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Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2021:4475184. [PMID: 34987564 PMCID: PMC8723864 DOI: 10.1155/2021/4475184] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 11/17/2021] [Accepted: 11/19/2021] [Indexed: 12/28/2022]
Abstract
Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.
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Park C, Rubchinsky LL, Ahn S. Mathematical model of subthalamic nucleus neuron: Characteristic activity patterns and bifurcation analysis. CHAOS (WOODBURY, N.Y.) 2021; 31:113121. [PMID: 34881610 DOI: 10.1063/5.0059773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 10/14/2021] [Indexed: 06/13/2023]
Abstract
The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease.
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Affiliation(s)
- Choongseok Park
- Department of Mathematics and Statistics, North Carolina A&T State University, Greensboro, North Carolina 27411, USA
| | - Leonid L Rubchinsky
- Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA
| | - Sungwoo Ahn
- Department of Mathematics, East Carolina University, Greenville, North Carolina 27858, USA
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Baertsch NA, Bush NE, Burgraff NJ, Ramirez JM. Dual mechanisms of opioid-induced respiratory depression in the inspiratory rhythm-generating network. eLife 2021; 10:e67523. [PMID: 34402425 PMCID: PMC8390004 DOI: 10.7554/elife.67523] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 08/14/2021] [Indexed: 12/20/2022] Open
Abstract
The analgesic utility of opioid-based drugs is limited by the life-threatening risk of respiratory depression. Opioid-induced respiratory depression (OIRD), mediated by the μ-opioid receptor (MOR), is characterized by a pronounced decrease in the frequency and regularity of the inspiratory rhythm, which originates from the medullary preBötzinger Complex (preBötC). To unravel the cellular- and network-level consequences of MOR activation in the preBötC, MOR-expressing neurons were optogenetically identified and manipulated in transgenic mice in vitro and in vivo. Based on these results, a model of OIRD was developed in silico. We conclude that hyperpolarization of MOR-expressing preBötC neurons alone does not phenocopy OIRD. Instead, the effects of MOR activation are twofold: (1) pre-inspiratory spiking is reduced and (2) excitatory synaptic transmission is suppressed, thereby disrupting network-driven rhythmogenesis. These dual mechanisms of opioid action act synergistically to make the normally robust inspiratory rhythm-generating network particularly prone to collapse when challenged with exogenous opioids.
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Affiliation(s)
- Nathan A Baertsch
- Center for Integrative Brain Research, Seattle Children’s Research InstituteSeattleUnited States
- Department of Pediatrics, University of WashingtonSeattleUnited States
| | - Nicholas E Bush
- Center for Integrative Brain Research, Seattle Children’s Research InstituteSeattleUnited States
| | - Nicholas J Burgraff
- Center for Integrative Brain Research, Seattle Children’s Research InstituteSeattleUnited States
| | - Jan-Marino Ramirez
- Center for Integrative Brain Research, Seattle Children’s Research InstituteSeattleUnited States
- Department of Pediatrics, University of WashingtonSeattleUnited States
- Department Neurological Surgery, University of WashingtonSeattleUnited States
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Yuan Q, Xu J, Chen H. Dynamics Analysis of Firing Patterns in Pre-Bötzinger Complex Neurons Model. Front Comput Neurosci 2021; 15:591037. [PMID: 34211383 PMCID: PMC8239244 DOI: 10.3389/fncom.2021.591037] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 05/25/2021] [Indexed: 11/29/2022] Open
Abstract
Pre-Bötzinger complex (PBC) neurons located in mammalian brain are the necessary conditions to produce respiratory rhythm, which has been widely verified experimentally and numerically. At present, one of the two different types of bursting mechanisms found in PBC mainly depends on the calcium-activated of non-specific cation current (ICaN). In order to study the influence of ICaN and stimulus current Iexc in PBC inspiratory neurons, a single compartment model was simplified, and firing patterns of the model was discussed by using stability theory, bifurcation analysis, fast, and slow decomposition technology combined with numerical simulation. Under the stimulation of different somatic applied currents, the firing behavior of neurons are studied and exhibit multiple mix bursting patterns, which is helpful to further understand the mechanism of respiratory rhythms of PBC neurons.
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Affiliation(s)
- Quan Yuan
- School of Mathematics and Information Science, Guangxi University, Guangxi, China
| | - Jieqiong Xu
- School of Mathematics and Information Science, Guangxi University, Guangxi, China
| | - Huiying Chen
- School of Mathematics and Information Science, Guangxi University, Guangxi, China
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Influence of Electric Current and Magnetic Flow on Firing Patterns of Pre-Bötzinger Complex Model. Neural Plast 2021; 2021:6655933. [PMID: 33927757 PMCID: PMC8049835 DOI: 10.1155/2021/6655933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Revised: 01/14/2021] [Accepted: 03/14/2021] [Indexed: 11/17/2022] Open
Abstract
The dynamics of neuronal firing activity is vital for understanding the pathological respiratory rhythm. Studies on electrophysiology show that the magnetic flow is an essential factor that modulates the firing activities of neurons. By adding the magnetic flow to Butera's neuron model, we investigate how the electric current and magnetic flow influence neuronal activities under certain parametric restrictions. Using fast-slow decomposition and bifurcation analysis, we show that the variation of external electric current and magnetic flow leads to the change of the bistable structure of the system and hence results in the switch of neuronal firing pattern from one type to another.
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Wang Y, Rubin JE. Complex bursting dynamics in an embryonic respiratory neuron model. CHAOS (WOODBURY, N.Y.) 2020; 30:043127. [PMID: 32357647 DOI: 10.1063/1.5138993] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2019] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
Pre-Bötzinger complex (pre-BötC) network activity within the mammalian brainstem controls the inspiratory phase of the respiratory rhythm. While bursting in pre-BötC neurons during the postnatal period has been extensively studied, less is known regarding inspiratory pacemaker neuron behavior at embryonic stages. Recent data in mouse embryo brainstem slices have revealed the existence of a variety of bursting activity patterns depending on distinct combinations of burst-generating INaP and ICAN conductances. In this work, we consider a model of an isolated embryonic pre-BötC neuron featuring two distinct bursting mechanisms. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to uncover mechanisms underlying several different types of intrinsic bursting dynamics observed experimentally including several forms of plateau bursts, bursts involving depolarization block, and various combinations of these patterns. Our analysis also yields predictions about how changes in the balance of the two bursting mechanisms contribute to alterations in an inspiratory pacemaker neuron activity during prenatal development.
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Affiliation(s)
- Yangyang Wang
- Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242, USA
| | - Jonathan E Rubin
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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A biophysical model explains the spontaneous bursting behavior in the developing retina. Sci Rep 2019; 9:1859. [PMID: 30755684 PMCID: PMC6372601 DOI: 10.1038/s41598-018-38299-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2017] [Accepted: 12/21/2018] [Indexed: 01/17/2023] Open
Abstract
During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During a particular phase of the retina development (stage II) these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. The underlying mechanisms of the spontaneous bursting and the transient excitability of immature SACs are not completely clear yet. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing V-gated calcium channels and hyperpolarizing V-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.
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Wang Y, Rubin JE. Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2017; 7:3. [PMID: 28589465 PMCID: PMC5461246 DOI: 10.1186/s13408-017-0045-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Accepted: 04/21/2017] [Indexed: 05/26/2023]
Abstract
Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, which can generate the eupneic rhythm associated with normal respiration as well as recurrent low-frequency, large-amplitude bursts associated with sighing. Two competing hypotheses have been proposed to explain sigh generation: the recruitment of a neuronal population distinct from the eupneic rhythm-generating subpopulation or the reconfiguration of activity within a single population. Here, we consider two recent computational models, one of which represents each of the hypotheses. We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model. In the course of our analysis, we discover that a third timescale is required to generate sighs in both models. Furthermore, we identify the similarities of the underlying mechanisms in the two models and the aspects in which they differ.
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Affiliation(s)
- Yangyang Wang
- Mathematical Biosciences Institute, Ohio State University, Jennings Hall 3rd Floor, 1735 Neil Ave., Columbus, 43210 USA
| | - Jonathan E. Rubin
- Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, 15260 USA
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Harris KD, Dashevskiy T, Mendoza J, Garcia AJ, Ramirez JM, Shea-Brown E. Different roles for inhibition in the rhythm-generating respiratory network. J Neurophysiol 2017; 118:2070-2088. [PMID: 28615332 PMCID: PMC5626906 DOI: 10.1152/jn.00174.2017] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Revised: 05/25/2017] [Accepted: 06/12/2017] [Indexed: 12/20/2022] Open
Abstract
Unraveling the interplay of excitation and inhibition within rhythm-generating networks remains a fundamental issue in neuroscience. We use a biophysical model to investigate the different roles of local and long-range inhibition in the respiratory network, a key component of which is the pre-Bötzinger complex inspiratory microcircuit. Increasing inhibition within the microcircuit results in a limited number of out-of-phase neurons before rhythmicity and synchrony degenerate. Thus unstructured local inhibition is destabilizing and cannot support the generation of more than one rhythm. A two-phase rhythm requires restructuring the network into two microcircuits coupled by long-range inhibition in the manner of a half-center. In this context, inhibition leads to greater stability of the two out-of-phase rhythms. We support our computational results with in vitro recordings from mouse pre-Bötzinger complex. Partial excitation block leads to increased rhythmic variability, but this recovers after blockade of inhibition. Our results support the idea that local inhibition in the pre-Bötzinger complex is present to allow for descending control of synchrony or robustness to adverse conditions like hypoxia. We conclude that the balance of inhibition and excitation determines the stability of rhythmogenesis, but with opposite roles within and between areas. These different inhibitory roles may apply to a variety of rhythmic behaviors that emerge in widespread pattern-generating circuits of the nervous system.NEW & NOTEWORTHY The roles of inhibition within the pre-Bötzinger complex (preBötC) are a matter of debate. Using a combination of modeling and experiment, we demonstrate that inhibition affects synchrony, period variability, and overall frequency of the preBötC and coupled rhythmogenic networks. This work expands our understanding of ubiquitous motor and cognitive oscillatory networks.
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Affiliation(s)
| | - Tatiana Dashevskiy
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Joshua Mendoza
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Alfredo J Garcia
- Institute for Integrative Physiology and Section of Emergency Medicine, University of Chicago, Chicago, Illinois; and
| | - Jan-Marino Ramirez
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
- Department of Neurological Surgery, University of Washington School of Medicine, Seattle, Washington
| | - Eric Shea-Brown
- Department of Applied Mathematics, University of Washington, Seattle, Washington
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Computational study on neuronal activities arising in the pre-Bötzinger complex. Cogn Neurodyn 2017; 11:443-451. [PMID: 29067132 DOI: 10.1007/s11571-017-9440-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Revised: 04/08/2017] [Accepted: 04/19/2017] [Indexed: 10/19/2022] Open
Abstract
Experimental investigations have shown that the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem generates the inspiratory phase of respiratory rhythm. Based on a single-compartment model of a pre-BötC inspiratory neuron, we, in this paper, use semi-analytical, numerical as well as fast-slow dynamical methods to investigate the effects of sodium conductance ([Formula: see text]) and potassium conductance ([Formula: see text]) on the firing activities of pre-BötC and try to reveal the dynamical mechanisms behind them. We show how [Formula: see text] and [Formula: see text] affect the bifurcations of the fast-subsystem and how the the firing patterns of pre-BötC transit according to the bifurcations.
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Molkov YI, Rubin JE, Rybak IA, Smith JC. Computational models of the neural control of breathing. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2016; 9. [PMID: 28009109 DOI: 10.1002/wsbm.1371] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2016] [Revised: 10/06/2016] [Accepted: 10/25/2016] [Indexed: 11/10/2022]
Abstract
The ongoing process of breathing underlies the gas exchange essential for mammalian life. Each respiratory cycle ensues from the activity of rhythmic neural circuits in the brainstem, shaped by various modulatory signals, including mechanoreceptor feedback sensitive to lung inflation and chemoreceptor feedback dependent on gas composition in blood and tissues. This paper reviews a variety of computational models designed to reproduce experimental findings related to the neural control of breathing and generate predictions for future experimental testing. The review starts from the description of the core respiratory network in the brainstem, representing the central pattern generator (CPG) responsible for producing rhythmic respiratory activity, and progresses to encompass additional complexities needed to simulate different metabolic challenges, closed-loop feedback control including the lungs, and interactions between the respiratory and autonomic nervous systems. The integrated models considered in this review share a common framework including a distributed CPG core network responsible for generating the baseline three-phase pattern of rhythmic neural activity underlying normal breathing. WIREs Syst Biol Med 2017, 9:e1371. doi: 10.1002/wsbm.1371 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Yaroslav I Molkov
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA
| | - Jonathan E Rubin
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
| | - Ilya A Rybak
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, USA
| | - Jeffrey C Smith
- Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland, USA
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Wang Y, Rubin JE. Multiple timescale mixed bursting dynamics in a respiratory neuron model. J Comput Neurosci 2016; 41:245-268. [PMID: 27491968 DOI: 10.1007/s10827-016-0616-6] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Revised: 07/01/2016] [Accepted: 07/08/2016] [Indexed: 11/29/2022]
Abstract
Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (I NaP) and intracellular Ca2+. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of I NaP, the calcium concentration, as well as the Ca2+-dependent inactivation of IP 3 as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both I NaP and Ca2+ oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.
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Affiliation(s)
- Yangyang Wang
- Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA
| | - Jonathan E Rubin
- Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA.
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Bertram R, Rubin JE. Multi-timescale systems and fast-slow analysis. Math Biosci 2016; 287:105-121. [PMID: 27424950 DOI: 10.1016/j.mbs.2016.07.003] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2016] [Revised: 07/01/2016] [Accepted: 07/10/2016] [Indexed: 11/28/2022]
Abstract
Mathematical models of biological systems often have components that vary on different timescales. This multi-timescale character can lead to problems when doing computer simulations, which can require a great deal of computer time so that the components that change on the fastest time scale can be resolved. Mathematical analysis of these multi-timescale systems can be greatly simplified by partitioning them into subsystems that evolve on different time scales. The subsystems are then analyzed semi-independently, using a technique called fast-slow analysis. In this review we describe the fast-slow analysis technique and apply it to relaxation oscillations, neuronal bursting oscillations, canard oscillations, and mixed-mode oscillations. Although these examples all involve neural systems, the technique can and has been applied to other biological, chemical, and physical systems. It is a powerful analysis method that will become even more useful in the future as new experimental techniques push forward the complexity of biological models.
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Affiliation(s)
- Richard Bertram
- Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University, Florida State University, Tallahassee, FL, United States.
| | - Jonathan E Rubin
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, United States
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Wang Y, Nan P, Kirk V, Rubin J. Understanding and distinguishing three time scale oscillations. BMC Neurosci 2014. [PMCID: PMC4126507 DOI: 10.1186/1471-2202-15-s1-p54] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
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