1
|
Adlakha N. Disturbances in system dynamics of [Formula: see text] and [Formula: see text] perturbing insulin secretion in a pancreatic [Formula: see text]-cell due to type-2 diabetes. J Bioenerg Biomembr 2023:10.1007/s10863-023-09966-7. [PMID: 37418135 DOI: 10.1007/s10863-023-09966-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 04/27/2023] [Indexed: 07/08/2023]
Abstract
The individual study of [Formula: see text] and [Formula: see text] dynamics respectively in a [Formula: see text]-cell has yielded limited information about the cell functions. But the systems biology approaches for such studies have received very little attention by the research workers in the past. In the present work, a system-dynamics model for the interdependent [Formula: see text] and [Formula: see text] signaling that controls insulin secretion in a [Formula: see text]-cell has been suggested. A two-way feedback system of [Formula: see text] and [Formula: see text] has been considered and one-way feedback between [Formula: see text] and insulin has been implemented in the model. The finite element method along with the Crank-Nicolson method have been applied for simulation. Numerical results have been used to analyze the impact of perturbations in [Formula: see text] and [Formula: see text] dynamics on insulin secretion for normal and Type-2 diabetic conditions. The results reveal that Type-2 diabetes comes from abnormalities in insulin secretion caused by the perturbation in buffers and pumps (SERCA and PMCA).
Collapse
Affiliation(s)
- Neeru Adlakha
- Department of Mathematics and Humanities, SVNIT, Surat, 395007, Gujarat, India
| |
Collapse
|
2
|
Moshkforoush A, Balachandar L, Moncion C, Montejo KA, Riera J. Unraveling ChR2-driven stochastic Ca2+ dynamics in astrocytes: A call for new interventional paradigms. PLoS Comput Biol 2021; 17:e1008648. [PMID: 33566841 PMCID: PMC7875401 DOI: 10.1371/journal.pcbi.1008648] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Accepted: 12/20/2020] [Indexed: 01/04/2023] Open
Abstract
Optogenetic targeting of astrocytes provides a robust experimental model to differentially induce Ca2+ signals in astrocytes in vivo. However, a systematic study quantifying the response of optogenetically modified astrocytes to light is yet to be performed. Here, we propose a novel stochastic model of Ca2+ dynamics in astrocytes that incorporates a light sensitive component-channelrhodopsin 2 (ChR2). Utilizing this model, we investigated the effect of different light stimulation paradigms on cells expressing select variants of ChR2 (wild type, ChETA, and ChRET/TC). Results predict that depending on paradigm specification, astrocytes might undergo drastic changes in their basal Ca2+ level and spiking probability. Furthermore, we performed a global sensitivity analysis to assess the effect of variation in parameters pertinent to the shape of the ChR2 photocurrent on astrocytic Ca2+ dynamics. Results suggest that directing variants towards the first open state of the ChR2 photocycle (o1) enhances spiking activity in astrocytes during optical stimulation. Evaluation of the effect of Ca2+ buffering and coupling coefficient in a network of ChR2-expressing astrocytes demonstrated basal level elevations in the stimulated region and propagation of calcium activity to unstimulated cells. Buffering reduced the diffusion range of Ca2+ within the network, thereby limiting propagation and influencing the activity of astrocytes. Collectively, the framework presented in this study provides valuable information for the selection of light stimulation paradigms that elicit desired astrocytic activity using existing ChR2 constructs, as well as aids in the engineering of future application-oriented optogenetic variants.
Collapse
Affiliation(s)
- Arash Moshkforoush
- Department of Biomedical Engineering, Florida International University, Miami, Florida, United States of America
| | - Lakshmini Balachandar
- Department of Biomedical Engineering, Florida International University, Miami, Florida, United States of America
| | - Carolina Moncion
- Department of Biomedical Engineering, Florida International University, Miami, Florida, United States of America
| | - Karla A. Montejo
- Department of Biomedical Engineering, Florida International University, Miami, Florida, United States of America
- Department of Neurologic Surgery, Mayo Clinic, Rochester, Minnesota, United States of America
| | - Jorge Riera
- Department of Biomedical Engineering, Florida International University, Miami, Florida, United States of America
- * E-mail:
| |
Collapse
|
3
|
Guse AH, Gil Montoya DC, Diercks BP. Mechanisms and functions of calcium microdomains produced by ORAI channels, d-myo-inositol 1,4,5-trisphosphate receptors, or ryanodine receptors. Pharmacol Ther 2021; 223:107804. [PMID: 33465399 DOI: 10.1016/j.pharmthera.2021.107804] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 01/04/2021] [Indexed: 12/24/2022]
Abstract
With the discovery of local Ca2+ signals in the 1990s the concept of 'elementary Ca2+ signals' and 'fundamental Ca2+ signals' was developed. While 'elementary Ca2+signals' relate to optical signals gained by activity of small clusters of Ca2+channels, 'fundamental signals' describe such optical signals that arise from opening of single Ca2+channels. In this review, we discuss (i) concepts of local Ca2+ signals and Ca2+ microdomains, (ii) molecular mechanisms underlying Ca2+ microdomains, (iii) functions of Ca2+ microdomains, and (iv) mathematical modelling of Ca2+ microdomains. We focus on Ca2+ microdomains produced by ORAI channels, D-myo-inositol 1,4,5-trisphosphate receptors, or ryanodine receptors. In summary, research on local Ca2+ signals in different cell models aims to better understand how cells use the Ca2+ toolkit to produce Ca2+ microdomains as relevant signals for specific cellular responses, but also how local Ca2+ signals as building blocks merge into global Ca2+ signaling.
Collapse
Affiliation(s)
- Andreas H Guse
- The Calcium Signalling Group, Dept of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Martinistrasse 52, D-20246 Hamburg, Germany.
| | - Diana C Gil Montoya
- The Calcium Signalling Group, Dept of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Martinistrasse 52, D-20246 Hamburg, Germany
| | - Björn-Philipp Diercks
- The Calcium Signalling Group, Dept of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Martinistrasse 52, D-20246 Hamburg, Germany
| |
Collapse
|
4
|
Kaimachnikov NP, Kotova PD, Kochkina EN, Rogachevskaja OA, Khokhlov AA, Bystrova MF, Kolesnikov SS. Modeling of Ca2+ transients initiated by GPCR agonists in mesenchymal stromal cells. BBA ADVANCES 2021; 1:100012. [PMID: 37082025 PMCID: PMC10074909 DOI: 10.1016/j.bbadva.2021.100012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Revised: 04/05/2021] [Accepted: 04/11/2021] [Indexed: 10/21/2022] Open
Abstract
The integrative study that included experimentation and mathematical modeling was carried out to analyze dynamic aspects of transient Ca2+ signaling induced by brief pulses of GPCR agonists in mesenchymal stromal cells from the human adipose tissue (AD-MSCs). The experimental findings argued for IP3/Ca2+-regulated Ca2+ release via IP3 receptors (IP3Rs) as a key mechanism mediating agonist-dependent Ca2+ transients. The consistent signaling circuit was proposed to formalize coupling of agonist binding to Ca2+ mobilization for mathematical modeling. The model properly simulated the basic phenomenology of agonist transduction in AD-MSCs, which mostly produced single Ca2+ spikes upon brief stimulation. The spike-like responses were almost invariantly shaped at different agonist doses above a threshold, while response lag markedly decreased with stimulus strength. In AD-MSCs, agonists and IP3 uncaging elicited similar Ca2+ transients but IP3 pulses released Ca2+ without pronounced delay. This suggested that IP3 production was rate-limiting in agonist transduction. In a subpopulation of AD-MSCs, brief agonist pulses elicited Ca2+ bursts crowned by damped oscillations. With properly adjusted parameters of IP3R inhibition by cytosolic Ca2+, the model reproduced such oscillatory Ca2+ responses as well. GEM-GECO1 and R-CEPIA1er, the genetically encoded sensors of cytosolic and reticular Ca2+, respectively, were co-expressed in HEK-293 cells that also responded to agonists in an "all-or-nothing" manner. The experimentally observed Ca2+ signals triggered by ACh in both compartments were properly simulated with the suggested signaling circuit. Thus, the performed modeling of the transduction process provides sufficient theoretical basis for deeper interpretation of experimental findings on agonist-induced Ca2+ signaling in AD-MSCs.
Collapse
|
5
|
Dunster JL, Panteleev MA, Gibbins JM, Sveshnikova AN. Mathematical Techniques for Understanding Platelet Regulation and the Development of New Pharmacological Approaches. Methods Mol Biol 2018; 1812:255-279. [PMID: 30171583 DOI: 10.1007/978-1-4939-8585-2_15] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Mathematical and computational modeling is currently in the process of becoming an accepted tool in the arsenal of methods utilized for the investigation of complex biological systems. For some problems in the field, like cellular metabolic regulation, neural impulse propagation, or cell cycle, progress is already unthinkable without use of such methods. Mathematical models of platelet signaling, function, and metabolism during the last years have not only been steadily increasing in their number, but have also been providing more in-depth insights, generating hypotheses, and allowing predictions to be made leading to new experimental designs and data. Here we describe the basic approaches to platelet mathematical model development and validation, highlighting the challenges involved. We then review the current theoretical models in the literature and how these are being utilized to increase our understanding of these complex cells.
Collapse
Affiliation(s)
- Joanna L Dunster
- Institute for Cardiovascular and Metabolic Research, School of Biological Sciences, University of Reading, Reading, UK.
| | - Mikhail A Panteleev
- Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia
- National Scientific and Practical Centre of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, Moscow, Russia
- Faculty of Biological and Medical Physics, Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
| | - Jonathan M Gibbins
- Institute for Cardiovascular and Metabolic Research, School of Biological Sciences, University of Reading, Reading, UK
| | - Anastacia N Sveshnikova
- Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
- Center for Theoretical Problems of Physicochemical Pharmacology, Russian Academy of Sciences, Moscow, Russia
- National Scientific and Practical Centre of Pediatric Hematology, Oncology and Immunology Named After Dmitry Rogachev, Moscow, Russia
| |
Collapse
|
6
|
Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations. PLoS Comput Biol 2016; 12:e1005298. [PMID: 28027301 PMCID: PMC5226835 DOI: 10.1371/journal.pcbi.1005298] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Revised: 01/11/2017] [Accepted: 12/07/2016] [Indexed: 12/20/2022] Open
Abstract
Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models. Rhythmic behavior is omnipresent in biology and has many crucial functions. In cells the activation levels and abundances of signaling molecules such as NF-κB, p53, EGFR or calcium repeatedly increase and decrease in response to stimuli. Such a dynamic behavior can also be observed monitoring the concentrations of mRNAs and proteins in the circadian clock and the cell cycle. Period and amplitude which are the time span between peaks and the peak height, respectively, as well as their variabilities are important features of oscillations. The circadian period is very stable allowing for proper time keeping, whereas in calcium signaling the period is very variable encoding different stimulation strengths. Our goal is to examine the origin of differences in sensitivities of periods and amplitudes using a computational approach. We use prototype oscillators and demonstrate that they can be used to derive general principles that explain the degree of robustness in period and amplitude for a set of commonly used models of cellular oscillators. Our findings imply that the robustness of oscillating systems can be influenced by feedback type and kinetic properties to which special attention should be paid when designing mathematical models of cellular rhythms.
Collapse
|
7
|
Liang J, Kulasiri D, Samarasinghe S. Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling. Biosystems 2015; 134:1-15. [PMID: 25998697 DOI: 10.1016/j.biosystems.2015.05.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2015] [Revised: 05/12/2015] [Accepted: 05/12/2015] [Indexed: 12/12/2022]
Abstract
Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.
Collapse
Affiliation(s)
- Jingyi Liang
- Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand; Department of Molecular Biosciences, Lincoln University, Christchurch, New Zealand
| | - Don Kulasiri
- Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand; Department of Molecular Biosciences, Lincoln University, Christchurch, New Zealand.
| | - Sandhya Samarasinghe
- Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand; Department of Informatics and Enabling Technologies, Lincoln University, Christchurch, New Zealand
| |
Collapse
|
8
|
Pecze L, Schwaller B. Characterization and modeling of Ca2+ oscillations in mouse primary mesothelial cells. BIOCHIMICA ET BIOPHYSICA ACTA-MOLECULAR CELL RESEARCH 2015; 1853:632-45. [DOI: 10.1016/j.bbamcr.2014.12.025] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Revised: 12/16/2014] [Accepted: 12/19/2014] [Indexed: 10/24/2022]
|
9
|
Sveshnikova AN, Ataullakhanov FI, Panteleev MA. Compartmentalized calcium signaling triggers subpopulation formation upon platelet activation through PAR1. MOLECULAR BIOSYSTEMS 2015; 11:1052-60. [DOI: 10.1039/c4mb00667d] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
A computational model of PAR1-stimulated platelet calcium signaling is developed to analyze the formation of platelet subpopulations. This occurs via a mitochondria-dependent decision-making mechanism. This is a stochastic phenomenon caused by a small number of PARs.
Collapse
Affiliation(s)
- Anastasia N. Sveshnikova
- Physics Department
- Moscow State University
- Moscow
- Russia
- Center for Theoretical Problems of Physicochemical Pharmacology
| | - Fazoil I. Ataullakhanov
- Physics Department
- Moscow State University
- Moscow
- Russia
- Center for Theoretical Problems of Physicochemical Pharmacology
| | - Mikhail A. Panteleev
- Physics Department
- Moscow State University
- Moscow
- Russia
- Center for Theoretical Problems of Physicochemical Pharmacology
| |
Collapse
|
10
|
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.
Collapse
|
11
|
Manhas N, Sneyd J, Pardasani KR. Modelling the transition from simple to complex Ca²⁺ oscillations in pancreatic acinar cells. J Biosci 2014; 39:463-84. [PMID: 24845510 DOI: 10.1007/s12038-014-9430-3] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic acinar cells. This model is based on calcium-induced calcium release via inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) and includes calcium modulation of inositol (1,4,5) trisphosphate (IP3) levels through feedback regulation of degradation and production. In our model, the apical and the basal regions are separated by a region containing mitochondria, which is capable of restricting Ca2+ responses to the apical region. We were able to reproduce the observed oscillatory patterns, from baseline spikes to sinusoidal oscillations. The model predicts that calcium-dependent production and degradation of IP3 is a key mechanism for complex calcium oscillations in pancreatic acinar cells. A partial bifurcation analysis is performed which explores the dynamic behaviour of the model in both apical and basal regions.
Collapse
Affiliation(s)
- Neeraj Manhas
- Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462 051, India,
| | | | | |
Collapse
|
12
|
Thul R. Translating intracellular calcium signaling into models. Cold Spring Harb Protoc 2014; 2014:2014/5/pdb.top066266. [PMID: 24786496 DOI: 10.1101/pdb.top066266] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca²⁺ signaling toolbox and determines the contribution of local Ca²⁺ release to global Ca²⁺ patterns, which at the moment cannot be resolved experimentally.
Collapse
Affiliation(s)
- Rüdiger Thul
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
13
|
Thul R. Exploring oscillations in a point model of the intracellular Ca²⁺ concentration. Cold Spring Harb Protoc 2014; 2014:2014/5/pdb.prot073221. [PMID: 24786498 DOI: 10.1101/pdb.prot073221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
Intracellular calcium (Ca²⁺) oscillations are a key signaling mechanism in most cell types. A prominent approach to modeling intracellular Ca²⁺ oscillations is the use of ordinary differential equations (ODEs), which treat the intracellular Ca²⁺ concentration as spatially homogenous. Although ODEs cannot account for the interaction of Ca²⁺ microdomains to form cell-wide Ca²⁺ patterns, modelers still choose ODEs because (a) the study of ODEs is computationally cheap, and a large body of techniques is available to investigate ODEs in great detail, or (b) sufficient experimental data are not available to develop a spatially extended model. Irrespective of the reason, analyzing ODEs is a key instrument in the toolbox of modelers. In this protocol, we look at a well-known model for Ca²⁺ oscillations, the De Young-Keizer model, along with the Li-Rinzel approximation of the De Young-Keizer model. The main emphasis of this protocol is the use of the open source software package XPPAUT to numerically study ODEs. The knowledge gained here can be directly transferred to other ODE systems and therefore may serve as a template for future studies.
Collapse
Affiliation(s)
- Rüdiger Thul
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| |
Collapse
|
14
|
Liu F, Heiner M. Multiscale modelling of coupled Ca2+ channels using coloured stochastic Petri nets. IET Syst Biol 2013; 7:106-13. [PMID: 23919953 DOI: 10.1049/iet-syb.2012.0017] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Stochastic modelling of coupled Ca2+ channels is a challenge, especially when the coupling of the channels, as determined by their spatial arrangement relative to each other, has to be considered at multiple spatial scales. In this study, the authors address this problem using coloured stochastic Petri nets (SPNc) as high-level description to generate continuous-time Markov chains. The authors develop several models with increasing complexity. They first apply SPNc to model single clusters of coupled Ca2+ channels arranged in a regular or irregular lattice, where they describe how to represent the geometrical arrangement of Ca2+ channels relative to each other using colours. They then apply this modelling idea to construct more complex models by modelling spatially arranged clusters of channels. The authors' models can be easily reproduced and adapted to different scenarios.
Collapse
Affiliation(s)
- Fei Liu
- Harbin Institute of Technology, Harbin, People's Republic of China.
| | | |
Collapse
|
15
|
Schmeitz C, Hernandez-Vargas EA, Fliegert R, Guse AH, Meyer-Hermann M. A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties. Front Immunol 2013; 4:277. [PMID: 24065966 PMCID: PMC3776162 DOI: 10.3389/fimmu.2013.00277] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2013] [Accepted: 08/29/2013] [Indexed: 11/25/2022] Open
Abstract
Fate decision processes of T lymphocytes are crucial for health and disease. Whether a T lymphocyte is activated, divides, gets anergic, or initiates apoptosis depends on extracellular triggers and intracellular signaling. Free cytosolic calcium dynamics plays an important role in this context. The relative contributions of store-derived calcium entry and calcium entry from extracellular space to T lymphocyte activation are still a matter of debate. Here we develop a quantitative mathematical model of T lymphocyte calcium dynamics in order to establish a tool which allows to disentangle cause-effect relationships between ion fluxes and observed calcium time courses. The model is based on single transmembrane protein characteristics which have been determined in independent experiments. This reduces the number of unknown parameters in the model to a minimum and ensures the predictive power of the model. Simulation results are subsequently used for an analysis of whole cell calcium dynamics measured under various experimental conditions. The model accounts for a variety of these conditions, which supports the suitability of the modeling approach. The simulation results suggest a model in which calcium dynamics dominantly relies on the opening of channels in calcium stores while calcium entry through calcium-release activated channels (CRAC) is more associated with the maintenance of the T lymphocyte calcium levels and prevents the cell from calcium depletion. Our findings indicate that CRAC guarantees a long-term stable calcium level which is required for cell survival and sustained calcium enhancement.
Collapse
Affiliation(s)
- Christine Schmeitz
- Department of Systems Immunology, Helmholtz Centre for Infection Research, Braunschweig, Germany
| | | | - Ralf Fliegert
- The Calcium Signalling Group, Department of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Andreas H. Guse
- The Calcium Signalling Group, Department of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Michael Meyer-Hermann
- Department of Systems Immunology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Department of Life Sciences, Technische Universität Braunschweig, Braunschweig, Germany
| |
Collapse
|
16
|
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.
Collapse
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
| |
Collapse
|
17
|
Comparison of models for IP3 receptor kinetics using stochastic simulations. PLoS One 2013; 8:e59618. [PMID: 23630568 PMCID: PMC3629942 DOI: 10.1371/journal.pone.0059618] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2012] [Accepted: 02/15/2013] [Indexed: 12/07/2022] Open
Abstract
Inositol 1,4,5-trisphosphate receptor (IP3R) is a ubiquitous intracellular calcium (Ca2+) channel which has a major role in controlling Ca2+ levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP3R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP3R when modeling local Ca2+ transients in dendrites or overall Ca2+ dynamics in large neuronal models. The goal of this study was to evaluate existing IP3R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson etal., 2003; Fraiman and Dawson, 2004; Doi etal., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP3R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP3R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP3R with different concentrations of Ca2+ and IP3 should be more carefully addressed when new models for IP3R are developed.
Collapse
|
18
|
Moenke G, Falcke M, Thurley K. Hierarchic stochastic modelling applied to intracellular Ca(2+) signals. PLoS One 2012; 7:e51178. [PMID: 23300536 PMCID: PMC3531454 DOI: 10.1371/journal.pone.0051178] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Accepted: 10/30/2012] [Indexed: 11/19/2022] Open
Abstract
Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011) which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to Ca(2+) signalling. Ca(2+) is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular Ca(2+) release events (puffs). We derive analytical expressions for a mechanistic Ca(2+) model, based on recent data from live cell imaging, and calculate Ca(2+) spike statistics in dependence on cellular parameters like stimulus strength or number of Ca(2+) channels. The new approach substantiates a generic Ca(2+) model, which is a very convenient way to simulate Ca(2+) spike sequences with correct spiking statistics.
Collapse
Affiliation(s)
- Gregor Moenke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Martin Falcke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Keven Thurley
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin, Berlin, Germany
| |
Collapse
|
19
|
Siekmann I, Wagner LE, Yule D, Crampin EJ, Sneyd J. A kinetic model for type I and II IP3R accounting for mode changes. Biophys J 2012; 103:658-68. [PMID: 22947927 PMCID: PMC3443778 DOI: 10.1016/j.bpj.2012.07.016] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2012] [Revised: 07/11/2012] [Accepted: 07/13/2012] [Indexed: 10/28/2022] Open
Abstract
Based upon an extensive single-channel data set, a Markov model for types I and II inositol trisphosphate receptors (IP(3)R) is developed. The model aims to represent accurately the kinetics of both receptor types of IP(3)R depending on the concentrations of inositol trisphosphate (IP(3)), adenosine trisphosphate (ATP), and intracellular calcium (Ca(2+)). In particular, the model takes into account that for some combinations of ligands the IP(3)R switches between extended periods of inactivity alternating with intervals of bursting activity (mode changes). In a first step, the inactive and active modes are modeled separately. It is found that, within modes, both receptor types are ligand-independent. In a second step, the submodels are connected by transition rates. Ligand-dependent regulation of the channel activity is achieved by modulating these transitions between active and inactive modes. As a result, a compact representation of the IP(3)R is obtained that accurately captures stochastic single-channel dynamics including mode changes in a model with six states and 10 rate constants, only two of which are ligand-dependent.
Collapse
Affiliation(s)
- Ivo Siekmann
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand.
| | | | | | | | | |
Collapse
|
20
|
Tewari SG, Majumdar KK. A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity. J Biol Phys 2012; 38:465-96. [PMID: 23729909 DOI: 10.1007/s10867-012-9267-7] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2012] [Accepted: 03/12/2012] [Indexed: 01/09/2023] Open
Abstract
In this paper, we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca(2 + ) dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been modeled. As an application, this model clearly shows synaptic potentiation in the hippocampal region, i.e., astrocyte Ca(2 + ) mediates synaptic plasticity, which is in conformity with the majority of the recent findings (Perea and Araque (Science 317, 1083-1086, 2007); Henneberger et al. (Nature 463, 232-236, 2010); Navarrete et al. (PLoS Biol. 10, e1001259, 2012)).
Collapse
Affiliation(s)
- Shivendra G Tewari
- Systems Science and Informatics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore, 560059 India ; Biotechnology & Bioengineering Center and Department of Physiology, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226 USA
| | | |
Collapse
|
21
|
A mathematical model for astrocytes mediated LTP at single hippocampal synapses. J Comput Neurosci 2012; 33:341-70. [PMID: 22454034 DOI: 10.1007/s10827-012-0389-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2011] [Revised: 02/21/2012] [Accepted: 02/22/2012] [Indexed: 02/07/2023]
Abstract
Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea and Araque (Science 317:1083-1086, 2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D-Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully imitates the experimental findings of Perea and Araque (Science 317:1083-1086, 2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.
Collapse
|
22
|
Fundamental properties of Ca2+ signals. Biochim Biophys Acta Gen Subj 2011; 1820:1185-94. [PMID: 22040723 DOI: 10.1016/j.bbagen.2011.10.007] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2011] [Revised: 10/16/2011] [Accepted: 10/17/2011] [Indexed: 11/21/2022]
Abstract
BACKGROUND Ca2+ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca2+ concentration. Recent investigations changed basic ideas on the dynamic character of Ca2+ signals and challenge traditional ideas on information transmission. SCOPE OF REVIEW We present recent findings on key characteristics of the cytosolic Ca2+ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca2+ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca2+ concentration to ideas about information transmission by stochastic signals. MAJOR CONCLUSIONS We demonstrate the importance of the hierarchal arrangement of Ca2+ release sites on the emergence of cellular Ca2+ spikes. Stochastic Ca2+ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties. GENERAL SIGNIFICANCE Robust and reliable signal transduction pathways that entail Ca2+ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2+ dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling.
Collapse
|
23
|
Dupont G, Combettes L, Bird GS, Putney JW. Calcium oscillations. Cold Spring Harb Perspect Biol 2011; 3:cshperspect.a004226. [PMID: 21421924 DOI: 10.1101/cshperspect.a004226] [Citation(s) in RCA: 185] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors.
Collapse
Affiliation(s)
- Geneviève Dupont
- Unité de Chronobiologie Théorique, Université Libre de Bruxelles, Faculté des Sciences, Brussels, Belgium
| | | | | | | |
Collapse
|
24
|
Oster AM, Thomas B, Terman D, Fall CP. The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model. J Theor Biol 2010; 273:216-31. [PMID: 21195090 DOI: 10.1016/j.jtbi.2010.12.023] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2010] [Revised: 10/31/2010] [Accepted: 12/13/2010] [Indexed: 11/30/2022]
Abstract
Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.
Collapse
Affiliation(s)
- Andrew M Oster
- Group for Neural Theory, Département d'Études Cognitives, École Normale Supérieure, Paris, France
| | | | | | | |
Collapse
|
25
|
Vais H, Foskett JK, Daniel Mak DO. Unitary Ca(2+) current through recombinant type 3 InsP(3) receptor channels under physiological ionic conditions. J Gen Physiol 2010; 136:687-700. [PMID: 21078871 PMCID: PMC2995152 DOI: 10.1085/jgp.201010513] [Citation(s) in RCA: 38] [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: 08/09/2010] [Accepted: 10/21/2010] [Indexed: 11/20/2022] Open
Abstract
The ubiquitous inositol 1,4,5-trisphosphate (InsP(3)) receptor (InsP(3)R) channel, localized primarily in the endoplasmic reticulum (ER) membrane, releases Ca(2+) into the cytoplasm upon binding InsP(3), generating and modulating intracellular Ca(2+) signals that regulate numerous physiological processes. Together with the number of channels activated and the open probability of the active channels, the size of the unitary Ca(2+) current (i(Ca)) passing through an open InsP(3)R channel determines the amount of Ca(2+) released from the ER store, and thus the amplitude and the spatial and temporal nature of Ca(2+) signals generated in response to extracellular stimuli. Despite its significance, i(Ca) for InsP(3)R channels in physiological ionic conditions has not been directly measured. Here, we report the first measurement of i(Ca) through an InsP(3)R channel in its native membrane environment under physiological ionic conditions. Nuclear patch clamp electrophysiology with rapid perfusion solution exchanges was used to study the conductance properties of recombinant homotetrameric rat type 3 InsP(3)R channels. Within physiological ranges of free Ca(2+) concentrations in the ER lumen ([Ca(2+)](ER)), free cytoplasmic [Ca(2+)] ([Ca(2+)](i)), and symmetric free [Mg(2+)] ([Mg(2+)](f)), the i(Ca)-[Ca(2+)](ER) relation was linear, with no detectable dependence on [Mg(2+)](f). i(Ca) was 0.15 +/- 0.01 pA for a filled ER store with 500 microM [Ca(2+)](ER). The i(Ca)-[Ca(2+)](ER) relation suggests that Ca(2+) released by an InsP(3)R channel raises [Ca(2+)](i) near the open channel to approximately 13-70 microM, depending on [Ca(2+)](ER). These measurements have implications for the activities of nearby InsP(3)-liganded InsP(3)R channels, and they confirm that Ca(2+) released by an open InsP(3)R channel is sufficient to activate neighboring channels at appropriate distances away, promoting Ca(2+)-induced Ca(2+) release.
Collapse
Affiliation(s)
- Horia Vais
- Department of Physiology and Department of Cell and Developmental Biology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104
| | - J. Kevin Foskett
- Department of Physiology and Department of Cell and Developmental Biology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104
| | - Don-On Daniel Mak
- Department of Physiology and Department of Cell and Developmental Biology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104
| |
Collapse
|
26
|
Rüdiger S, Nagaiah C, Warnecke G, Shuai JW. Calcium domains around single and clustered IP3 receptors and their modulation by buffers. Biophys J 2010; 99:3-12. [PMID: 20655827 DOI: 10.1016/j.bpj.2010.02.059] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2009] [Revised: 02/12/2010] [Accepted: 02/26/2010] [Indexed: 02/04/2023] Open
Abstract
We study Ca(2+) release through single and clustered IP(3) receptor channels on the ER membrane under presence of buffer proteins. Our computational scheme couples reaction-diffusion equations and a Markovian channel model and allows our investigating the effects of buffer proteins on local calcium concentrations and channel gating. We find transient and stationary elevations of calcium concentrations around active channels and show how they determine release amplitude. Transient calcium domains occur after closing of isolated channels and constitute an important part of the channel's feedback. They cause repeated openings (bursts) and mediate increased release due to Ca(2+) buffering by immobile proteins. Stationary domains occur during prolonged activity of clustered channels, where the spatial proximity of IP(3)Rs produces a distinct [Ca(2+)] scale (0.5-10 microM), which is smaller than channel pore concentrations (>100 microM) but larger than transient levels. While immobile buffer affects transient levels only, mobile buffers in general reduce both transient and stationary domains, giving rise to Ca(2+) evacuation and biphasic modulation of release amplitude. Our findings explain recent experiments in oocytes and provide a general framework for the understanding of calcium signals.
Collapse
Affiliation(s)
- S Rüdiger
- Institute of Physics, Humboldt-Universität zu Berlin, Berlin, Germany
| | | | | | | |
Collapse
|
27
|
Foskett JK, Daniel Mak DO. Regulation of IP(3)R Channel Gating by Ca(2+) and Ca(2+) Binding Proteins. CURRENT TOPICS IN MEMBRANES 2010; 66:235-72. [PMID: 22353483 PMCID: PMC6707373 DOI: 10.1016/s1063-5823(10)66011-5] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- J Kevin Foskett
- Department of Physiology, University of Pennsylvania, Philadelphia, Pennsylvania, USA; Department of Cell and Developmental Biology, University of Pennsylvania, Philadelphia, Pennsylvania, USA
| | | |
Collapse
|
28
|
Slepchenko BM, Loew LM. Use of virtual cell in studies of cellular dynamics. INTERNATIONAL REVIEW OF CELL AND MOLECULAR BIOLOGY 2010; 283:1-56. [PMID: 20801417 DOI: 10.1016/s1937-6448(10)83001-1] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems. In this chapter, we discuss modeling capabilities of VCell and demonstrate representative examples of the models published by the VCell users.
Collapse
Affiliation(s)
- Boris M Slepchenko
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, USA
| | | |
Collapse
|
29
|
Gin E, Wagner LE, Yule DI, Sneyd J. Inositol trisphosphate receptor and ion channel models based on single-channel data. CHAOS (WOODBURY, N.Y.) 2009; 19:037104. [PMID: 19792029 PMCID: PMC5848693 DOI: 10.1063/1.3184540] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2009] [Accepted: 07/01/2009] [Indexed: 05/28/2023]
Abstract
The inositol trisphosphate receptor (IPR) plays an important role in controlling the dynamics of intracellular Ca(2+). Single-channel patch-clamp recordings are a typical way to study these receptors as well as other ion channels. Methods for analyzing and using this type of data have been developed to fit Markov models of the receptor. The usual method of parameter fitting is based on maximum-likelihood techniques. However, Bayesian inference and Markov chain Monte Carlo techniques are becoming more popular. We describe the application of the Bayesian methods to real experimental single-channel data in three ion channels: the ryanodine receptor, the K(+) channel, and the IPR. One of the main aims of all three studies was that of model selection with different approaches taken. We also discuss the modeling implications for single-channel data that display different levels of channel activity within one recording.
Collapse
Affiliation(s)
- Elan Gin
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | | | | | | |
Collapse
|
30
|
Shuai JW, Yang DP, Pearson JE, Rüdiger S. An investigation of models of the IP3R channel in Xenopus oocyte. CHAOS (WOODBURY, N.Y.) 2009; 19:037105. [PMID: 19792030 PMCID: PMC2771705 DOI: 10.1063/1.3156402] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2009] [Accepted: 05/29/2009] [Indexed: 05/28/2023]
Abstract
We consider different models of inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) channels in order to fit nuclear membrane patch clamp data of the stationary open probability, mean open time, and mean close time of channels in the Xenopus oocyte. Our results indicate that rather than to treat the tetrameric IP(3)R as four independent and identical subunits, one should assume sequential binding-unbinding processes of Ca(2+) ions and IP(3) messengers. Our simulations also favor the assumption that a channel opens through a conformational transition from a close state to an active state.
Collapse
Affiliation(s)
- J W Shuai
- Department of Physics, Xiamen University, Xiamen, China.
| | | | | | | |
Collapse
|
31
|
Gin E, Falcke M, Wagner LE, Yule DI, Sneyd J. A kinetic model of the inositol trisphosphate receptor based on single-channel data. Biophys J 2009; 96:4053-62. [PMID: 19450477 DOI: 10.1016/j.bpj.2008.12.3964] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2008] [Revised: 12/14/2008] [Accepted: 12/16/2008] [Indexed: 11/28/2022] Open
Abstract
In many cell types, the inositol trisphosphate receptor is one of the important components controlling intracellular calcium dynamics, and an understanding of this receptor is necessary for an understanding of calcium oscillations and waves. Based on single-channel data from the type-I inositol trisphosphate receptor, and using a Markov chain Monte Carlo approach, we show that the most complex time-dependent model that can be unambiguously determined from steady-state data is one with three closed states and one open state, and we determine how the rate constants depend on calcium. Because the transitions between these states are complex functions of calcium concentration, each model state must correspond to a group of physical states. We fit two different topologies and find that both models predict that the main effect of [Ca(2+)] is to modulate the probability that the receptor is in a state that is able to open, rather than to modulate the transition rate to the open state.
Collapse
Affiliation(s)
- Elan Gin
- Department of Mathematics, The University of Auckland, Auckland, New Zealand
| | | | | | | | | |
Collapse
|
32
|
Higgins ER, Schmidle H, Falcke M. Waiting time distributions for clusters of receptors. J Theor Biol 2009; 259:338-49. [DOI: 10.1016/j.jtbi.2009.03.018] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2008] [Revised: 02/02/2009] [Accepted: 03/11/2009] [Indexed: 10/20/2022]
|
33
|
Taufiq-Ur-Rahman, Skupin A, Falcke M, Taylor CW. Clustering of InsP3 receptors by InsP3 retunes their regulation by InsP3 and Ca2+. Nature 2009; 458:655-9. [PMID: 19348050 PMCID: PMC2702691 DOI: 10.1038/nature07763] [Citation(s) in RCA: 147] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
The versatility of Ca2+ signals derives from their spatio-temporal organization. For Ca2+ signals initiated by inositol-1,4,5-trisphosphate (InsP3), this requires local interactions between InsP3 receptors (InsP3Rs) mediated by their rapid stimulation and slower inhibition\ by cytosolic Ca2+. This allows hierarchical recruitment of Ca2+ release events as the InsP3 concentration increases. Single InsP3Rs respond first, then clustered InsP3Rs open together giving a local 'Ca2+ puff', and as puffs become more frequent they ignite regenerative Ca2+ waves. Using nuclear patch-clamp recording, here we demonstrate that InsP3Rs are initially randomly distributed with an estimated separation of 1 m. Low concentrations of InsP3 cause InsP3Rs to aggregate rapidly and reversibly into small clusters of about four closely associated InsP3Rs. At resting cytosolic [Ca2+], clustered InsP3Rs open independently, but with lower open probability, shorter open time, and less InsP3 sensitivity than lone InsP3Rs. Increasing cytosolic [Ca2+] reverses the inhibition caused by clustering, InsP3R gating becomes coupled, and the duration of multiple openings is prolonged. Clustering both exposes InsP3Rs to local Ca2+ rises and increases the effects of Ca2+. Dynamic regulation of clustering by InsP3 retunes InsP3R sensitivity to InsP3 and Ca2+, facilitating hierarchical recruitment of the elementary events that underlie all InsP3-evoked Ca2+ signals.
Collapse
Affiliation(s)
- Taufiq-Ur-Rahman
- Department of Pharmacology, Tennis Court Road, Cambridge CB2 1PD, UK
| | | | | | | |
Collapse
|
34
|
Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors. J Theor Biol 2008; 257:460-74. [PMID: 19168073 DOI: 10.1016/j.jtbi.2008.12.020] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2008] [Revised: 12/15/2008] [Accepted: 12/15/2008] [Indexed: 11/21/2022]
Abstract
In many cell types, the inositol trisphosphate receptor (IPR) is one of the important components that control intracellular calcium dynamics, and an understanding of this receptor (which is also a calcium channel) is necessary for an understanding of calcium oscillations and waves. Recent advances in experimental techniques now allow for the measurement of single-channel activity of the IPR in conditions similar to its native environment, and these data can be used to determine the rate constants in Markov models of the IPR. We illustrate a parameter estimation method based on Markov chain Monte Carlo, which can be used to fit directly to single-channel data, and determining, as an intrinsic part of the fit, the times at which the IPR is opening and closing. We show, using simulated data, the most complex Markov model that can be unambiguously determined from steady-state data and show that non-steady-state data is required to determine more complex models.
Collapse
|
35
|
Shi X, Zheng Y, Liu Z, Yang W. A model of calcium signaling and degranulation dynamics induced by laser irradiation in mast cells. Sci Bull (Beijing) 2008. [DOI: 10.1007/s11434-008-0255-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
|
36
|
Modeling Ca2+ feedback on a single inositol 1,4,5-trisphosphate receptor and its modulation by Ca2+ buffers. Biophys J 2008; 95:3738-52. [PMID: 18641077 DOI: 10.1529/biophysj.108.137182] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The inositol 1,4,5-trisphosphate receptor/channel (IP(3)R) is a major regulator of intracellular Ca(2+) signaling, and liberates Ca(2+) ions from the endoplasmic reticulum in response to binding at cytosolic sites for both IP(3) and Ca(2+). Although the steady-state gating properties of the IP(3)R have been extensively studied and modeled under conditions of fixed [IP(3)] and [Ca(2+)], little is known about how Ca(2+) flux through a channel may modulate the gating of that same channel by feedback onto activating and inhibitory Ca(2+) binding sites. We thus simulated the dynamics of Ca(2+) self-feedback on monomeric and tetrameric IP(3)R models. A major conclusion is that self-activation depends crucially on stationary cytosolic Ca(2+) buffers that slow the collapse of the local [Ca(2+)] microdomain after closure. This promotes burst-like reopenings by the rebinding of Ca(2+) to the activating site; whereas inhibitory actions are substantially independent of stationary buffers but are strongly dependent on the location of the inhibitory Ca(2+) binding site on the IP(3)R in relation to the channel pore.
Collapse
|
37
|
Thul R, Bellamy TC, Roderick HL, Bootman MD, Coombes S. Calcium oscillations. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2008; 641:1-27. [PMID: 18783168 DOI: 10.1007/978-0-387-09794-7_1] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Changes in cellular Ca2+ concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Ca2+ can also trigger cell death through both apoptosis and necrosis, and so the regulation of cellular Ca2+ concentration must be tightly controlled through the concerted action of pumps, channels and buffers that transport Ca2+ into and out of the cell cytoplasm. A hallmark of cellular Ca2+ signalling is its spatiotemporal complexity: stimulation of cells by a hormone or neurotransmitter leads to oscillations in cytoplasmic Ca2+ concentration that can vary markedly in time course, amplitude, frequency, and spatial range. In this chapter we review some of the biological roles of Ca2+, the experimental characterisation of complex dynamic changes in Ca2+ concentration, and attempts to explain this complexity using computational models. We consider the 'toolkit' of cellular proteins which influence Ca2+ concentrarion, describe mechanistic models of key elements of the toolkit, and fit these into the framework of whole cell models of Ca2+ oscillations and waves. Finally, we will touch on recent efforts to use stochastic modelling to elucidate elementary Ca2+ signal events, and how these may evolve into global signals.
Collapse
Affiliation(s)
- Ruediger Thul
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | | | | | | |
Collapse
|
38
|
Ullah G, Jung P, Machaca K. Modeling Ca2+ signaling differentiation during oocyte maturation. Cell Calcium 2007; 42:556-64. [PMID: 17349690 DOI: 10.1016/j.ceca.2007.01.010] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2006] [Revised: 01/19/2007] [Accepted: 01/25/2007] [Indexed: 10/23/2022]
Abstract
Ca2+ is a fundamental intracellular signal that mediates a variety of disparate physiological functions often in the same cell. Ca2+ signals span a wide range of spatial and temporal scales, which endow them with the specificity required to induce defined cellular functions. Furthermore, Ca2+ signaling is highly plastic as it is modulated dynamically during normal physiological development and under pathological conditions. However, the molecular mechanisms underlying Ca2+ signaling differentiation during cellular development remain poorly understood. Oocyte maturation in preparation for fertilization provides an exceptionally well-suited model to elucidate Ca2+ signaling regulation during cellular development. This is because a Ca2+ signal with specialized spatial and temporal dynamics is universally essential for egg activation at fertilization. Here we use mathematical modeling to define the critical determinants of Ca2+ signaling differentiation during oocyte maturation. We show that increasing IP3 receptor (IP3R) affinity replicates both elementary and global Ca2+ dynamics observed experimentally following oocyte maturation. Furthermore, our model reveals that because of the Ca2+ dependency of both SERCA and the IP3R, increased IP3R affinity shifts the system's equilibrium to a new steady state of high cytosolic Ca2+, which is essential for fertilization. Therefore our model provides unique insights into how relatively small alterations of the basic molecular mechanisms of Ca2+ signaling components can lead to dramatic alterations in the spatio-temporal properties of Ca2+ dynamics.
Collapse
Affiliation(s)
- Ghanim Ullah
- Department of Physics and Astronomy and Quantitative Biology Institute, Ohio University, Athens, OH 45701, USA
| | | | | |
Collapse
|
39
|
Rapid ligand-regulated gating kinetics of single inositol 1,4,5-trisphosphate receptor Ca2+ release channels. EMBO Rep 2007; 8:1044-51. [PMID: 17932510 DOI: 10.1038/sj.embor.7401087] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2007] [Revised: 08/20/2007] [Accepted: 08/31/2007] [Indexed: 11/08/2022] Open
Abstract
The ubiquitous inositol 1,4,5-trisphosphate receptor (InsP(3)R) intracellular Ca(2+) release channel is engaged by thousands of plasma membrane receptors to generate Ca(2+) signals in all cells. Understanding how complex Ca(2+) signals are generated has been hindered by a lack of information on the kinetic responses of the channel to its primary ligands, InsP(3) and Ca(2+), which activate and inhibit channel gating. Here, we describe the kinetic responses of single InsP(3)R channels in native endoplasmic reticulum membrane to rapid ligand concentration changes with millisecond resolution, using a new patch-clamp configuration. The kinetics of channel activation and deactivation showed novel Ca(2+) regulation and unexpected ligand cooperativity. The kinetics of Ca(2+)-mediated channel inhibition showed the single-channel bases for fundamental Ca(2+) release events and Ca(2+) release refractory periods. These results provide new insights into the channel regulatory mechanisms that contribute to complex spatial and temporal features of intracellular Ca(2+) signals.
Collapse
|
40
|
Livshitz LM, Rudy Y. Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents. Am J Physiol Heart Circ Physiol 2007; 292:H2854-66. [PMID: 17277017 PMCID: PMC2274911 DOI: 10.1152/ajpheart.01347.2006] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention.
Collapse
Affiliation(s)
- Leonid M Livshitz
- Cardiac Bioelectricity and Arrhythmia Center, Washington University in St. Louis, Missouri 63130-4899, USA
| | | |
Collapse
|
41
|
Shuai J, Pearson JE, Foskett JK, Mak DOD, Parker I. A kinetic model of single and clustered IP3 receptors in the absence of Ca2+ feedback. Biophys J 2007; 93:1151-62. [PMID: 17526578 PMCID: PMC1929031 DOI: 10.1529/biophysj.107.108795] [Citation(s) in RCA: 79] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Ca2+ liberation through inositol 1,4,5-trisphosphate receptor (IP3R) channels generates complex patterns of spatiotemporal cellular Ca2+ signals owing to the biphasic modulation of channel gating by Ca2+ itself. These processes have been extensively studied in Xenopus oocytes, where imaging studies have revealed local Ca2+ signals ("puffs") arising from clusters of IP3R, and patch-clamp studies on isolated oocyte nuclei have yielded extensive data on IP3R gating kinetics. To bridge these two levels of experimental data, we developed an IP3R model and applied stochastic simulation and transition matrix theory to predict the behavior of individual and clustered IP3R channels. The channel model consists of four identical, independent subunits, each of which has an IP3-binding site together with one activating and one inactivating Ca2+-binding site. The channel opens when at least three subunits undergo a conformational change to an "active" state after binding IP3 and Ca2+. The model successfully reproduces patch-clamp data; including the dependence of open probability, mean open duration, and mean closed duration on [IP3] and [Ca2+]. Notably, the biexponential distribution of open-time duration and the dependence of mean open time on [Ca2+] are explained by populations of openings involving either three or four active subunits. As a first step toward applying the single IP3R model to describe cellular responses, we then simulated measurements of puff latency after step increases of [IP3]. Assuming that stochastic opening of a single IP3R at basal cytosolic [Ca2+] and any given [IP3] has a high probability of rapidly triggering neighboring channels by calcium-induced calcium release to evoke a puff, optimal correspondence with experimental data of puff latencies after photorelease of IP3 was obtained when the cluster contained a total of 40-70 IP3Rs.
Collapse
Affiliation(s)
- Jianwei Shuai
- Department of Neurobiology and Behavior, University of California, Irvine, California 92697-4550, USA.
| | | | | | | | | |
Collapse
|
42
|
Parthimos D, Haddock RE, Hill CE, Griffith TM. Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment. Biophys J 2007; 93:1534-56. [PMID: 17483163 PMCID: PMC1948040 DOI: 10.1529/biophysj.107.106278] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The effects of pharmacological interventions that modulate Ca(2+) homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca(2+)] in the cytosol, [Ca(2+)] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca(2+) stores and transmembrane ion fluxes via K(+) channels, Cl(-) channels, and voltage-operated Ca(2+) channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca(2+)] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.
Collapse
Affiliation(s)
- D Parthimos
- Wales Heart Research Institute, Department of Diagnostic Radiology, Cardiff University, Cardiff, UK
| | | | | | | |
Collapse
|
43
|
Joshi RP, Nguyen A, Sridhara V, Hu Q, Nuccitelli R, Beebe SJ, Kolb J, Schoenbach KH. Simulations of intracellular calcium release dynamics in response to a high-intensity, ultrashort electric pulse. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:041920. [PMID: 17500934 DOI: 10.1103/physreve.75.041920] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2007] [Revised: 03/06/2007] [Indexed: 05/15/2023]
Abstract
Numerical simulations for electrically induced, intracellular calcium release from the endoplasmic reticulum are reported. A two-step model is used for self-consistency. Distributed electrical circuit representation coupled with the Smoluchowski equation yields the ER membrane nanoporation for calcium outflow based on a numerical simulation. This is combined with the continuum Li-Rinzel model and drift diffusion for calcium dynamics. Our results are shown to be in agreement with reported calcium release data. A modest increase (rough doubling) of the cellular calcium is predicted in the absence of extra-cellular calcium. In particular, the applied field of 15 kV/cm with 60 ns pulse duration makes for a strong comparison. No oscillations are predicted and the net recovery period of about 5 min are both in agreement with published experimental results. A quantitative explanation for the lack of such oscillatory behavior, based on the density dependent calcium fluxes, is also provided.
Collapse
Affiliation(s)
- R P Joshi
- Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA 23529-0246, USA
| | | | | | | | | | | | | | | |
Collapse
|
44
|
Zhu CL, Jia Y, Liu Q, Yang LJ, Zhan X. A mesoscopic stochastic mechanism of cytosolic calcium oscillations. Biophys Chem 2007; 125:201-12. [PMID: 16952419 DOI: 10.1016/j.bpc.2006.08.001] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2006] [Revised: 08/01/2006] [Accepted: 08/02/2006] [Indexed: 10/24/2022]
Abstract
Based on a model of intracellular calcium (Ca(2+)) oscillation with self-modulation of inositol 1,4,5-trisphosphate signal, the mesoscopic stochastic differential equations for the intracellular Ca(2+) oscillations are theoretically derived by using the chemical Langevin equation method. The effects of the finite biochemical reaction molecule number on both simple and complex cytosolic Ca(2+) oscillations are numerically studied. In the case of simple intracellular Ca(2+) oscillation, it is found that, with the increase of molecule number, the coherence resonance or autonomous resonance phenomena can occur for some external stimulation parameter values. In the cases of complex cytosolic Ca(2+) oscillations, each extremum of concentration of cytosolic Ca(2+) oscillations corresponds to a peak in the histogram of Ca(2+) concentration, and the most probability appeared during the bursting plateau level for bursting, but at the largest minimum of Ca(2+) concentration for chaos. For quasi-periodicity, however, there are only two peaks in the histogram of Ca(2+) concentration, and the most probability is located at low concentration state.
Collapse
Affiliation(s)
- Chun-Lian Zhu
- Department of Physics, Jianghan University, Wuhan 430056, China
| | | | | | | | | |
Collapse
|
45
|
Barabote RD, Tamang DG, Abeywardena SN, Fallah NS, Fu JYC, Lio JK, Mirhosseini P, Pezeshk R, Podell S, Salampessy ML, Thever MD, Saier MH. Extra domains in secondary transport carriers and channel proteins. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2006; 1758:1557-79. [PMID: 16905115 DOI: 10.1016/j.bbamem.2006.06.018] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2006] [Revised: 06/16/2006] [Accepted: 06/20/2006] [Indexed: 01/06/2023]
Abstract
"Extra" domains in members of the families of secondary transport carrier and channel proteins provide secondary functions that expand, amplify or restrict the functional nature of these proteins. Domains in secondary carriers include TrkA and SPX domains in DASS family members, DedA domains in TRAP-T family members (both of the IT superfamily), Kazal-2 and PDZ domains in OAT family members (of the MF superfamily), USP, IIA(Fru) and TrkA domains in ABT family members (of the APC superfamily), ricin domains in OST family members, and TrkA domains in AAE family members. Some transporters contain highly hydrophilic domains consisting of multiple repeat units that can also be found in proteins of dissimilar function. Similarly, transmembrane alpha-helical channel-forming proteins contain unique, conserved, hydrophilic domains, most of which are not found in carriers. In some cases the functions of these domains are known. They may be ligand binding domains, phosphorylation domains, signal transduction domains, protein/protein interaction domains or complex carbohydrate-binding domains. These domains mediate regulation, subunit interactions, or subcellular targeting. Phylogenetic analyses show that while some of these domains are restricted to closely related proteins derived from specific organismal types, others are nearly ubiquitous within a particular family of transporters and occur in a tremendous diversity of organisms. The former probably became associated with the transporters late in the evolutionary process; the latter probably became associated with the carriers much earlier. These domains can be located at either end of the transporter or in a central region, depending on the domain and transporter family. These studies provide useful information about the evolution of extra domains in channels and secondary carriers and provide novel clues concerning function.
Collapse
Affiliation(s)
- Ravi D Barabote
- Division of Biological Sciences, University of California at San Diego, La Jolla, CA 92093-0116, USA
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
46
|
Kowalewski JM, Uhlén P, Kitano H, Brismar H. Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. Math Biosci 2006; 204:232-49. [PMID: 16620876 DOI: 10.1016/j.mbs.2006.03.001] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2005] [Accepted: 03/02/2006] [Indexed: 11/28/2022]
Abstract
Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.
Collapse
Affiliation(s)
- Jacob M Kowalewski
- Cell Physics, Royal Institute of Technology, Roslagstullsbacken 21, 106 91 Stockholm, Sweden
| | | | | | | |
Collapse
|
47
|
Means S, Smith AJ, Shepherd J, Shadid J, Fowler J, Wojcikiewicz RJH, Mazel T, Smith GD, Wilson BS. Reaction diffusion modeling of calcium dynamics with realistic ER geometry. Biophys J 2006; 91:537-57. [PMID: 16617072 PMCID: PMC1483115 DOI: 10.1529/biophysj.105.075036] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations.
Collapse
Affiliation(s)
- Shawn Means
- Sandia National Laboratory, Albuquerque, New Mexico, USA
| | | | | | | | | | | | | | | | | |
Collapse
|
48
|
Kusters JMAM, Dernison MM, van Meerwijk WPM, Ypey DL, Theuvenet APR, Gielen CCAM. Stabilizing role of calcium store-dependent plasma membrane calcium channels in action-potential firing and intracellular calcium oscillations. Biophys J 2005; 89:3741-56. [PMID: 16169971 PMCID: PMC1366943 DOI: 10.1529/biophysj.105.062984] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP3)-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP3-mediated intracellular calcium oscillator. The IP3 receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP3 and Ca2+. We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP3 concentrations, our integrated NRK cell model is at rest at -70 mV. For higher IP3 concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP3 concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near -20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes.
Collapse
Affiliation(s)
- J M A M Kusters
- Department of Medical Physics and Biophysics, Institute for Neuroscience, Radboud University Nijmegen, Nijmegen, The Netherlands
| | | | | | | | | | | |
Collapse
|