Mathematical Modeling in Neuroendocrinology

Bertram, Richard

doi:10.1002/cphy.c140034

Cited by 13 publications

(11 citation statements)

References 81 publications

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“…The review in [1] covers general principles of modelling in neuroendocrinology using the growth hormone system as an example, while a recent review by the same authors addresses the contributions of modelling to hypothalamic–pituitary neurosecretory systems [2]. The review in [3] describes in detail several mathematical modelling tools such as types of equations, analysis of their dynamic behaviour (e.g., bistability , oscillations), and approaches to deal with biological noise and systems with multiple timescales in view of applications in endocrinology. This demonstrates a growing interest in the use of quantitative tools and methods to investigate complex hormone dynamics, particularly in relation to stress, reproduction, and metabolism 4, 5, 6, 7, 8, 9.…”

Section: Understanding the Complexity Of Endocrine Regulation Demandsmentioning

confidence: 99%

Mathematical Modelling of Endocrine Systems

Zavala

Wedgwood

Voliotis

et al. 2019

Trends in Endocrinology & Metabolism

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Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

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Section: Understanding the Complexity Of Endocrine Regulation Demandsmentioning

confidence: 99%

Mathematical Modelling of Endocrine Systems

Zavala

Wedgwood

Voliotis

et al. 2019

Trends in Endocrinology & Metabolism

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“…Other models have focused on showing whether endogenous ultradian oscillations are allowed in a class of models of the HPA axis (Savić, Jelić, & Burić, 2006 ; Vinther, Andersen, & Ottesen, 2011 ) or have investigated the feedback mechanism between the HPA axis and the memory system (Savić, Knežević, & Opačić, 2000 ). Further discussion on the structure and features of previous mathematical models can be found in Kim, D’Orsogna, and Chou ( 2016 ) and Bertram ( 2015 ).…”

mentioning

confidence: 99%

Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests

Kim

D’Orsogna

Chou

2018

Computational Psychiatry

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We use a dynamical systems model of the hypothalamic–pituitary–adrenal (HPA) axis to understand the mechanisms underlying clinical protocols used to probe patient stress response. Specifically, we address dexamethasone (DEX) and ACTH challenge tests, which probe pituitary and adrenal gland responses, respectively. We show that some previously observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific and permanent parameter changes due to physiological disruption. Moreover, we show that the timing of a perturbation relative to the intrinsic oscillation of the HPA axis can affect challenge test responses. Conventional mechanistic hypotheses supported and refuted by the challenge tests are reexamined by varying parameters in our mathematical model associated with these hypotheses. We show that (a) adrenal hyposensitivity can give rise to the responses seen in ACTH challenge tests and (b) enhanced cortisol-mediated suppression of the pituitary in subjects with PTSD is not necessary to explain the responses observed in DEX stress tests. We propose a new two-stage DEX/external stressor protocol to more clearly distinguish between the conventional hypothesis of enhanced suppression of the pituitary and bistable dynamics hypothesized in our model.

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“…This branch switches back and gains stability at a saddle node of periodics (SNP) bifurcation, beyond which there are stable periodic solutions corresponding to tonic spiking. (see Bertram, 2015 for a description of subHB and SNP bifurcations). In the parameter interval between the SNP and the subHB the system is bistable, although the basin of attraction of the periodic solutions is much larger.…”

Section: Resultsmentioning

confidence: 99%

The Effects of GABAergic Polarity Changes on Episodic Neural Network Activity in Developing Neural Systems

Blanco

Bertram

Tabak

2017

Front. Comput. Neurosci.

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Early in development, neural systems have primarily excitatory coupling, where even GABAergic synapses are excitatory. Many of these systems exhibit spontaneous episodes of activity that have been characterized through both experimental and computational studies. As development progress the neural system goes through many changes, including synaptic remodeling, intrinsic plasticity in the ion channel expression, and a transformation of GABAergic synapses from excitatory to inhibitory. What effect each of these, and other, changes have on the network behavior is hard to know from experimental studies since they all happen in parallel. One advantage of a computational approach is that one has the ability to study developmental changes in isolation. Here, we examine the effects of GABAergic synapse polarity change on the spontaneous activity of both a mean field and a neural network model that has both glutamatergic and GABAergic coupling, representative of a developing neural network. We find some intuitive behavioral changes as the GABAergic neurons go from excitatory to inhibitory, shared by both models, such as a decrease in the duration of episodes. We also find some paradoxical changes in the activity that are only present in the neural network model. In particular, we find that during early development the inter-episode durations become longer on average, while later in development they become shorter. In addressing this unexpected finding, we uncover a priming effect that is particularly important for a small subset of neurons, called the “intermediate neurons.” We characterize these neurons and demonstrate why they are crucial to episode initiation, and why the paradoxical behavioral change result from priming of these neurons. The study illustrates how even arguably the simplest of developmental changes that occurs in neural systems can present non-intuitive behaviors. It also makes predictions about neural network behavioral changes that occur during development that may be observable even in actual neural systems where these changes are convoluted with changes in synaptic connectivity and intrinsic neural plasticity.

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Mathematical Modeling in Neuroendocrinology

Cited by 13 publications

References 81 publications

Mathematical Modelling of Endocrine Systems

Mathematical Modelling of Endocrine Systems

Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests

The Effects of GABAergic Polarity Changes on Episodic Neural Network Activity in Developing Neural Systems

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