# Browsing by Author "Reed, Michael C"

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Item Open Access A population model of folate-mediated one-carbon metabolism.(Nutrients, 2013-07-05) Duncan, Tanya M; Reed, Michael C; Nijhout, H FrederikBACKGROUND: Previous 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 plasma are related to their respective intracellular concentrations. METHODS: The model consists of a set of ordinary differential equations, one for each metabolite in each compartment, and kinetic equations for metabolism and for transport between compartments. The model was validated by comparison to a variety of experimental data such as the methionine load test and variation in folate intake. We further extended this model by introducing random and systematic variation in enzyme activity. OUTCOMES AND CONCLUSIONS: A database of 10,000 virtual individuals was generated, each with a quantitatively different one-carbon metabolism. Our population has distributions of folate and homocysteine in the plasma and tissues that are similar to those found in the NHANES data. The model reproduces many other sets of clinical data. We show that tissue and plasma folate is highly correlated, but liver and plasma folate much less so. Oxidative stress increases the plasma S-adenosylmethionine/S-adenosylhomocysteine (SAM/SAH) ratio. We show that many relationships among variables are nonlinear and in many cases we provide explanations. Sampling of subpopulations produces dramatically different apparent associations among variables. The model can be used to simulate populations with polymorphisms in genes for folate metabolism and variations in dietary input.Item Open Access An Application of Abstract Algebra to the Neural Code for Sound Localization in the Barn Owl(2016-04-25) Brown, LindseyPatterns of neural firing can be viewed as a binary code with each neuron as a bit, with neurons which actively fire in response to a stimulus associated to a 1 and those which do not fire associated to a 0. In previous work, Curto et al. demonstrate that by studying the neural code as a ring, information can be recovered about the ways the regions over which the different neurons fire intersect as well as the convexity of these regions. In this work, these ideas are applied to the system of sound localization in the owl. One of the properties of the sound used to determine its location is the interaural time difference, which is represented in the nucleus laminaris when a neuron fires in response to being stimulated by signals coming from both ears at the same time. Though the signals arrive at the same time at the neuron, it is still ambiguous by how many periods the two sound waves differ, resulting in periodic firing in the columns of the nucleus laminaris and behavioral errors in the owl's response in locating the sound. Using the concepts from neural coding theory, it is demonstrated that neural codes with a perfectly patterned periodic form do not correspond to a set of convex sets, reflecting this ambiguity. It is further shown that by introducing stochasticity into these patterns, hence introducing new codewords, the new code may have a convex realization. This suggests that the stochastic nature of neural firing may be necessary for disambiguating stimuli.Item Open Access An In Vivo Definition of Brain Histamine Dynamics Reveals Critical Neuromodulatory Roles for This Elusive Messenger.(International journal of molecular sciences, 2022-11) Berger, Shane N; Baumberger, Beatrice; Samaranayake, Srimal; Hersey, Melinda; Mena, Sergio; Bain, Ian; Duncan, William; Reed, Michael C; Nijhout, H Frederik; Best, Janet; Hashemi, ParastooHistamine 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 histamine's neurochemistry remain undefined. In this work, we undertake the first in-depth characterization of real time in vivo histamine dynamics using fast electrochemical tools. We find that histamine release is sensitive to pharmacological manipulation at the level of synthesis, packaging, autoreceptors and metabolism. We find two breakthrough aspects of histamine modulation. First, differences in H3 receptor regulation between sexes show that histamine release in female mice is much more tightly regulated than in male mice under H3 or inflammatory drug challenge. We hypothesize that this finding may contribute to hormone-mediated neuroprotection mechanisms in female mice. Second, a high dose of a commonly available antihistamine, the H1 receptor inverse agonist diphenhydramine, rapidly decreases serotonin levels. This finding highlights the sheer significance of pharmaceuticals on neuromodulation. Our study opens the path to better understanding and treating histamine related disorders of the brain (such as neuroinflammation), emphasizing that sex and modulation (of serotonin) are critical factors to consider when studying/designing new histamine targeting therapeutics.Item Open Access Homeostasis-Bifurcation Singularities and Identifiability of Feedforward Networks(2020) Duncan, WilliamThis dissertation addresses two aspects of dynamical systems arising from biological networks: homeostasis-bifurcation and identifiability.

Homeostasis occurs when a biological quantity does not change very much as a parameter is varied over a wide interval. Local bifurcation occurs when the multiplicity or stability of equilibria changes at a point. Both phenomena can occur simultaneously and as the result of a single mechanism. We show that this is the case in the feedback inhibition network motif. In addition we prove that longer feedback inhibition networks are less stable. Towards understanding interactions between homeostasis and bifurcations, we define a new type of singularity, the homeostasis-bifurcation point. Using singularity theory, the behavior of dynamical systems with homeostasis-bifurcation points is characterized. In particular, we show that multiple homeostatic plateaus separated by hysteretic switches and homeostatic limit cycle periods and amplitudes are common when these singularities occur.

Identifiability asks whether it is possible to infer model parameters from measurements. We characterize the structural identifiability properties for feedforward networks with linear reaction rate kinetics. Interestingly, the set of reaction rates corresponding to the edges of the graph are identifiable, but the assignment of rates to edges is not; Permutations of the reaction rates leads to the same measurements. We show how the identifiability results for linear kinetics can be extended to Michaelis-Menten kinetics using asymptotics.

Item Open Access Inflammation-Induced Histamine Impairs the Capacity of Escitalopram to Increase Hippocampal Extracellular Serotonin.(The Journal of neuroscience : the official journal of the Society for Neuroscience, 2021-07) Hersey, Melinda; Samaranayake, Srimal; Berger, Shane N; Tavakoli, Navid; Mena, Sergio; Nijhout, H Frederik; Reed, Michael C; Best, Janet; Blakely, Randy D; Reagan, Lawrence P; Hashemi, ParastooCommonly 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 significant and growing number of individuals are resistant to SSRIs. There is emerging evidence that inflammation plays a significant role in the clinical variability of SSRIs, though how SSRIs and inflammation intersect with synaptic serotonin modulation remains unknown. In this work, we use fast*in vivo*serotonin measurement tools to investigate the nexus between serotonin, inflammation, and SSRIs. Upon acute systemic lipopolysaccharide (LPS) administration in male and female mice, we find robust decreases in extracellular serotonin in the mouse hippocampus. We show that these decreased serotonin levels are supported by increased histamine activity (because of inflammation), acting on inhibitory histamine H3 heteroreceptors on serotonin terminals. Importantly, under LPS-induced histamine increase, the ability of escitalopram to augment extracellular serotonin is impaired because of an off-target action of escitalopram to inhibit histamine reuptake. Finally, we show that a functional decrease in histamine synthesis boosts the ability of escitalopram to increase extracellular serotonin levels following LPS. This work reveals a profound effect of inflammation on brain chemistry, specifically the rapidity of inflammation-induced decreased extracellular serotonin, and points the spotlight at a potentially critical player in the pathology of depression, histamine. The serotonin/histamine homeostasis thus, may be a crucial new avenue in improving serotonin-based treatments for depression.**SIGNIFICANCE STATEMENT**Acute LPS-induced inflammation (1) increases CNS histamine, (2) decreases CNS serotonin (via inhibitory histamine receptors), and (3) prevents a selective serotonin reuptake inhibitor (SSRI) from effectively increasing extracellular serotonin. A targeted depletion of histamine recovers SSRI-induced increases in extracellular hippocampal serotonin.Item Open Access Mathematical Modeling of Perifusion Cell Culture Experiments(2016) Temamogullari, NIhal EzgiIn perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Item Open Access Mathematical Modelling of Immuno-Oncology and Related Immunology(2019) Hanson, Shalla DImmunotherapy offers new and promising treatments for many different types of cancer, but the problem of how to practically regulate the immune response in a way that allows it to fight cancer without overwhelming patients with potentially fatal inflammatory toxicity has yet to be solved. This partly results from lingering unanswered questions in immunology and partly results from the inevitable variability between one patient and the next. Here we look specifically at Chimeric Antigen Receptor (CAR)-T cell therapy, explore the mechanisms by which this living drug grows and changes inside the body, and explore how and why this process differs so dramatically between patients.

We develop two ordinary differential equation models -- one which unifies several currently conflicting theories on T cell differentiation pathways, and one which serves as a framework for a Simulated Randomized Clinical Trial (SRCT) to evaluate CAR-T cell therapy as a treatment for patients with leukemia. Our results provide a plausible mechanistic explanation for widely variable patient responses to CAR-T cell therapy seen clinically, and suggest possible ways to improve patient outcomes, even and especially when the patient population is highly heterogeneous. In particular, our results suggest that improvements in patient outcomes can be obtained by reintroducing key characteristics of the endogenous T-cell response that are lost with the dosing protocols currently being used in clinical trials. Our primary conclusion is that single or (homogeneously) split dose protocols should be replaced with protocols for achieving, during the initial stages of therapy, low serum concentrations of effector CAR-T cells, followed by higher serum concentrations of effector CAR-T cells as the tumor burden decreases, and finally substantial serum concentrations of memory CAR-T cells at the end of the treatment period.

Item Open Access Modeling the interactions between the circadian clock, dopamine, and metabolism(2022) Kim, RubyThis dissertation includes three projects in mathematical biology: (1) Mathematical modeling of the circadian clock and dopamine, (2) Mathematical analysis of a circadian clock model, and (3) Mathematical modeling of sex differences in one-carbon metabolism. Circadian rhythms, dopamine, and metabolism are all important aspects of human physiology and we use methods from dynamical systems and scientific computing to investigate these systems at the molecular level.

First, we create a mathematical model to understand the influences of the mammalian circadian clock on the neurotransmitter dopamine (DA). The circadian clock circuitry in the suprachiasmatic nucleus (SCN) drives 24-hour rhythms in many important physiological processes, including the dopaminergic system. DA imbalances have been linked to various neurological and psychiatric conditions such as Parkinson's disease, attention-deficit/hyperactivity disorder (ADHD), and mood disorders. Previous studies have shown that these conditions are often accompanied by disrupted circadian rhythms, but it has not been well understood why. We use our mathematical model to explain the mechanisms by which the circadian clock influences DA in the brain. We show that the model corresponds well with a host of experimental data and accurately predicts daily variation in extracellular DA.

The model is comprised of a system of nonlinear ordinary differential equations with solutions displaying a remarkably robust 24-hour period consistent with the biology. We further investigate different dynamical behaviors in the model, including periodicity, quasiperiodicity, and decoupling. We show that these behaviors are biologically meaningful and may help to explain clinically observed circadian or dopaminergic disruptions. In addition, experiments have suggested several links between the mammalian clock and one-carbon metabolism (OCM). OCM is essential for the synthesis of DNA and proteins, and we use mathematical modeling to understand how the biochemical reactions in OCM are influenced by sex hormones and micronutrients like folate, vitamin B12, and vitamin B6.

Item Open Access Probabilistic methods for multiscale evolutionary dynamics(2013) Luo, Shishi ZhigeEvolution by natural selection can occur at multiple biological scales. This is particularly the case for host-pathogen systems, where selection occurs both within each infected host as well as through transmission between hosts. Despite there being established mathematical models for understanding evolution at a single biological scale, fewer tractable models exist for multiscale evolutionary dynamics. Here I present mathematical approaches using tools from probability and stochastic processes as well as dynamical systems to handle multiscale evolutionary systems. The first problem I address concerns the antigenic evolution of influenza. Using a combination of ordinary differential equations and inhomogeneous Poisson processes, I study how immune selection pressures at the within-host level impact population-level evolutionary dynamics. The second problem involves the more general question of evolutionary dynamics when selection occurs antagonistically at two biological scales. In addition to host-pathogen systems, such situations arise naturally in the evolution of traits such as the production of a public good and the use of a common resource. I introduce a model for this general phenomenon that is intuitively visualized as a a stochastic ball-and-urn system and can be used to systematically obtain general properties of antagonistic multiscale evolution. Lastly, this ball-and-urn framework is in itself an interesting mathematical object which can studied as either a measure-valued process or an interacting particle system. In this mathematical context, I show that under different scalings, the measure-valued process can have either a propagation of chaos or Fleming-Viot limit.

Item Open Access Propagation of fluctuations in biochemical systems, I: Linear SSC networks(Bulletin of Mathematical Biology, 2007-08-01) Anderson, David F; Mattingly, Jonathan C; Nijhout, H Frederik; Reed, Michael CWe 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 topology on the emergent properties of the reaction system by characterizing the behavior of variance as fluctuations propagate down chains and studying the effect of side chains and feedback loops. We also investigate the asymptotic behavior of the system as one reaction becomes fast relative to the others. © 2007 Springer Science+Business Media, Inc.Item Open Access Sensitivity to switching rates in stochastically switched ODEs(Communications in Mathematical Sciences, 2014-01-01) Lawley, Sean D; Mattingly, Jonathan C; Reed, Michael CWe consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.Item Open Access Serotonin is a Common Thread Linking Different Classes of Antidepressants.(Res Sq, 2023-03-28) Witt, Colby E; Mena, Sergio; Holmes, Jordan; Hersey, Melinda; Buchanan, Anna Marie; Parke, Brenna; Saylor, Rachel; Honan, Lauren E; Berger, Shane N; Lumbreras, Sara; Nijhout, Frederik H; Reed, Michael C; Best, Janet; Fadel, James; Schloss, Patrick; Lau, Thorsten; Hashemi, ParastooDepression 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 plasticity and neurogenesis theory of antidepressant action). There is evidence that different classes of antidepressants may affect serotonin levels; a notion we test here. We measure hippocampal serotonin in mice with voltammetry and study the effects of acute challenges of antidepressants. We find that pseudo-equivalent doses of these drugs similarly raise ambient serotonin levels, despite their differing pharmacodynamics because of differences in Uptake 1 and 2, rapid SERT trafficking and modulation of serotonin by histamine. These antidepressants have different pharmacodynamics but have strikingly similar effects on extracellular serotonin. Our findings suggest that serotonin is a common thread that links clinically effective antidepressants, synergizing different theories of depression (synaptic plasticity, neurogenesis and the monoamine hypothesis).Item Open Access Stochastic Switching in Evolution Equations(2014) Lawley, Sean DavidWe consider stochastic hybrid systems that stem from evolution equations with right-hand sides that stochastically switch between a given set of right-hand sides. To begin our study, we consider a linear ordinary differential equation whose right-hand side stochastically switches between a collection of different matrices. Despite its apparent simplicity, we prove that this system can exhibit surprising behavior.

Next, we construct mathematical machinery for analyzing general stochastic hybrid systems. This machinery combines techniques from various fields of mathematics to prove convergence to a steady state distribution and to analyze its structure.

Finally, we apply the tools from our general framework to partial differential equations with randomly switching boundary conditions. There, we see that these tools yield explicit formulae for statistics of the process and make seemingly intractable problems amenable to analysis.

Item Open Access Stochastic switching in infinite dimensions with applications to random parabolic PDE(SIAM Journal on Mathematical Analysis, 2015-01-01) Lawley, Sean D; Mattingly, Jonathan C; Reed, Michael C© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.Item Open Access Systems Biology of Phenotypic Robustness and Plasticity.(Integr Comp Biol, 2017-08-01) Nijhout, H Frederik; Sadre-Marandi, Farrah; Best, Janet; Reed, Michael CSYNOPSIS: Gene 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 variation. Animals also often have plastic responses to environmental variables, which means that many different phenotypes can correspond to a single genotype. Since natural selection acts on phenotypes, this raises the question of how selection can act on the genome if genotypes are decoupled from phenotypes by robustness and plasticity mechanisms. The answer can be found in the systems biology of the homeostatic mechanisms themselves. First, all such mechanisms operate over a limited range and outside that range the controlled variable changes rapidly allowing natural selection to act. Second, mutations and environmental stressors can disrupt homeostatic mechanisms, exposing cryptic genetic variation and allowing natural selection to act. We illustrate these ideas by examining the systems biology of four specific examples. We show how it is possible to analyze and visualize the roles of specific genes and specific polymorphisms in robustness in the context of large and realistic nonlinear systems. We also describe a new method, system population models, that allows one to connect causal dynamics to the variable outcomes that one sees in biological populations with large variation.Item Open Access Time-Scaled Stochastic Input to Biochemical Reaction Networks(2010) Thomas, Rachel LeeBiochemical reaction networks with a sufficiently large number of molecules may be represented as systems of differential equations. Many networks receive inputs that fluctuate continuously in time. These networks may never settle down to a static equilibrium and are of great interest both mathematically and biologically. Biological systems receive inputs that vary on multiple time scales. Hormonal and neural inputs vary on a scale of seconds or minutes; inputs from meals and circadian rhythms vary on a scale of hours or days; and long term environmental changes (such as diet, disease, and pollution) vary on a scale of years. In this thesis, we consider the limiting behavior of networks in which the input is on a different time scale compared to the reaction kinetics within the network.

We prove analytic results of how the variance of reaction rates within a system compares to the variance of the input when the input is on a different time scale than the reaction kinetics within the network. We consider the behavior of simple chains, single species complex networks, reversible chains, and certain classes of non-linear systems with time-scaled stochastic input, as the input speeds up and slows down. In all cases, as the input fluctuates more and more quickly, the variance of species within the system approaches to zero. As the input fluctuates more and more slowly, the variance of the species approaches the variance of the input, up to a normalization factor.