# ECC_MSK (Rios et al. 1993)

### About this model

Original publication: | |
---|---|

Rios, E., et al. (1993): "An Allosteric Model of the Molecular Interactions of Excitation-Contraction Coupling in Skeletal Muscle." The Journal of general physiology 102.3 (1993): 449-481. | |

DOI: | 10.1085/jgp.102.3.449 |

### Model status

The current CellML implementation runs in OpenCOR.
The results have been validated against the data extracted from the figures in the published Rios, E., et al. (1993). We provide the settings used for the figure reproduction with the simulation results shown under `Experiments`. The model structure can be found in this documentation. The curation process has been summarized in the Model history and Known issues.

### Model overview

Rios, E., et al. (1993) proposed a quantitative formulation describing the allosteric transition in MWC model proposed by Monod, J., Wyman, J., & Changeux, J. P. (1965). The allosteric model includes four independent voltate sensor molecules in contact with the calcium release channel. Two states of the release channel (closed and open) are modelled, as well as two of five possible dispositions of the voltage sensors. The model is therefore a 10-state Markov system, and we refer it as `MWC-10 model`. In the Appendix, the model is generalized to include 8 sensors with 18 states in total, and we refer the generalized model as `MWC-18 model`. This workspace holds a CellML encoding of the Rios, E., et al. (1993) `MWC-10 model` and `MWC-18 model`.

### Modular description

#### Components

CellML divides the mathematical model into distinct components, which are able to be re-used. We reuse Markov states model MarkovS defined in the workspace cellLib. MarkovS defines Markov state change rate, in which `S1`, `S2`, and `S3` are the state connected with one, two, and three neighbors, respectively.

In Rios, E., et al. (1993) model, the form of the rate constants in transitions can be formalized as follows, where *N* is the number of the sensors, *j* is the number of activated sensors, C is a closed state, and O is an open state:

- The rate constants from
*C*_{j}to*C*_{j + 1}is (*N*−*j*)**k*_{C} - The rate constants from
*C*_{j + 1}to*C*_{j}is (*j*+ 1)**k*_{C}^{ − } - The rate constants from
*C*_{j}to*O*_{j}is*k*_{L}⁄*f*^{j} - The rate constants from
*O*_{j}to*C*_{j}is*k*_{L}^{ − }**f*^{j}

Hence, the main CellML components are:

The closed and open states when all the sensors in rest are

*C*_{0}to*O*_{0}, which have two neighbors, modelled as C0_S2 and O0_S2.The closed and open states when all the sensors being active are

*C*_{N}to*O*_{N}, which have two neighbors, modelled as CN_S2 and ON_S2.The closed states when some sensors are in rest and some are active, which have three neighbors, modelled as C_S3.

The open states when some sensors are in rest and some are active, which have three neighbors, modelled as O_S3.

Each of these blocks is itself a CellML model, which enables us to reuse the various components in future studies and models.

#### Experiments

Following best practices, this model separates the mathematics from the parameterisation of the model. The mathematical model is imported into a specific parameterised instance in order to perform numerical simulations. The default parameters are defined in Para. The parameterisation would include defining the stimulus protocol to be applied.

This workspace encodes MWC_10_experiment, MWC_18_experiment , and corresponding simulation results.

#### Simulation settings

Simulation settings are encoded in SED-ML files for experiment execution. It is common that we may need to vary experimental settings to obtain data under various conditions. Hence, the full experimental settings are encoded in the simulation scripts.
The Python scripts to run simulation and reproduce the figures in the original paper are included under the `Simulation/src` folder. The `runSim.ps1` is used to run the simulation in PowerShell, while `plotFig4.py`, `plotFig9_r.py`, `plotFig9_p.py` , `plotFig11.py`, `plotFig11_1.py`, `plotFig13_p.py` and `plotFig13_r.py` and `plotFig14.py` are ready to plot the figures in MWC_10_experiment and MWC_18_experiment .

We adopted the same stimulation protocol as discussed in primary Fig 1, where there is 100-ms 20 mV conditioning pulse followed by 100-ms -80 mV holding potential, then the test voltage is applied.

### Model history

There is no publicly available code for this model.

### Known issues

- The parameters we used to produce the figures are listed in Table 1.

- In the primary paper, Fig 11 caption says "the parameters are similar to those used for Fig. 9 (908 entries in Table I)" , however, Fig 9 says "Parameters are the same as those listed in Table I for fiber 827 ". We do not know which one is correct, so we tried both.
- Fig 4 and 13 are steady states of
`MWC-10 model`and`MWC-18 model`, respectively, which matches the original data very well. - Other figures are dynamic behaviors of the models, where we see discrepancy especially in case of perchlorate simulation.