Lees_Green_2014

Original Paper

Model status

The current CellML model implementation runs in OpenCOR. The CellML model parameters and equations must be updated regarding each specific model variation to reproduce the related simulations; see Model Experiments below for more detailed information. The results have been validated against the data extracted from the figures in the published Lees-Green, Rachel, et al (2014); see the section Model Validation. Using the default parameters provided in the paper except for the modification listed in the following sections, Figures 4 and 5 can be reproduced. See Model Modifications below.

Model Summary

Interstitial cells of Cajal (ICC) pacemaker activity begins when IP3-mediated Ca² release from the ER leads to depletion of the ER Ca² stores, activating SOCE via SOC channels. Ano1 channels colocalized with SOC channels are activated by the local rise in Ca² in microdomains surrounding the open SOC channels, causing depolarization of the ICC. The depolarization initiates a slow wave by activating voltage-dependent ion channels. The morphology of the slow wave, including the plateau phase and repolarization, is determined by the balance of voltage- and Ca²-dependent ion currents. The pacemaker cycle concludes when Ca² influx via SOC channels and uptake via SERCA pumps is sufficient to refill the ER stores, resulting in deactivation of the SOC channels and Ano1 channels.

Model Equations

The model is implemented using a Hodgkin-Huxley type formulation, where the cell membrane lipid bilayer is expresses capacitance (Cm), and the ion channels in the membrane express conductance. The change in the transmembrane potential (Vm) over time depends on the sum of the individual ion currents through each class of ion channel in the cell current:

where there are 12 different ion channels contributing to the total current I_tot.

Model Variations

A high chloride environment ( E_Cl =  − 20.2 mV, C_Cl = 78 mM) is categorized into four different variations:

• High-Cl (NaV): Ion current specific to Voltage-gated Na channel
• High-Cl (NSCC): Ion currents specific to Ca²-activated nonselective channel
• High-Cl (CaV): Ion current specific to Voltage-gated Ca channel

A low chloride environment is modelled (E_Cl =  − 49.7 mV, C_Cl = 25.85 mM) where the low chloride simulations are categorized into two different variations:

• Low-Cl (NaV) : Ion currents specific to Voltage-gated Na channel
• Low-Cl (NSCC): Ion currents specific to Ca²-activated nonselective channel

Model Experiments

This workspace contains two sets of experiments and corresponding simulation results. The first sets reproduce the four variations for the high chloride concentration and therefore E_Cl =  − 20mV, and the results are demonstrated in Figure. 4. The second sets of variations represent the low chloride environment with the E_Cl =  − 50mV (Figure 5 in the original paper).

• Figure 4A-4E (HIGH-CL(NaV): Sodium Voltage Activated Channel): the file HCl-NaV.json contains the HIGH-CL(NAV) model's parameters and initial conditions. The wild-type (WT) simulation's result (full model simulation) is saved in 'Fig4_1a.csv'. For the Ano1 knockout (KO) scenarios, data is saved in 'Fig4_1b.csv'.
• Figure 4B-4F (HIGH-CL(NSV): Non-Selective Voltage Activated Channel): the file HCl-NSV.json contains the HIGH-CL(NSV) model's parameters and initial conditions. The data relating to HIGH-CL(NSV) wild-type simulation is saved in 'Fig4_2a.csv'. For the Ano1 knockout (KO) scenarios, data is saved in 'Fig4_2b.csv'.
• Figure 4C-4G (HIGH-CL(NSCC): Non-Selective Ca Activated Channel): the file HCl-NSCC.json contains the HIGH-CL(NSCC) model's parameters and initial conditions. The WT and KO results are saved in 'Fig4_3a.csv' and 'Fig4_3b.csv', respectively.
• Figure 4D-4H (HIGH-CL(CaV): Ca Voltage Activated Channel): the file HCl-CaV.json contains the HIGH-CL(CaV) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig4_4a.csv' and 'Fig4_4b.csv', respectively.
• Figure 5A-5C (LOW-CL(NaV): Sodium Voltage Activated Channel) : the file LCl-NaV.json contains the LOW-CL(NAV) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig5_1a.csv' and 'Fig5_1b.csv', respectively.
• Figure 5B-5D (LOW-CL(NSCC): Non-Selective Ca Activated Channel): the file LCl-NSCC.json contains the LOW-CL(NSCC) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig5_2a.csv' and 'Fig5_2b.csv', respectively.

Model Modifications

In the case of reproducibility and reusability, there are a couple of issues with the model equations and model default parameters. We point them as below:

• There are no definitions of the fluxes for some ion channels; definitions are defined from the references and compared to the similar descriptions of the other fluxes with similar behaviour in the original work and confirmed through the MATLAB updated model of ICC.
• To reproduce Figure 5A-5C: the K parameter for voltage-dependent gating equation for the NaV channel inactivation F_NaV is changed from -4.5 mV to 4.5 mV as the K parameter for voltage-dependent gating equation in the case of inactivation is always positive.

To reproduce Figure 5B-5D: the conductance value for the CaV channel is reduced to g = 3.72 nS from the original value g = 4 nS. As shown in the below diagram at g = 4 nS, there are damped oscillations that indicate that the dominant eigenvalue has a negative real value for stable system. These damped oscillations switch to the slow-wave oscillations for g = 3.72 nS.

Model Validations

The results have been validated against the data extracted from the figures in the published Lees-Green, Rachel, et al (2014). Reproduction of Figure 4:

Reproduction of figure 5, with modifications listed in Model Modifications performed: