Yoast_2020 ============== :Original publication: The native ORAI channel trio underlies the diversity of Ca2+ signaling events :Published By: Nature communications :DOI: https://doi.org/10.1038/s41467-020-16232-6 Sneyd_2016 =============== :Reference: On the dynamical structure of calcium oscillations :Published By: National Academy of Sciences :DOI: https://doi.org/10.1073/pnas.1614613114 Model status ============= The current CellML model implementation runs in OpenCOR_. Using the default parameters provided in the paper except for the modification listed in the sections :ref:` Model Issues`. Figure 6 in the main article and Figure 10 in the supporting material can be reproduced by CellML implementation with marginal difference. Model Summary ============== The Ca2+ dynamics model is an adapted version of that in :ref:` Sneyd_2016`. The major difference from :ref:` Sneyd_2016` is the modeling of the Ca2+ influx across the PM, is done by a simple ORAI binding model. ORAI1 (O1), ORAI2 (O2), and ORAI3 (O3) bind to form dimers according to the reactions. The essential role of ORAI1 channels in receptor-evoked Ca2+ signaling is well understood, yet little is known about the physiological activation of the ORAI channel trio natively expressed in all cells. The roles of ORAI2 and ORAI3 have remained unknown. In the current work, the authors aim to show the role of ORAI channels in mediating the regenerative Ca2+ oscillations. Model Components ================ The model is implemented using the current formulation which is based on :ref:`Sneyd_2016`. There are four main Components in the model: 1. Cytoplasm Ca2+ concentration (Ca2+): - Jserca : the uptake of Ca2+ into the SR by SERCA pumps. - Jin : Sum of main Ca2+ influxes including Jrocc (receptor-operated Ca2+ channel), Jsocc (store-operated Ca2+ channel). - Jpm : the flux through plasma pump. - JIPR : the flux through the IPRs, which is the most complex component contains at least 7 subcomponents. 2. Endoplasmic reticulum (ER) Ca2+ concentration (ca_e): - Jserca : the uptake of Ca2+ into the SR by SERCA pumps. - JIPR : the flux through the IPRs 3. IPRs activation rate (h) 4. ORAI channels (indicated as Jin in the :ref:`Yoast_2020`, while is not exactly the same as Jin, for more details see; :ref:` Model Issues`) Model Issues =================== - There were rescaling factors concerning ER ca+ generations, with the aim to have a better values. To do that, all the related parameters that appear in the :ref:`Sneyd_2016` needed to be modified. - There were no clear instructions on how to add extra Ca+ to the mathematical model. - There were not any explicit instructions about how to add Tg in the calcium dynamic system equations. - There wasn't any clear protocol about the IP3 concentration for Figure 6D. - The initial values for state variables were not defined. Model Validations =================== Applying the default parameters in the model, we were not able to reproduce the model predictions, . - There is a constant IP3 concentrations in the :ref:`Yoast_2020` model; the IP3 response in the supporting information document :ref:`Sneyd_2016` is not applicable in the current work. - The Algebraic definition :math:`J_{in}` was modified to the formulation taken from MATLAB code provided by authors. - The Algebraic definition :math:`J_{serca}` was modified to the formulation taken from MATLAB code provided by authors, please see the table below: ================= ================================ ====================================================================================== ====================================================================================== Param Yoast_2020 Sneyd_2016 Modified Version ------------------ -------------------------------- -------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------- :math:`J_{in}` :math:` J_{orai}` :math:`\alpha_{0}+\alpha_{1}\frac{K_{e}^{4}}{K_{e}^{4}+C_{e}^{4}}` :math:`\alpha_{0}+(J_{ORAI})*\frac{K_{e}^{2}}{K_{e}^{2}+C_{e}^{2}}` :math:`J_{serca}` No indication of the Equation :math:`V_{serca}*\frac{ca_{c}^{2}-k_{bar}ca_{e}^{2}}{ca_{c}^{2}+k_{serca}^{2}}` :math:` v_{serca} * \frac{thaps*ca_{c}^{2}-k_{bar}ca_{e}^{2}}{ca_{c}^{2}+k_{serca}^{2}}` :math:`p` Constant values :math:`\frac{dp}{dt} = \tau (p-ps)` --------------- ================= ================================ ====================================================================================== ====================================================================================== - Authors rescaled related parameters for the ER ca+ generations to magnify the ER ca+ concentrations. The rescaling process was not mentioned in the paper; please check the updated values in the table below: =================== ========================== ============================ Parameters Yoast_2020 & Sneyd_2016 Modified Yoast_2020 ================== ========================== ============================ :math:`\tau_{max}` :math:`1000 ~s^{-1}` :math:`20~ s^{-1}` :math:`\alpha_{0}` :math:`0.0027 ~\mu M s^{-1}` :math:`0.0003~ \mu Ms^{-1}` :math:`K_{Ce}` :math:`8 ~ \mu M` :math:`200~ \mu M` :math:`k_{f}` :math:`10~ s^{-1}` :math:`0.2 ~ s^{-1}` :math:`\gamma` :math:`5.5` :math:`275` :math:`thapa` :math:`2~ mM~(Yoast)` :math:`0.2 ~ n M` :math:`k_{bar}` :math:`1.957e-5` :math:`7.82e-9` ================ ========================== ============================ Figure. 6: Mathematical modeling shows native CRAC channels are ORAI heteromultimers. .. image::Doc/Figure_6.png :width: 100% :align: center :alt: Fig. 6 Mathematical modeling shows native CRAC channels are ORAI heteromultimers. Figure. 10: ER Ca2+ concentrations in response to agonist stimulation. .. image::Doc/Figure_10.png :width: 100% :align: center :alt: Different pulse responses to the Calcium model. Model Simulation ================ Simulation setting: ------------------- Simulation settings are encoded in SED-ML_ documents for the experiment execution. The python scripts (Fig6_10_sim.py & Fig6D-10D_sim.py) to run the simulations (Yoast_2020.sedml & Yoast_2020_SubplotD.sedml). Simulation process: ------------------- Execute 'Fig6_10_sim.py' in the Python console in OpenCOR_. This can be done with the following commands at the prompt in the OpenCOR_ Python console: In [1]: cd path/to/folder_this_file_is_in In [2]: run Fig6_10_sim.py To reproduce Figure 6, after collection of the required data, run the Python script Fig6_Plot.py. To reproduce Figure 10, run the Python script Fig6_Plot.py. To reproduce data related to ORAI channels, run the Python script Yoast_2020_ORAI.py in Python console.