Scholars@Duke
Michael C. Reed

Michael C. Reed

Arts and Sciences Distinguished Professor of Mathematics
Mathematics
reed@math.duke.edu
Box 90320, Duke University 90320, Durham, NC 27708-0320
237 Physics Bldg., Duke University, Box 90320, Durham, NC 27708

Selected Publications

A mathematical model of melatonin synthesis and interactions with the circadian clock.

Journal Article Mathematical biosciences · November 2024 A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregula ... Full text Cite

Modulation of serotonin transporter expression by escitalopram under inflammation.

Journal Article Communications biology · June 2024 Selective serotonin reuptake inhibitors (SSRIs) are widely used for depression based on the monoamine deficiency hypothesis. However, the clinical use of these agents is controversial, in part because of their variable clinical efficacy and in part because ... Full text Cite

Serotonin as a biomarker of toxin-induced Parkinsonism.

Journal Article Molecular medicine (Cambridge, Mass.) · March 2024 BackgroundLoss of dopaminergic neurons underlies the motor symptoms of Parkinson's disease (PD). However stereotypical PD symptoms only manifest after approximately 80% of dopamine neurons have died making dopamine-related motor phenotypes unrelia ... Full text Cite

Sex differences in glutathione metabolism and acetaminophen toxicity

Journal Article Metabolism and Target Organ Damage · January 1, 2024 Aims: Clinical and experimental evidence has shown that females in humans and other mammals have higher glutathione (GSH) levels than males, which are caused by higher levels of estradiol. Understanding how hepatic GSH level and synthesis velocity depend o ... Full text Cite

Lower hepatic CBS and PEMT expression in advanced NAFLD: inferencing strategies to lower homocysteine with a mathematical model

Journal Article Metabolism and Target Organ Damage · January 1, 2024 Aim: Hepatic homocysteine (Hcy) accumulation promotes inflammation and fibrosis in experimental nonalcoholic fatty liver disease (NAFLD), while vitamin B12 and folate reduce hepatic Hcy and protect animals from nonalcoholic steatohepatitis. This suggests c ... Full text Cite

Homeostasis Patterns

Journal Article SIAM Journal on Applied Dynamical Systems · January 1, 2024 Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distin ... Full text Cite

Dynamical questions in volume transmission.

Journal Article Journal of biological dynamics · December 2023 In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including seroto ... Full text Cite

Serotonin is a common thread linking different classes of antidepressants.

Journal Article Cell chemical biology · December 2023 Depression pathology remains elusive. The monoamine hypothesis has placed much focus on serotonin, but due to the variable clinical efficacy of monoamine reuptake inhibitors, the community is looking for alternative therapies such as ketamine (neurogenesis ... Full text Cite

Serotonin is a Common Thread Linking Different Classes of Antidepressants.

Journal Article Res Sq · March 28, 2023 Depression pathology remains elusive. The monoamine hypothesis has placed much focus on serotonin, but due to the variable clinical efficacy of monoamine reuptake inhibitors, the community is looking for alternative therapies such as ketamine (synaptic pla ... Full text Open Access Link to item Cite

Mathematical insights into the role of dopamine signaling in circadian entrainment.

Journal Article Mathematical biosciences · February 2023 The circadian clock in the mammalian brain comprises interlocked molecular feedback loops that have downstream effects on important physiological functions such as the sleep-wake cycle and hormone regulation. Experiments have shown that the circadian clock ... Full text Cite

An In Vivo Definition of Brain Histamine Dynamics Reveals Critical Neuromodulatory Roles for This Elusive Messenger.

Journal Article International journal of molecular sciences · November 2022 Histamine is well known for mediating peripheral inflammation; however, this amine is also found in high concentrations in the brain where its roles are much less known. In vivo chemical dynamics are difficult to measure, thus fundamental aspects of histam ... Full text Open Access Cite

Voltammetric Approach for Characterizing the Biophysical and Chemical Functionality of Human Induced Pluripotent Stem Cell-Derived Serotonin Neurons.

Journal Article Analytical chemistry · June 2022 Depression is quickly becoming one of the world's most pressing public health crises, and there is an urgent need for better diagnostics and therapeutics. Behavioral models in animals and humans have not adequately addressed the diagnosis and treatment of ... Full text Cite

Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.

Journal Article Journal of mathematical biology · April 2022 In insect respiration, oxygen from the air diffuses through a branching system of air-filled tubes to the cells of the body and carbon dioxide produced in cellular respiration diffuses out. The tracheal system has a very large surface area, so water loss i ... Full text Cite

Inflammation-Induced Histamine Impairs the Capacity of Escitalopram to Increase Hippocampal Extracellular Serotonin.

Journal Article The Journal of neuroscience : the official journal of the Society for Neuroscience · July 2021 Commonly prescribed selective serotonin reuptake inhibitors (SSRIs) inhibit the serotonin transporter to correct a presumed deficit in extracellular serotonin signaling during depression. These agents bring clinical relief to many who take them; however, a ... Full text Open Access Cite

A mathematical model of circadian rhythms and dopamine

Journal Article Theoretical Biology and Medical Modelling · January 30, 2021 Cite

Autoreceptor control of serotonin dynamics.

Journal Article BMC neuroscience · September 2020 BackgroundSerotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and aff ... Full text Cite

Fast serotonin voltammetry as a versatile tool for mapping dynamic tissue architecture: I. Responses at carbon fibers describe local tissue physiology.

Journal Article Journal of neurochemistry · April 2020 It is important to monitor serotonin neurochemistry in the context of brain disorders. Specifically, a better understanding of biophysical alterations and associated biochemical functionality within subregions of the brain will enable better of understandi ... Full text Cite

Systems biology of robustness and homeostatic mechanisms.

Journal Article Wiley interdisciplinary reviews. Systems biology and medicine · May 2019 All organisms are subject to large amounts of genetic and environmental variation and have evolved mechanisms that allow them to function well in spite of these challenges. This property is generally referred to as robustness. We start with the premise tha ... Full text Cite

Voltammetric evidence for discrete serotonin circuits, linked to specific reuptake domains, in the mouse medial prefrontal cortex.

Journal Article Neurochemistry international · February 2019 The medial prefrontal cortex (mPFC) is an important brain region, that controls a variety of behavioral and functional outputs. As an important step in characterizing mPFC functionality, in this paper we focus on chemically defining serotonin transmission ... Full text Cite

In vivo Hippocampal Serotonin Dynamics in Male and Female Mice: Determining Effects of Acute Escitalopram Using Fast Scan Cyclic Voltammetry.

Journal Article Frontiers in neuroscience · January 2019 Depression is a highly prevalent psychiatric disorder, impacting females at a rate roughly twice that of males. This disparity has become the focus of many studies which are working to determine if there are environmental or biological underpinnings to dep ... Full text Cite

Corrigendum: In vivo Hippocampal Serotonin Dynamics in Male and Female Mice: Determining Effects of Acute Escitalopram Using Fast Scan Cyclic Voltammetry.

Journal Article Frontiers in neuroscience · January 2019 [This corrects the article DOI: 10.3389/fnins.2019.00362.]. ... Full text Cite

Sex differences in hepatic one-carbon metabolism.

Journal Article BMC systems biology · October 2018 BackgroundThere are large differences between men and women of child-bearing age in the expression level of 5 key enzymes in one-carbon metabolism almost certainly caused by the sex hormones. These male-female differences in one-carbon metabolism ... Full text Cite

Neurotransmitter Receptors

Chapter · January 1, 2018 Neurotransmitter receptors play a vital role in the normal functioning of the nervous system. Controlled modulation of neurotransmitter receptors is critical for proper signaling between nerve cells and effector organs. Factors that disrupt normal neurotra ... Full text Cite

Analysis of Homeostatic Mechanisms in Biochemical Networks.

Journal Article Bulletin of mathematical biology · November 2017 Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This "homeostasis" does not mean that the dynamical system is rigid and fixed. Typically, large changes in external va ... Full text Cite

Systems Biology of Phenotypic Robustness and Plasticity.

Journal Article Integrative and comparative biology · August 2017 SynopsisGene regulatory networks, cellular biochemistry, tissue function, and whole body physiology are imbued with myriad overlapping and interacting homeostatic mechanisms that ensure that many phenotypes are robust to genetic and environmental ... Full text Open Access Cite

Neurotransmitter concentrations in the presence of neural switching in one dimension

Journal Article Discrete and Continuous Dynamical Systems - Series B · September 1, 2016 In volume transmission, neurons in one brain nucleus send their axons to a second nucleus where neurotransmitter is released into the extracellular space. One would like methods to calculate the average amount of neurotransmitter at different parts of the ... Full text Cite

A voltammetric and mathematical analysis of histaminergic modulation of serotonin in the mouse hypothalamus.

Journal Article Journal of neurochemistry · August 2016 Histamine and serotonin are neuromodulators which facilitate numerous, diverse neurological functions. Being co-localized in many brain regions, these two neurotransmitters are thought to modulate one another's chemistry and are often implicated in the eti ... Full text Cite

Mathematical modeling of perifusion cell culture experiments on GnRH signaling.

Journal Article Mathematical biosciences · June 2016 The effects of pulsatile GnRH stimulation on anterior pituitary cells are studied using perifusion cell cultures, where constantly moving culture medium over the immobilized cells allows intermittent GnRH delivery. The LH content of the outgoing medium ser ... Full text Cite

Mathematical biology is good for mathematics

Journal Article Notices of the American Mathematical Society · November 1, 2015 Full text Cite

Mathematical analysis of the regulation of competing methyltransferases.

Journal Article BMC systems biology · October 2015 BackgroundMethyltransferase (MT) reactions, in which methyl groups are attached to substrates, are fundamental to many aspects of cell biology and human physiology. The universal methyl donor for these reactions is S-adenosylmethionine (SAM) and t ... Full text Cite

Using mathematical models to understand metabolism, genes, and disease.

Journal Article BMC biology · September 2015 Mathematical models are a useful tool for investigating a large number of questions in metabolism, genetics, and gene-environment interactions. A model based on the underlying biology and biochemistry is a platform for in silico biological experimentation ... Full text Cite

The role of skeletal muscle in liver glutathione metabolism during acetaminophen overdose.

Journal Article Journal of theoretical biology · July 2015 Marked alterations in systemic glutamate-glutamine metabolism characterize the catabolic state, in which there is an increased breakdown and decreased synthesis of skeletal muscle protein. Among these alterations are a greatly increased net release of glut ... Full text Cite

Escape from homeostasis.

Journal Article Mathematical biosciences · November 2014 Many physiological systems, from gene networks to biochemistry to whole organism physiology, exhibit homeostatic mechanisms that keep certain variables within a fairly narrow range. Because homeostatic mechanisms buffer traits against environmental and gen ... Full text Cite

Voltammetric and mathematical evidence for dual transport mediation of serotonin clearance in vivo.

Journal Article Journal of neurochemistry · August 2014 The neurotransmitter serotonin underlies many of the brain's functions. Understanding serotonin neurochemistry is important for improving treatments for neuropsychiatric disorders such as depression. Antidepressants commonly target serotonin clearance via ... Full text Cite

Homeostasis and dynamic stability of the phenotype link robustness and plasticity.

Journal Article Integrative and comparative biology · July 2014 Phenotypes are remarkably robust to genetic and environmental variation. Although the general control principles of robustness are well understood in simple systems, the actual mechanisms that convey robustness in realistically complex systems have been li ... Full text Cite

Targeted metabolomics and mathematical modeling demonstrate that vitamin B-6 restriction alters one-carbon metabolism in cultured HepG2 cells.

Journal Article American journal of physiology. Endocrinology and metabolism · July 2014 Low vitamin B-6 nutritional status is associated with increased risk for cardiovascular disease and certain cancers. Pyridoxal 5'-phosphate (PLP) serves as a coenzyme in many cellular processes, including several reactions in one-carbon (1C) metabolism and ... Full text Cite

Mathematical modeling of the effects of glutathione on arsenic methylation.

Journal Article Theoretical biology & medical modelling · May 2014 BackgroundArsenic is a major environmental toxin that is detoxified in the liver by biochemical mechanisms that are still under study. In the traditional metabolic pathway, arsenic undergoes two methylation reactions, each followed by a reduction, ... Full text Cite

Projecting biochemistry over long distances

Journal Article Mathematical Modelling of Natural Phenomena · February 20, 2014 Mathematical and computational neuroscience have contributed to the brain sciences by the study of the dynamics of individual neurons and more recently the study of the dynamics of electrophysiological networks. Often these studies treat individual neurons ... Full text Cite

Sensitivity to switching rates in stochastically switched ODEs

Journal Article Communications in Mathematical Sciences · 2014 Full text Open Access Cite

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.

Journal Article The Journal of nutrition · September 2013 Vitamin B-6 deficiency is associated with impaired tryptophan metabolism because of the coenzyme role of pyridoxal 5'-phosphate (PLP) for kynureninase and kynurenine aminotransferase. To investigate the underlying mechanism, we developed a mathematical mod ... Full text Cite

A population model of folate-mediated one-carbon metabolism.

Journal Article Nutrients · July 2013 BackgroundPrevious mathematical models for hepatic and tissue one-carbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites that can be measured in the ... Full text Open Access Cite

The relationship between intracellular and plasma levels of folate and metabolites in the methionine cycle: a model.

Journal Article Molecular nutrition & food research · April 2013 ScopeFolate status and the status of the methionine cycle are typically assessed by measuring folate and metabolites in the plasma. It is assumed that plasma metabolite levels are proportional to their levels in tissues, but there is little inform ... Full text Cite

Stimulus encoding within the barn owl optic tectum using gamma oscillations vs. spike rate: a modeling approach.

Journal Article Network (Bristol, England) · January 2013 The optic tectum of the barn owl is a multimodal structure with multiple layers, with each layer topographically organized according to spatial receptive field. The response of a site to a stimulus can be measured as either spike rate or local field potent ... Full text Cite

Computational studies of the role of serotonin in the basal ganglia.

Journal Article Frontiers in integrative neuroscience · January 2013 It has been well established that serotonin (5-HT) plays an important role in the striatum. For example, during levodopa therapy for Parkinson's disease (PD), the serotonergic projections from the dorsal raphe nucleus (DRN) release dopamine as a false tran ... Full text Cite

The impact of host immune status on the within-host and population dynamics of antigenic immune escape.

Journal Article J R Soc Interface · October 7, 2012 Antigenically evolving pathogens such as influenza viruses are difficult to control owing to their ability to evade host immunity by producing immune escape variants. Experimental studies have repeatedly demonstrated that viral immune escape variants emerg ... Full text Open Access Link to item Cite

Blood biomarkers of methylation in Down syndrome and metabolic simulations using a mathematical model.

Journal Article Molecular nutrition & food research · October 2012 ScopeThe study tests the metabolites of the methylation cycle in individuals with Down syndrome (DS) and applies a mathematical model in order to change this cycle by nutritional factors.Methods and resultsWe measured concentrations of th ... Full text Cite

A mathematical modelling approach to assessing the reliability of biomarkers of glutathione metabolism.

Journal Article European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences · July 2012 One of the main pathways for the detoxification of reactive metabolites in the liver involves glutathione conjugation. Metabolic profiling studies have shown paradoxical responses in glutathione-related biochemical pathways. One of these is the increase in ... Full text Cite

Do Real Neurons Have Time Windows?

Journal Article Journal of Computational Neuroscience · 2012 Cite

Mathematical insights into the effects of levodopa

Journal Article Frontiers in Integrative Neuroscience · 2012 Cite

The biochemistry of acetaminophen hepatotoxicity and rescue: a mathematical model

Journal Article Theoretical Biology and Medical Modeling · 2012 Cite

A stochastic compartmental model for fast axonal transport

Journal Article SIAM Journal on Applied Mathematics · September 19, 2011 In this paper we develop a probabilistic micro scale compartmental model and use it to study macroscale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale inter ... Full text Cite

Mathematical modeling predicts the effect of folate deficiency and excess on cancer-related biomarkers.

Journal Article Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology · September 2011 BackgroundFolate is an essential B-vitamin that mediates one-carbon metabolism reactions, including nucleotide synthesis and others related to carcinogenesis. Both low- and high-folate status influences carcinogenesis.MethodsWe used a mat ... Full text Cite

Mathematical model insights into arsenic detoxification

Journal Article Theoretical Biology and Medical Modelling · August 30, 2011 Background: Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic ... Full text Cite

Mathematical model insights into arsenic detoxification.

Journal Article Theoretical biology & medical modelling · August 2011 BackgroundArsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methyl ... Full text Cite

Bursts and the efficacy of selective serotonin reuptake inhibitors.

Journal Article Pharmacopsychiatry · May 2011 We present a new hypothesis for the efficacy of selective serotonin reuptake inhibitors (SSRIs). We propose that SSRIs bring the response to the phasic firing of raphe nucleus cells back to normal, even though the average extracellular 5HT concentration re ... Full text Cite

Serotonin synthesis, release and reuptake in terminals: a mathematical model.

Journal Article Theoretical biology & medical modelling · August 2010 BackgroundSerotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and aff ... Full text Open Access Cite

Mathematical biology

Chapter · July 18, 2010 Cite

The biological significance of substrate inhibition: a mechanism with diverse functions.

Journal Article BioEssays : news and reviews in molecular, cellular and developmental biology · May 2010 Many enzymes are inhibited by their own substrates, leading to velocity curves that rise to a maximum and then descend as the substrate concentration increases. Substrate inhibition is often regarded as a biochemical oddity and experimental annoyance. We s ... Full text Cite

Models of dopaminergic and serotonergic signaling.

Journal Article Pharmacopsychiatry · May 2010 Mathematical models of dopaminergic and serotonergic synapses have enabled the authors to study quantitative aspects of the synthesis, release and reuptake of dopamine and serotonin, to investigate the effects of autoreceptors, and to explore the influence ... Full text Cite

Biological Significance of Substrate Inhibition

Journal Article BioEssays · 2010 Cite

Singularity in polarization: rewiring yeast cells to make two buds.

Journal Article Cell · November 13, 2009 For budding yeast to ensure formation of only one bud, cells must polarize toward one, and only one, site. Polarity establishment involves the Rho family GTPase Cdc42, which concentrates at polarization sites via a positive feedback loop. To assess whether ... Full text Link to item Cite

Use of pathway information in molecular epidemiology.

Journal Article Human genomics · October 2009 Candidate gene studies are generally motivated by some form of pathway reasoning in the selection of genes to be studied, but seldom has the logic of the approach been carried through to the analysis. Marginal effects of polymorphisms in the selected genes ... Full text Cite

Use of pathway information in molecular epidemiology

Journal Article Human Genomics · October 1, 2009 © 2009 Henry Stewart Publications. Candidate gene studies are generally motivated by some form of pathway reasoning in the selection of genes to be studied, but seldom has the logic of the approach been carried through to the analysis. Marginal effects of ... Full text Cite

Passive and active stabilization of dopamine in the striatum

Journal Article Bioscience Hypotheses · June 3, 2009 Parkinson's disease is a neurodegenerative disorder associated with cell loss from the substantia nigra pars compacta (SNc). The dopaminergic cells of the SNc project to the striatum where the loss of dopaminergic tone is thought to be the main cause of Pa ... Full text Cite

A mathematical model gives insights into the effects of vitamin B-6 deficiency on 1-carbon and glutathione metabolism.

Journal Article The Journal of nutrition · April 2009 We experimented with a mathematical model for 1-carbon metabolism and glutathione (GSH) synthesis to investigate the effects of vitamin B-6 deficiency on the reaction velocities and metabolite concentrations in this metabolic network. The mathematical mode ... Full text Cite

Homeostatic mechanisms in dopamine synthesis and release: a mathematical model.

Journal Article Theoretical Biology and Medical Modeling · 2009 Cite

Modeling folate, one-carbon metabolism, and DNA methylation.

Journal Article Nutrition reviews · August 2008 Full text Cite

Mathematical modeling of folate metabolism: predicted effects of genetic polymorphisms on mechanisms and biomarkers relevant to carcinogenesis.

Journal Article Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology · July 2008 Low-folate status and genetic polymorphisms in folate metabolism have been linked to several cancers. Possible biological mechanisms for this association include effects on purine and thymidine synthesis, DNA methylation, or homocysteine concentrations. Th ... Full text Cite

A mathematical model of glutathione metabolism.

Journal Article Theoretical biology & medical modelling · April 2008 BackgroundGlutathione (GSH) plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by othe ... Full text Cite

A Mathematical Model for Juvenile Hormone Titers

Journal Article Journal of Insect Physiology · 2008 Cite

A mathematical model for the regulation of juvenile hormone titers.

Journal Article Journal of insect physiology · January 2008 The titer of juvenile hormone (JH) is determined by three factors: its rate of synthesis, its rate of degradation, and the degree to which JH is protected from degradation by binding to a diversity of JH-binding proteins. All three of these factors vary th ... Full text Cite

Mathematical models of folate-mediated one-carbon metabolism.

Journal Article Vitamins and hormones · January 2008 Folate-mediated one-carbon metabolism is an unusually complex metabolic network, consisting of several interlocking cycles, and compartmentation between cytosol and mitochondria. The cycles have diverse functions, the primary being thymidylate synthesis (t ... Full text Cite

Neural timing in highly convergent systems

Journal Article SIAM Journal on Applied Mathematics · December 1, 2007 In order to study how the convergence of many variable-response neurons on a single target can sharpen timing information, we investigate the limit as the number of input neurons and the number of incoming spikes required to fire the target both get large ... Full text Cite

Flavin-dependent thymidylate synthase ThyX activity: implications for the folate cycle in bacteria.

Journal Article Journal of bacteriology · December 2007 Although flavin-dependent ThyX proteins show thymidylate synthase activity in vitro and functionally complement thyA defects in heterologous systems, direct proof of their cellular functions is missing. Using insertional mutagenesis of Rhodobacter capsulat ... Full text Cite

Propagation of fluctuations in biochemical systems, I: linear SSC networks.

Journal Article Bulletin of mathematical biology · August 2007 We investigate the propagation of random fluctuations through biochemical networks in which the number of molecules of each species is large enough so that the concentrations are well modeled by differential equations. We study the effect of network topolo ... Full text Open Access Cite

A day in the life of cell metabolism.

Journal Article Biological Theory (in press) · 2007 Cite

In silico experimentation with a model of hepatic mitochondrial folate metabolism.

Journal Article Theoretical biology & medical modelling · December 2006 BackgroundIn eukaryotes, folate metabolism is compartmentalized and occurs in both the cytosol and the mitochondria. The function of this compartmentalization and the great changes that occur in the mitochondrial compartment during embryonic devel ... Full text Cite

A mathematical model gives insights into nutritional and genetic aspects of folate-mediated one-carbon metabolism.

Journal Article The Journal of nutrition · October 2006 Impaired folate-mediated 1-carbon metabolism has been linked to multiple disease outcomes. A better understanding of the nutritional and genetic influences on this complex biochemical pathway is needed to comprehend their impact on human health. To this en ... Full text Cite

Neural tube defects and folate pathway genes: family-based association tests of gene-gene and gene-environment interactions.

Journal Article Environ Health Perspect · October 2006 BACKGROUND: Folate metabolism pathway genes have been examined for association with neural tube defects (NTDs) because folic acid supplementation reduces the risk of this debilitating birth defect. Most studies addressed these genes individually, often wit ... Full text Link to item Cite

Mathematical modeling: epidemiology meets systems biology.

Journal Article Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology · May 2006 Full text Cite

Parabolic behavior of a hyperbolic delay equation

Journal Article SIAM Journal on Mathematical Analysis · March 1, 2006 It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e., is approximately Gaussian, as t → ∞. The proof uses ideas from the DeMoivre proof of the central limit theo ... Full text Cite

A mathematical model of the folate cycle: new insights into folate homeostasis.

Journal Article The Journal of biological chemistry · December 2004 A mathematical model is developed for the folate cycle based on standard biochemical kinetics. We use the model to provide new insights into several different mechanisms of folate homeostasis. The model reproduces the known pool sizes of folate substrates ... Full text Cite

Why is mathematical biology so hard?

Journal Article Notices of the American Mathematical Society · March 1, 2004 Cite

A mathematical model for LH release in response to continuous and pulsatile exposure of gonadotrophs to GnRH

Journal Article Theoretical Biology and Medical Modeling · 2004 In a previous study, a model was developed to investigate the release of luteinizing hormone (LH) from pituitary cells in response to a short pulse of gonadotropin-releasing hormone (GnRH). The model included: binding of GnRH to its receptor (R), dimeriz ... Cite

A mathematical model of the methionine cycle.

Journal Article Journal of theoretical biology · January 2004 Building on the work of Martinov et al. (2000), a mathematical model is developed for the methionine cycle. A large amount of information is available about the enzymes that catalyse individual reaction steps in the cycle, from methionine to S-adenosylmeth ... Full text Cite

Precision of neural timing: effects of convergence and time-windowing.

Journal Article Journal of computational neuroscience · July 2002 We study the improvement in timing accuracy in a neural system having n identical input neurons projecting to one target neuron. The n input neurons receive the same stimulus but fire at stochastic times selected from one of four specified probability dens ... Full text Cite

Robustness of a neural network model for differencing.

Journal Article Journal of computational neuroscience · September 2001 A neural network, originally proposed as a model for nuclei in the auditory brainstem, uses gradients of cell thresholds to reliably compute the difference of inputs over wide input ranges. The encoding of difference is linear even though the individual co ... Full text Cite

Model calculations of time dependent responses to binaural stimuli in the dorsal nucleus of the lateral lemniscus.

Journal Article Hearing research · November 2000 In a previous paper (Reed and Blum, 1999), we examined the connectional hypotheses put forward by Markovitz and Pollak (1994) to explain the steady-state behavior of cells in the dorsal nucleus of the lateral lemniscus (DNLL). We found that the steady-stat ... Full text Cite

A mathematical model quantifying GnRH-induced LH secretion from gonadotropes.

Journal Article Am J Physiol Endocrinol Metab · February 2000 A mathematical model is developed to investigate the rate of release of luteinizing hormone (LH) from pituitary gonadotropes in response to short pulses of gonadotropin-releasing hormone (GnRH). The model includes binding of the hormone to its receptor, di ... Full text Link to item Cite

Model calculations of steady state responses to binaural stimuli in the dorsal nucleus of the lateral lemniscus.

Journal Article Hearing research · October 1999 Several studies have been performed in which both the time-dependent and steady state output of cells in the dorsal nucleus of the lateral lemniscus (DNLL) have been measured in response to binaural sound stimulation. In this paper, a mathematical and comp ... Full text Cite

Effects of wide band inhibitors in the dorsal cochlear nucleus. II. Model calculations of the responses to complex sounds.

Journal Article The Journal of the Acoustical Society of America · April 1998 In a previous modeling study of signal processing in the dorsal cochlear nucleus [Reed and Blum, J. Acoust. Soc. Am 96, 1442-1453 (1997)] it was shown that inclusion of a wideband inhibitor (WBI) greatly improved the fit between model response maps and the ... Full text Cite

Model calculations of the effects of wide-band inhibitors in the dorsal cochlear nucleus.

Journal Article The Journal of the Acoustical Society of America · October 1997 In two previous papers [Reed and Blum, J. Acoust. Soc. Am. 97, 425-438 (1995), Blum et al., J. Acoust. Soc. Am. 98, 181-191 (1995)] a computational model for signal processing in the dorsal cochlear nucleus (DCN) was developed. In those modelling studies, ... Full text Cite

Envelope coding in the auditory brainstem

Conference SIMULATION IN THE MEDICAL SCIENCES · January 1, 1997 Link to item Cite

A computational model for signal processing by the dorsal cochlear nucleus. II. Responses to broadband and notch noise.

Journal Article The Journal of the Acoustical Society of America · July 1995 In a previous paper a computational model was developed which was shown to account for most of the essential features of the variety of experimentally observed response maps of type-IV cells in the dorsal cochlear nucleus to pure tones. In the present stud ... Full text Cite

A computational model for signal processing by the dorsal cochlear nucleus. I. Responses to pure tones.

Journal Article The Journal of the Acoustical Society of America · January 1995 Much information is available on the anatomical organization and neurophysiological properties of the major cell types in the dorsal cochlear nucleus (DCN). The complicated response properties of individual cells and units in the DCN indicate that substant ... Full text Cite

THE TRANSPORT OF MATERIALS IN NERVE AXONS

Journal Article MOLECULAR BIOLOGY OF THE CELL · September 1, 1992 Link to item Cite

Theoretical analysis of lipid transport in sciatic nerve.

Journal Article Biochimica et biophysica acta · May 1992 We modify our previous mathematical model of axonal transport to analyze data on the fast transport of lipids in rat sciatic nerve given in Toews et al. (J. Neurochem. 40, 555-562 (1983)). The theoretical model accounts well for the shapes of the profiles ... Full text Cite

Further studies of a model for azimuthal encoding: lateral superior olive neuron response curves and developmental processes.

Journal Article The Journal of the Acoustical Society of America · October 1991 A number of investigators have published measurements of the outputs of single neurons from the lateral superior olive (LSO) of the cat for a variety of auditory signals. The response curves show a very wide range of shapes and thresholds. In this paper, t ... Full text Cite

A model for the computation and encoding of azimuthal information by the lateral superior olive.

Journal Article The Journal of the Acoustical Society of America · September 1990 A structural model is proposed for the processing of interaural intensity differences by the lateral superior olive. One fundamental assumption is that the incoming excitatory projections from the ipsilateral anteroventral cochlear nucleus innervate column ... Full text Cite

Approximate traveling waves in linear reaction-hyperbolic equations

Journal Article SIAM Journal on Applied Mathematics · January 1, 1990 Linear reaction-hyperbolic equations of a general type arising in certain physiological problems do not have traveling wave solutions, but numerical computations have shown that they possess approximate traveling waves. Using singular perturbation theory, ... Full text Cite

Effect of cytoskeletal geometry on intracellular diffusion.

Journal Article Biophysical journal · November 1989 A method is presented for determining the retardation of diffusion of particles inside cells owing to cytoskeletal barriers. The cytoskeletal meshwork is treated as a repeating periodic two-dimensional or three-dimensional lattice composed of elements of g ... Full text Cite

A model for slow axonal transport and its application to neurofilamentous neuropathies.

Journal Article Cell motility and the cytoskeleton · January 1989 A model for slow axonal transport is developed in which the essential features are reversible binding of cytoskeletal elements and of soluble cytosolic proteins to each other and to motile elements such as actin microfilaments. Computer simulation of the e ... Full text Cite

The transport of organelles in axons

Journal Article Mathematical Biosciences · January 1, 1988 The fast anterograde and retrograde transport systems in axons convey organelles from the soma, where synthesis occurs, to the synaptic region and back. Studies of label incorporation into newly synthesized organelles show that they move along the axon wit ... Full text Cite

Nonlinear superposition and absorption of delta waves in one space dimension

Journal Article Journal of Functional Analysis · January 1, 1987 Full text Cite

A REACTION-HYPERBOLIC SYSTEM IN PHYSIOLOGY

Journal Article LECTURE NOTES IN MATHEMATICS · January 1, 1987 Link to item Cite

ON THE ABSORPTION OF SINGULARITIES IN DISSIPATIVE NONLINEAR EQUATIONS

Journal Article LECTURE NOTES IN MATHEMATICS · January 1, 1987 Link to item Cite

ULTRASINGULARITIES IN NONLINEAR-WAVES

Journal Article LECTURE NOTES IN MATHEMATICS · January 1, 1987 Link to item Cite

Theoretical analysis of radioactivity profiles during fast axonal transport: effects of deposition and turnover.

Journal Article Cell motility and the cytoskeleton · January 1986 In a preceding study [Blum, J.J., and Reed, M.C. (1985): Cell Motil. 5:507-527], factors responsible for the shape and velocity of the leading edge of the radiolabeled organelle profile were analyzed, but processes that might influence the shape of the pla ... Full text Cite

A model for fast axonal transport.

Journal Article Cell motility · January 1985 A model for fast axonal transport is developed in which the essential features are that organelles may interact with mechanochemical cross-bridges that in turn interact with microtubules, forming an organelle-engine-microtubule complex which is transported ... Full text Cite

Discontinuous progressing waves for semilinear systems

Journal Article Communications in Partial Differential Equations · January 1985 Full text Cite

Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems

Journal Article Transactions of the American Mathematical Society · January 1, 1984 The authors develop a calculus of pseudodifferential operators with nonsmooth coefficients in order to study the regularity of solutions to linear equations P(x, D)u = f. The regularity theorems are similar to those of Bony, but the calculus and the method ... Full text Cite

DECAY TO EQUILIBRIUM FOR THE CARLEMAN MODEL IN A BOX.

Journal Article SIAM Journal on Applied Mathematics · January 1, 1984 We prove global decay to the homogeneous equilibrium state for the simplest discrete velocity approximation to the Boltzmann equation. ... Full text Cite

Geometry and Discrete Velocity Approximations to the Boltzmann Equation

Journal Article North-Holland Mathematics Studies · January 1, 1984 Full text Cite

A general regularity theorem for semilinear hyperbolic waves in one space dimension

Journal Article Bulletin of the American Mathematical Society · January 1, 1982 Full text Cite

Propagation of singularities for hyperbolic pseudo differential operators with non‐smooth coefficients

Journal Article Communications on Pure and Applied Mathematics · January 1, 1982 Full text Cite

Propagation of singularities in non‐strictly hyperbolic semilinear systems: Examples

Journal Article Communications on Pure and Applied Mathematics · January 1, 1982 Full text Cite

Singularities Produced by the Nonlinear Interaction of Three Progressing Waves;Examples

Journal Article Communications in Partial Differential Equations · January 1, 1982 Full text Cite

Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation

Journal Article Communications in Mathematical Physics · June 1, 1981 The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}i=1 n, of jump discontinuities. Let S be the smallest closed set which sat ... Full text Cite

The decay of solutions of the Carleman model

Journal Article Mathematical Methods in the Applied Sciences · January 1, 1981 We prove that for positive initial data u0, v0 ϵ C1 (R) ∩ L1 (R) vanishing at infinity, the solution u(x, t) v(x, t) of the Carleman model satisfies the estimate The constant C depends only on the initial mass m. Copyright © 1981 John Wiley & Sons, Ltd ... Full text Cite

Reflection of singularities of one-dimensional semilinear wave equations at boundaries

Journal Article Journal of Mathematical Analysis and Applications · January 1, 1979 Full text Cite

Propagation of singularities for non-linear wave equations in one dimension

Journal Article Communications in Partial Differential Equations · January 1, 1978 Full text Cite

The scattering of classical waves from inhomogeneous media

Journal Article Mathematische Zeitschrift · June 1, 1977 By extending Kato's theory of two Hilbert space scattering, we are able to formulate both optical and accoustical scattering from inhomogeneous media as strictly elliptic problems. We use this formulation to present simple proofs of the existence and compl ... Full text Cite

CONSTRUCTION OF SCATTERING OPERATOR FOR ABSTRACT NONLINEAR-WAVE EQUATIONS

Journal Article INDIANA UNIVERSITY MATHEMATICS JOURNAL · January 1, 1976 Full text Link to item Cite

Higher order estimates and smoothness of nonlinear wave equations

Journal Article Proceedings of the American Mathematical Society · January 1, 1975 A completely elementary proof is given for Segal's nonlinear semigroup theorem. © 1975 American Mathematical Society. ... Full text Cite

Support properties of the free measure for Boson fields

Journal Article Communications in Mathematical Physics · June 1, 1974 Let μ be the measure on I′ (ℝd) corresponding to the Gaussian process with mean zero and covariance (f,(-Δ+1)-1g) on I (ℝd). It is proven that the set {Mathematical expression} has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δd ... Full text Cite

Two examples illustrating the differences between classical and quantum mechanics

Journal Article Communications in Mathematical Physics · June 1, 1973 Two examples are presented: The first shows that a potential V(x) can be in the limit circle case at ∞ even if the classical travel time to ∞ is infinite. The second shows that V(x) can be in the limit point case at ∞ even though the classical travel time ... Full text Cite

Tensor products of closed operators on Banach spaces

Journal Article Journal of Functional Analysis · January 1, 1973 Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let α be a uniform cross norm on X ⊗ Y. Using the Gelfand theory and resolvent algebra techniques, a s ... Full text Cite

A spectral mapping theorem for tensor products of unbounded operators

Journal Article Bulletin of the American Mathematical Society · January 1, 1972 Full text Cite

Covariant representations of infinite tensor product algebras

Journal Article Pacific Journal of Mathematics · January 1, 1972 In this paper myriad covariant representations of a class of C*-algebras and automorphism groups are constructed. The Hilbert spaces on which the representations are realized have an unusual structure: they are direct integrals of measurable families S(·) ... Full text Cite

Torus invariance for the clifford algebra i

Journal Article Transactions of the American Mathematical Society · January 1, 1971 A problem in Quantum Field Theory leads to the study of a representation of the torus, T3, as automorphisms of the infinite dimensional Clifford algebra. It is shown that the irreducible product representations of the Clifford algebra fall into two categor ... Full text Cite

Torus invariance for the Clifford algebra, II

Journal Article Journal of Functional Analysis · January 1, 1971 The structure of the representations of the infinite-dimensional Clifford algebra generated by states symmetric about a basis is studied. In particular, it is shown where they fit into the Gårding-Wightman classification. These representations have an unus ... Full text Cite

On self-adjointness in infinite tensor product spaces

Journal Article Journal of Functional Analysis · January 1, 1970 Full text Cite

The damped self-interaction

Journal Article Communications in Mathematical Physics · December 1, 1969 A self-interaction with damped off-diagonal coefficients is used to illustrate techniques for dealing directly with Hamiltonians in strange representations of the CCR. © 1969 Springer-Verlag. ... Full text Cite

A Gårding domain for quantum fields

Journal Article Communications in Mathematical Physics · December 1, 1969 In all representations of the canonical commutation relations, there is a common, invariant domain of essential self-adjointness for quantum fields and conjugate momenta. © 1969 Springer-Verlag. ... Full text Cite

Homeostasis Despite Instability

Journal Article Mathematical Biosciences Open Access Cite

A mathematical model of circadian rhythms and dopamine.

Journal Article Theoretical Biology and Medical Modelling Cite