  Effective therapy of complex diseases requires control of highly non-linear
complex networks that remain incompletely characterized. In particular, drug
intervention can be seen as control of signaling in cellular networks.
Identification of control parameters presents an extreme challenge due to the
combinatorial explosion of control possibilities in combination therapy and to
the incomplete knowledge of the systems biology of cells. In this review paper
we describe the main current and proposed approaches to the design of
combinatorial therapies, including the empirical methods used now by clinicians
and alternative approaches suggested recently by several authors. New
approaches for designing combinations arising from systems biology are
described. We discuss in special detail the design of algorithms that identify
optimal control parameters in cellular networks based on a quantitative
characterization of control landscapes, maximizing utilization of incomplete
knowledge of the state and structure of intracellular networks. The use of new
technology for high-throughput measurements is key to these new approaches to
combination therapy and essential for the characterization of control
landscapes and implementation of the algorithms. Combinatorial optimization in
medical therapy is also compared with the combinatorial optimization of
engineering and materials science and similarities and differences are
delineated.
