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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Gao ZX, Li TT, Jiang HY, He J. Calcium oscillation on homogeneous and heterogeneous networks of ryanodine receptor. Phys Rev E 2023; 107:024402. [PMID: 36932487 DOI: 10.1103/physreve.107.024402] [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: 07/26/2022] [Accepted: 01/20/2023] [Indexed: 06/18/2023]
Abstract
Calcium oscillation is an important calcium homeostasis, imbalance of which is the key mechanism of initiation and progression of many major diseases. The formation and maintenance of calcium homeostasis are closely related to the spatial distribution of calcium channels on endoplasmic reticulum, whose complex structure was unveiled by recent observations with superresolution imaging techniques. In the current paper, a theoretical framework is established by abstracting the spatial distribution of the calcium channels as a nonlinear biological complex network with calcium channels as nodes and Ca^{2+} as edges. A dynamical model for a ryanodine receptor (RyR) is adopted to investigate the effect of spatial distribution on calcium oscillation. The mean-field model can be well reproduced from the complete graph and dense Erdös-Rényi network. The synchronization of RyRs is found important to generate a global calcium oscillation. Below a critical density of the Erdös-Rényi or BaraBási-Albert network, the amplitude and interspike interval decrease rapidly with the end of disappearance of oscillation due to the desynchronization. The clique graph with a cluster structure cannot produce a global oscillation due to the failure of synchronization between clusters. A more realistic geometric network is constructed in a two-dimensional plane based on the experimental information about the RyR arrangement of clusters and the frequency distribution of cluster sizes. Different from the clique graph, the global oscillation can be generated with reasonable parameters on the geometric network. The simulation also suggests that existence of small clusters and rogue RyRs plays an important role in the maintenance of global calcium oscillation through keeping synchronization between large clusters. Such results support the heterogeneous distribution of RyRs with different-size clusters, which is helpful to understand recent observations with superresolution nanoscale imaging techniques. The current theoretical framework can also be extent to investigate other phenomena in calcium signal transduction.
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Affiliation(s)
- Zhong-Xue Gao
- School of Physics and Technology, Nanjing Normal University, Nanjing 210097, China
| | - Tian-Tian Li
- School of Physics and Technology, Nanjing Normal University, Nanjing 210097, China
| | - Han-Yu Jiang
- School of Physics and Technology, Nanjing Normal University, Nanjing 210097, China
| | - Jun He
- School of Physics and Technology, Nanjing Normal University, Nanjing 210097, China
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3
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Curcic S, Erkan-Candag H, Pilic J, Malli R, Wiedner P, Tiapko O, Groschner K. TRPC3 governs the spatiotemporal organization of cellular Ca 2+ signatures by functional coupling to IP 3 receptors. Cell Calcium 2022; 108:102670. [PMID: 36375273 DOI: 10.1016/j.ceca.2022.102670] [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: 09/08/2022] [Revised: 10/12/2022] [Accepted: 10/31/2022] [Indexed: 11/06/2022]
Abstract
Communication between TRPC channels and IP3 receptors (IP3R) is considered pivotal in the generation of spatiotemporal Ca2+signaling patterns. Here we revisited the role of TRPC3-IP3R coupling for local Ca2+ signaling within TRPC3-harbouring micro/nanodomains using R-GECO as a reporter, fused to the channel´s C-terminus. Cytoplasmic Ca2+ changes at TRPC3 originated from both the entry of Ca2+ through the TRPC channel and Ca2+ mobilization via IP3R. Local Ca2+ changes at TRPC3 channels expressed in HEK293 cells were predominantly biphasic with IP3R-dependent initial Ca2+ transients, while exclusively monophasic signals were recorded when all three IP3R isoforms were lacking. Abrogation of Ca2+ entry through TRPC3 by point mutations, which impair Ca2+ permeability (E630Q), cation permeation (E630K), or DAG sensitivity (G652A), promoted microdomain Ca2+ oscillations. Ca2+ signals at E630Q, E630K, and G652A channels featured initial Ca2+ transients along with oscillatory activity. Similarly, when extracellular Ca2+ was omitted, IP3R-mediated Ca2+ transients and Ca2+ oscillations were promoted at the cytoplasmic face of wild-type TRPC3 channels. By contrast, oscillations, as well as initial Ca2+ transients, were virtually lacking, when the TRPC3 channels were sensitized by preexposure to low-level PLC activity. TIRF imaging provided evidence for dynamic colocalization of TRPC3 and IP3R. We suggest that TRPC3-mediated Ca2+ entry controls IP3R activity at ER-PM junctions to determine Ca2+ signaling signatures and enable specificity of downstream signaling.
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Affiliation(s)
- Sanja Curcic
- Gottfried-Schatz Research Center (Biophysics), Medical University of Graz, Austria.
| | - Hazel Erkan-Candag
- Gottfried-Schatz Research Center (Biophysics), Medical University of Graz, Austria
| | - Johannes Pilic
- Gottfried-Schatz Research Center (Molecular Biology and Biochemistry), Medical University of Graz, Austria
| | - Roland Malli
- Gottfried-Schatz Research Center (Molecular Biology and Biochemistry), Medical University of Graz, Austria
| | - Patrick Wiedner
- Gottfried-Schatz Research Center (Biophysics), Medical University of Graz, Austria
| | - Oleksandra Tiapko
- Gottfried-Schatz Research Center (Biophysics), Medical University of Graz, Austria
| | - Klaus Groschner
- Gottfried-Schatz Research Center (Biophysics), Medical University of Graz, Austria.
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4
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Shen S, Wang Z, Sun H, Ma L. Role of NLRP3 Inflammasome in Myocardial Ischemia-Reperfusion Injury and Ventricular Remodeling. Med Sci Monit 2022; 28:e934255. [PMID: 35042840 PMCID: PMC8790935 DOI: 10.12659/msm.934255] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Reperfusion therapy is the optimal therapy for acute myocardial infarction (AMI), but acute inflammatory injury and chronic heart failure (HF) after myocardial ischemia and reperfusion (MI/R) remain the leading cause of death after AMI. Pyroptosis, a newly discovered form of cell death, has been proven to play a significant role in the acute reperfusion process and the subsequent chronic process of ventricular remodeling. Current research shows that multiple stimuli activate the pyroptotic signaling pathway and contribute to cell death and nonbacterial inflammation after MI/R. These stimuli promote the assembly of the nucleotide-binding and oligomerization-like receptor pyrin domain-containing protein 3 (NLRP3) inflammasome by activating NLRP3. The mature NLRP3 inflammasome cleaves procaspase-1 to active caspase-1, which leads to mature processing of interleukin (IL)-18, IL-1β, and gasdermin D (GSDMD) protein. That eventually results in cell lysis and generation of nonbacterial inflammation. The present review summarizes the mechanism of NLRP3 inflammasome activation after MI/R and discusses the role that NLRP3-mediated pyroptosis plays in the pathophysiology of MI/R injury and ventricular remodeling. We also discuss potential mechanisms and targeted therapy for which there is evidence supporting treatment of ischemic heart disease.
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Affiliation(s)
- Shichun Shen
- Department of Cardiology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China (mainland)
| | - Zhen Wang
- Department of Cardiology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China (mainland)
| | - Haozhong Sun
- Department of Cardiology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China (mainland)
| | - Likun Ma
- Department of Cardiology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China (mainland)
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5
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Ottolini M, Sonkusare SK. The Calcium Signaling Mechanisms in Arterial Smooth Muscle and Endothelial Cells. Compr Physiol 2021; 11:1831-1869. [PMID: 33792900 PMCID: PMC10388069 DOI: 10.1002/cphy.c200030] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
The contractile state of resistance arteries and arterioles is a crucial determinant of blood pressure and blood flow. Physiological regulation of arterial contractility requires constant communication between endothelial and smooth muscle cells. Various Ca2+ signals and Ca2+ -sensitive targets ensure dynamic control of intercellular communications in the vascular wall. The functional effect of a Ca2+ signal on arterial contractility depends on the type of Ca2+ -sensitive target engaged by that signal. Recent studies using advanced imaging methods have identified the spatiotemporal signatures of individual Ca2+ signals that control arterial and arteriolar contractility. Broadly speaking, intracellular Ca2+ is increased by ion channels and transporters on the plasma membrane and endoplasmic reticular membrane. Physiological roles for many vascular Ca2+ signals have already been confirmed, while further investigation is needed for other Ca2+ signals. This article focuses on endothelial and smooth muscle Ca2+ signaling mechanisms in resistance arteries and arterioles. We discuss the Ca2+ entry pathways at the plasma membrane, Ca2+ release signals from the intracellular stores, the functional and physiological relevance of Ca2+ signals, and their regulatory mechanisms. Finally, we describe the contribution of abnormal endothelial and smooth muscle Ca2+ signals to the pathogenesis of vascular disorders. © 2021 American Physiological Society. Compr Physiol 11:1831-1869, 2021.
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Affiliation(s)
- Matteo Ottolini
- Department of Pharmacology, University of Virginia, Charlottesville, Virginia, USA
| | - Swapnil K Sonkusare
- Department of Pharmacology, University of Virginia, Charlottesville, Virginia, USA.,Department of Molecular Physiology & Biological Physics, University of Virginia, Charlottesville, Virginia, USA.,Robert M. Berne Cardiovascular Research Center, University of Virginia, Charlottesville, Virginia, USA
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6
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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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7
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Li X, Wu Y, Gao X, Cai M, Shuai J. Wave failure at strong coupling in intracellular Ca^{2+} signaling system with clustered channels. Phys Rev E 2018; 97:012406. [PMID: 29448381 DOI: 10.1103/physreve.97.012406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Indexed: 01/04/2023]
Abstract
As an important intracellular signal, Ca^{2+} ions control diverse cellular functions. In this paper, we discuss the Ca^{2+} signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate (IP_{3}) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large Ca^{2+} diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological Ca^{2+} signaling systems.
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Affiliation(s)
- Xiang Li
- 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
| | - Yuning Wu
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Xuejuan Gao
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - Meichun Cai
- Department of Physics, Xiamen University, Xiamen 361005, China
| | - 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.,Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Xiamen University, Xiamen 361102, China
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8
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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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9
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Rückl M, Rüdiger S. Calcium waves in a grid of clustered channels with synchronous IP 3 binding and unbinding. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:108. [PMID: 27848113 DOI: 10.1140/epje/i2016-16108-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Accepted: 10/26/2016] [Indexed: 06/06/2023]
Abstract
Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca2+ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP 3) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP 3 from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP 3 stimulation. Finally the model allows for a new explanation of oscillating [IP 3], which is not based on metabolic production and degradation of IP 3.
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Affiliation(s)
- M Rückl
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany.
| | - S Rüdiger
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany
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10
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Cai X, Li X, Qi H, Wei F, Chen J, Shuai J. Comparison of gating dynamics of different IP 3R channels with immune algorithm searching for channel parameter distributions. Phys Biol 2016; 13:056005. [PMID: 27749281 DOI: 10.1088/1478-3975/13/5/056005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The gating properties of the inositol 1, 4, 5-trisphosphate (IP3) receptor (IP3R) are determined by the binding and unbinding capability of Ca2+ ions and IP3 messengers. With the patch clamp experiments, the stationary properties have been discussed for Xenopus oocyte type-1 IP3R (Oo-IP3R1), type-3 IP3R (Oo-IP3R3) and Spodoptera frugiperda IP3R (Sf-IP3R). In this paper, in order to provide insights about the relation between the observed gating characteristics and the gating parameters in different IP3Rs, we apply the immune algorithm to fit the parameters of a modified DeYoung-Keizer model. By comparing the fitting parameter distributions of three IP3Rs, we suggest that the three types of IP3Rs have the similar open sensitivity in responding to IP3. The Oo-IP3R3 channel is easy to open in responding to low Ca2+ concentration, while Sf-IP3R channel is easily inhibited in responding to high Ca2+ concentration. We also show that the IP3 binding rate is not a sensitive parameter for stationary gating dynamics for three IP3Rs, but the inhibitory Ca2+ binding/unbinding rates are sensitive parameters for gating dynamics for both Oo-IP3R1 and Oo-IP3R3 channels. Such differences may be important in generating the spatially and temporally complex Ca2+ oscillations in cells. Our study also demonstrates that the immune algorithm can be applied for model parameter searching in biological systems.
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Affiliation(s)
- Xiuhong Cai
- Department of Physics, Xiamen University, Xiamen 361000, People's Republic of China
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11
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Emergence of ion channel modal gating from independent subunit kinetics. Proc Natl Acad Sci U S A 2016; 113:E5288-97. [PMID: 27551100 DOI: 10.1073/pnas.1604090113] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca(2+) concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.
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12
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Chen Y, Qi H, Li X, Cai M, Chen X, Liu W, Shuai J. Suppressing effect of Ca^{2+} blips on puff amplitudes by inhibiting channels to prevent recovery. Phys Rev E 2016; 94:022411. [PMID: 27627339 DOI: 10.1103/physreve.94.022411] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2016] [Indexed: 11/07/2022]
Abstract
As local signals, calcium puffs arise from the concerted opening of a few nearby inositol 1,4,5-trisphospate receptor channels to release Ca^{2+} ions from the endoplasmic reticulum. Although Ca^{2+} puffs have been well studied, little is known about the modulation of cytosolic basal Ca^{2+} concentration ([Ca^{2+}]_{Basal}) on puff dynamics. In this paper we consider a puff model to study how the statistical properties of puffs are modulated by [Ca^{2+}]_{Basal}. The puff frequency and lifetime trivially increase with the increasing [Ca^{2+}]_{Basal}, but an unexpected result is that the puff amplitude and the maximum open-channel number of the puff show decreasing relationship with the increasing [Ca^{2+}]_{Basal}. The underlying dynamics is related not only to the increasing puff frequency which gives a shorter recovery time, but also to the increasing frequency of blips with only one channel open. We indicate that Ca^{2+} blips cause the channels to be inhibited and prevent their recovery during interpuff intervals, resulting in the suppressing effect on puff amplitudes. With increasing [Ca^{2+}]_{Basal}, more blips occur to cause more channels to be inhibited, leaving fewer channels available for puff events. This study shows that the blips may play relevant functions in global Ca^{2+} waves through modulating puff dynamics.
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Affiliation(s)
- Yuan Chen
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China
| | - Hong Qi
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - Xiang Li
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China
| | - Meichun Cai
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China
| | - Xingqiang Chen
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China
| | - Wen Liu
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China
| | - Jianwei Shuai
- Department of Physics, College of Physics Science and Technology, Xiamen University, Xiamen 361005, China.,State Key Laboratory of Cellular Stress Biology, Innovation Center for Cell Signaling Network, Xiamen University, Xiamen 361102, China
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13
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Weinberg SH, Smith GD. The influence of Ca²⁺ buffers on free [Ca²⁺] fluctuations and the effective volume of Ca²⁺ microdomains. Biophys J 2015; 106:2693-709. [PMID: 24940787 DOI: 10.1016/j.bpj.2014.04.045] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2013] [Revised: 04/28/2014] [Accepted: 04/30/2014] [Indexed: 02/06/2023] Open
Abstract
Intracellular calcium (Ca(2+)) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca(2+) binding proteins (Ca(2+) buffers) play an important role in regulating Ca(2+) concentration ([Ca(2+)]). Buffers typically slow [Ca(2+)] temporal dynamics and increase the effective volume of Ca(2+) domains. Because fluctuations in [Ca(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca(2+)] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca(2+) signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca(2+) influx with passive exchange of both Ca(2+) and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca(2+)] fluctuations for different buffer parameters (e.g., dissociation constant and concentration). In marked contrast to expectations based on a naive application of the principle of effective volume as employed in deterministic models of Ca(2+) signaling, we find that mobile and rapid buffers typically increase the magnitude of domain [Ca(2+)] fluctuations during periods of Ca(2+) influx, whereas stationary (immobile) Ca(2+) buffers do not. Also contrary to expectations, we find that in the absence of Ca(2+) influx, buffers influence the temporal characteristics, but not the magnitude, of [Ca(2+)] fluctuations. We derive an analytical formula describing the influence of rapid Ca(2+) buffers on [Ca(2+)] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca(2+) buffers alter the dynamics of [Ca(2+)] fluctuations in a nonintuitive manner. The finding that Ca(2+) buffers do not suppress intrinsic domain [Ca(2+)] fluctuations raises the intriguing question of whether or not [Ca(2+)] fluctuations are a physiologically significant aspect of local Ca(2+) signaling.
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Affiliation(s)
- Seth H Weinberg
- Department of Applied Science, The College of William & Mary, Williamsburg, Virginia
| | - Gregory D Smith
- Department of Applied Science, The College of William & Mary, Williamsburg, Virginia.
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14
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Frequency and relative prevalence of calcium blips and puffs in a model of small IP₃R clusters. Biophys J 2015; 106:2353-63. [PMID: 24896114 DOI: 10.1016/j.bpj.2014.04.027] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2013] [Revised: 03/07/2014] [Accepted: 04/15/2014] [Indexed: 11/22/2022] Open
Abstract
In this work, we model the local calcium release from clusters with a few inositol 1,4,5-trisphosphate receptor (IP3R) channels, focusing on the stochastic process in which an open channel either triggers other channels to open (as a puff) or fails to cause any channel to open (as a blip). We show that there are linear relations for the interevent interval (including blips and puffs) and the first event latency against the inverse cluster size. However, nonlinearity is found for the interpuff interval and the first puff latency against the inverse cluster size. Furthermore, the simulations indicate that the blip fraction among all release events and the blip frequency are increasing with larger basal [Ca(2+)], with blips in turn giving a growing contribution to basal [Ca(2+)]. This result suggests that blips are not just lapses to trigger puffs, but they may also possess a biological function to contribute to the initiation of calcium waves by a preceding increase of basal [Ca(2+)] in cells that have small IP3R clusters.
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15
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Rückl M, Parker I, Marchant JS, Nagaiah C, Johenning FW, Rüdiger S. Modulation of elementary calcium release mediates a transition from puffs to waves in an IP3R cluster model. PLoS Comput Biol 2015; 11:e1003965. [PMID: 25569772 PMCID: PMC4288706 DOI: 10.1371/journal.pcbi.1003965] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Accepted: 10/06/2014] [Indexed: 11/18/2022] Open
Abstract
The oscillating concentration of intracellular calcium is one of the most important examples for collective dynamics in cell biology. Localized releases of calcium through clusters of inositol 1,4,5-trisphosphate receptor channels constitute elementary signals called calcium puffs. Coupling by diffusing calcium leads to global releases and waves, but the exact mechanism of inter-cluster coupling and triggering of waves is unknown. To elucidate the relation of puffs and waves, we here model a cluster of IP3R channels using a gating scheme with variable non-equilibrium IP3 binding. Hybrid stochastic and deterministic simulations show that puffs are not stereotyped events of constant duration but are sensitive to stimulation strength and residual calcium. For increasing IP3 concentration, the release events become modulated at a timescale of minutes, with repetitive wave-like releases interspersed with several puffs. This modulation is consistent with experimental observations we present, including refractoriness and increase of puff frequency during the inter-wave interval. Our results suggest that waves are established by a random but time-modulated appearance of sustained release events, which have a high potential to trigger and synchronize activity throughout the cell.
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Affiliation(s)
- Martin Rückl
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany
| | - Ian Parker
- Departments of Neurobiology and Behavior, Physiology and Biophysics, University of California, Irvine, Irvine, California, United States of America
| | - Jonathan S. Marchant
- Department of Pharmacology, University of Minnesota, Minneapolis, Minnesota, United States of America
| | - Chamakuri Nagaiah
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
| | | | - Sten Rüdiger
- Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany
- * E-mail:
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16
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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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17
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Rüdiger S. Excitability in a stochastic differential equation model for calcium puffs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062717. [PMID: 25019824 DOI: 10.1103/physreve.89.062717] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2013] [Indexed: 06/03/2023]
Abstract
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
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Affiliation(s)
- S Rüdiger
- Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
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18
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Christian N, Skupin A, Morante S, Jansen K, Rossi G, Ebenhöh O. Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels. J Theor Biol 2013; 343:102-12. [PMID: 24270093 DOI: 10.1016/j.jtbi.2013.11.010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Revised: 09/03/2013] [Accepted: 11/13/2013] [Indexed: 11/19/2022]
Abstract
A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.
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Affiliation(s)
- Nils Christian
- University of Aberdeen, Department of Physics, Meston Walk, Aberdeen AB24 3UE, UK; University Luxembourg, Luxembourg Centre for Systems Biomedicine, 7, Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg.
| | - Alexander Skupin
- University Luxembourg, Luxembourg Centre for Systems Biomedicine, 7, Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, Luxembourg; Institute for Systems Biology, 401 Terry Ave N, Seattle, WA 98109, USA
| | - Silvia Morante
- Università di Roma Tor Vergata and INFN, Sezione di Roma 2, Via della Ricerca Scientifica, I-00133 Roma, Italy
| | - Karl Jansen
- NIC/DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen, Germany
| | - Giancarlo Rossi
- Università di Roma Tor Vergata and INFN, Sezione di Roma 2, Via della Ricerca Scientifica, I-00133 Roma, Italy
| | - Oliver Ebenhöh
- University of Aberdeen, Department of Physics, Meston Walk, Aberdeen AB24 3UE, UK; Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany; Cluster of Excellence on Plant Sciences (CEPLAS), Heinrich-Heine-University, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
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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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