Browsing by Author "Duncan, William"

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    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, Parastoo
    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 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.
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    Coincidence of Homeostasis and Bifurcation in Feedforward Networks
    (International Journal of Bifurcation and Chaos) Duncan, William; Golubitsky, Martin
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    Homeostasis despite instability.
    (Mathematical biosciences, 2018-06) Reed, MC; Duncan, William; Nijhout, HF; Best, J; Golubitsky, M
    We have shown previously that different homeostatic mechanisms in biochemistry create input-output curves with a "chair" shape. At equilibrium, for intermediate values of a parameter (often an input), a variable, Z, changes very little (the homeostatic plateau), but for low and high values of the parameter, Z changes rapidly (escape from homeostasis). In all cases previously studied, the steady state was stable for each value of the input parameter. Here we show that, for the feedback inhibition motif, stability may be lost through a Hopf bifurcation on the homeostatic plateau and then regained by another Hopf bifurcation. If the limit cycle oscillations are relatively small in the unstable interval, then the variable Z maintains homeostasis despite the instability. We show that the existence of an input interval in which there are oscillations, the length of the interval, and the size of the oscillations depend in interesting and complicated ways on the properties of the inhibition function, f, the length of the chain, and the size of a leakage parameter.
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    Homeostasis-Bifurcation Singularities and Identifiability of Feedforward Networks
    (2020) Duncan, William

    This 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.