Sparse grid-based modeling and control of biological systems

Maia Mahoney Donahue, Purdue University

Abstract

The goal of systems biology is to utilize quantitative, mathematical models in order to advance the understanding of complex biological processes as well as determine strategies to modify or control these processes. Achieving these goals could aid the development of novel disease interventions and therapy strategies. The major challenge that systems biology faces is uncertainty. Uncertainty arises from incomplete knowledge of the biological pathways, which are encoded in the mathematical equations of the model, and the dynamical rates at which the processes proceed, which are encoded in values of the model parameters. Knowledge is hampered by the fact that biological data is usually noisy, due to biological variation and experimental error, is often taken at sparse times points, and typically does not include measurements for every element of the system. A set of systems biology tools has been developed that appropriately deal with these sources of biological uncertainty, including experiment design, control, and robustness analysis algorithms. These algorithms rely on a thorough exploration of the global parameter space to characterize uncertainty, in terms of the data-consistent dynamics of the system. Such an examination of a global space is unusual, due to the high computational demand and the problem of the curse of dimensionality (where the computational effort is on the order of the problem's dimension). Therefore, this work presents a new implementation of sparse grids, which can be less dependent on dimension then other sampling techniques, in order to make this exploration computationally feasible, even in high dimensional spaces. In this work, a sequential experiment design algorithm helps reduce the uncertainty in the dynamics of a biological system. In addition, an adaptive predictive control algorithm determines the appropriate input to predictably alter the behavior of a biological system with uncertainty in its model parameter values. Furthermore, a robust open loop controller was designed to control biological systems with uncertainty in the model structure. These developed algorithms are broadly applicable in the field of systems biology: they place no restrictions on the type of model used, the amount of data or knowledge of the system already available, or the quality of data. As a result, it is expected that the algorithms can be widely applied to many systems biology applications. Examples for both intracellular and biomedical applications are demonstrated.

Degree

Ph.D.

Advisors

Rundell, Purdue University.

Subject Area

Systematic|Biomedical engineering

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