"Quantitative Experiment Design for Highly Uncertain Biological Systems"
April 2 @ 3:00 PM - 4:00 PM - Birck Nanotechnology Center, Room 2001
Abstract: Many biological systems are highly uncertain thus their descriptive mathematical models have structures that are not fully defined by underlying physical and chemical principles and have parameters that are not well constrained by existing data. Experiments to resolve the biological system behaviors and their associated mathematical model are expensive, so it is vital to design experiments that will be nearly optimal among available experiments in terms of constraining the model structure and parameters the most. Our sequential experiment design approach addresses these issues by using sparse grid interpolation to identify multiple areas of parameter space that are consistent with available data and clustering these identified parameters based on simulated model response and the limits of experimental measurement. By analyzing the expected experimental variance and the variance due to different model responses, we choose a measurement to provide maximal discrimination among currently acceptable solutions. This experiment design criterion is similar to the Hunter-Reiner criterion since it looks for the largest difference in predicted dynamics, but it also avoids design points with large expected measurement error as recommended by Buzzi-Ferraris & Forzatti. This approach further differs from other experiment design methods in that it simultaneously addresses both parameter- and structural- based uncertainty, is applicable to some ill-posed problems where the number of uncertain parameters exceeds the amount of data, places very few requirements on the model type, available data, and a priori parameter estimates, and is performed over the global uncertain parameter space. We illustrate this approach on models of the mitogen-activated protein kinase cascade, one with 3 uncertain parameters and one with 18 uncertain parameters. The results show that system dynamics are highly uncertain with an initial set of limited experimental data. Nevertheless, the algorithm requires only three additional experimental data points to simultaneously discriminate between possible model structures and acceptable parameter values. This sparse grid-based experiment design process provides a systematic and computationally efficient exploration over the entire uncertain parameter space of potential model structures to resolve the uncertainty in the nonlinear systems biology model dynamics.
- Mari-Ellyn Brock