Experimental Prediction of | Model selection based on parameter estimation permits the selection of the best model structure. |
Ordinary differential equation model selection | For each model structure, parameter estimation was performed to determine the model performance in relation to the experimental data. |
Ordinary differential equation model selection | To reduce the complexity of combining all model structures, we applied a “backward selection” based on the removal of single building blocks from the complete model structure followed by parameter estimation to obtain a new ranking (Fig 5B). |
Ordinary differential equation model selection | Based on the backward selection result, we generated combinations of model structures focusing on these four minimal models and performed parameter estimation for all eleven possible combinations (Fig 5C). |
Ordinary differential equation modeling | Parameter estimation . |
Ordinary differential equation modeling | To find the optimal parameter sets that describe the experimental data for each model structure, we performed parameter estimations . |
Ordinary differential equation modeling | The procedure of parameter estimation is based on multiple local optimizations of different parameter starting values. |
Parameter estimation | Parameter estimation |
Parameter estimation | Here, we used the data for glucose and ethanol for parameter estimation . |
Parameter estimation | Model-1 and Model-2 were fitted independently using a custom evolutionary parameter estimation algorithm (81 Text). |
Results | We used the data for glucose and ethanol for parameter estimation and the data for galactose and raff1nose for validation of the models (Fig 3A). |
Supporting Information | Convergence of the objective value during parameter estimation . |
Supporting Information | Shown is the evolution of the objective values (thin lines) and the mean objective value (thick lines) over the number of iterations for 100 rounds of parameter estimation for Model-1 (red) and Model-2 (blue), respectively. |
Supporting Information | Note that in every iteration of the parameter estimation , the algorithm runs through a population of 12 different parameter sets for each model. |
Dynamic electrophysiology protocols and optimization improve model fit to in vitro experimental data | The parameter estimation method was next applied to four guinea pig left basal ventricular myocytes from four different animals. |
Extending the protocol: Adding multi-step voltage clamp data | To improve parameter estimation accuracy, more improvement is typically gained from adding measurements of a different state variable than adding additional measurements of the same state variable [36]. |
Extending the protocol: Adding multi-step voltage clamp data | Therefore, to improve the parameter estimation accuracy, we added a multi-step voltage clamp protocol to the objective function. |
GA optimization using a single action potential | We first developed our parameter estimation strategy using a guinea pig ventricular myocyte model (Faber and Rudy [34], the “FR” model) and tested the ability of the optimization procedure to return the original parameter values. |
GA optimization using a single action potential | Therefore, we first ran the parameter estimation using a single FR model action potential as the target objective. |
Introduction | In neuroscience, considerably more research has been carried out on parameter estimation problems (e.g., [27—30]) and a few studies have developed protocols that allow parameterization of cell-specific models [31,32]. |
Stochastic stimulation protocol improves model fit and predictability over single action potential protocol | We used this stochastic stimulation protocol and resulting voltage response as an optimization sequence to test the extent to which dynamic stimulus timing would improve the parameter estimation . |
Stochastic stimulation protocol improves model fit and predictability over single action potential protocol | Because the GA parameter estimation is a stochastic method, it was run 10 times with 10 different initial populations. |
Stochastic stimulation protocol improves model fit and predictability over single action potential protocol | Compared to the single action potential, the stochastic stimulation leads to a modest overall improvement of the parameter estimation , but it did notably better in determining the maximal conductances of IKr, ICaL, and 1K3 (Fig 2C). |
The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation | The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation |
The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation | Running the optimization with the combined objective does indeed lead to improved accuracy of the parameter estimation , with all nine current parameters being recovered to within one standard deviation (orange symbols, Fig 4B). |
Methods | Sensitivity of the parameter estimates was explored by performing MCMC separately using different subsets of the data. |
Year | The black dots are US disease incidence data, and the shaded regions represent the credible intervals (50% and 95%) obtained through model parameter estimation of model 8. |
Year | Parameter estimates for the best-fitting model, Model 8 (models outlined in Table 1). |
Application to real outbreaks | However, when we simulated 150 or 250 spillover events instead, the uncertainty in our estimates shrank, and we were able to obtain more precise parameter estimates (88 Fig). |
Discussion | We tested the accuracy of parameter estimation when the transmission process was mis-specif1ed, and found that it was still possible to distinguish between different scenarios as long as transmission matrices in both the simulation and inference models were dominated by intense mixing between children. |
Inference | For a higher dimensional model, it might be necessary to use an alternative technique, such as Markov chain Monte Carlo [41], to ensure robust and efficient parameter estimation . |