Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale (original) (raw)
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Subcellular calcium dynamics in a whole-cell model of an atrial myocyte
Proceedings of the National Academy of Sciences, 2012
In this study, we present an innovative mathematical modelling approach that allows detailed characterisation of Ca 2+ movement within the 3-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic representation of Ca 2+ release sites and physiological Ca 2+ flux parameters, coupled with a computationally inexpensive framework. By translating non-linear Ca 2+ excitability into threshold dynamics, we avoid the computationally demanding time-stepping of the full partial differential equations that are often used to model Ca 2+ transport. Our approach successfully reproduces key features of atrial myocyte Ca 2+ signalling observed using confocal imaging. In particular, the model displays the centripetal Ca 2+ waves that occur within atrial myocytes during excitation-contraction coupling, and the effect of positive inotropic stimulation on the spatial profile of the Ca 2+ signals. Beyond this validation of the model, our simulation reveals novel observations about the spread of Ca 2+ within an atrial myocyte. In particular, the model describes the movement of Ca 2+ between ryanodine receptor (RyR) clusters within a specific z-disk of an atrial myocyte. Furthermore, we demonstrate that altering the strength of Ca 2+ release, RyR refractoriness, the magnitude of initiating stimulus, or the introduction of stochastic Ca 2+ channel activity can cause the nucleation of pro-arhythmic travelling Ca 2+ waves. The model provides clinically-relevant insights into the initiation and propagation of subcellular Ca 2+ signals that are currently beyond the scope of imaging technology. atrial myocytes, calcium signalling, computational cell biology
Intracellular Calcium Dynamics - Sparks of Insight
Journal of Basic and Clinical Physiology and Pharmacology, 2000
3.3.1 Endoplasmic reticulum (ER) and sarcoplasmic reticulum (SR) 3.3.2 Mitochondria 3.3.3 Golgi complex 3.3.4 Nucleus 3.3.5 Secretory granules and vesicles 4. Calcium Sparks in the Heart 4.1 Calcium and heart function 4.2 The discovery of heart sparks and the local control theory 4.3 Heart calcium sparks: L-type calcium channels and what else? 4.4 The termination of the calcium spark 4.5 How many RyR channels open to produce a spark?
A basic model of calcium homeostasis in non-excitable cells
bioRxiv (Cold Spring Harbor Laboratory), 2022
The level of cytosolic calcium (Ca 2+) in cells is tightly regulated to about 100 nM (pCa ≈ 7). Due to external stimuli, the basal cytosolic Ca 2+ level can temporarily be raised to much higher values. The resulting Ca 2+ transients take part in cell-intrinsic signals, which result in cellular responses. Because of its signaling importance and that high levels of Ca 2+ can lead to apoptosis, regulation and homeostatic control of cytosolic Ca 2+ is essential. Based on experimentally known molecular interactions and kinetic data together with control theoretic concepts (integral feedback) we developed a basic computational model describing robust cytosolic Ca 2+ homeostasis. The aim of the model is to describe the integrative mechanisms involved in cytosolic Ca 2+ homeostasis in non-excitable cells. From a model perspective, the cytosolic steady state value (set point) of 100 nM is determined by negative feedback loops (outflow controllers), one of these represented by the plasma membrane Ca 2+ ATPase (PMCA)-calmodulin (CaM) pump and its activation by cytosolic Ca 2+. Hysteretic behaviors of the Ca pumps and transporters have been added leading to improved kinetic behaviors indicating that hysteretic properties of the Ca 2+ pumps appear important how cytosolic Ca 2+ transients are formed. Supported by experimental data the model contains new findings that the activation of the inositol 1,4,5,-tris-phosphate receptor by cytosolic Ca 2+ has a cooperativity of 1, while increased Ca 2+ leads to a pronounced inhibition with a cooperativity of 2. The model further suggests that the capacitative inflow of Ca 2+ into the cytosol at low Ca 2+ storage levels in the ER undergoes a successive change in the cooperativity of the Store Operated calcium Channel (SOCC) as Ca 2+ levels in the ER change. Integrating these aspects the model can show sustained oscillations with period lengths between 2 seconds and 30 hours.
PLoS Computational Biology, 2011
Electrophysiological studies of the human heart face the fundamental challenge that experimental data can be acquired only from patients with underlying heart disease. Regarding human atria, there exist sizable gaps in the understanding of the functional role of cellular Ca 2+ dynamics, which differ crucially from that of ventricular cells, in the modulation of excitation-contraction coupling. Accordingly, the objective of this study was to develop a mathematical model of the human atrial myocyte that, in addition to the sarcolemmal (SL) ion currents, accounts for the heterogeneity of intracellular Ca 2+ dynamics emerging from a structurally detailed sarcoplasmic reticulum (SR). Based on the simulation results, our model convincingly reproduces the principal characteristics of Ca 2+ dynamics: 1) the biphasic increment during the upstroke of the Ca 2+ transient resulting from the delay between the peripheral and central SR Ca 2+ release, and 2) the relative contribution of SL Ca 2+ current and SR Ca 2+ release to the Ca 2+ transient. In line with experimental findings, the model also replicates the strong impact of intracellular Ca 2+ dynamics on the shape of the action potential. The simulation results suggest that the peripheral SR Ca 2+ release sites define the interface between Ca 2+ and AP, whereas the central release sites are important for the fire-diffuse-fire propagation of Ca 2+ diffusion. Furthermore, our analysis predicts that the modulation of the action potential duration due to increasing heart rate is largely mediated by changes in the intracellular Na + concentration. Finally, the results indicate that the SR Ca 2+ release is a strong modulator of AP duration and, consequently, myocyte refractoriness/ excitability. We conclude that the developed model is robust and reproduces many fundamental aspects of the tight coupling between SL ion currents and intracellular Ca 2+ signaling. Thus, the model provides a useful framework for future studies of excitation-contraction coupling in human atrial myocytes.
Researchers have made good progress in unraveling the molecular mechanisms of excitation-contraction (EC) coupling in striated muscle. Despite this progress, paradoxes abound. In skeletal muscle, the existence of a mechanical coupling between membrane charge movement and activation of sarcoplasmic reticulum (SR) release channels is essentially established, but the contribution of Ca 2+induced Ca 2+ release (CICR) to the transient and steady-state components of Ca 2+ release remains controversial. In cardiac muscle, the role of CICR as the primary mechanism of EC coupling is well established, but the stability and tight coupling between membrane Ca 2+ current and release are paradoxical. Answers may lie in microdomain issues, and in the examination of discrete elementary release events, although quantitative treatments are needed. This review explores the theoretical and experimental methods used and the observations made in the study of microdomain Ca 2+ . 47 1056-8700/97/0610-0047$08.00 Annu. Rev. Biophys. Biomol. Struct. 1997.26:47-82. Downloaded from arjournals.annualreviews.org by RUSH UNIVERSITY on 08/30/09. For personal use only. TOOLS FOR STUDYING MICRODOMAIN Ca 2+ DISTRIBUTION Recognizing that the possibilities of measuring microdomain [Ca 2+ ] are still limited and evolving, this section first discusses theoretical tools that led to the recognition of the importance of gradients long before their measurement. In addition to developing the theory, attention is given to several simplifications that add computational ease and physical insight. Experimental tools, mostly the spatially resolved detection of [Ca 2+ ] by confocal microscopy, are also considered. Theoretical and Computational GENERAL THEORY The theoretical analysis and modeling of EC coupling depends heavily on the properties of calcium diffusion. In a myocyte, calcium Annu. Rev. Biophys. Biomol. Struct. 1997.26:47-82. Downloaded from arjournals.annualreviews.org by RUSH UNIVERSITY on 08/30/09. For personal use only.
Identification and modeling of calcium dynamics in cardiac myocytes
Simulation Practice and Theory, 2000
Calcium plays an essential role as a messenger and as a factor in cardiac contraction. In the present study, a model for Ca2+ handling in cardiac cells is presented. After the identification of the sarcoplasmic reticulum (SR) parameters, the SERCA pump and ryanodine channels activities, a comparison is made between experimental and calculated responses. The model's parameters were identified using optimization methods. This identification is based on the response of the digitonin permeabilized cells. The model deals with the dynamics of the calcium exchange between the different compartments of the cell. Cell compartments involved are the SR, the cytosol and the extra-cellular medium. The different components of the mathematical models are discussed and compared. The modeling and simulation are run within Ψlab,1 a freeware for modeling and simulation of dynamic systems.
Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level
International Review of Cytology, 2007
Many essential physiological processes are controlled by calcium. To ensure reliability and specificity, calcium signals are highly organized in time and space in the form of oscillations and waves. Interesting findings have been obtained at various scales, ranging from the stochastic opening of a single calcium channel to the intercellular calcium wave spreading through an entire organ. A detailed understanding of calcium dynamics thus requires a link between observations at different scales. It appears that some regulations such as calcium-induced calcium release or PLC activation by calcium, as well as the weak diffusibility of calcium ions play a role at all levels of organization in most cell types. To comprehend how calcium waves spread from one cell to another, specific gap-junctional coupling and paracrine signaling must also be taken into account. On the basis of a pluridisciplinar approach ranging from physics to physiology, a unified description of calcium dynamics is emerging, which could help understanding how such a small ion can mediate so many vital functions in living systems.
Model of Intracellular Calcium Cycling in Ventricular Myocytes
Biophysical Journal, 2003
We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.
A membrane model for cytosolic calcium oscillations. A study using Xenopus oocytes
Biophysical Journal, 1992
Cytosolic calcium oscillations occur in a wide variety of cells and are involved in different cellular functions. We describe these calcium oscillations by a mathematical model based on the putative electrophysiological properties of the endoplasmic reticulum (ER) membrane. The salient features of our membrane model are calcium-dependent calcium channels and calcium pumps in the ER membrane, constant entry of calcium into the cytosol, calcium dependent removal from the cytosol, and buffering by cytoplasmic calcium binding proteins. Numerical integration of the model allows us to study the fluctuations in the cytosolic calcium concentration, the ER membrane potential, and the concentration of free calcium binding sites on a calcium binding protein. The model demonstrates the physiological features necessary for calcium oscillations and suggests that the level of calcium flux into the cytosol controls the frequency and amplitude of oscillations. The model also suggests that the level of buffering affects the frequency and amplitude of the oscillations. The model is supported by experiments indirectly measuring cytosolic calcium by calcium-induced chloride currents in Xenopus oocytes as well as cytosolic calcium oscillations observed in other preparations.
Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes
Biophysical chemistry, 1998
Using a modular approach, in which kinetic models of various mechanisms of calcium handling in cells are fine-tuned to in vivo and in vitro measurements before combining them into whole-cell models, three distinct modes of transmission of calcium waves in mature and immature frog eggs have been defined. Two modes of transmission are found in immature eggs, where the inositol 1,4,5-trisphosphate receptor (IP 3 R) controls release of calcium from the endoplasmic reticulum (ER). The first mode corresponds to an excitable physiological state of the cytoplasm and results in solitary waves that can appear as circular or spiral waves in two dimensions with the wave speed proportional to the square root of the diffusion constant of calcium. A second mode occurs when the state of the cytoplasm is oscillatory and because of the small size of the buffered diffusion constant for calcium, the wave speed can appear to be weakly dependent on diffusion. In the mature frog egg, where the sperm-induced Ca 2+ fertilization wave is a propagating front, the cytoplasm appears to be bistable and in this mode the wave speed is also proportional to the square root of the diffusion constant. Here we investigate a fourth mode of propagation for cardiac myocytes, in which calcium release from the sarcoplasmic reticulum (SR) is dominated by clusters of ryanodine receptors spaced at regular intervals. In myocytes a stochastically excitable myoplasm leads to the spontaneous production of calcium 'sparks' that under certain conditions can merge into saltatory waves with a speed proportional to the diffusion constant.