Fig 1.
(A) Illustration of wound healing/scratch assay.
(B) Diffusion, advection, and reaction mechanisms for cell random motion, directed motion and proliferation, respectively.
Fig 2.
Experimental wound healing data (symbols), the model inferred by Jin et al. [11] (dashed curves), and the model inferred by Variational System Identification and refined by PDE-constrained optimization (solid curves).
For the 18000 initial density data, the 4-term model was used. Inferred model parameters appear in Table 1.
Table 1.
Model terms learnt by Variational System Identification and PDE-constrained parameter optimization for each experimental condition presented in Jin et al.
As in the text, C is the cell number density measured in the units of cells/.
Fig 3.
Elbow curve illustrating the Variational System Identification (VSI) loss at each step of stepwise regression.
At each step, the loss is computed as the minimum residual norm over the space of all admissible parameters for the current model.
Fig 4.
Root mean squared error (RMSE) calculated between experimental data and reaction-diffusion models from Jin et al. (blue), and a model obtained by PDE-constrained optimization following Variational System Identification (red) for each case with different initial number of seeded cells.
For the 18000 initial density data, the 4-term model was used. The model parameters inferred in this work are shown in Table 1.
Fig 5.
Fractional wound closure Eq (1) calculated for a range of trametinib concentrations and an untreated control (labeled NT), with N = 4 wells for all conditions.
Individual datapoints are shown in red, and the mean +/- standard deviation is shown by the bars and error bars, respectively.
Fig 6.
(A) Comparison of experimental data and predictions of a model inferred by Variational System Identification followed by PDE-constrained parameter optimization under the same initial conditions.
The experimental condition is with no treatment. (B) Variational System Identification loss as a function of the number of terms in the model inferred for the untreated and 100 nM trametinib conditions. (C-D) PDE-constrained and optimized diffusivity (C) and reaction (cell proliferation) (D) terms as functions of density. Diffusivity is constant, while reaction/proliferation is a combination of linear and quadratic terms. The horizontal axis ranges were chosen to represent the densities present in the experimental data.
Fig 7.
Loss minimization during PDE-constrained optimization process.
Fig 8.
RMSE evaluated between the forward prediction of VSI+Optim models (Variational System Identification and PDE-constrained parameter optimization) presented in Table 2.
The red dots represent the RMSE for each replicate, and the bar represents the mean value.
Table 2.
Model terms inferred by Variational System Identification and PDE-constrained parameter optimization for each experimental condition shown in Fig 3.
As in the text, C is the cell number density measured in the units of cells/.
Fig 9.
Sensitivity analysis of the inferred parameters in the 3-term model: .
Contour plots show the normalized loss function from Eq (16a) as a function of parameter variations. Each column represents a case where one parameter– C2 (left), C1 (middle), or D0 (right)–is held fixed at its inferred value, while the remaining two parameters are varied in a neighborhood around their inferred values: ,
, and
, respectively. Each row corresponds to one of the six experimental conditions. Contours illustrate the sensitivity of the loss function to changes in the inferred parameters, where sharp minima indicate high sensitivity (well-constrained parameters), and broader regions suggest lower sensitivity (potential parameter degeneracy).