Set membership experimental design for biological systems

Experimental design approaches for biological systems are needed to help conserve the limited resources that are allocated for performing experiments. The assumptions used when assigning probability density functions to characterize uncertainty in biological systems are unwarranted when only a small number of measurements can be obtained. In these situations, the uncertainty in biological systems is more appropriately characterized in a bounded-error context. Additionally, effort must be made to improve the connection between modelers and experimentalists by relating design metrics to biologically relevant information. Bounded-error experimental design approaches that can assess the impact of additional measurements on model uncertainty are needed to identify the most appropriate balance between the collection of data and the availability of resources.

In this work we develop a bounded-error experimental design framework for nonlinear continuous-time systems when few data measurements are available. This approach leverages many of the recent advances in bounded-error parameter and state estimation methods that use interval analysis to generate parameter sets and state bounds consistent with uncertain data measurements. We devise a novel approach using set-based uncertainty propagation to estimate measurement ranges at candidate time points. We then use these estimated measurements at the candidate time points to evaluate which candidate measurements furthest reduce model uncertainty. A method for quickly combining multiple candidate time points is presented and allows for determining the effect of adding multiple measurements. Biologically relevant metrics are developed and used to predict when new data measurements should be acquired, which system components should be measured and how many additional measurements should be obtained.

The practicability of our approach is illustrated with a case study. This study shows that our approach is able to 1) identify candidate measurement time points that maximize information corresponding to biologically relevant metrics and 2) determine the number at which additional measurements begin to provide insignificant information. This framework can be used to balance the availability of resources with the addition of one or more measurement time points to improve the predictability of resulting models.