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Creators/Authors contains: "Rubin, Jonathan E."

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  1. Free, publicly-accessible full text available July 1, 2024
  2. Abstract Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and specifically to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity. 
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    Free, publicly-accessible full text available May 12, 2024
  3. Abstract

    Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.

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  4. Despite considerable study of population cycles, the striking variability of cycle periods in many cyclic populations has received relatively little attention. Mathematical models of cyclic population dynamics have historically exhibited much greater regularity in cycle periods than many real populations, even when accounting for environmental stochasticity. We contend, however, that the recent focus on understanding the impact of long, transient but recurrent epochs within population oscillations points the way to a previously unrecognized means by which environmental stochasticity can create cycle period variation. Specifically, consumer–resource cycles that bring the populations near a saddle point (a combination of population sizes toward which the populations tend, before eventually transitioning to substantially different levels) may be subject to a slow passage effect that has been dubbed a ‘saddle crawlby'. In this study, we illustrate how stochasticity that generates variability in how close predator and prey populations come to saddles can result in substantial variability in the durations of crawlbys and, as a result, in the periods of population cycles. Our work suggests a new mechanistic hypothesis to explain an important factor in the irregular timing of population cycles and provides a basis for understanding when environmental stochasticity is, and is not, expected to generate cyclic dynamics with variability across periods. 
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  5. Inspiratory breathing rhythms arise from synchronized neuronal activity in a bilaterally distributed brainstem structure known as the preBötzinger complex (preBötC). In in vitro slice preparations containing the preBötC, extracellular potassium must be elevated above physiological levels (to 7–9 mM) to observe regular rhythmic respiratory motor output in the hypoglossal nerve to which the preBötC projects. Reexamination of how extracellular K + affects preBötC neuronal activity has revealed that low-amplitude oscillations persist at physiological levels. These oscillatory events are subthreshold from the standpoint of transmission to motor output and are dubbed burstlets. Burstlets arise from synchronized neural activity in a rhythmogenic neuronal subpopulation within the preBötC that in some instances may fail to recruit the larger network events, or bursts, required to generate motor output. The fraction of subthreshold preBötC oscillatory events (burstlet fraction) decreases sigmoidally with increasing extracellular potassium. These observations underlie the burstlet theory of respiratory rhythm generation. Experimental and computational studies have suggested that recruitment of the non-rhythmogenic component of the preBötC population requires intracellular Ca 2+ dynamics and activation of a calcium-activated nonselective cationic current. In this computational study, we show how intracellular calcium dynamics driven by synaptically triggered Ca 2+ influx as well as Ca 2+ release/uptake by the endoplasmic reticulum in conjunction with a calcium-activated nonselective cationic current can reproduce and offer an explanation for many of the key properties associated with the burstlet theory of respiratory rhythm generation. Altogether, our modeling work provides a mechanistic basis that can unify a wide range of experimental findings on rhythm generation and motor output recruitment in the preBötC. 
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  6. Previously our computational modeling studies (Phillips et al., 2019) proposed that neuronal persistent sodium current (I NaP ) and calcium-activated non-selective cation current (I CAN ) are key biophysical factors that, respectively, generate inspiratory rhythm and burst pattern in the mammalian preBötzinger complex (preBötC) respiratory oscillator isolated in vitro. Here, we experimentally tested and confirmed three predictions of the model from new simulations concerning the roles of I NaP and I CAN : (1) I NaP and I CAN blockade have opposite effects on the relationship between network excitability and preBötC rhythmic activity; (2) I NaP is essential for preBötC rhythmogenesis; and (3) I CAN is essential for generating the amplitude of rhythmic output but not rhythm generation. These predictions were confirmed via optogenetic manipulations of preBötC network excitability during graded I NaP or I CAN blockade by pharmacological manipulations in slices in vitro containing the rhythmically active preBötC from the medulla oblongata of neonatal mice. Our results support and advance the hypothesis that I NaP and I CAN mechanistically underlie rhythm and inspiratory burst pattern generation, respectively, in the isolated preBötC. 
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