1
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Gil Montoya DC, Ornelas-Guevara R, Diercks BP, Guse AH, Dupont G. T cell Ca 2+ microdomains through the lens of computational modeling. Front Immunol 2023; 14:1235737. [PMID: 37860008 PMCID: PMC10582754 DOI: 10.3389/fimmu.2023.1235737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 09/18/2023] [Indexed: 10/21/2023] Open
Abstract
Cellular Ca2+ signaling is highly organized in time and space. Locally restricted and short-lived regions of Ca2+ increase, called Ca2+ microdomains, constitute building blocks that are differentially arranged to create cellular Ca2+ signatures controlling physiological responses. Here, we focus on Ca2+ microdomains occurring in restricted cytosolic spaces between the plasma membrane and the endoplasmic reticulum, called endoplasmic reticulum-plasma membrane junctions. In T cells, these microdomains have been finely characterized. Enough quantitative data are thus available to develop detailed computational models of junctional Ca2+ dynamics. Simulations are able to predict the characteristics of Ca2+ increases at the level of single channels and in junctions of different spatial configurations, in response to various signaling molecules. Thanks to the synergy between experimental observations and computational modeling, a unified description of the molecular mechanisms that create Ca2+ microdomains in the first seconds of T cell stimulation is emerging.
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Affiliation(s)
- Diana C. Gil Montoya
- The Calcium Signalling Group, Department of Biochemistry and Molecular Cell Biology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - Roberto Ornelas-Guevara
- Unit of Theoretical Chronobiology, Faculté des Sciences CP231, Université Libre de Bruxelles (ULB), Brussels, Belgium
| | - Björn-Philipp Diercks
- 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
| | - Geneviève Dupont
- Unit of Theoretical Chronobiology, Faculté des Sciences CP231, Université Libre de Bruxelles (ULB), Brussels, Belgium
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2
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Matveev VV. Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion. Biophys J 2022; 121:4569-4584. [PMID: 36815708 PMCID: PMC9748373 DOI: 10.1016/j.bpj.2022.10.033] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2022] [Revised: 09/13/2022] [Accepted: 10/24/2022] [Indexed: 11/22/2022] Open
Abstract
Ca2+-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion, and Ca2+ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering, and sensing if Ca2+ channel gating is not Ca2+ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.
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Affiliation(s)
- Victor V Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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3
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Villarruel C, Dawson SP. Quantification of fluctuations from fluorescence correlation spectroscopy experiments in reaction-diffusion systems. Phys Rev E 2020; 102:052407. [PMID: 33327184 DOI: 10.1103/physreve.102.052407] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 10/12/2020] [Indexed: 11/07/2022]
Abstract
Fluorescence correlation spectroscopy (FCS) is commonly used to estimate diffusion and reaction rates. In FCS the fluorescence coming from a small volume is recorded and the autocorrelation function (ACF) of the fluorescence fluctuations is computed. Scaling out the fluctuations due to the emission process, this ACF can be related to the ACF of the fluctuations in the number of observed fluorescent molecules. In this paper the ACF of the molecule number fluctuations is studied theoretically, with no approximations, for a reaction-diffusion system in which the fluorescence changes with binding and unbinding. Theoretical ACFs are usually derived assuming that fluctuations in the number of molecules of one species are instantaneously uncorrelated to those of the others and obey Poisson statistics. Under these assumptions, the ACF derived in this paper is characterized only by the diffusive timescale of the fluorescent species and its total weight is the inverse of the mean number of observed fluorescent molecules. The theory is then scrutinized in view of previous experimental results which, for a similar system, gave a different total weight and correct estimates of other diffusive timescales. The total weight mismatch is corrected by assuming that the variance of the number of fluorescent molecules depends on the variance of the particle numbers of the other species, as in the variance decomposition formula. Including the finite acquisition time in its computation, it is shown that the ACF depends on various timescales of the system and that its total weight coincides with the one obtained with the variance decomposition formula. This calculation implies that diffusion coefficients of nonobservable species can be estimated with FCS experiments performed in reaction-diffusion systems. Ways to proceed in future experiments are also discussed.
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Affiliation(s)
- Cecilia Villarruel
- Departamento de Física, FCEN-UBA, and IFIBA, UBA-CONICET, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina.,IFIBYNE, UBA-CONICET, Buenos Aires, Argentina
| | - Silvina Ponce Dawson
- Departamento de Física, FCEN-UBA, and IFIBA, UBA-CONICET, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina
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4
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Powell J, Falcke M, Skupin A, Bellamy TC, Kypraios T, Thul R. A Statistical View on Calcium Oscillations. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020; 1131:799-826. [PMID: 31646535 DOI: 10.1007/978-3-030-12457-1_32] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.
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Affiliation(s)
- Jake Powell
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Martin Falcke
- Max Delbrück Centre for Molecular Medicine, Berlin, Germany.,Department of Physics, Humboldt University, Berlin, Germany
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belval, Luxembourg.,National Biomedical Computation Resource, University California San Diego, La Jolla, CA, USA
| | - Tomas C Bellamy
- School of Life Sciences, University of Nottingham, Nottingham, UK
| | - Theodore Kypraios
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Rüdiger Thul
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK.
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5
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Simulation Strategies for Calcium Microdomains and Calcium Noise. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020; 1131:771-797. [DOI: 10.1007/978-3-030-12457-1_31] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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6
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Swaminathan D, Dickinson GD, Demuro A, Parker I. Noise analysis of cytosolic calcium image data. Cell Calcium 2019; 86:102152. [PMID: 31918030 DOI: 10.1016/j.ceca.2019.102152] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Revised: 12/15/2019] [Accepted: 12/16/2019] [Indexed: 11/28/2022]
Abstract
Cellular Ca2+ signals are often constrained to cytosolic micro- or nano-domains where stochastic openings of Ca2+ channels cause large fluctuations in local Ca2+ concentration (Ca2+ 'noise'). With the advent of TIRF microscopy to image the fluorescence of Ca2+-sensitive probes from attoliter volumes it has become possible to directly monitor these signals, which closely track the gating of plasmalemmal and ER Ca2+-permeable channels. Nevertheless, it is likely that many physiologically important Ca2+ signals are too small to resolve as discrete events in fluorescence recordings. By analogy with noise analysis of electrophysiological data, we explore here the use of statistical approaches to detect and analyze such Ca2+ noise in images obtained using Ca2+-sensitive indicator dyes. We describe two techniques - power spectrum analysis and spatio-temporal correlation - and demonstrate that both effectively identify discrete, spatially localized calcium release events (Ca2+ puffs). Moreover, we show they are able to detect localized noise fluctuations in a case where discrete events cannot directly be resolved.
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Affiliation(s)
- Divya Swaminathan
- Department of Neurobiology & Behavior, University of California, Irvine, CA92697, USA.
| | - George D Dickinson
- Department of Neurobiology & Behavior, University of California, Irvine, CA92697, USA
| | - Angelo Demuro
- Department of Neurobiology & Behavior, University of California, Irvine, CA92697, USA
| | - Ian Parker
- Department of Neurobiology & Behavior, University of California, Irvine, CA92697, USA; Department of Physiology & Biophysics, University of California, Irvine, CA92697, USA
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7
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Abstract
Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca2+) signals resulting from brief openings of trans-membrane Ca2+ channels. On short temporal and spatial scales, the corresponding local Ca2+ nanodomains formed in the vicinity of a single or several open Ca2+ channels can be effectively approximated by quasi-stationary solutions. The rapid buffering approximation (RBA) is one of the most powerful of such approximations, and is based on the assumption of instantaneous equilibration of the bimolecular Ca2+ buffering reaction, combined with the conservation condition for the total Ca2+ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca2+ channels on a flat membrane, in the presence of any number of simple Ca2+ buffers with one-to-one Ca2+ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca2+-binding domains (lobes), with each domain binding two Ca2+ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca2+ binding sites. We show that in the presence of such buffers, RBA solution is given by the solution to a cubic equation, analogous to the quadratic equation describing RBA in the case of a simple, one-to-one Ca2+ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.
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Affiliation(s)
- Victor Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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8
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Clarke SE. Analog Signaling With the "Digital" Molecular Switch CaMKII. Front Comput Neurosci 2018; 12:92. [PMID: 30524260 PMCID: PMC6262075 DOI: 10.3389/fncom.2018.00092] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Accepted: 10/31/2018] [Indexed: 11/13/2022] Open
Abstract
Molecular switches, such as the protein kinase CaMKII, play a fundamental role in cell signaling by decoding inputs into either high or low states of activity; because the high activation state can be turned on and persist after the input ceases, these switches have earned a reputation as "digital." Although this on/off, binary perspective has been valuable for understanding long timescale synaptic plasticity, accumulating experimental evidence suggests that the CaMKII switch can also control plasticity on short timescales. To investigate this idea further, a non-autonomous, nonlinear ordinary differential equation, representative of a general bistable molecular switch, is analyzed. The results suggest that switch activity in regions surrounding either the high- or low-stable states of activation could act as a reliable analog signal, whose short timescale fluctuations relative to equilibrium track instantaneous input frequency. The model makes intriguing predictions and is validated against previous work demonstrating its suitability as a minimal representation of switch dynamics; in combination with existing experimental evidence, the theory suggests a multiplexed encoding of instantaneous frequency information over short timescales, with integration of total activity over longer timescales.
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Affiliation(s)
- Stephen E Clarke
- Department of Bioengineering, Department of Neurosurgery, Stanford University, Stanford, CA, United States
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9
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Zhong M, Rees CM, Terentyev D, Choi BR, Koren G, Karma A. NCX-Mediated Subcellular Ca 2+ Dynamics Underlying Early Afterdepolarizations in LQT2 Cardiomyocytes. Biophys J 2018; 115:1019-1032. [PMID: 30173888 DOI: 10.1016/j.bpj.2018.08.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Revised: 07/18/2018] [Accepted: 08/02/2018] [Indexed: 12/12/2022] Open
Abstract
Long QT syndrome type 2 (LQT2) is a congenital disease characterized by loss of function mutations in hERG potassium channels (IKr). LQT2 is associated with fatal ventricular arrhythmias promoted by triggered activity in the form of early afterdepolarizations (EADs). We previously demonstrated that intracellular Ca2+ handling is remodeled in LQT2 myocytes. Remodeling leads to aberrant late RyR-mediated Ca2+ releases that drive forward-mode Na+-Ca2+ exchanger (NCX) current and slow repolarization to promote reopening of L-type calcium channels and EADs. Forward-mode NCX was found to be enhanced despite the fact that these late releases do not significantly alter the whole-cell cytosolic calcium concentration during a vulnerable period of phase 2 of the action potential corresponding to the onset of EADs. Here, we use a multiscale ventricular myocyte model to explain this finding. We show that because the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration, a larger number of smaller-amplitude discrete Ca2+ release events can produce a large increase in whole-cell forward-mode NCX current without increasing significantly the whole-cell cytosolic calcium concentration. Furthermore, we develop novel insights, to our knowledge, into how alterations of stochastic RyR activity at the single-channel level cause late aberrant Ca2+ release events. Experimental measurements in transgenic LTQ2 rabbits confirm the critical arrhythmogenic role of NCX and identify this current as a potential target for antiarrhythmic therapies in LQT2.
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Affiliation(s)
- Mingwang Zhong
- Physics Department and Center for Interdisciplinary Research in Complex Systems, Northeastern University, Boston, Massachusetts
| | - Colin M Rees
- Physics Department and Center for Interdisciplinary Research in Complex Systems, Northeastern University, Boston, Massachusetts
| | - Dmitry Terentyev
- Cardiovascular Research Centre, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island
| | - Bum-Rak Choi
- Cardiovascular Research Centre, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island
| | - Gideon Koren
- Cardiovascular Research Centre, Rhode Island Hospital, Warren Alpert Medical School of Brown University, Providence, Rhode Island
| | - Alain Karma
- Physics Department and Center for Interdisciplinary Research in Complex Systems, Northeastern University, Boston, Massachusetts.
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10
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Heart rate variability alters cardiac repolarization and electromechanical dynamics. J Theor Biol 2018; 442:31-43. [DOI: 10.1016/j.jtbi.2018.01.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2017] [Revised: 01/05/2018] [Accepted: 01/10/2018] [Indexed: 11/23/2022]
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11
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Matveev V. Padé Approximation of a Stationary Single-Channel Ca 2+ Nanodomain. Biophys J 2017; 111:2062-2074. [PMID: 27806286 DOI: 10.1016/j.bpj.2016.09.019] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Revised: 09/09/2016] [Accepted: 09/14/2016] [Indexed: 11/30/2022] Open
Abstract
We consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain, in the presence of a single mobile buffer with one-to-one Ca2+ binding stoichiometry. Previously, a number of Ca2+ nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca2+ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca2+ distribution on crucial parameters such as buffer mobility and its Ca2+ binding properties. In this study, we present a different form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a "dual" Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and we show that this provides an accurate approximation to the nanodomain Ca2+ and buffer concentrations. We compare this approximation with the previously obtained approximations and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca2+ channels. However, it may be possible to extend the Padé method to estimate Ca2+ nanodomains in the presence of cooperative Ca2+ buffers with two Ca2+ binding sites, the case that existing methods do not address.
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Affiliation(s)
- V Matveev
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey.
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12
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Ji H, Li Y, Weinberg SH. Calcium Ion Fluctuations Alter Channel Gating in a Stochastic Luminal Calcium Release Site Model. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2017; 14:611-619. [PMID: 26561478 DOI: 10.1109/tcbb.2015.2498552] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Stochasticity and small system size effects in complex biochemical reaction networks can greatly alter transient and steady-state system properties. A common approach to modeling reaction networks, which accounts for system size, is the chemical master equation that governs the dynamics of the joint probability distribution for molecular copy number. However, calculation of the stationary distribution is often prohibitive, due to the large state-space associated with most biochemical reaction networks. Here, we analyze a network representing a luminal calcium release site model and investigate to what extent small system size effects and calcium fluctuations, driven by ion channel gating, influx and diffusion, alter steady-state ion channel properties including open probability. For a physiological ion channel gating model and number of channels, the state-space may be between approximately 106-108 elements, and a novel modified block power method is used to solve the associated dominant eigenvector problem required to calculate the stationary distribution. We demonstrate that both small local cytosolic domain volume and a small number of ion channels drive calcium fluctuations that result in deviation from the corresponding model that neglects small system size effects.
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13
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Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes. Proc Natl Acad Sci U S A 2017; 114:E270-E279. [PMID: 28049836 DOI: 10.1073/pnas.1614051114] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023] Open
Abstract
Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca2+) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na+/Ca2+ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca2+ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca2+ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.
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14
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Weinberg SH. Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study. CLINICAL MEDICINE INSIGHTS-CARDIOLOGY 2016; 10:1-15. [PMID: 27385917 PMCID: PMC4920205 DOI: 10.4137/cmc.s39709] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 05/26/2016] [Accepted: 05/27/2016] [Indexed: 02/01/2023]
Abstract
Cardiac electrical dynamics are governed by cellular-level properties, such as action potential duration (APD) restitution and intracellular calcium (Ca) handling, and tissue-level properties, including conduction velocity restitution and cell-cell coupling. Irregular dynamics at the cellular level can lead to instabilities in cardiac tissue, including alternans, a beat-to-beat alternation in the action potential and/or the intracellular Ca transient. In this study, we incorporate a detailed single cell coupled map model of Ca cycling and bidirectional APD-Ca coupling into a spatially extended tissue model to investigate the influence of sarcoplasmic reticulum (SR) Ca uptake and release properties on alternans and conduction block. We find that an intermediate SR Ca uptake rate and larger SR Ca release resulted in the widest range of stimulus periods that promoted alternans. However, both reduced SR Ca uptake and release promote arrhythmogenic spatially and electromechanically discordant alternans, suggesting a complex interaction between SR Ca handling and alternans characteristics at the cellular and tissue level.
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Affiliation(s)
- Seth H Weinberg
- Department of Biomedical Engineering, Virginia Commonwealth University, Richmond, VA, USA
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15
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Weinberg SH. Microdomain [Ca(2+)] Fluctuations Alter Temporal Dynamics in Models of Ca(2+)-Dependent Signaling Cascades and Synaptic Vesicle Release. Neural Comput 2016; 28:493-524. [PMID: 26735745 DOI: 10.1162/neco_a_00811] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Ca(2+)-dependent signaling is often localized in spatially restricted microdomains and may involve only 1 to 100 Ca(2+) ions. Fluctuations in the microdomain Ca(2+) concentration (Ca(2+)) can arise from a wide range of elementary processes, including diffusion, Ca(2+) influx, and association/dissociation with Ca(2+) binding proteins or buffers. However, it is unclear to what extent these fluctuations alter Ca(2+)-dependent signaling. We construct Markov models of a general Ca(2+)-dependent signaling cascade and Ca(2+)-triggered synaptic vesicle release. We compare the hitting (release) time distribution and statistics for models that account for [Ca(2+)] fluctuations with the corresponding models that neglect these fluctuations. In general, when Ca(2+) fluctuations are much faster than the characteristic time for the signaling event, the hitting time distributions and statistics for the models with and without Ca(2+) fluctuation are similar. However, when the timescale of Ca(2+) fluctuations is on the same order as the signaling cascade or slower, the hitting time mean and variability are typically increased, in particular when the average number of microdomain Ca(2+) ions is small, a consequence of a long-tailed hitting time distribution. In a model of Ca(2+)-triggered synaptic vesicle release, we demonstrate the conditions for which [Ca(2+)] fluctuations do and do not alter the distribution, mean, and variability of release timing. We find that both the release time mean and variability can be increased, demonstrating that Ca(2+) fluctuations are an important aspect of microdomain Ca(2+) signaling and further suggesting that Ca(2+) fluctuations in the presynaptic terminal may contribute to variability in synaptic vesicle release and thus variability in neuronal spiking.
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Affiliation(s)
- Seth H Weinberg
- Virginia Modeling, Analysis and Simulation Center, Old Dominion University, Suffolk, Virginia 23435, U.S.A
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16
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Matolcsi M, Giordano N. A novel explanation for observed CaMKII dynamics in dendritic spines with added EGTA or BAPTA. Biophys J 2015; 108:975-985. [PMID: 25692602 DOI: 10.1016/j.bpj.2014.12.044] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2014] [Revised: 12/11/2014] [Accepted: 12/12/2014] [Indexed: 10/24/2022] Open
Abstract
We present a simplified reaction network in a single well-mixed volume that captures the general features of CaMKII dynamics observed during both synaptic input and spine depolarization. Our model can also account for the greater-than-control CaMKII activation observed with added EGTA during depolarization. Calcium input currents are modeled after experimental observations, and existing models of calmodulin and CaMKII autophosphorylation are used. After calibration against CaMKII activation data in the absence of chelators, CaMKII activation dynamics due to synaptic input via n-methyl-d-aspartate receptors are qualitatively accounted for in the presence of the chelators EGTA and BAPTA without additional adjustments to the model. To account for CaMKII activation dynamics during spine depolarization with added EGTA or BAPTA, the model invokes the modulation of CaV2.3 (R-type) voltage-dependent calcium channel (VDCC) currents observed in the presence of EGTA or BAPTA. To our knowledge, this is a novel explanation for the increased CaMKII activation seen in dendritic spines with added EGTA, and suggests that differential modulation of VDCCs by EGTA and BAPTA offers an alternative or complementary explanation for other experimental results in which addition of EGTA or BAPTA produces different effects. Our results also show that a simplified reaction network in a single, well-mixed compartment is sufficient to account for the general features of observed CaMKII dynamics.
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Affiliation(s)
- Matt Matolcsi
- Department of Physics, Purdue University, West Lafayette, Indiana.
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17
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Ca2+-activation kinetics modulate successive puff/spark amplitude, duration and inter-event-interval correlations in a Langevin model of stochastic Ca2+ release. Math Biosci 2015; 264:101-7. [DOI: 10.1016/j.mbs.2015.03.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2014] [Revised: 03/16/2015] [Accepted: 03/27/2015] [Indexed: 01/12/2023]
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18
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Weinberg SH. Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model. PLoS One 2015; 10:e0126629. [PMID: 25970534 PMCID: PMC4430543 DOI: 10.1371/journal.pone.0126629] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2015] [Accepted: 04/04/2015] [Indexed: 12/17/2022] Open
Abstract
Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.
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Affiliation(s)
- Seth H. Weinberg
- Virginia Modeling, Analysis and Simulation Center, Old Dominion University, 1030 University Boulevard, Suffolk, Virginia, USA
- * E-mail:
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19
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The phototransduction machinery in the rod outer segment has a strong efficacy gradient. Proc Natl Acad Sci U S A 2015; 112:E2715-24. [PMID: 25941368 DOI: 10.1073/pnas.1423162112] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Rod photoreceptors consist of an outer segment (OS) and an inner segment. Inside the OS a biochemical machinery transforms the rhodopsin photoisomerization into electrical signal. This machinery has been treated as and is thought to be homogenous with marginal inhomogeneities. To verify this assumption, we developed a methodology based on special tapered optical fibers (TOFs) to deliver highly localized light stimulations. By using these TOFs, specific regions of the rod OS could be stimulated with spots of light highly confined in space. As the TOF is moved from the OS base toward its tip, the amplitude of saturating and single photon responses decreases, demonstrating that the efficacy of the transduction machinery is not uniform and is 5-10 times higher at the base than at the tip. This gradient of efficacy of the transduction machinery is attributed to a progressive depletion of the phosphodiesterase along the rod OS. Moreover we demonstrate that, using restricted spots of light, the duration of the photoresponse along the OS does not increase linearly with the light intensity as with diffuse light.
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20
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Coddou C, Yan Z, Stojilkovic SS. Role of domain calcium in purinergic P2X2 receptor channel desensitization. Am J Physiol Cell Physiol 2015; 308:C729-36. [PMID: 25673774 DOI: 10.1152/ajpcell.00399.2014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Accepted: 02/10/2015] [Indexed: 11/22/2022]
Abstract
Activation of P2X2 receptor channels (P2X2Rs) is characterized by a rapid current growth accompanied by a decay of current during sustained ATP application, a phenomenon known as receptor desensitization. Using rat, mouse, and human receptors, we show here that two processes contribute to receptor desensitization: bath calcium-independent desensitization and calcium-dependent desensitization. Calcium-independent desensitization is minor and comparable during repetitive agonist application in cells expressing the full size of the receptor but is pronounced in cells expressing shorter versions of receptors, indicating a role of the COOH terminus in control of receptor desensitization. Calcium-dependent desensitization is substantial during initial agonist application and progressively increases during repetitive agonist application in bath ATP and calcium concentration-dependent manners. Experiments with substitution of bath Na(+) with N-methyl-d-glucamine (NMDG(+)), a large organic cation, indicate that receptor pore dilation is a calcium-independent process in contrast to receptor desensitization. A decrease in the driving force for calcium by changing the holding potential from -60 to +120 mV further indicates that calcium influx through the channel pores at least partially accounts for receptor desensitization. Experiments with various receptor chimeras also indicate that the transmembrane and/or intracellular domains of P2X2R are required for development of calcium-dependent desensitization and that a decrease in the amplitude of current slows receptor desensitization. Simultaneous calcium and current recording shows development of calcium-dependent desensitization without an increase in global intracellular calcium concentrations. Combined with experiments with clamping intrapipette concentrations of calcium at various levels, these experiments indicate that domain calcium is sufficient to establish calcium-dependent receptor desensitization in experiments with whole-cell recordings.
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Affiliation(s)
- Claudio Coddou
- From the Section on Cellular Signaling, Program in Developmental Neuroscience, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland; Department of Biomedical Sciences, Faculty of Medicine, Universidad Católica del Norte, Coquimbo, Chile
| | - Zonghe Yan
- From the Section on Cellular Signaling, Program in Developmental Neuroscience, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
| | - Stanko S Stojilkovic
- From the Section on Cellular Signaling, Program in Developmental Neuroscience, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
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Wieder N, Fink R, von Wegner F. Exact stochastic simulation of a calcium microdomain reveals the impact of Ca²⁺ fluctuations on IP₃R gating. Biophys J 2015; 108:557-67. [PMID: 25650923 PMCID: PMC4317541 DOI: 10.1016/j.bpj.2014.11.3458] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Revised: 11/04/2014] [Accepted: 11/18/2014] [Indexed: 01/07/2023] Open
Abstract
In this study, we numerically analyzed the nonlinear Ca(2+)-dependent gating dynamics of a single, nonconducting inositol 1,4,5-trisphosphate receptor (IP₃R) channel, using an exact and fully stochastic simulation algorithm that includes channel gating, Ca(2+) buffering, and Ca(2+) diffusion. The IP₃R is a ubiquitous intracellular Ca(2+) release channel that plays an important role in the formation of complex spatiotemporal Ca(2+) signals such as waves and oscillations. Dynamic subfemtoliter Ca(2+) microdomains reveal low copy numbers of Ca(2+) ions, buffer molecules, and IP₃Rs, and stochastic fluctuations arising from molecular interactions and diffusion do not average out. In contrast to models treating calcium dynamics deterministically, the stochastic approach accounts for this molecular noise. We varied Ca(2+) diffusion coefficients and buffer reaction rates to tune the autocorrelation properties of Ca(2+) noise and found a distinct relation between the autocorrelation time τac, the mean channel open and close times, and the resulting IP₃R open probability PO. We observed an increased PO for shorter noise autocorrelation times, caused by increasing channel open times and decreasing close times. In a pure diffusion model the effects become apparent at elevated calcium concentrations, e.g., at [Ca(2+)] = 25 μM, τac = 0.082 ms, the IP₃R open probability increased by ≈20% and mean open times increased by ≈4 ms, compared to a zero noise model. We identified the inactivating Ca(2+) binding site of IP₃R subunits as the primarily noise-susceptible element of the De Young and Keizer model. Short Ca(2+) noise autocorrelation times decrease the probability of Ca(2+) association and consequently increase IPvR activity. These results suggest a functional role of local calcium noise properties on calcium-regulated target molecules such as the ubiquitous IP₃R. This finding may stimulate novel experimental approaches analyzing the role of calcium noise properties on microdomain behavior.
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Affiliation(s)
- Nicolas Wieder
- Medical Biophysics Unit, Department of Physiology and Pathophysiology, Universität Heidelberg, Heidelberg, Germany.
| | - Rainer Fink
- Medical Biophysics Unit, Department of Physiology and Pathophysiology, Universität Heidelberg, Heidelberg, Germany
| | - Frederic von Wegner
- Medical Biophysics Unit, Department of Physiology and Pathophysiology, Universität Heidelberg, Heidelberg, Germany
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von Wegner F, Wieder N, Fink RHA. Microdomain calcium fluctuations as a colored noise process. Front Genet 2014; 5:376. [PMID: 25404938 PMCID: PMC4217525 DOI: 10.3389/fgene.2014.00376] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Accepted: 10/10/2014] [Indexed: 12/02/2022] Open
Abstract
Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca2+ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.
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Affiliation(s)
- Frederic von Wegner
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
| | - Nicolas Wieder
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
| | - Rainer H A Fink
- Medical Biophysics Group, Institute of Physiology and Pathophysiology, Heidelberg University Heidelberg, Germany
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