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Duncan PJ, Romanò N, Nair SV, Murray JF, Le Tissier P, Shipston MJ. Sex differences in pituitary corticotroph excitability. Front Physiol 2023; 14:1205162. [PMID: 37534368 PMCID: PMC10391550 DOI: 10.3389/fphys.2023.1205162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 07/05/2023] [Indexed: 08/04/2023] Open
Abstract
Stress-related illness represents a major burden on health and society. Sex differences in stress-related disorders are well documented, with women having twice the lifetime rate of depression compared to men and most anxiety disorders. Anterior pituitary corticotrophs are central components of the hypothalamic-pituitary-adrenal (HPA) axis, receiving input from hypothalamic neuropeptides corticotrophin-releasing hormone (CRH) and arginine vasopressin (AVP), while regulating glucocorticoid output from the adrenal cortex. The dynamic control of electrical excitability by CRH/AVP and glucocorticoids is critical for corticotroph function; however, whether corticotrophs contribute to sexually differential responses of the HPA axis, which might underlie differences in stress-related disorders, is very poorly understood. Using perforated patch clamp electrophysiology in corticotrophs from mice expressing green fluorescent protein under the control of the Pomc promoter, we characterized basal and secretagogue-evoked excitability. Both male and female corticotrophs show predominantly single-spike action potentials under basal conditions; however, males predominantly display spikes with small-amplitude (<20 mV) afterhyperpolarizations (B-type), whereas females displayed a mixture of B-type spikes and spikes with a large-amplitude (>25 mV) afterhyperpolarization (A-type). In response to CRH, or CRH/AVP, male cells almost exclusively transition to a predominantly pseudo-plateau bursting, whereas only female B-type cells display bursting in response to CRH±AVP. Treatment of male or female corticotrophs with 1 nM estradiol (E2) for 24-72 h has no effect on the proportion of cells with A- or B-type spikes in either sex. However, E2 results in the cessation of CRH-induced bursting in both male and female corticotrophs, which can be partially reversed by adding a BK current using a dynamic clamp. RNA-seq analysis of purified corticotrophs reveals extensive differential gene expression at the transcriptional level, including more than 71 mRNAs encoding ion channel subunits. Interestingly, there is a two-fold lower level (p < 0.01) of BK channel pore-forming subunit (Kcnma1) expression in females compared to males, which may partially explain the decrease in CRH-induced bursting. This study identified sex differences at the level of the anterior pituitary corticotroph ion channel landscape and control of both spontaneous and CRH-evoked excitability. Determining the mechanisms of sex differences of corticotroph and HPA activity at the cellular level could be an important step for better understanding, diagnosing, and treating stress-related disorders.
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Ghosh S, Mondal A, Ji P, Mishra A, Dana SK, Antonopoulos CG, Hens C. Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling. Front Comput Neurosci 2020; 14:49. [PMID: 32581757 PMCID: PMC7294985 DOI: 10.3389/fncom.2020.00049] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 05/04/2020] [Indexed: 11/21/2022] Open
Abstract
In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.
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Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
| | - Argha Mondal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
| | - Peng Ji
- The Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
| | - Arindam Mishra
- Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, India
| | - Syamal K Dana
- Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, India.,Division of Dynamics, Faculty of Mechanical Engineering, Lodz University of Technology, Lodz, Poland
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
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A computational model for gonadotropin releasing cells in the teleost fish medaka. PLoS Comput Biol 2019; 15:e1006662. [PMID: 31437161 PMCID: PMC6726249 DOI: 10.1371/journal.pcbi.1006662] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Revised: 09/04/2019] [Accepted: 08/01/2019] [Indexed: 01/16/2023] Open
Abstract
Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na+ currents (INa), high-voltage activated Ca2+ currents (ICa), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where INa is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by ICa. Unlike in rats, spontaneous INa-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by INa, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, INa and ICa, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire ICa-based APs. We put a particular focus on how the big conductance K+ current (IBK) modulates the AP shape. Interestingly, we find that IBK can prolong AP duration in models that fire ICa-based APs, while it consistently shortens the duration of the predominantly INa-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire INa-mediated APs. Excitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. Since one type of ion channels is permeable to Ca2+ ions, there is typically an influx of Ca2+ during an AP. Pituitary cells therefore use AP firing to regulate their cytosolic Ca2+ concentration, which in turn controls their hormone secretion rate. The amount of Ca2+ that enters during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Pituitary APs are generally mediated by a combination of Ca2+ channels and Na+ channels, and the relative contributions of from the two vary between cell types, animal species and biological conditions. Previous computer models have predominantly been adapted to data from pituitary cells which tend to fire Ca2+-based APs. Here we develop a new model, adapted to data from pituitary cells in the fish medaka, which APs that are predominantly Na+-based, and compare its dynamical properties to the previous models that fire Ca2+-based APs.
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Kaper TJ, Vo T. Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction-diffusion equations. CHAOS (WOODBURY, N.Y.) 2018; 28:091103. [PMID: 30278640 DOI: 10.1063/1.5050508] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Accepted: 09/11/2018] [Indexed: 06/08/2023]
Abstract
This article presents the delayed loss of stability due to slow passage through Hopf bifurcations in reaction-diffusion equations with slowly-varying parameters, generalizing a well-known result about delayed Hopf bifurcations in analytic ordinary differential equations to spatially-extended systems. We focus on the Hodgkin-Huxley partial differential equation (PDE), the cubic Complex Ginzburg-Landau PDE as an equation in its own right, the Brusselator PDE, and a spatially-extended model of a pituitary clonal cell line. Solutions which are attracted to quasi-stationary states (QSS) sufficiently before the Hopf bifurcations remain near the QSS for long times after the states have become repelling, resulting in a significant delay in the loss of stability and the onset of oscillations. Moreover, the oscillations have large amplitude at onset, and may be spatially homogeneous or inhomogeneous. Space-time boundaries are identified that act as buffer curves beyond which solutions cannot remain near the repelling QSS, and hence before which the delayed onset of oscillations must occur, irrespective of initial conditions. In addition, a method is developed to derive the asymptotic formulas for the buffer curves, and the asymptotics agree well with the numerically observed onset in the Complex Ginzburg-Landau (CGL) equation. We also find that the first-onset sites act as a novel pulse generation mechanism for spatio-temporal oscillations.
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Affiliation(s)
- Tasso J Kaper
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Theodore Vo
- Department of Mathematics, Florida State University, Tallahassee, Florida 32306, USA
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McKiernan EC, Marrone DF. CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging. PeerJ 2017; 5:e3836. [PMID: 28948109 PMCID: PMC5609525 DOI: 10.7717/peerj.3836] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Accepted: 08/31/2017] [Indexed: 12/04/2022] Open
Abstract
Neuron types (e.g., pyramidal cells) within one area of the brain are often considered homogeneous, despite variability in their biophysical properties. Here we review literature demonstrating variability in the electrical activity of CA1 hippocampal pyramidal cells (PCs), including responses to somatic current injection, synaptic stimulation, and spontaneous network-related activity. In addition, we describe how responses of CA1 PCs vary with development, experience, and aging, and some of the underlying ionic currents responsible. Finally, we suggest directions that may be the most impactful in expanding this knowledge, including the use of text and data mining to systematically study cellular heterogeneity in more depth; dynamical systems theory to understand and potentially classify neuron firing patterns; and mathematical modeling to study the interaction between cellular properties and network output. Our goals are to provide a synthesis of the literature for experimentalists studying CA1 PCs, to give theorists an idea of the rich diversity of behaviors models may need to reproduce to accurately represent these cells, and to provide suggestions for future research.
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Affiliation(s)
- Erin C McKiernan
- Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, México
| | - Diano F Marrone
- Department of Psychology, Wilfrid Laurier University, Waterloo, Ontario, Canada.,McKnight Brain Institute, University of Arizona, Tucson, AZ, United States of America
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V-Ghaffari B, Kouhnavard M, Elbasiouny SM. Mixed-mode oscillations in pyramidal neurons under antiepileptic drug conditions. PLoS One 2017; 12:e0178244. [PMID: 28591171 PMCID: PMC5462370 DOI: 10.1371/journal.pone.0178244] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2016] [Accepted: 05/10/2017] [Indexed: 11/19/2022] Open
Abstract
Subthreshold oscillations in combination with large-amplitude oscillations generate mixed-mode oscillations (MMOs), which mediate various spatial and temporal cognition and memory processes and behavioral motor tasks. Although many studies have shown that canard theory is a reliable method to investigate the properties underlying the MMOs phenomena, the relationship between the results obtained by applying canard theory and conductance-based models of neurons and their electrophysiological mechanisms are still not well understood. The goal of this study was to apply canard theory to the conductance-based model of pyramidal neurons in layer V of the Entorhinal Cortex to investigate the properties of MMOs under antiepileptic drug conditions (i.e., when persistent sodium current is inhibited). We investigated not only the mathematical properties of MMOs in these neurons, but also the electrophysiological mechanisms that shape spike clustering. Our results show that pyramidal neurons can display two types of MMOs and the magnitude of the slow potassium current determines whether MMOs of type I or type II would emerge. Our results also indicate that slow potassium currents with large time constant have significant impact on generating the MMOs, as opposed to fast inward currents. Our results provide complete characterization of the subthreshold activities in MMOs in pyramidal neurons and provide explanation to experimental studies that showed MMOs of type I or type II in pyramidal neurons under antiepileptic drug conditions.
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Affiliation(s)
- Babak V-Ghaffari
- Department of Neuroscience, Cell Biology and Physiology, Boonshoft School of Medicine and College of Science & Mathematics, Wright State University, Dayton, Ohio, United States of America
- * E-mail: (SME); (BV)
| | - M. Kouhnavard
- Malaysia-Japan Int. Inst. of Tech, University Technology Malaysia, Kuala Lumpur, Malaysia
| | - Sherif M. Elbasiouny
- Department of Neuroscience, Cell Biology and Physiology, Boonshoft School of Medicine and College of Science & Mathematics, Wright State University, Dayton, Ohio, United States of America
- Department of Biomedical, Industrial and Human Factors Engineering, College of Engineering & Computer Science, Wright State University, Dayton, Ohio, United States of America
- * E-mail: (SME); (BV)
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Fletcher P, Bertram R, Tabak J. From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability. J Comput Neurosci 2016; 40:331-45. [PMID: 27033230 DOI: 10.1007/s10827-016-0600-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2015] [Revised: 03/02/2016] [Accepted: 03/07/2016] [Indexed: 01/25/2023]
Abstract
Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial parameter set. In this study we combined global sampling of parameter space and local analysis of representative parameter sets in a pituitary cell model to understand the effects of adding K (+) conductances, which mediate some effects of hormone action on these cells. Global sampling ensured that the effects of introducing K (+) conductances were captured across a wide variety of contexts of model parameters. For each type of K (+) conductance we determined the types of behavioral transition that it evoked. Some transitions were counterintuitive, and may have been missed without the use of global sampling. In general, the wide range of transitions that occurred when the same current was applied to the model cell at different locations in parameter space highlight the challenge of making accurate model predictions in light of cell-to-cell heterogeneity. Finally, we used bifurcation analysis and fast/slow analysis to investigate why specific transitions occur in representative individual models. This approach relies on the use of a graphics processing unit (GPU) to quickly map parameter space to model behavior and identify parameter sets for further analysis. Acceleration with modern low-cost GPUs is particularly well suited to exploring the moderate-sized (5-20) parameter spaces of excitable cell and signaling models.
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Affiliation(s)
- Patrick Fletcher
- Currently at the Laboratory of Biological Modeling, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Richard Bertram
- Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA.
| | - Joel Tabak
- Currently at the University of Exeter Medical School, Biomedical Neuroscience Research Group, EX4 4PS, Exeter, UK
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8
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Tomaiuolo M, Bertram R, Leng G, Tabak J. Models of electrical activity: calibration and prediction testing on the same cell. Biophys J 2013. [PMID: 23199930 DOI: 10.1016/j.bpj.2012.09.034] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022] Open
Abstract
Mathematical models are increasingly important in biology, and testability is becoming a critical issue. One limitation is that one model simulation tests a parameter set representing one instance of the biological counterpart, whereas biological systems are heterogeneous in their properties and behavior, and a model often is fitted to represent an ideal average. This is also true for models of a cell's electrical activity; even within a narrowly defined population there can be considerable variation in electrophysiological phenotype. Here, we describe a computational experimental approach for parameterizing a model of the electrical activity of a cell in real time. We combine the inexpensive parallel computational power of a programmable graphics processing unit with the flexibility of the dynamic clamp method. The approach involves 1), recording a cell's electrical activity, 2), parameterizing a model to the recording, 3), generating predictions, and 4), testing the predictions on the same cell used for the calibration. We demonstrate the experimental feasibility of our approach using a cell line (GH4C1). These cells are electrically active, and they display tonic spiking or bursting. We use our approach to predict parameter changes that can convert one pattern to the other.
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Affiliation(s)
- Maurizio Tomaiuolo
- Department of Biological Science and Program in Neuroscience, Florida State University, Tallahassee, Florida, USA
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Vo T, Bertram R, Wechselberger M. Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model. ACTA ACUST UNITED AC 2012. [DOI: 10.3934/dcds.2012.32.2879] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Osinga HM, Sherman A, Tsaneva-Atanasova K. CROSS-CURRENTS BETWEEN BIOLOGY AND MATHEMATICS: THE CODIMENSION OF PSEUDO-PLATEAU BURSTING. ACTA ACUST UNITED AC 2012; 32:2853-2877. [PMID: 22984340 DOI: 10.3934/dcds.2012.32.2853] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A great deal of work has gone into classifying bursting oscillations, periodic alternations of spiking and quiescence modeled by fast-slow systems. In such systems, one or more slow variables carry the fast variables through a sequence of bifurcations that mediate transitions between oscillations and steady states. A rigorous classification approach is to characterize the bifurcations found in the neighborhood of a singularity; a measure of the complexity of the bursting oscillation is then given by the smallest codimension of the singularities near which it occurs. Fold/homoclinic bursting, along with most other burst types of interest, has been shown to occur near a singularity of codimension three by examining bifurcations of a cubic Liénard system; hence, these types of bursting have at most codimension three. Modeling and biological considerations suggest that fold/homoclinic bursting should be found near fold/subHopf bursting, a more recently identified burst type whose codimension has not been determined yet. One would expect that fold/subHopf bursting has the same codimension as fold/homoclinic bursting, because models of these two burst types have very similar underlying bifurcation diagrams. However, no codimension-three singularity is known that supports fold/subHopf bursting, which indicates that it may have codimension four. We identify a three-dimensional slice in a partial unfolding of a doubly-degenerate Bodganov-Takens point, and show that this codimension-four singularity gives rise to almost all known types of bursting.
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Affiliation(s)
- Hinke M Osinga
- Bristol Centre for Applied Nonlinear Mathematics Department of Engineering Mathematics University of Bristol, Queen's Building, University Walk Bristol BS8 1TR, UK
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Tsaneva-Atanasova K, Osinga HM, Tabak J, Pedersen MG. Modeling mechanisms of cell secretion. Acta Biotheor 2010; 58:315-27. [PMID: 20661627 DOI: 10.1007/s10441-010-9115-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2010] [Accepted: 07/05/2010] [Indexed: 11/25/2022]
Abstract
Secretion is a fundamental cellular process involving the regulated release of intracellular products from cells. Physiological functions such as neurotransmission, or the release of hormones and digestive enzymes, are all governed by cell secretion. Anomalies in the processes involved in secretion contribute to the development and progression of diseases such as diabetes and other hormonal disorders. To unravel the mechanisms that govern such diseases, it is essential to understand how hormones, growth factors and neurotransmitters are synthesized and processed, and how their signals are recognized, amplified and transmitted by intracellular signaling pathways in the target cells. Here, we discuss diverse aspects of the detailed mechanisms involved in secretion based on mathematical models. The models range from stochastic ones describing the trafficking of secretory vesicles to deterministic ones investigating the regulation of cellular processes that underlie hormonal secretion. In all cases, the models are closely related to experimental results and suggest theoretical predictions for the secretion mechanisms.
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Affiliation(s)
- Krasimira Tsaneva-Atanasova
- Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK.
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12
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Abstract
We present a mathematical analysis of the dynamics that underlies plateau bursting in models of endocrine cells under variation of the location of the (unstable) equilibrium around which these bursting patterns are organised. We focus primarily on the less well-studied case of pseudo-plateau bursting, but also consider the square-wave case. The behaviour of such models is explained using the theory for systems with multiple time scales and it is well known that the underlying so-called fast subsystem organises their dynamics. However, such results are valid only in a sufficiently small neighbourhood of the singular limit that defines the fast subsystem. Hence, the slow variable (intracellular calcium concentration) must be very slow, which is actually not the case for pseudo-plateau bursting. Furthermore, the theoretical predictions are also only valid for parameter values such that the equilibrium is close to a homoclinic bifurcation occuring in the fast subsystem. In the present study, we use numerical explorations to discuss what happens outside this theoretically known neighbourhood of parameter space. In particular, we consider what happens as the equilibrium moves outside a small neighbourhood of the homoclinic bifurcation that occurs in the fast subsystem, and relatively fast speeds are allowed for the slow variable which is controlled by a relatively large value of a parameter ε. The results obtained complement our earlier work [Tsaneva-Atanasova et al. (2010) J Theor Biol264, 1133-1146], which focussed on how the bursting patterns vary with the rate of change ε of the slow variable: we fix ε and move the equilibrium over the full range of the bursting regime. Our findings show that the transitions between different bursting patterns are rather similar for square-wave and pseudo-plateau bursting, provided that the value of ε for the pseudo-plateau-bursting model is chosen so that it is much larger than for the square-wave bursting model. Furthermore, the two families of tonic spiking and plateau bursting, which are generally viewed as two separately generated families, are actually connected into a single family in the two-parameter plane through branches of unstable periodic orbits.
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Affiliation(s)
- H M Osinga
- Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics, University of Bristol, Bristol, UK.
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13
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Vo T, Bertram R, Tabak J, Wechselberger M. Mixed mode oscillations as a mechanism for pseudo-plateau bursting. J Comput Neurosci 2010; 28:443-58. [PMID: 20186476 DOI: 10.1007/s10827-010-0226-7] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2009] [Revised: 01/29/2010] [Accepted: 02/12/2010] [Indexed: 10/19/2022]
Abstract
We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called "pseudo-plateau bursting". Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic beta-cells.
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Affiliation(s)
- Theodore Vo
- School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia
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Zhang Y, Bose A, Nadim F. Predicting the activity phase of a follower neuron with A-current in an inhibitory network. BIOLOGICAL CYBERNETICS 2008; 99:171-84. [PMID: 18719938 PMCID: PMC2702225 DOI: 10.1007/s00422-008-0248-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2008] [Accepted: 08/04/2008] [Indexed: 05/26/2023]
Abstract
The transient potassium A-current is present in most neurons and plays an important role in determining the timing of action potentials. We examine the role of the A-current in the activity phase of a follower neuron in a rhythmic feed-forward inhibitory network with a reduced three-variable model and conduct experiments to verify the usefulness of our model. Using geometric analysis of dynamical systems, we explore the factors that determine the onset of activity in a follower neuron following release from inhibition. We first analyze the behavior of the follower neuron in a single cycle and find that the phase plane structure of the model can be used to predict the potential behaviors of the follower neuron following release from inhibition. We show that, depending on the relative scales of the inactivation time constant of the A-current and the time constant of the recovery variable, the follower neuron may or may not reach its active state following inhibition. Our simple model is used to derive a recursive set of equations to predict the contribution of the A-current parameters in determining the activity phase of a follower neuron as a function of the duration and frequency of the inhibitory input it receives. These equations can be used to demonstrate the dependence of activity phase on the period and duty cycle of the periodic inhibition, as seen by comparing the predictions of the model with the activity of the pyloric constrictor (PY) neurons in the crustacean pyloric network.
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Affiliation(s)
- Yu Zhang
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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