Multi-scale Modeling and Sensitivity Analysis in Biological Systems

We develop a multi-method sensitivity framework, which incorporates two variance-based methods, namely Sobol\u27s method, eFAST and Derivative-based global measures to identify which parameters are most influential to the model outputs. A new implementation version of eFAST, namely DeFAST, was developed to address some critical issues in an existing published algorithm. Sensitivity analysis is a powerful tool in the modeling process that can be leveraged in various ways including model reduction and model fitting to data. There are two novel models that have been developed in this work where sensitivity analysis was applied. A stochastic computational model was constructed to understand mechanistic division event in Caulobacter crecentus bacterium in order to investigate how precise measurements can be made at the micron scale in the face of stochastic fluctuations. In this context, sensitivity analysis is used to derive a minimal PDE model in a minimal intermittent-search framework that could capture key results of the computational model closely. In addition, a new single compartment mathematical model for type I diabetes was analyzed to understand which parameters are the main driver of the blood glucose dynamics with the intention to understand the curative potential of dendritic-cell-based vaccine therapies. In this case, the sensitivity analysis was used to rank parameters and reduce the parameter space so that we can calibrate the model with in-vivo data in the future. The novelty of this work is that we validate our sensitivity analysis approach on highly nonlinear and stochastic models. These complex models present significant challenges for the application of sensitivity analysis algorithms as compared to the simpler case-study models that are typically used for testing sensitivity analysis methods