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Gao H, Liu L, Zaikin A, Chen S. An efficient reduced-lattice model of IP 3R for probing Ca 2+ dynamics. BIOCHIMICA ET BIOPHYSICA ACTA. BIOMEMBRANES 2023; 1865:184195. [PMID: 37353068 DOI: 10.1016/j.bbamem.2023.184195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 06/15/2023] [Accepted: 06/16/2023] [Indexed: 06/25/2023]
Abstract
Numerous cellular processes are regulated by Ca2+ signals, and the endoplasmic reticulum (ER) membrane's inositol triphosphate receptor (IP3R) is critical for modulating intracellular Ca2+ dynamics. The IP3Rs are seen to be clustered in a variety of cell types. The combination of IP3Rs clustering and IP3Rs-mediated Ca2+-induced Ca2+ release results in the hierarchical organization of the Ca2+ signals, which challenges the numerical simulation given the multiple spatial and temporal scales that must be covered. The previous methods rather ignore the spatial feature of IP3Rs or fail to coordinate the conflicts between the real biological relevance and the computational cost. In this work, a general and efficient reduced-lattice model is presented for the simulation of IP3Rs-mediated multiscale Ca2+ dynamics. The model highlights biological details that make up the majority of the calcium events, including IP3Rs clustering and calcium domains, and it reduces the complexity by approximating the minor details. The model's extensibility provides fresh insights into the function of IP3Rs in producing global Ca2+ events and supports the research under more physiological circumstances. Our work contributes to a novel toolkit for modeling multiscale Ca2+ dynamics and advances knowledge of Ca2+ signals.
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Affiliation(s)
- Huayi Gao
- Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology, Wuhan, China; MoE Key Laboratory for Biomedical Photonics, School of Engineering Sciences, Huazhong University of Science and Technology, Wuhan, China
| | - Langzhou Liu
- Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology, Wuhan, China; MoE Key Laboratory for Biomedical Photonics, School of Engineering Sciences, Huazhong University of Science and Technology, Wuhan, China
| | - Alexey Zaikin
- Institute for Women's Health and Department of Mathematics, University College London, Gower St., London, WC1E 6BT, UK; Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Ave., 7 Nizhniy Novgorod, 603022, Russia; Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University, Moscow, 119019, Russia
| | - Shangbin Chen
- Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology, Wuhan, China; MoE Key Laboratory for Biomedical Photonics, School of Engineering Sciences, Huazhong University of Science and Technology, Wuhan, China.
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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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Abstract
Inositol 1,4,5-trisphosphate (IP3) plays a key role in calcium signaling. After stimulation, it diffuses from the plasma membrane where it is produced to the endoplasmic reticulum where its receptors are localized. Based on in vitro measurements, IP3 was long thought to be a global messenger characterized by a diffusion coefficient of ~ 280 μm2s-1. However, in vivo observations revealed that this value does not match with the timing of localized Ca2+ increases induced by the confined release of a non-metabolizable IP3 analog. A theoretical analysis of these data concluded that in intact cells diffusion of IP3 is strongly hindered, leading to a 30-fold reduction of the diffusion coefficient. Here, we performed a new computational analysis of the same observations using a stochastic model of Ca2+ puffs. Our simulations concluded that the value of the effective IP3 diffusion coefficient is close to 100 μm2s-1. Such moderate reduction with respect to in vitro estimations quantitatively agrees with a buffering effect by non-fully bound inactive IP3 receptors. The model also reveals that IP3 spreading is not much affected by the endoplasmic reticulum, which represents an obstacle to the free displacement of molecules, but can be significantly increased in cells displaying elongated, 1-dimensional like geometries.
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Voorsluijs V, Dawson SP, De Decker Y, Dupont G. Deterministic Limit of Intracellular Calcium Spikes. PHYSICAL REVIEW LETTERS 2019; 122:088101. [PMID: 30932600 DOI: 10.1103/physrevlett.122.088101] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 01/09/2019] [Indexed: 06/09/2023]
Abstract
In nonexcitable cells, global Ca^{2+} spikes emerge from the collective dynamics of clusters of Ca^{2+} channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin, while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.
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Affiliation(s)
- V Voorsluijs
- Nonlinear Physical Chemistry Unit and Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles, Boulevard du Triomphe, C.P. 231, B-1050 Brussels, Belgium
| | - S Ponce Dawson
- Departamento de Física, FCEN-UBA and IFIBA, UBA-CONICET, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
| | - Y De Decker
- Nonlinear Physical Chemistry Unit and Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles, Boulevard du Triomphe, C.P. 231, B-1050 Brussels, Belgium
| | - G Dupont
- Unité de Chronobiologie Théorique, Université libre de Bruxelles, Boulevard du Triomphe, C.P. 231, B-1050 Brussels, Belgium
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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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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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Lopez L, Piegari E, Sigaut L, Ponce Dawson S. Intracellular calcium signals display an avalanche-like behavior over multiple lengthscales. Front Physiol 2012; 3:350. [PMID: 22969730 PMCID: PMC3432517 DOI: 10.3389/fphys.2012.00350] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2012] [Accepted: 08/15/2012] [Indexed: 12/01/2022] Open
Abstract
Many natural phenomena display “self-organized criticality” (SOC), (Bak et al., 1987). This refers to spatially extended systems for which patterns of activity characterized by different lengthscales can occur with a probability density that follows a power law with pattern size. Differently from power laws at phase transitions, systems displaying SOC do not need the tuning of an external parameter. Here we analyze intracellular calcium (Ca2+) signals, a key component of the signaling toolkit of almost any cell type. Ca2+ signals can either be spatially restricted (local) or propagate throughout the cell (global). Different models have suggested that the transition from local to global signals is similar to that of directed percolation. Directed percolation has been associated, in turn, to the appearance of SOC. In this paper we discuss these issues within the framework of simple models of Ca2+ signal propagation. We also analyze the size distribution of local signals (“puffs”) observed in immature Xenopus Laevis oocytes. The puff amplitude distribution obtained from observed local signals is not Gaussian with a noticeable fraction of large size events. The experimental distribution of puff areas in the spatio-temporal record of the image has a long tail that is approximately log-normal. The distribution can also be fitted with a power law relationship albeit with a smaller goodness of fit. The power law behavior is encountered within a simple model that includes some coupling among individual signals for a wide range of parameter values. An analysis of the model shows that a global elevation of the Ca2+ concentration plays a major role in determining whether the puff size distribution is long-tailed or not. This suggests that Ca2+-clearing from the cytosol is key to determine whether IP3-mediated Ca2+ signals can display a SOC-like behavior or not.
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Affiliation(s)
- Lucía Lopez
- Departamento de Física FCEN-UBA and IFIBA, Ciudad Universitaria, Pabellón I Buenos Aires, Argentina
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