1
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Friedhoff VN, Lindner B, Falcke M. Modeling IP 3-induced Ca 2+ signaling based on its interspike interval statistics. Biophys J 2023; 122:2818-2831. [PMID: 37312455 PMCID: PMC10398346 DOI: 10.1016/j.bpj.2023.06.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Revised: 04/24/2023] [Accepted: 06/06/2023] [Indexed: 06/15/2023] Open
Abstract
Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca2+ signaling on all structural levels. We compile eight general properties of Ca2+ spiking common to all cell types investigated and suggest a theory of Ca2+ spiking starting from the random behavior of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum capturing all general properties and pathway-specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the interspike interval SD and its robustness properties, sensitive dependency of Tav on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+-induced Ca2+ release, the number of clusters, and IP3 pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP3] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.
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Affiliation(s)
- Victor Nicolai Friedhoff
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany; Department of Physics, Humboldt University, Berlin, Germany
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany; Department of Physics, Humboldt University, Berlin, Germany
| | - Martin Falcke
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany; Department of Physics, Humboldt University, Berlin, Germany.
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2
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Araujo R, Brumley D, Cursons J, Day K, Faria M, Flegg JA, Germano D, Hunt H, Hunter P, Jenner A, Johnston S, McCaw JM, Maini P, Miller C, Muskovic W, Osborne J, Pan M, Rajagopal V, Shahidi N, Siekmann I, Stumpf M, Zanca A. Frontiers of Mathematical Biology: A workshop honouring Professor Edmund Crampin. Math Biosci 2023; 359:109007. [PMID: 37062447 DOI: 10.1016/j.mbs.2023.109007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Revised: 03/28/2023] [Accepted: 04/02/2023] [Indexed: 04/18/2023]
Affiliation(s)
- Robyn Araujo
- School of Mathematical Sciences, Queensland University of Technology, Australia
| | - Douglas Brumley
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | | | - Karen Day
- Bio21 Institute, The University of Melbourne, Australia
| | - Matthew Faria
- Department of Biomedical Engineering, The University of Melbourne, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | - Domenic Germano
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | - Hilary Hunt
- Department of Biology, University of Oxford, United Kingdom
| | - Peter Hunter
- Auckland Bioengineering Institute, University of Auckland, New Zealand
| | - Adrianne Jenner
- School of Mathematical Sciences, Queensland University of Technology, Australia
| | - Stuart Johnston
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | - James M McCaw
- School of Mathematics and Statistics, The University of Melbourne, Australia; Melbourne School of Population and Global Health, The University of Melbourne, Australia.
| | - Philip Maini
- Mathematical Institute, University of Oxford, United Kingdom
| | - Claire Miller
- Auckland Bioengineering Institute, University of Auckland, New Zealand
| | | | - James Osborne
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | - Michael Pan
- School of Mathematics and Statistics, The University of Melbourne, Australia
| | - Vijay Rajagopal
- Department of Biomedical Engineering, The University of Melbourne, Australia
| | - Niloofar Shahidi
- Auckland Bioengineering Institute, University of Auckland, New Zealand
| | - Ivo Siekmann
- School of Computer Science and Mathematics, Liverpool John Moores University, United Kingdom
| | - Michael Stumpf
- School of Mathematics and Statistics, The University of Melbourne, Australia; Melbourne Integrative Genomics, The University of Melbourne, Australia
| | - Adriana Zanca
- School of Mathematics and Statistics, The University of Melbourne, Australia
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3
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Ramlow L, Falcke M, Lindner B. An integrate-and-fire approach to Ca 2+ signaling. Part I: Renewal model. Biophys J 2023; 122:713-736. [PMID: 36635961 PMCID: PMC9989887 DOI: 10.1016/j.bpj.2023.01.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Revised: 12/13/2022] [Accepted: 01/06/2023] [Indexed: 01/13/2023] Open
Abstract
In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.
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Affiliation(s)
- Lukas Ramlow
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany; Physics Department of Humboldt University Berlin, Berlin, Germany.
| | - Martin Falcke
- Physics Department of Humboldt University Berlin, Berlin, Germany; Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany; Physics Department of Humboldt University Berlin, Berlin, Germany
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4
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Chung J, Tilūnaitė A, Ladd D, Hunt H, Soeller C, Crampin EJ, Johnston ST, Roderick HL, Rajagopal V. IP 3R activity increases propensity of RyR-mediated sparks by elevating dyadic [Ca 2+]. Math Biosci 2023; 355:108923. [PMID: 36395827 DOI: 10.1016/j.mbs.2022.108923] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 10/15/2022] [Accepted: 10/15/2022] [Indexed: 11/16/2022]
Abstract
Calcium (Ca2+) plays a critical role in the excitation contraction coupling (ECC) process that mediates the contraction of cardiomyocytes during each heartbeat. While ryanodine receptors (RyRs) are the primary Ca2+ channels responsible for generating the cell-wide Ca2+ transients during ECC, Ca2+ release, via inositol 1,4,5-trisphosphate (IP3) receptors (IP3Rs) are also reported in cardiomyocytes to elicit ECC-modulating effects. Recent studies suggest that the localization of IP3Rs at dyads grant their ability to modify the occurrence of Ca2+ sparks (elementary Ca2+ release events that constitute cell wide Ca2+ releases associated with ECC) which may underlie their modulatory influence on ECC. Here, we aim to uncover the mechanism by which dyad-localized IP3Rs influence Ca2+ spark dynamics. To this end, we developed a mathematical model of the dyad that incorporates the behaviour of IP3Rs, in addition to RyRs, to reveal the impact of their activity on local Ca2+ handling and consequent Ca2+ spark occurrence and its properties. Consistent with published experimental data, our model predicts that the propensity for Ca2+ spark formation increases in the presence of IP3R activity. Our simulations support the hypothesis that IP3Rs elevate Ca2+ in the dyad, sensitizing proximal RyRs towards activation and hence Ca2+ spark formation. The stochasticity of IP3R gating is an important aspect of this mechanism. However, dyadic IP3R activity lowers the Ca2+ available in the junctional sarcoplasmic reticulum (JSR) for release, thus resulting in Ca2+ sparks with similar durations but lower amplitudes.
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Affiliation(s)
- Joshua Chung
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia; Laboratory of Experimental Cardiology, Department of Cardiovascular Sciences, KU Leuven, 3000, Leuven, Belgium
| | - Agnė Tilūnaitė
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia; School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia
| | - David Ladd
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia; School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia; ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, School of Chemical and Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia
| | - Hilary Hunt
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia
| | | | - Edmund J Crampin
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia; School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia; ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, School of Chemical and Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia
| | - Stuart T Johnston
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC 3010, Australia; ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, School of Chemical and Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia
| | - H Llewelyn Roderick
- Laboratory of Experimental Cardiology, Department of Cardiovascular Sciences, KU Leuven, 3000, Leuven, Belgium.
| | - Vijay Rajagopal
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia; Baker Department of Cardiometabolic Health, The University of Melbourne, Melbourne, VIC 3010, Australia.
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5
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Shapovalov G, Ritaine A, Essonghe NC, de Ridder I, Ivanova H, Karamanou S, Economou A, Bultynck G, Skryma R, Prevarskaya N. Allosteric cross-talk between the hydrophobic cleft and the BH4 domain of Bcl-2 in control of inositol 1,4,5-trisphosphate receptor activity. EXPLORATION OF TARGETED ANTI-TUMOR THERAPY 2022; 3:375-391. [PMID: 36045908 PMCID: PMC9400710 DOI: 10.37349/etat.2022.00088] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 04/13/2022] [Indexed: 12/12/2022] Open
Abstract
Aim: Inositol 1,4,5-trisphosphate receptor (IP3R) is a ubiquitous calcium (Ca2+) channel involved in the regulation of cellular fate and motility. Its modulation by anti-apoptotic protein B-cell lymphoma 2 (Bcl-2) plays an important role in cancer progression. Disrupting this interaction could overcome apoptosis avoidance, one of the hallmarks of cancer, and is, thus, of great interest. Earlier reports have shown the involvement of both the Bcl-2 homology 4 (BH4) and the transmembrane domains (TMDs) of Bcl-2 in regulating IP3R activity, while the Bcl-2 hydrophobic cleft was associated primarily with its anti-apoptotic and IP3R-independent action at the mitochondria (Oncotarget. 2016;7:55704–20. doi: 10.18632/oncotarget.11005). The aim of this study was to investigate how targeting the BH3 hydrophobic cleft of Bcl-2 affects IP3R:Bcl-2 interaction. Methods: Organelle membrane-derived (OMD) patch-clamp and circular dichroism (CD) thermal melting experiments were used to elucidate the effects of the ABT-199 (venetoclax) on the IP3R:Bcl-2 interaction. Molecular dynamics (MD) simulations of free and ABT-199 bound Bcl-2 were used to propose a molecular model of such interaction. Results: It was shown that occlusion of Bcl-2’s hydrophobic cleft by the drug ABT-199 finely modulates IP3R gating in the low open probability (Po) regime, characteristic of the basal IP3R activity in non-excited cells. Complementary MD simulations allowed to propose a model of this modulation, involving an allosteric interaction with the BH4 domain on the opposite side of Bcl-2. Conclusions: Bcl-2 is an important regulator of IP3R activity and, thus of Ca2+ release from internal stores and associated processes, including cellular proliferation and death. The presence of multiple regulatory domains in both proteins suggests a complex interaction. Thus, it was found that the occlusion of the hydrophobic cleft of Bcl-2 by ABT-199 disrupts IP3R activity, leading to Bcl-2 rebinding with smaller affinity and lesser inhibitory effect. MDs simulations of free and ABT-199 bound Bcl-2 propose a molecular model of such disruption, involving an allosteric interaction with the BH4 domain on the opposite side of Bcl-2.
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Affiliation(s)
- George Shapovalov
- Univ. Lille, Inserm, U1003 - PHYCEL - Physiologie Cellulaire, F-59000 Lille, France.,Laboratory of Excellence, Ion Channels Science and Therapeutics, 59655 Villeneuve d'Ascq, France
| | - Abigaël Ritaine
- Univ. Lille, Inserm, U1003 - PHYCEL - Physiologie Cellulaire, F-59000 Lille, France.,Laboratory of Excellence, Ion Channels Science and Therapeutics, 59655 Villeneuve d'Ascq, France.,KU Leuven, Laboratory of Molecular and Cellular Signaling, Department of Cellular and Molecular Medicine, Campus Gasthuisberg O/N-I bus 802, Herestraat 49, B-3000 Leuven, Belgium
| | - Nadege Charlene Essonghe
- Univ. Lille, Inserm, U1003 - PHYCEL - Physiologie Cellulaire, F-59000 Lille, France.,Laboratory of Excellence, Ion Channels Science and Therapeutics, 59655 Villeneuve d'Ascq, France
| | - Ian de Ridder
- KU Leuven, Laboratory of Molecular and Cellular Signaling, Department of Cellular and Molecular Medicine, Campus Gasthuisberg O/N-I bus 802, Herestraat 49, B-3000 Leuven, Belgium
| | - Hristina Ivanova
- KU Leuven, Laboratory of Molecular and Cellular Signaling, Department of Cellular and Molecular Medicine, Campus Gasthuisberg O/N-I bus 802, Herestraat 49, B-3000 Leuven, Belgium
| | - Spyridoula Karamanou
- KU Leuven, Department of Microbiology and Immunology, Rega Institute of Medical Research, Laboratory of Molecular Bacteriology, Herestraat 49, B-3000 Leuven, Belgium
| | - Anastassios Economou
- KU Leuven, Department of Microbiology and Immunology, Rega Institute of Medical Research, Laboratory of Molecular Bacteriology, Herestraat 49, B-3000 Leuven, Belgium
| | - Geert Bultynck
- KU Leuven, Laboratory of Molecular and Cellular Signaling, Department of Cellular and Molecular Medicine, Campus Gasthuisberg O/N-I bus 802, Herestraat 49, B-3000 Leuven, Belgium
| | - Roman Skryma
- Univ. Lille, Inserm, U1003 - PHYCEL - Physiologie Cellulaire, F-59000 Lille, France.,Laboratory of Excellence, Ion Channels Science and Therapeutics, 59655 Villeneuve d'Ascq, France
| | - Natalia Prevarskaya
- Univ. Lille, Inserm, U1003 - PHYCEL - Physiologie Cellulaire, F-59000 Lille, France.,Laboratory of Excellence, Ion Channels Science and Therapeutics, 59655 Villeneuve d'Ascq, France
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6
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Affiliation(s)
- Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
| | - Peter J Hunter
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Peter J Gawthrop
- Systems Biology Laboratory, Department of Biomedical Engineering, Faculty of Engineering and Information Technology, University of Melbourne, Victoria, 3010, Australia
- Systems Biology Laboratory, School of Mathematics and Statistics, University of Melbourne, Victoria, 3010, Australia
| | - Nic P Smith
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
- Queensland University of Technology, Brisbane, Australia
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7
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Zhang Y, Pang X, Yang Y, Yan S. Effect of calcium ion on the morphology structure and compression elasticity of muscle fibers from honeybee abdomen. J Biomech 2021; 127:110652. [PMID: 34358879 DOI: 10.1016/j.jbiomech.2021.110652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Revised: 07/21/2021] [Accepted: 07/25/2021] [Indexed: 10/20/2022]
Abstract
Muscle contraction activated by calcium ion is the key to reveal that honeybee abdomen can achieve various physiological activities through flexible exercises and contributes to a powerful mechanical function of muscle fibers. To investigate the stimulating effect of calcium ion on muscle fibers of honeybee abdomen, atomic force microscopy was used to measure the morphology structure and mechanical properties of muscle fibers from honeybee abdomen in different calcium ion solutions. The periodic morphology structure of muscle fibers stimulated by different calcium ion concentration changed greatly, and the sarcomere length contracted from 6.53 μm to 4.29 μm as the calcium ion concentration increased from 0.11 mM to 10 mM. The mechanical measurement showed that the elastic modulus of Z-line reached the maximum, followed by M-line, overlap zone and I-band in sequence at the same calcium ion concentration, and was approximately 3.636, 2.450, 2.284, 2.748 times that of I-band from 0.11 mM to 10 mM calcium ion concentration. Combining the experimental analysis, the calcium ion threshold range was obtained based on the response surface method. This work adequately elucidates biological structure and biomechanics of muscle fibers from honeybee abdomen and could provide reference for other similar muscle system.
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Affiliation(s)
- Yuling Zhang
- Division of Intelligent and Biomechanical Systems, State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
| | - Xu Pang
- School of Engineering and Technology, China University of Geosciences (Beijing), 100083 Beijing, PR China
| | - Yunqiang Yang
- School of Engineering and Technology, China University of Geosciences (Beijing), 100083 Beijing, PR China
| | - Shaoze Yan
- Division of Intelligent and Biomechanical Systems, State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China.
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8
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Takano T, Wahl AM, Huang KT, Narita T, Rugis J, Sneyd J, Yule DI. Highly localized intracellular Ca 2+ signals promote optimal salivary gland fluid secretion. eLife 2021; 10:66170. [PMID: 34240705 PMCID: PMC8352588 DOI: 10.7554/elife.66170] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Accepted: 07/08/2021] [Indexed: 11/23/2022] Open
Abstract
Salivary fluid secretion involves an intricate choreography of membrane transporters to result in the trans-epithelial movement of NaCl and water into the acinus lumen. Current models are largely based on experimental observations in enzymatically isolated cells where the Ca2+ signal invariably propagates globally and thus appears ideally suited to activate spatially separated Cl and K channels, present on the apical and basolateral plasma membrane, respectively. We monitored Ca2+ signals and salivary secretion in live mice expressing GCamp6F, following stimulation of the nerves innervating the submandibular gland. Consistent with in vitro studies, Ca2+ signals were initiated in the apical endoplasmic reticulum. In marked contrast to in vitro data, highly localized trains of Ca2+ transients that failed to fully propagate from the apical region were observed. Following stimuli optimum for secretion, large apical-basal gradients were elicited. A new mathematical model, incorporating these data was constructed to probe how salivary secretion can be optimally stimulated by apical Ca2+ signals.
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Affiliation(s)
- Takahiro Takano
- Department of Pharmacology and Physiology, University of Rochester, Rochester, United States
| | - Amanda M Wahl
- Department of Pharmacology and Physiology, University of Rochester, Rochester, United States
| | - Kai-Ting Huang
- Department of Pharmacology and Physiology, University of Rochester, Rochester, United States
| | - Takanori Narita
- Department of Veterinary Medicine, College of Bioresource Sciences, Nihon University, Fujisawa, Japan
| | - John Rugis
- Department of Mathematics, University of Auckland, Auckland, New Zealand
| | - James Sneyd
- Department of Mathematics, University of Auckland, Auckland, New Zealand
| | - David I Yule
- Department of Pharmacology and Physiology, University of Rochester, Rochester, United States
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9
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Sneyd J, Vera-Sigüenza E, Rugis J, Pages N, Yule DI. Calcium Dynamics and Water Transport in Salivary Acinar Cells. Bull Math Biol 2021; 83:31. [PMID: 33594615 PMCID: PMC8018713 DOI: 10.1007/s11538-020-00841-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 11/25/2020] [Indexed: 01/07/2023]
Abstract
Saliva is secreted from the acinar cells of the salivary glands, using mechanisms that are similar to other types of water-transporting epithelial cells. Using a combination of theoretical and experimental techniques, over the past 20 years we have continually developed and modified a quantitative model of saliva secretion, and how it is controlled by the dynamics of intracellular calcium. However, over approximately the past 5 years there have been significant developments both in our understanding of the underlying mechanisms and in the way these mechanisms should best be modelled. Here, we review the traditional understanding of how saliva is secreted, and describe how our work has suggested important modifications to this traditional view. We end with a brief description of the most recent data from living animals and discuss how this is now contributing to yet another iteration of model construction and experimental investigation.
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Affiliation(s)
- James Sneyd
- Department of Mathematics, The University of Auckland, Level 2, Building 303, 38 Princes Street, Auckland, New Zealand.
| | | | | | | | - David I Yule
- School of Medicine and Dentistry, University of Rochester Medical Center, 601 Elmwood Ave, Box 711, Rochester, NY, USA
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10
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Ca 2+ Release via IP 3 Receptors Shapes the Cardiac Ca 2+ Transient for Hypertrophic Signaling. Biophys J 2020; 119:1178-1192. [PMID: 32871099 DOI: 10.1016/j.bpj.2020.08.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Revised: 06/16/2020] [Accepted: 08/04/2020] [Indexed: 12/27/2022] Open
Abstract
Calcium (Ca2+) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca2+ channels trigger release of Ca2+ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca2+ release via inositol 1,4,5-trisphosphate receptors (IP3Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca2+ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP3Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP3R channels on the Ca2+ transient and examine the sensitivity of the Ca2+ transient shape to properties of IP3R activation. A key result of our study is that IP3R activation increases Ca2+ transient duration for a broad range of IP3R properties, but the effect of IP3R activation on Ca2+ transient amplitude is dependent on IP3 concentration. Furthermore we demonstrate that IP3-mediated Ca2+ release in the cytosol increases the duty cycle of the Ca2+ transient, the fraction of the cycle for which [Ca2+] is elevated, across a broad range of parameter values and IP3 concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca2+ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca2+ duty cycle as a plausible mechanism for IP3-dependent hypertrophic signaling via Ca2+-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.
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11
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Huang Y, Qu J, Li X, Wei F, Zhong J, Wu Y, Cai M, Gao X, Pearson JE, Shuai J. Anti-cross-correlation between the adjacent open and closed durations of Markovian channels. Phys Rev E 2020; 101:012418. [PMID: 32069561 DOI: 10.1103/physreve.101.012418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Indexed: 11/07/2022]
Abstract
We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of N independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with N>M>0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.
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Affiliation(s)
- Yandong Huang
- College of Computer Engineering, Jimei University, Xiamen 361021, China
| | - Jing Qu
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Xiang Li
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Fang Wei
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Jinjin Zhong
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Yuning Wu
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Meichun Cai
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Xuejuan Gao
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - John E Pearson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Jianwei Shuai
- Department of Physics, Xiamen University, Xiamen 361005, China.,State Key Laboratory of Cellular Stress Biology, Innovation Center for Cell Signaling Network, Xiamen University, Xiamen 361102, China.,National Institute for Data Science in Health and Medicine, Xiamen University, Xiamen 361102, China
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12
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Simulation Strategies for Calcium Microdomains and Calcium Noise. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020; 1131:771-797. [DOI: 10.1007/978-3-030-12457-1_31] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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13
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A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes. PLoS Comput Biol 2019; 15:e1006661. [PMID: 31437152 PMCID: PMC6726250 DOI: 10.1371/journal.pcbi.1006661] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2018] [Revised: 09/04/2019] [Accepted: 08/03/2019] [Indexed: 12/27/2022] Open
Abstract
Multiple cellular organelles tightly orchestrate intracellular calcium (Ca2+) dynamics to regulate cellular activities and maintain homeostasis. The interplay between the endoplasmic reticulum (ER), a major store of intracellular Ca2+, and mitochondria, an important source of adenosine triphosphate (ATP), has been the subject of much research, as their dysfunction has been linked with metabolic diseases. Interestingly, throughout the cell’s cytosolic domain, these two organelles share common microdomains called mitochondria-associated ER membranes (MAMs), where their membranes are in close apposition. The role of MAMs is critical for intracellular Ca2+ dynamics as they provide hubs for direct Ca2+ exchange between the organelles. A recent experimental study reported correlation between obesity and MAM formation in mouse liver cells, and obesity-related cellular changes that are closely associated with the regulation of Ca2+ dynamics. We constructed a mathematical model to study the effects of MAM Ca2+ dynamics on global Ca2+ activities. Through a series of model simulations, we investigated cellular mechanisms underlying the altered Ca2+ dynamics in the cells under obesity. We predict that, as the dosage of stimulus gradually increases, liver cells from obese mice will reach the state of saturated cytosolic Ca2+ concentration at a lower stimulus concentration, compared to cells from healthy mice. It is well known that intracellular Ca2+ oscillations carry encoded signals in their amplitude and frequency to regulate various cellular processes, and accumulating evidence supports the importance of the interplay between the ER and mitochondria in cellular Ca2+ homeostasis. Miscommunications between the organelles may be involved in the development of metabolic diseases. Based on a recent experimental study that spotlighted a correlation between obesity and physical interactions of the ER and mitochondria in mouse hepatic cells, we constructed a mathematical model as a tool to probe the effects of the cellular changes linked with obesity on global cellular Ca2+ dynamics. Our model successfully reproduced the experimental study that observed a positive correlation between an increase in ER-mitochondrial junctions and the magnitude of mitochondrial Ca2+ responses. We postulate that hepatic cells from lean animals exhibit Ca2+ oscillations that are more robust under higher concentrations of stimulus, compared to cells from obese animals.
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Denizot A, Arizono M, Nägerl UV, Soula H, Berry H. Simulation of calcium signaling in fine astrocytic processes: Effect of spatial properties on spontaneous activity. PLoS Comput Biol 2019; 15:e1006795. [PMID: 31425510 PMCID: PMC6726244 DOI: 10.1371/journal.pcbi.1006795] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Revised: 09/04/2019] [Accepted: 07/08/2019] [Indexed: 12/20/2022] Open
Abstract
Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including the spatial organization of calcium channels IP3R, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on the spatial organization of the channels. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy and predicts that local variations of calcium indicators might contribute to the diversity of calcium signals observed in astrocytes. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability.
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Affiliation(s)
- Audrey Denizot
- INRIA, F-69603, Villeurbanne, France
- Univ Lyon, LIRIS, UMR5205 CNRS, F-69621, Villeurbanne, France
| | - Misa Arizono
- Interdisciplinary Institute for Neuroscience, Université de Bordeaux, Bordeaux, France
- Interdisciplinary Institute for Neuroscience, CNRS UMR 5297, Bordeaux, France
| | - U. Valentin Nägerl
- Interdisciplinary Institute for Neuroscience, Université de Bordeaux, Bordeaux, France
- Interdisciplinary Institute for Neuroscience, CNRS UMR 5297, Bordeaux, France
| | - Hédi Soula
- INRIA, F-69603, Villeurbanne, France
- Univ P&M Curie, CRC, INSERM UMRS 1138, F-75006, Paris, France
| | - Hugues Berry
- INRIA, F-69603, Villeurbanne, France
- Univ Lyon, LIRIS, UMR5205 CNRS, F-69621, Villeurbanne, France
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15
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Wacquier B, Voorsluijs V, Combettes L, Dupont G. Coding and decoding of oscillatory Ca 2+ signals. Semin Cell Dev Biol 2019; 94:11-19. [PMID: 30659886 DOI: 10.1016/j.semcdb.2019.01.008] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 01/11/2019] [Accepted: 01/14/2019] [Indexed: 01/08/2023]
Abstract
About 30 years after their first observation, Ca2+ oscillations are now recognised as a universal mechanism of signal transduction. These oscillations are driven by periodic cycles of release and uptake of Ca2+ between the cytoplasm and the endoplasmic reticulum. Their frequency often increases with the level of stimulation, which can be decoded by some molecules. However, it is becoming increasingly evident that the widespread core oscillatory mechanism is modulated in many ways, depending on the cell type and on the physiological conditions. Interplay with inositol 1,4,5-trisphosphate metabolism and with other Ca2+ stores as the extracellular medium or mitochondria can much affect the properties of these oscillations. In many cases, these finely tuned characteristics of Ca2+ oscillations impact the physiological response that is triggered by the signal. Moreover, oscillations are intrinsically irregular. This randomness can also be exploited by the cell. In this review, we discuss evidences of these additional manifestations of the versatility of Ca2+ signalling.
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Affiliation(s)
- Benjamin Wacquier
- Unit of Theoretical Chronobiology, Faculté des Sciences, Université Libre de Bruxelles (ULB), Brussels, Belgium
| | - Valérie Voorsluijs
- Nonlinear Physical Chemistry Unit & Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université Libre de Bruxelles (ULB), Brussels, Belgium
| | | | - Geneviève Dupont
- Unit of Theoretical Chronobiology, Faculté des Sciences, Université Libre de Bruxelles (ULB), Brussels, Belgium.
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Toglia P, Demuro A, Mak DOD, Ullah G. Data-driven modeling of mitochondrial dysfunction in Alzheimer's disease. Cell Calcium 2018; 76:23-35. [PMID: 30248575 DOI: 10.1016/j.ceca.2018.09.003] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2018] [Revised: 09/02/2018] [Accepted: 09/03/2018] [Indexed: 02/06/2023]
Abstract
Intracellular accumulation of oligomeric forms of β amyloid (Aβ) are now believed to play a key role in the earliest phase of Alzheimer's disease (AD) as their rise correlates well with the early symptoms of the disease. Extensive evidence points to impaired neuronal Ca2+ homeostasis as a direct consequence of the intracellular Aβ oligomers. However, little is known about the downstream effects of the resulting Ca2+ rise on the many intracellular Ca2+-dependent pathways. Here we use multiscale modeling in conjunction with patch-clamp electrophysiology of single inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and fluorescence imaging of whole-cell Ca2+ response, induced by exogenously applied intracellular Aβ42 oligomers to show that Aβ42 inflicts cytotoxicity by impairing mitochondrial function. Driven by patch-clamp experiments, we first model the kinetics of IP3R, which is then extended to build a model for the whole-cell Ca2+ signals. The whole-cell model is then fitted to fluorescence signals to quantify the overall Ca2+ release from the endoplasmic reticulum by intracellular Aβ42 oligomers through G-protein-mediated stimulation of IP3 production. The estimated IP3 concentration as a function of intracellular Aβ42 content together with the whole-cell model allows us to show that Aβ42 oligomers impair mitochondrial function through pathological Ca2+ uptake and the resulting reduced mitochondrial inner membrane potential, leading to an overall lower ATP and increased production of reactive oxygen species and H2O2. We further show that mitochondrial function can be restored by the addition of Ca2+ buffer EGTA, in accordance with the observed abrogation of Aβ42 cytotoxicity by EGTA in our live cells experiments.
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Affiliation(s)
- Patrick Toglia
- Department of Physics, University of South Florida, Tampa, FL 33620, USA
| | - Angelo Demuro
- Department of Neurobiology and Behavior and Physiology and Biophysics, University of California, Irvine, CA 92697, USA
| | - Don-On Daniel Mak
- Department of Physiology, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL 33620, USA.
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17
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Abstract
Analysis of Rosen's theories with a focus on their mathematical content. Provides links of Rosen's work with most recent research into mathematical modelling. Possible implementations of ’closure to efficient causation’ in models are discussed. Critical analysis of Rosen's use of category theory.
The theoretical biologist Robert Rosen developed a highly original approach for investigating the question “What is life?”, the most fundamental problem of biology. Considering that Rosen made extensive use of mathematics it might seem surprising that his ideas have only rarely been implemented in mathematical models. On the one hand, Rosen propagates relational models that neglect underlying structural details of the components and focus on relationships between the elements of a biological system, according to the motto “throw away the physics, keep the organisation”. Rosen's strong rejection of mechanistic models that he implicitly associates with a strong form of reductionism might have deterred mathematical modellers from adopting his ideas for their own work. On the other hand Rosen's presentation of his modelling framework, (M, R) systems, is highly abstract which makes it hard to appreciate how this approach could be applied to concrete biological problems. In this article, both the mathematics as well as those aspects of Rosen's work are analysed that relate to his philosophical ideas. It is shown that Rosen's relational models are a particular type of mechanistic model with specific underlying assumptions rather than a fundamentally different approach that excludes mechanistic models. The strengths and weaknesses of relational models are investigated by comparison with current network biology literature. Finally, it is argued that Rosen's definition of life, “organisms are closed to efficient causation”, should be considered as a hypothesis to be tested and ideas how this postulate could be implemented in mathematical models are presented.
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Abstract
Decoding how tissue properties emerge across multiple spatial and temporal scales from the integration of local signals is a grand challenge in quantitative biology. For example, the collective behavior of epithelial cells is critical for shaping developing embryos. Understanding how epithelial cells interpret a diverse range of local signals to coordinate tissue-level processes requires a systems-level understanding of development. Integration of multiple signaling pathways that specify cell signaling information requires second messengers such as calcium ions. Increasingly, specific roles have been uncovered for calcium signaling throughout development. Calcium signaling regulates many processes including division, migration, death, and differentiation. However, the pleiotropic and ubiquitous nature of calcium signaling implies that many additional functions remain to be discovered. Here we review a selection of recent studies to highlight important insights into how multiple signals are transduced by calcium transients in developing epithelial tissues. Quantitative imaging and computational modeling have provided important insights into how calcium signaling integration occurs. Reverse-engineering the conserved features of signal integration mediated by calcium signaling will enable novel approaches in regenerative medicine and synthetic control of morphogenesis.
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Affiliation(s)
- Pavel A. Brodskiy
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 205 McCourtney Hall, Notre Dame, IN 46556, USA
| | - Jeremiah J. Zartman
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, 205 McCourtney Hall, Notre Dame, IN 46556, USA
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19
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Falcke M, Moein M, Tilūnaitė A, Thul R, Skupin A. On the phase space structure of IP 3 induced Ca 2+ signalling and concepts for predictive modeling. CHAOS (WOODBURY, N.Y.) 2018; 28:045115. [PMID: 31906671 DOI: 10.1063/1.5021073] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.
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Affiliation(s)
- Martin Falcke
- Max Delbrück Centre for Molecular Medicine, Robert Rössler Strasse 10, 13125 Berlin, Germany and Department of Physics, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany
| | - Mahsa Moein
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 7, Rue de Swing, Belval L-4367, Luxembourg
| | - Agne Tilūnaitė
- Systems Biology Laboratory, School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Rüdiger Thul
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 7, Rue de Swing, Belval L-4367, Luxembourg
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20
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Toglia P, Ullah G, Pearson JE. Analyzing optical imaging of Ca 2+ signals via TIRF microscopy: The limits on resolution due to chemical rates and depth of the channels. Cell Calcium 2017; 67:65-73. [PMID: 29029792 DOI: 10.1016/j.ceca.2017.08.010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Revised: 08/22/2017] [Accepted: 08/23/2017] [Indexed: 11/17/2022]
Abstract
High resolution total internal reflection (TIRF) microscopy (TIRFM) together with detailed computational modeling provides a powerful approach towards the understanding of a wide range of Ca2+ signals mediated by the ubiquitous inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) channel. Exploiting this fruitful collaboration further requires close agreement between the models and observations. However, elementary Ca2+ release events, puffs, imaged through TIRFM do not show the rapid single-channel openings and closings during and between puffs as are present in simulated puffs using data-driven single channel models. TIRFM also shows a rapid equilibration of 10ms after a channel opens or closes which is not achievable in simulation using standard Ca2+ diffusion coefficients and reaction rates between indicator dye and Ca2+. Furthermore, TIRFM imaging cannot decipher the depth of the channel with respect to the microscope, which will affect the change in fluorescence that the microscope detects, thereby affecting its sensitivity to fast single-channel activity. Using the widely used Ca2+ diffusion coefficients and reaction rates, our simulations show equilibration rates that are eight times slower than TIRFM imaging. We show that to get equilibrium rates consistent with observed values, the diffusion coefficients and reaction rates have to be significantly higher than the values reported in the literature, and predict the channel depth to be 200-250nm. Finally, we show that with the addition of noise, short events due to 1-2ms opening and closing of channels that are observed in computational models can be missed in TIRFM.
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Affiliation(s)
- Patrick Toglia
- Department of Physics, University of South Florida, Tampa, FL 33620, USA
| | - Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL 33620, USA.
| | - John E Pearson
- T-6 Theoretical Biology and Biophysics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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21
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Cao P, Falcke M, Sneyd J. Mapping Interpuff Interval Distribution to the Properties of Inositol Trisphosphate Receptors. Biophys J 2017; 112:2138-2146. [PMID: 28538151 DOI: 10.1016/j.bpj.2017.03.019] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Revised: 03/14/2017] [Accepted: 03/24/2017] [Indexed: 01/24/2023] Open
Abstract
Tightly clustered inositol trisphosphate receptors (IP3Rs) control localized Ca2+ liberation from the endoplasmic reticulum to generate repetitive Ca2+ puffs. Distributions of the interpuff interval (IPI), i.e., the waiting time between successive puffs, are found to be well characterized by a probability density function involving only two parameters, λ and ξ, which represent the basal rate of puff generation and the recovery rate from refractoriness, respectively. However, how the two parameters depend on the kinetic parameters of single IP3Rs in a cluster is still unclear. In this article, using a stochastic puff model and a single-channel data-based IP3R model, we establish the dependencies of λ and ξ on two important IP3R model parameters, IP3 concentration ([IP3]) and the recovery rate from Ca2+ inhibition (rlow). By varying [IP3] and rlow in physiologically plausible ranges, we find that the ξ-λ plane is comprised of only two disjoint regions, a biologically impermissible region and a region where each parameter set (ξ, λ) can be caused by using two different combinations of [IP3] and rlow. The two combinations utilize very different mechanisms to maintain the same IPI distribution, and the mechanistic difference provides a way of identifying IP3R kinetic parameters by observing properties of the IPI.
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Affiliation(s)
- Pengxing Cao
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, Australia
| | - Martin Falcke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Auckland, New Zealand.
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22
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23
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Oschmann F, Berry H, Obermayer K, Lenk K. From in silico astrocyte cell models to neuron-astrocyte network models: A review. Brain Res Bull 2017; 136:76-84. [PMID: 28189516 DOI: 10.1016/j.brainresbull.2017.01.027] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Revised: 01/30/2017] [Accepted: 01/31/2017] [Indexed: 01/25/2023]
Abstract
The idea that astrocytes may be active partners in synaptic information processing has recently emerged from abundant experimental reports. Because of their spatial proximity to neurons and their bidirectional communication with them, astrocytes are now considered as an important third element of the synapse. Astrocytes integrate and process synaptic information and by doing so generate cytosolic calcium signals that are believed to reflect neuronal transmitter release. Moreover, they regulate neuronal information transmission by releasing gliotransmitters into the synaptic cleft affecting both pre- and postsynaptic receptors. Concurrent with the first experimental reports of the astrocytic impact on neural network dynamics, computational models describing astrocytic functions have been developed. In this review, we give an overview over the published computational models of astrocytic functions, from single-cell dynamics to the tripartite synapse level and network models of astrocytes and neurons.
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Affiliation(s)
- Franziska Oschmann
- Technical University Berlin, Neural Information Processing Group, Sekr. MAR 5-6, Marchstrasse 23, 10587 Berlin, Germany; Bernstein Center for Computational Neuroscience, Berlin, Germany.
| | - Hugues Berry
- INRIA, 69603 Villeurbanne, France; LIRIS UMR5205, University of Lyon, 69622 Villeurbanne, France
| | - Klaus Obermayer
- Technical University Berlin, Neural Information Processing Group, Sekr. MAR 5-6, Marchstrasse 23, 10587 Berlin, Germany; Bernstein Center for Computational Neuroscience, Berlin, Germany
| | - Kerstin Lenk
- Tampere University of Technology, BioMediTech, PL100, 33014 Tampere, Finland.
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24
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Han JM, Tanimura A, Kirk V, Sneyd J. A mathematical model of calcium dynamics in HSY cells. PLoS Comput Biol 2017; 13:e1005275. [PMID: 28199326 PMCID: PMC5310762 DOI: 10.1371/journal.pcbi.1005275] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Accepted: 11/30/2016] [Indexed: 12/03/2022] Open
Abstract
Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations.
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Affiliation(s)
- Jung Min Han
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Akihiko Tanimura
- Department of Pharmacology, School of Dentistry, Health Sciences University of Hokkaido, Ishikari-Tobetsu, Hokkaido 061-0293, Japan
| | - Vivien Kirk
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
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25
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Abstract
Oscillations in the concentration of free cytosolic Ca2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca2+ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca2+ oscillation period can be controlled by modulation of the rate of activation by Ca2+ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables.
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26
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Ullah G, Ullah A. Mode switching of Inositol 1,4,5-trisphosphate receptor channel shapes the Spatiotemporal scales of Ca 2+ signals. J Biol Phys 2016; 42:507-524. [PMID: 27154029 PMCID: PMC5059592 DOI: 10.1007/s10867-016-9419-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 04/12/2016] [Indexed: 01/24/2023] Open
Abstract
The inositol 1,4,5-trisphosphate (InsP3) receptor (InsP3R) channel is crucial for the generation and modulation of highly specific intracellular Ca2+ signals performing numerous functions in animal cells. However, the single channel behavior during Ca2+ signals of different spatiotemporal scales is not well understood. To elucidate the correlation between the gating dynamics of single InsP3Rs and spatiotemporal Ca2+ patterns, we simulate a cluster of InsP3Rs under varying ligand concentrations and extract comprehensive gating statistics of all channels during events of different sizes and durations. Our results show that channels gating predominantly in the low activity mode with negligible occupancy of intermediate and high modes leads to single channel Ca2+ release event blips. Increasing occupancies of intermediate and high modes results in events with increasing size. When the channel has more than 50% probability of gating in the intermediate and high modes, the cluster generates very large puffs that would most likely result in global Ca2+ signals. The size, duration and frequency of Ca2+ signals all increase linearly with the total probability of channel gating in the intermediate and high modes. To our knowledge, this is the first study that quantitatively relates the modal characteristics of InsP3R to the shaping of different spatiotemporal scales of Ca2+ signals.
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Affiliation(s)
- Ghanim Ullah
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA.
| | - Aman Ullah
- Department of Molecular Neuroscience, Krasnow Institute for Advanced Study, George Mason University, Fairfax, VA, 22030, USA
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27
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Boie S, Chen J, Sanderson MJ, Sneyd J. The relative contributions of store-operated and voltage-gated Ca 2+ channels to the control of Ca 2+ oscillations in airway smooth muscle. J Physiol 2016; 595:3129-3141. [PMID: 27502470 DOI: 10.1113/jp272996] [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: 06/24/2016] [Accepted: 08/03/2016] [Indexed: 02/02/2023] Open
Abstract
KEY POINTS Agonist-dependent oscillations in the concentration of free cytosolic calcium are a vital mechanism for the control of airway smooth muscle contraction and thus are a critical factor in airway hyper-responsiveness. Using a mathematical model, closely tied to experimental work, we show that the oscillations in membrane potential accompanying the calcium oscillations have no significant effect on the properties of the calcium oscillations. In addition, the model shows that calcium entry through store-operated calcium channels is critical for calcium oscillations, but calcium entry through voltage-gated channels has much less effect. The model predicts that voltage-gated channels are less important than store-operated channels in the control of airway smooth muscle tone. ABSTRACT Airway smooth muscle contraction is typically the key mechanism underlying airway hyper-responsiveness, and the strength of muscle contraction is determined by the frequency of oscillations of intracellular calcium (Ca2+ ) concentration. In airway smooth muscle cells, these Ca2+ oscillations are caused by cyclic Ca2+ release from the sarcoplasmic reticulum, although Ca2+ influx via plasma membrane channels is also necessary to sustain the oscillations over longer times. To assess the relative contributions of store-operated and voltage-gated Ca2+ channels to this Ca2+ influx, we generated a comprehensive mathematical model, based on experimental Ca2+ measurements in mouse precision-cut lung slices, to simulate Ca2+ oscillations and changes in membrane potential. Agonist-induced Ca2+ oscillations are accompanied by oscillations in membrane potential, although the membrane potential oscillations are too small to generate large Ca2+ currents through voltage-gated Ca2+ channels, and thus have little effect on the Ca2+ oscillations. Ca2+ entry through voltage-gated channels only becomes important when the cell is depolarized (e.g. by a high external K+ concentration). As a result, agonist-induced Ca2+ oscillations are critically dependent on Ca2+ entry through store-operated channels but do not depend strongly on Ca2+ entry though voltage-gated channels.
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Affiliation(s)
- Sebastian Boie
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | - Jun Chen
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, MA, USA
| | - Michael J Sanderson
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, MA, USA
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
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28
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Siekmann I, Fackrell M, Crampin EJ, Taylor P. Modelling modal gating of ion channels with hierarchical Markov models. Proc Math Phys Eng Sci 2016; 472:20160122. [PMID: 27616917 PMCID: PMC5014102 DOI: 10.1098/rspa.2016.0122] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Accepted: 07/22/2016] [Indexed: 11/12/2022] Open
Abstract
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models.
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Affiliation(s)
- Ivo Siekmann
- Systems Biology Laboratory, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia
- Centre for Systems Genomics, University of Melbourne, Melbourne, Australia
| | - Mark Fackrell
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
| | - Edmund J. Crampin
- Systems Biology Laboratory, Melbourne School of Engineering, University of Melbourne, Melbourne, Australia
- Centre for Systems Genomics, University of Melbourne, Melbourne, Australia
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
- School of Medicine, University of Melbourne, Melbourne, Australia
- Australian Research Council Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne, Australia
| | - Peter Taylor
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
- Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Australia
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Sneyd J, Means S, Zhu D, Rugis J, Won JH, Yule DI. Modeling calcium waves in an anatomically accurate three-dimensional parotid acinar cell. J Theor Biol 2016; 419:383-393. [PMID: 27155044 DOI: 10.1016/j.jtbi.2016.04.030] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Revised: 04/20/2016] [Accepted: 04/25/2016] [Indexed: 11/24/2022]
Abstract
We construct a model of calcium waves in a three-dimensional anatomically accurate parotid acinar cell, constructed from experimental data. Gradients of inositol trisphosphate receptor (IPR) density are imposed, with the IPR density being greater closer to the lumen, which has a branched structure, and inositol trisphosphate (IP3) is produced only at the basal membrane. We show (1) that IP3 equilibrates so quickly across the cell that it can be assumed to be spatially homogeneous; (2) spatial separation of the sites of IP3 action and IP3 production does not preclude the formation of stable oscillatory Ca2+ waves. However, these waves are not waves in the mathematical sense of a traveling wave with fixed profile. They result instead from a time delay between the Ca2+ rise in the apical and basal regions; (3) the ryanodine receptors serve to reinforce the Ca2+ wave, but are not necessary for the wave to exist; (4) a spatially independent model is not sufficient to study saliva secretion, although a one-dimensional model might be sufficient. Our results here form the first stages of the construction of a multiscale and multicellular model of saliva secretion in an entire acinus.
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Affiliation(s)
- James Sneyd
- Department of Mathematics, University of Auckland, New Zealand.
| | - Shawn Means
- Department of Mathematics, University of Auckland, New Zealand
| | - Di Zhu
- Department of Mathematics, University of Auckland, New Zealand
| | - John Rugis
- Department of Mathematics, University of Auckland, New Zealand
| | - Jong Hak Won
- Department of Pharmacology and Physiology, University of Rochester Medical Centre, Rochester, USA
| | - David I Yule
- Department of Pharmacology and Physiology, University of Rochester Medical Centre, Rochester, USA
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陈 圆. Modeling of Ca<sup>2+</sup> Channels and Ca<sup>2+</sup> Signal Oscillations. Biophysics (Nagoya-shi) 2016. [DOI: 10.12677/biphy.2016.41001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
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Mak DOD, Foskett JK. Inositol 1,4,5-trisphosphate receptors in the endoplasmic reticulum: A single-channel point of view. Cell Calcium 2014; 58:67-78. [PMID: 25555684 DOI: 10.1016/j.ceca.2014.12.008] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Revised: 12/09/2014] [Accepted: 12/10/2014] [Indexed: 10/24/2022]
Abstract
As an intracellular Ca(2+) release channel at the endoplasmic reticulum membrane, the ubiquitous inositol 1,4,5-trisphosphate (InsP3) receptor (InsP3R) plays a crucial role in the generation, propagation and regulation of intracellular Ca(2+) signals that regulate numerous physiological and pathophysiological processes. This review provides a concise account of the fundamental single-channel properties of the InsP3R channel: its conductance properties and its regulation by InsP3 and Ca(2+), its physiological ligands, studied using nuclear patch clamp electrophysiology.
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Affiliation(s)
- Don-On Daniel Mak
- Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, United States.
| | - J Kevin Foskett
- Department of Physiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, United States; Department of Cell and Developmental Biology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, United States
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Cao P, Tan X, Donovan G, Sanderson MJ, Sneyd J. A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells. PLoS Comput Biol 2014; 10:e1003783. [PMID: 25121766 PMCID: PMC4133161 DOI: 10.1371/journal.pcbi.1003783] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2014] [Accepted: 06/24/2014] [Indexed: 11/18/2022] Open
Abstract
The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model. The inositol trisphosphate receptor () is one of the most important cellular components responsible for calcium oscillations. Over the past decade, two major questions about the have arisen. Firstly, what fundamental properties of the allow it to perform its function? Secondly, although calcium oscillations are caused by the stochastic properties of small numbers of is it possible for a deterministic model to be a reliable predictor of calcium dynamics? Using airway smooth muscle cells as an example, we show that calcium dynamics can be accurately modeled using simplified models, and, secondly, that deterministic models are qualitatively accurate predictors of calcium dynamics. These results are important for the study of calcium dynamics in many cell types.
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Affiliation(s)
- Pengxing Cao
- Department of Mathematics, University of Auckland, Auckland, New Zealand
| | - Xiahui Tan
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America
| | - Graham Donovan
- Department of Mathematics, University of Auckland, Auckland, New Zealand
| | - Michael J. Sanderson
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America
| | - James Sneyd
- Department of Mathematics, University of Auckland, Auckland, New Zealand
- * E-mail:
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Multiscale modelling of saliva secretion. Math Biosci 2014; 257:69-79. [PMID: 25014770 DOI: 10.1016/j.mbs.2014.06.017] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2014] [Revised: 06/18/2014] [Accepted: 06/26/2014] [Indexed: 01/28/2023]
Abstract
We review a multiscale model of saliva secretion, describing in brief how the model is constructed and what we have so far learned from it. The model begins at the level of inositol trisphosphate receptors (IPR), and proceeds through the cellular level (with a model of acinar cell calcium dynamics) to the multicellular level (with a model of the acinus), finally to a model of a saliva production unit that includes an acinus and associated duct. The model at the level of the entire salivary gland is not yet completed. Particular results from the model so far include (i) the importance of modal behaviour of IPR, (ii) the relative unimportance of Ca(2+) oscillation frequency as a controller of saliva secretion, (iii) the need for the periodic Ca(2+) waves to be as fast as possible in order to maximise water transport, (iv) the presence of functional K(+) channels in the apical membrane increases saliva secretion, (v) the relative unimportance of acinar spatial structure for isotonic water transport, (vi) the prediction that duct cells are highly depolarised, (vii) the prediction that the secondary saliva takes at least 1mm (from the acinus) to reach ionic equilibrium. We end with a brief discussion of future directions for the model, both in construction and in the study of scientific questions.
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Means SA, Cheng LK. Mitochondrial calcium handling within the interstitial cells of Cajal. Am J Physiol Gastrointest Liver Physiol 2014; 307:G107-21. [PMID: 24789203 PMCID: PMC4080165 DOI: 10.1152/ajpgi.00380.2013] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The interstitial cells of Cajal (ICC) drive rhythmic pacemaking contractions in the gastrointestinal system. The ICC generate pacemaking signals by membrane depolarizations associated with the release of intracellular calcium (Ca(2+)) in the endoplasmic reticulum (ER) through inositol-trisphosphate (IP3) receptors (IP3R) and uptake by mitochondria (MT). This Ca(2+) dynamic is hypothesized to generate pacemaking signals by calibrating ER Ca(2+) store depletions and membrane depolarization with ER store-operated Ca(2+) entry mechanisms. Using a biophysically based spatio-temporal model of integrated Ca(2+) transport in the ICC, we determined the feasibility of ER depletion timescale correspondence with experimentally observed pacemaking frequencies while considering the impact of IP3R Ca(2+) release and MT uptake on bulk cytosolic Ca(2+) levels because persistent elevations of free intracellular Ca(2+) are toxic to the cell. MT densities and distributions are varied in the model geometry to observe MT influence on free cytosolic Ca(2+) and the resulting frequencies of ER Ca(2+) store depletions, as well as the sarco-endoplasmic reticulum Ca(2+) ATP-ase (SERCA) and IP3 agonist concentrations. Our simulations show that high MT densities observed in the ICC are more relevant to ER establishing Ca(2+) depletion frequencies than protection of the cytosol from elevated free Ca(2+), whereas the SERCA pump is more relevant to containing cytosolic Ca(2+) elevations. Our results further suggest that the level of IP3 agonist stimulating ER Ca(2+) release, subsequent MT uptake, and eventual activation of ER store-operated Ca(2+) entry may determine frequencies of rhythmic pacemaking exhibited by the ICC across species and tissue types.
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Affiliation(s)
- Shawn A. Means
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Leo K. Cheng
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
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Siekmann I, Sneyd J, Crampin EJ. Statistical analysis of modal gating in ion channels. Proc Math Phys Eng Sci 2014. [DOI: 10.1098/rspa.2014.0030] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Ion channels regulate the concentrations of ions within cells. By stochastically opening and closing its pore, they enable or prevent ions from crossing the cell membrane. However, rather than opening with a constant probability, many ion channels switch between several different levels of activity even if the experimental conditions are unchanged. This phenomenon is known as modal gating: instead of directly adapting its activity, the channel seems to mix sojourns in active and inactive modes in order to exhibit intermediate open probabilities. Evidence is accumulating that modal gating rather than modulation of opening and closing at a faster time scale is the primary regulatory mechanism of ion channels. However, currently, no method is available for reliably calculating sojourns in different modes. In order to address this challenge, we develop a statistical framework for segmenting single-channel datasets into segments that are characteristic for particular modes. The algorithm finds the number of mode changes, detects their locations and infers the open probabilities of the modes. We apply our approach to data from the inositol-trisphosphate receptor. Based upon these results, we propose that mode changes originate from alternative conformational states of the channel protein that determine a certain level of channel activity.
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Affiliation(s)
- Ivo Siekmann
- National ICT Australia, Victorian Research Laboratory, Melbourne, Australia
- Systems Biology Laboratory, Melbourne School of Engineering, The University of Melbourne, Melbourne, Australia
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | - Edmund J. Crampin
- National ICT Australia, Victorian Research Laboratory, Melbourne, Australia
- Systems Biology Laboratory, Melbourne School of Engineering, The University of Melbourne, Melbourne, Australia
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Wagner LE, Groom LA, Dirksen RT, Yule DI. Characterization of ryanodine receptor type 1 single channel activity using "on-nucleus" patch clamp. Cell Calcium 2014; 56:96-107. [PMID: 24972488 DOI: 10.1016/j.ceca.2014.05.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Revised: 05/27/2014] [Accepted: 05/28/2014] [Indexed: 12/13/2022]
Abstract
In this study, we provide the first description of the biophysical and pharmacological properties of ryanodine receptor type 1 (RyR1) expressed in a native membrane using the on-nucleus configuration of the patch clamp technique. A stable cell line expressing rabbit RyR1 was established (HEK-RyR1) using the FLP-in 293 cell system. In contrast to untransfected cells, RyR1 expression was readily demonstrated by immunoblotting and immunocytochemistry in HEK-RyR1 cells. In addition, the RyR1 agonists 4-CMC and caffeine activated Ca(2+) release that was inhibited by high concentrations of ryanodine. On nucleus patch clamp was performed in nuclei prepared from HEK-RyR1 cells. Raising the [Ca(2+)] in the patch pipette resulted in the appearance of a large conductance cation channel with well resolved kinetics and the absence of prominent subconductance states. Current versus voltage relationships were ohmic and revealed a chord conductance of ∼750pS or 450pS in symmetrical 250mM KCl or CsCl, respectively. The channel activity was markedly enhanced by caffeine and exposure to ryanodine resulted in the appearance of a subconductance state with a conductance ∼40% of the full channel opening with a Po near unity. In total, these properties are entirely consistent with RyR1 channel activity. Exposure of RyR1 channels to cyclic ADP ribose (cADPr), nicotinic acid adenine dinucleotide phosphate (NAADP) or dantrolene did not alter the single channel activity stimulated by Ca(2+), and thus, it is unlikely these molecules directly modulate RyR1 channel activity. In summary, we describe an experimental platform to monitor the single channel properties of RyR channels. We envision that this system will be influential in characterizing disease-associated RyR mutations and the molecular determinants of RyR channel modulation.
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Affiliation(s)
- Larry E Wagner
- Department of Pharmacology and Physiology, University of Rochester, 601 Elmwood Ave, Rochester, NY 14642, United States
| | - Linda A Groom
- Department of Pharmacology and Physiology, University of Rochester, 601 Elmwood Ave, Rochester, NY 14642, United States
| | - Robert T Dirksen
- Department of Pharmacology and Physiology, University of Rochester, 601 Elmwood Ave, Rochester, NY 14642, United States
| | - David I Yule
- Department of Pharmacology and Physiology, University of Rochester, 601 Elmwood Ave, Rochester, NY 14642, United States.
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37
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Hohendanner F, McCulloch AD, Blatter LA, Michailova AP. Calcium and IP3 dynamics in cardiac myocytes: experimental and computational perspectives and approaches. Front Pharmacol 2014; 5:35. [PMID: 24639654 PMCID: PMC3944219 DOI: 10.3389/fphar.2014.00035] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2013] [Accepted: 02/18/2014] [Indexed: 11/22/2022] Open
Abstract
Calcium plays a crucial role in excitation-contraction coupling (ECC), but it is also a pivotal second messenger activating Ca2+-dependent transcription factors in a process termed excitation-transcription coupling (ETC). Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor (IP3R)-mediated Ca2+ release in the regulation of cytosolic and nuclear Ca2+ signals. IP3 is generated by stimulation of plasma membrane receptors that couple to phospholipase C (PLC), liberating IP3 from phosphatidylinositol 4,5-bisphosphate (PIP2). An intriguing aspect of IP3 signaling is the presence of the entire PIP2-PLC-IP3 signaling cascade as well as the presence of IP3Rs at the inner and outer membranes of the nuclear envelope (NE) which functions as a Ca2+ store. The observation that the nucleus is surrounded by its own putative Ca2+ store raises the possibility that nuclear IP3-dependent Ca2+ release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca2+ signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca2+ store; (ii) the nuclear pore complex is the major gateway for Ca2+ and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca2+ handling proteins including the Na+/Ca2+ exchanger (NCX)/GM1 complex, ryanodine receptors (RyRs), nicotinic acid adenine dinucleotide phosphate receptors (NAADPRs), Na+/K+ ATPase, and Na+/H+ exchanger. Thus, it appears that the nucleus represents a Ca2+ signaling domain equipped with its own ion channels and transporters that allow for complex local Ca2+ signals. Many experimental and modeling approaches have been used for the study of intracellular Ca2+ signaling but the key to the understanding of the dual role of Ca2+ mediating ECC and ECT lays in quantitative differences of local [Ca2+] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca2+ transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca2+ and IP3 signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca2+ signals are required to translocate and activate Ca2+-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.
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Affiliation(s)
- Felix Hohendanner
- Department of Molecular Biophysics and Physiology, Rush University Medical Center Chicago, IL, USA
| | - Andrew D McCulloch
- Department of Bioengineering, University of California San Diego La Jolla, CA, USA
| | - Lothar A Blatter
- Department of Molecular Biophysics and Physiology, Rush University Medical Center Chicago, IL, USA
| | - Anushka P Michailova
- Department of Bioengineering, University of California San Diego La Jolla, CA, USA
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Dupont G. Modeling the intracellular organization of calcium signaling. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2014; 6:227-37. [PMID: 24604723 DOI: 10.1002/wsbm.1261] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Revised: 12/24/2013] [Accepted: 12/26/2013] [Indexed: 12/29/2022]
Abstract
Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.
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Affiliation(s)
- Geneviève Dupont
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Brussels, Belgium
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Falkenburger BH, Dickson EJ, Hille B. Quantitative properties and receptor reserve of the DAG and PKC branch of G(q)-coupled receptor signaling. ACTA ACUST UNITED AC 2014; 141:537-55. [PMID: 23630338 PMCID: PMC3639584 DOI: 10.1085/jgp.201210887] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
Gq protein–coupled receptors (GqPCRs) of the plasma membrane activate the phospholipase C (PLC) signaling cascade. PLC cleaves the membrane lipid phosphatidylinositol 4,5-bisphosphate (PIP2) into the second messengers diacylgycerol (DAG) and inositol 1,4,5-trisphosphate (IP3), leading to calcium release, protein kinase C (PKC) activation, and in some cases, PIP2 depletion. We determine the kinetics of each of these downstream endpoints and also ask which is responsible for the inhibition of KCNQ2/3 (KV7.2/7.3) potassium channels in single living tsA-201 cells. We measure DAG production and PKC activity by Förster resonance energy transfer–based sensors, and PIP2 by KCNQ2/3 channels. Fully activating endogenous purinergic receptors by uridine 5′triphosphate (UTP) leads to calcium release, DAG production, and PKC activation, but no net PIP2 depletion. Fully activating high-density transfected muscarinic receptors (M1Rs) by oxotremorine-M (Oxo-M) leads to similar calcium, DAG, and PKC signals, but PIP2 is depleted. KCNQ2/3 channels are inhibited by the Oxo-M treatment (85%) and not by UTP (<1%), indicating that depletion of PIP2 is required to inhibit KCNQ2/3 in response to receptor activation. Overexpression of A kinase–anchoring protein (AKAP)79 or calmodulin (CaM) does not increase KCNQ2/3 inhibition by UTP. From these results and measurements of IP3 and calcium presented in our companion paper (Dickson et al. 2013. J. Gen. Physiol.http://dx.doi.org/10.1085/jgp.201210886), we extend our kinetic model for signaling from M1Rs to DAG/PKC and IP3/calcium signaling. We conclude that calcium/CaM and PKC-mediated phosphorylation do not underlie dynamic KCNQ2/3 channel inhibition during GqPCR activation in tsA-201 cells. Finally, our experimental data provide indirect evidence for cleavage of PI(4)P by PLC in living cells, and our modeling revisits/explains the concept of receptor reserve with measurements from all steps of GqPCR signaling.
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Affiliation(s)
- Björn H Falkenburger
- Department of Physiology and Biophysics, University of Washington, Seattle, WA 98195, USA
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40
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Abstract
Puffs are localized Ca(2 +) signals that arise in oocytes in response to inositol 1,4,5-trisphosphate (IP3). They are the result of the liberation of Ca(2 +) from the endoplasmic reticulum through the coordinated opening of IP3 receptor/channels clustered at a functional release site. The presence of buffers that trap Ca(2 +) provides a mechanism that enriches the spatio-temporal dynamics of cytosolic calcium. The expression of different types of buffers along the cell's life provides a tool with which Ca(2 +) signals and their responses can be modulated. In this paper we extend the stochastic model of a cluster of IP3R-Ca(2 +) channels introduced previously to elucidate the effect of buffers on sequences of puffs at the same release site. We obtain analytically the probability laws of the interpuff time and of the number of channels that participate of the puffs. Furthermore, we show that under typical experimental conditions the effect of buffers can be accounted for in terms of a simple inhibiting function. Hence, by exploring different inhibiting functions we are able to study the effect of a variety of buffers on the puff size and interpuff time distributions. We find the somewhat counter-intuitive result that the addition of a fast Ca(2 +) buffer can increase the average number of channels that participate of a puff.
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Affiliation(s)
- Daniel Fraiman
- Laboratorio de Investigación en Neurociencia, Departamento de Matemática y Ciencias, Universidad de San Andrés, (1644) Buenos Aires, Argentina. CONICET, Argentina
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Cao P, Donovan G, Falcke M, Sneyd J. A stochastic model of calcium puffs based on single-channel data. Biophys J 2013; 105:1133-42. [PMID: 24010656 PMCID: PMC3852038 DOI: 10.1016/j.bpj.2013.07.034] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2013] [Revised: 07/03/2013] [Accepted: 07/24/2013] [Indexed: 11/17/2022] Open
Abstract
Calcium puffs are local transient Ca(2+) releases from internal Ca(2+) stores such as the endoplasmic reticulum or the sarcoplasmic reticulum. Such release occurs through a cluster of inositol 1,4,5-trisphosphate receptors (IP3Rs). Based on the IP3R model (which is determined by fitting to stationary single-channel data) and nonstationary single-channel data, we construct a new IP3R model that includes time-dependent rates of mode switches. A point-source model of Ca(2+) puffs is then constructed based on the new IP3R model and is solved by a hybrid Gillespie method with adaptive timing. Model results show that a relatively slow recovery of an IP3R from Ca(2+) inhibition is necessary to reproduce most of the experimental outcomes, especially the nonexponential interpuff interval distributions. The number of receptors in a cluster could be severely underestimated when the recovery is sufficiently slow. Furthermore, we find that, as the number of IP3Rs increases, the average duration of puffs initially increases but then becomes saturated, whereas the average decay time keeps increasing linearly. This gives rise to the observed asymmetric puff shape.
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Affiliation(s)
- Pengxing Cao
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | - Graham Donovan
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | - Martin Falcke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - James Sneyd
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
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42
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Croisier H, Tan X, Perez-Zoghbi JF, Sanderson MJ, Sneyd J, Brook BS. Activation of store-operated calcium entry in airway smooth muscle cells: insight from a mathematical model. PLoS One 2013; 8:e69598. [PMID: 23936056 PMCID: PMC3723852 DOI: 10.1371/journal.pone.0069598] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2013] [Accepted: 06/10/2013] [Indexed: 11/30/2022] Open
Abstract
Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.
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Affiliation(s)
- Huguette Croisier
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
- * E-mail:
| | - Xiahui Tan
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachussetts, United States of America
| | - Jose F. Perez-Zoghbi
- Department of Cell Physiology and Molecular Biophysics, Texas Tech University Health Sciences Center, Lubbock, Texas, United States of America
| | - Michael J. Sanderson
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachussetts, United States of America
| | - James Sneyd
- Department of Mathematics, University of Auckland, Auckland, New Zealand
| | - Bindi S. Brook
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
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Siekmann I, Sneyd J, Crampin EJ. MCMC can detect nonidentifiable models. Biophys J 2013; 103:2275-86. [PMID: 23283226 DOI: 10.1016/j.bpj.2012.10.024] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2012] [Revised: 06/14/2012] [Accepted: 10/18/2012] [Indexed: 11/26/2022] Open
Abstract
Continuous-time Markov models have been considered the best representation for the stochastic dynamics of ion channels for more than thirty years. For most single-channel data sets, several open and closed states are required for accurately representing the dynamics. However, each data point only shows if the channel is open or closed but not in which state it is. Consequently, some model structures are inherently overparameterized and therefore, in principle, unsuitable for representing any data--those models are called "nonidentifiable". As of this writing, it seems to be poorly understood which continuous-time Markov models are identifiable and which are not, therefore the unconscious use of a nonidentifiable model is a considerable concern. To address this problem, an improved variant of a recently published Markov-chain Monte Carlo method is presented. The algorithm is tested using test data as well as experimental data. We demonstrate that, opposed to a widely used maximum-likelihood estimator, it gives clear warning signs when a nonidentifiable model is used for fitting. Furthermore, for test data that was generated from a nonidentifiable model, the Markov-chain Monte Carlo results recover much more information from the data than maximum-likelihood estimation.
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Affiliation(s)
- Ivo Siekmann
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand.
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Patterson K, Catalán MA, Melvin JE, Yule DI, Crampin EJ, Sneyd J. A quantitative analysis of electrolyte exchange in the salivary duct. Am J Physiol Gastrointest Liver Physiol 2012; 303:G1153-63. [PMID: 22899825 PMCID: PMC3517652 DOI: 10.1152/ajpgi.00364.2011] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
A healthy salivary gland secretes saliva in two stages. First, acinar cells generate primary saliva, a plasma-like, isotonic fluid high in Na(+) and Cl(-). In the second stage, the ducts exchange Na(+) and Cl(-) for K(+) and HCO(3)(-), producing a hypotonic final saliva with no apparent loss in volume. We have developed a tool that aims to understand how the ducts achieve this electrolyte exchange while maintaining the same volume. This tool is part of a larger multiscale model of the salivary gland and can be used at the duct or gland level to investigate the effects of genetic and chemical alterations. In this study, we construct a radially symmetric mathematical model of the mouse salivary gland duct, representing the lumen, the cell, and the interstitium. For a given flow and primary saliva composition, we predict the potential differences and the luminal and cytosolic concentrations along a duct. Our model accounts well for experimental data obtained in wild-type animals as well as knockouts and chemical inhibitors. Additionally, the luminal membrane potential of the duct cells is predicted to be very depolarized compared with acinar cells. We investigate the effects of an electrogenic vs. electroneutral anion exchanger in the luminal membrane on concentration and the potential difference across the luminal membrane as well as how impairing the cystic fibrosis transmembrane conductance regulator channel affects other ion transporting mechanisms. Our model suggests the electrogenicity of the anion exchanger has little effect in the submandibular duct.
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Affiliation(s)
- Kate Patterson
- Dept. of Mathematics, Univ. of Auckland, Auckland, New Zealand.
| | - Marcelo A. Catalán
- 2Secretory Mechanisms and Dysfunction Section, Division of Intramural Research, National Institute of Dental and Craniofacial Research, National Institutes of Health, Bethesda, Maryland;
| | - James E. Melvin
- 2Secretory Mechanisms and Dysfunction Section, Division of Intramural Research, National Institute of Dental and Craniofacial Research, National Institutes of Health, Bethesda, Maryland;
| | - David I. Yule
- 3Department of Pharmacology and Physiology and the Center for Oral Biology, University of Rochester Medical Center, Rochester, New York; and
| | - Edmund J. Crampin
- 4Auckland Bioengineering Institute and Department of Engineering Science, University of Auckland, Auckland, New Zealand
| | - James Sneyd
- 1Department of Mathematics, University of Auckland, Auckland, New Zealand;
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