Parameter Identification with Adaptive Sparse Grid-based Optimization for Models of Cellular Processes

Identifying parameter values in mathematical models of cellular processes is crucial to ascertain if the hypotheses reflected in the model structure is consistent with the available experimental data. Due to the uncertainty in the parameter values, partially attributed to the necessary model abstraction of any cellular process, parameters are pragmatically estimated by varying their values to minimize a cost function that represents the difference between the simulated results and available experimental data. Local searches for these parameter values rarely result in an adequate fit of the model to the experimental data since the optimization gets caught in a local minimum near the initial guess. Typically, larger regions of the parameter space must be searched for acceptable parameter values to support model simulations that replicate the experimental data. Most of these global algorithms use stochastic sampling of the parameter space; however, these methods are not computationally efficient and cannot guarantee convergence. Alternatively, adaptive sparse grid-based optimization samples the parameter space in a more systematic manner and employs selective evaluations of the cost function at support nodes to build an error-controlled interpolated approximation of the cost function from basis functions. The search for the global minimum is performed on the surrogate interpolant rather than relying extensively on simulations of the model; this tends to be more computationally efficient for smooth, continuous models. Additional insight is provided by the cost function 2 mapping on the parameter space, which can be useful for evaluating and refining the model and parameter identification problem. This chapter describes the methods to create and use an adaptive sparse grid and interpolant to find parameter values, including an example that demonstrates that this method performs more accurately, consistently, and efficiently than the genetic algorithm, a standard global stochastic optimization method.