Robust Calibration of High Dimension Nonlinear Dynamical Models for Omics Data: An Application in Cancer Systems Biology

In computational mathematical modeling of biological systems, most model parameters, such as initial conditions, kinetics, and scale factors, are usually unknown because they cannot be directly measured. Therefore, key issues in system identification of nonlinear systems are model calibration and identifiability analysis. Currently, existing methodologies for parameter estimation are divided in two classes: frequentist and Bayesian methods. The first optimize a cost function, while the second estimate the posterior distribution of parameters through different sampling techniques. However, when dealing with high-dimensional models, these methodologies suffer from an increasing computational cost due to the important volume of -omic data necessary to carry out reliable and robust solutions. Here, we present an innovative Bayesian method, called conditional robust calibration (CRC), for model calibration and identifiability analysis. The algorithm is an iterative procedure based on a uniform and joint perturbation of the parameter space. At each step the algorithm returns the probability density functions of all parameters that progressively shrink toward specific points in the parameter space. These distributions are estimated on parameter samples that guarantee a certain level of agreement between each observable and the corresponding in silico measure. We apply CRC to a nonlinear high-dimensional ordinary differential equations model representing the signaling pathway of p38MAPK in multiple myeloma. The available data set consists of time courses of proteomic cancerous data. We test CRC performances in comparison with profile-likelihood and approximate Bayesian computation sequential Monte Carlo. We obtain a more precise and robust solution with a reduced computational cost.