CC. "Precision of neural timing: effects of convergence and timewindowing." J Comput Neurosci 13, no. 1 (July 2002): 3547. Link to Item
 Solodovnikov, A, and Reed, MC. "Robustness of a neural network model for differencing." J Comput Neurosci 11, no. 2 (September 2001): 165173. Link to Item
 Blum, JJ, and Reed, MC. "Model calculations of time dependent responses to binaural stimuli in the dorsal nucleus of the lateral lemniscus." Hear Res 149, no. 12 (November 2000): 7790. Link to Item
 Blum, JJ, Reed, MC, Janovick, JA, and Conn, PM. "A mathematical model quantifying GnRHinduced LH secretion from gonadotropes." Am J Physiol Endocrinol Metab 278, no. 2 (February 2000): E263E272. Full Text Link to Item
 Reed, MC, and Blum, JJ. "Model calculations of steady state responses to binaural stimuli in the dorsal nucleus of the lateral lemniscus." Hear Res 136, no. 12 (October 1999): 1328. Link to Item
 Blum, JJ, and Reed, MC. "Effects of wide band inhibitors in the dorsal cochlear nucleus. II. Model calculations of the responses to complex sounds." J Acoust Soc Am 103, no. 4 (April 1998): 20002009. Link to Item
 Reed, MC, and Blum, JJ. "Model calculations of the effects of wideband inhibitors in the dorsal cochlear nucleus." J Acoust Soc Am 102, no. 4 (October 1997): 22382244. Link to Item
 Blum, JJ, Reed, MC, and Davies, JM. "A computational model for signal processing by the dorsal cochlear nucleus. II. Responses to broadband and notch noise." J Acoust Soc Am 98, no. 1 (July 1995): 181191. Link to Item
 Reed, MC, and Blum, JJ. "A computational model for signal processing by the dorsal cochlear nucleus. I. Responses to pure tones." J Acoust Soc Am 97, no. 1 (January 1995): 425438. Link to Item
 REED, MC. "THE TRANSPORT OF MATERIALS IN NERVE AXONS." MOLECULAR BIOLOGY OF THE CELL 3 (September 1992): A6A6. Link to Item
 Blum, JJ, Carr, DD, and Reed, MC. "Theoretical analysis of lipid transport in sciatic nerve." Biochim Biophys Acta 1125, no. 3 (May 8, 1992): 313320. Link to Item
 Blum, JJ, and Reed, MC. "Further studies of a model for azimuthal encoding: lateral superior olive neuron response curves and developmental processes." J Acoust Soc Am 90, no. 4 Pt 1 (October 1991): 19681978. Link to Item
 Blum, JJ, and Reed, MC. "Further studies of a model for azimuthal encoding: Lateral superior olive neuron response curves and developmental processes." Journal of the Acoustical Society of America 90, no. 4 I (1991): 19681978. Full Text
 Reed, MC, and Blum, JJ. "A model for the computation and encoding of azimuthal information by the lateral superior olive." J Acoust Soc Am 88, no. 3 (September 1990): 14421453. Link to Item
 Reed, MC, Venakides, S, and Blum, JJ. "Approximate traveling waves in linear reactionhyperbolic equations." SIAM Journal on Applied Mathematics 50, no. 1 (1990): 167180.
 Blum, JJ, Lawler, G, Reed, M, and Shin, I. "Effect of cytoskeletal geometry on intracellular diffusion." Biophys J 56, no. 5 (November 1989): 9951005. Full Text Link to Item
 Blum, JJ, and Reed, MC. "A model for slow axonal transport and its application to neurofilamentous neuropathies." Cell Motil Cytoskeleton 12, no. 1 (1989): 5365. Full Text Link to Item
 Blum, JJ, and Reed, MC. "The transport of organelles in axons." Mathematical Biosciences 90, no. 12 (1988): 233245. Full Text
 RAUCH, J, and REED, MC. "ON THE ABSORPTION OF SINGULARITIES IN DISSIPATIVE NONLINEAR EQUATIONS." LECTURE NOTES IN MATHEMATICS 1285 (1987): 403407. Link to Item
 RAUCH, J, and REED, MC. "ULTRASINGULARITIES IN NONLINEARWAVES." LECTURE NOTES IN MATHEMATICS 1248 (1987): 127133. Link to Item
 REED, MC, and BLUM, JJ. "A REACTIONHYPERBOLIC SYSTEM IN PHYSIOLOGY." LECTURE NOTES IN MATHEMATICS 1248 (1987): 134141. Link to Item
 Rauch, J, and Reed, MC. "Nonlinear superposition and absorption of delta waves in one space dimension." Journal of Functional Analysis 73, no. 1 (1987): 152178. Full Text
 Reed, MC, and Blum, JJ. "Theoretical analysis of radioactivity profiles during fast axonal transport: Effects of deposition and turnover." Cell Motility and the Cytoskeleton 6, no. 6 (1986): 620627.
 Blum, JJ, and Reed, MC. "A model for fast axonal transport." Cell Motility 5, no. 6 (1985): 507527.
 RAUCH, J, and REED, MC. "DISCONTINUOUS PROGRESSING WAVES FOR SEMILINEAR SYSTEMS." COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 10, no. 9 (1985): 10331075. Full Text Link to Item
 Beals, M, and Reed, M. "Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems." Transactions of the American Mathematical Society 285, no. 1 (January 1, 1984): 159159. Full Text
 Illner, R, and Reed, MC. "DECAY TO EQUILIBRIUM FOR THE CARLEMAN MODEL IN A BOX." SIAM Journal on Applied Mathematics 44, no. 6 (1984): 10671075.
 Reed, MC. "Geometry and Discrete Velocity Approximations to the Boltzmann Equation." NorthHolland Mathematics Studies 92, no. C (1984): 477483. Full Text
 Rauch, J, and Reed, MC. "Propagation of singularities in nonstrictly hyperbolic semilinear systems: Examples." Communications on Pure and Applied Mathematics 35, no. 4 (July 1982): 555565. Full Text
 Rauch, J, and Reed, M. "A general regularity theorem for semilinear hyperbolic waves in one space dimension." Bulletin of the American Mathematical Society 6, no. 3 (May 1, 1982): 445449. Full Text
 Beals, M, and Reed, M. "Propagation of singularities for hyperbolic pseudo differential operators with nonsmooth coefficients." Communications on Pure and Applied Mathematics 35, no. 2 (March 1982): 169184. Full Text
 RAUCH, J, and REED, MC. "SINGULARITIES PRODUCED BY THE NONLINEAR INTERACTION OF 3 PROGRESSING WAVES  EXAMPLES." COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 7, no. 9 (1982): 11171133. Full Text Link to Item
 Rauch, J, and Reed, M. "Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension." Duke Mathematical Journal 49, no. 2 (January 1, 1982): 397475. Full Text
 Illner, R, Reed, MC, and Neunzert, H. "The decay of solutions of the Carleman model." Mathematical Methods in the Applied Sciences 3, no. 1 (1981): 121127. Full Text
 Rauch, J, and Reed, M. "Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation." Communications in Mathematical Physics 81, no. 2 (1981): 203227. Full Text
 RAUCH, J, and REED, MC. "PROPAGATION OF SINGULARITIES FOR SEMILINEAR HYPERBOLICEQUATIONS IN ONE SPACE VARIABLE." ANNALS OF MATHEMATICS 111, no. 3 (1980): 531552. Full Text Link to Item
 Reed, MC, and Jr, JAB. "Reflection of singularities of onedimensional semilinear wave equations at boundaries." Journal of Mathematical Analysis and Applications 72, no. 2 (1979): 635653.
 Reed, MC. "Propagation of singularities for nonlinear wave equations in one dimension." Communications in Partial Differential Equations 3, no. 2 (January 1978): 153199. Full Text
 Reed, M, and Simon, B. "The scattering of classical waves from inhomogeneous media." Mathematische Zeitschrift 155, no. 2 (June 1977): 163180. Full Text
 REED, MC. "CONSTRUCTION OF SCATTERING OPERATOR FOR ABSTRACT NONLINEARWAVE EQUATIONS." INDIANA UNIVERSITY MATHEMATICS JOURNAL 25, no. 11 (1976): 10171027. Full Text Link to Item
 Reed, MC. "Higher order estimates and smoothness of nonlinear wave equations." Proceedings of the American Mathematical Society 51, no. 1 (January 1, 1975): 7979. Full Text
 Reed, M, and Rosen, L. "Support properties of the free measure for Boson fields." Communications in Mathematical Physics 36, no. 2 (1974): 123132. Full Text
 Reed, M, and Simon, B. "Tensor products of closed operators on Banach spaces." Journal of Functional Analysis 13, no. 2 (June 1973): 107124. Full Text
 Rauch, J, and Reed, M. "Two examples illustrating the differences between classical and quantum mechanics." Communications in Mathematical Physics 29, no. 2 (1973): 105111. Full Text
 Reed, MC, and Simon, B. "A spectral mapping theorem for tensor products of unbounded operators." Bulletin of the American Mathematical Society 78, no. 5 (September 1, 1972): 730734. Full Text
 Herman, R, and Reed, M. "Covariant representations of infinite tensor product algebras." Pacific Journal of Mathematics 40, no. 2 (February 1, 1972): 311326. Full Text
 Reed, MC. "Torus invariance for the Clifford algebra. I." Transactions of the American Mathematical Society 154 (1971): 177177. Full Text
 Reed, MC. "Torus invariance for the Clifford algebra, II." Journal of Functional Analysis 8, no. 3 (1971): 450468.
 Reed, MC. "On selfadjointness in infinite tensor product spaces." Journal of Functional Analysis 5, no. 1 (1970): 94124.
 Reed, M. "The damped selfinteraction." Communications in Mathematical Physics 11, no. 4 (1969): 346357. Full Text
 Reed, MC. "A Gårding domain for quantum fields." Communications in Mathematical Physics 14, no. 4 (1969): 336346. Full Text

 Teaching & Mentoring

Recent Courses
 MATH 89S: FirstYear Seminar 2018
 MATH 431: Advanced Calculus I 2018
 MATH 731: Advanced Calculus I 2018
 MATH 394: Research Independent Study 2017
 MATH 494: Research Independent Study 2017
 MATH 79077: Current Research in Mathematical Biology 2017
 MATH 393: Research Independent Study 2016
 MATH 493: Research Independent Study 2016
 MATH 631: Real Analysis 2016
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 New Mathematics in Cell Metabolism. Danish Mathematical Society. June 2018 2018
 Population Models in Cell Metabolism. Howard University. December 2, 2017 2017
 Mathematics, Cell Metabolism, and Public Health. Tulane University. November 16, 2017 2017
 Projecting Biochemistry over Long Distances in the Brain. Howard University. April 29, 2017 2017
 Acetaminophen Toxicity and Rescue. Duke University. April 7, 2017 2017
 Interactions between electrophysiology and neuropharmacology. SIAM Life Sciences Meeting. SIAM. July 2016 2016
 Deterministic and Statistical Models for Precision Medicine. MBI summer REU program. Mathematical Biosciences Institute. June 2016 2016
 Deterministic and Statistical Models for Precision Medicine. Precision Medicine Workshop. Howard University. April 2016 2016
 Deterministic and Statistical Models for Precision Medicine. SAMSI conference on precision medicine. SAMSI. April 2016 2016
 Stochastics in biological networks. MBI conference on Networks. Mathematical Bioscience Institute. February 2016 2016
 Mathematics and Precision Medicine. Field of Dreams Conference. November 2015 2015
 Homeostasis, cryptic genetic variation, predisposition to disease, and precision medicine. Duke Mathematical Biology Colloquium. Duke University. September 2015 2015
 Depression? Parkinson's Disease? Why is it so hard to understand the brain?. Duke Mathematical Biology Workshop. Duke University. May 2015 2015
 Metabolism and Neurobiology. Lysosomal Therapeutics, Inc.. February 2015 2015
 How to get into mathematical biology. Howard University Awards Ceremony. Howard University. December 2014 2014
 Axonal transport led to new mathematics. Duke Mathematical Biology Colloquium. Duke University. November 2014 2014
 Homeostatic mechanisms in Biochemical Systems. SIAM LIfe Sciences Conference. SIAM. August 2014 2014
 How mathematics can contribute to genomic medicine. MBI Conference. Mathematical Biosciences Institute. May 2014 2014
 Mathematics and Human Physiology. Science Sundays lecture. Ohio State University. March 2014 2014
 Mathematics, Cell Metabolism, and Public Health. Duke CBB seminar. Duke University. February 2014 2014
 New Challenges for Mathematical Neuroscience. Mathematics Colloquium. University of Pittsburgh. January 2014 2014
 Mathematics, Cell Metabolism, and Public Health. November 21, 2013 2013
 Mathematics, Cell Metabolism, and Public health. November 12, 2013 2013
 Metabolic Stories. October 4, 2013 2013
 Projecting Biochemistry over Long Distances. June 6, 2013 2013
 Stochastic Models of the Lateral Superior Olive. May 22, 2013 2013
 Why is Epidemiology so hard?. April 15, 2013 2013
 Mathematics, Cell Metabolism, and Public health. March 6, 2013 2013
 Consequences of Levodopa Therapy. Dept. of Biophysics, Rush Medical Center. March 4, 2013 2013
 Serotonin and the mysteries of depression and SSRIs. February 6, 2013 2013
 Consequences of levodopa therapy. MBI Neurological Disease Conference. Ohio State University. February 2013 2013
 Consequences of levodopa therapy. October 26, 2012 2012
 New Mathematics from Human Physiology. October 26, 2012 2012
 The Mysteries of human physiology can only be solved with mathematics. August 7, 2012 2012
 Serotonin metabolism in Health and Disease. July 19, 2011 2011
 Serotonin Metabolism in Health and Disease. June 30, 2011 2011
 Introduction to the Auditory System. August 3, 2010 2010
 Serotonin Chemistry and Neural Firing Patterns. July 15, 2010 2010
 Why Metabolism is a Challenge for Statistical Analysis: The Case of Substrate Inhibition. July 14, 2010 2010
 The Biological Significance of Substrate Inhibition. July 12, 2010 2010
 New Mathematics from Biology. March 27, 2010 2010
 New Questions in Metabolism. November 20, 2009 2009
 Deep PDE Questions Arising from Biology. November 9, 2009 2009
 Diet and Brain Serotonin. October 30, 2009 2009
 Mathematics, Cell Metabolism, and Public Health. October 17, 2009 2009
 Dopamine Stabilization in Parkinson’s Disease. October 16, 2009 2009
 Cell Metabolism and Public Health. April 2, 2009 2009
 Dynamical Systems in Chemistry. December 12, 2008 2008
 Mathematics, Cell Metabolism, and Public Health. December 12, 2008 2008
 Mathematics, Cell metabolism, and Public Health. December 12, 2008 2008
 Metabolism of Neurons: Substrate Inhibition of Tyrosine Hydroxylase. December 12, 2008 2008
 Stochastic Analysis and Biological Function. December 12, 2008 2008
 Cell Metabolism, Mathematics, and Public Health. November 7, 2008 2008

Service to the Profession
 refereed articles for the Bulletin of Mathematical Biology, the SIAM Journal of Applied Mathematics, the SIAM Journal of Analysis, and Synapse. December 10, 2011 2011
 invited symposium organizor for the International Conference on Applied Mathematics, Vancouver, 2011. July 19, 2011 2011
 NSF Panel on Career awards. November 1, 2010 2010
 NSF Site Visit Committee for NIMBios. June 5, 2010 2010
 Senior Scientific Advisor, Mathematical Biosciences Institute, Ohio State : Consultant. 2009 2009

Service to Duke
 Provost's Committee on Misconduct in Research. December 21, 2013 2013
 Provost's Standing Committee on Misconduct in Research. December 10, 2011 2011
 Hiring committee for applied ARP postdoc. December 21, 2010 2010
 Provost's Standing Committee of Misconduct in Research. December 21, 2010 2010
 hiring committee for the RTG postdoc. December 21, 2010 2010
 promotion committee for Tom Witelski. December 21, 2010 2010
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