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Systems approaches and algorithms for discovery of combinatorial therapies

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Abstract Effective therapy of complex diseases requires control of highly nonlinear complex networks that remain incompletely characterized. In particular, drug intervention can be seen as control of cellular network activity. 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 heuristic 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. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Translational, Genomic, and Systems Medicine > Therapeutic Methods

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The nonsystematic method. This approach designs combinations based on the clinical experience of doctors, knowledge of biological mechanisms, and practical constraints in the design of clinical trials.

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Modeling approaches integrated with experimental search. A more systematic approach could integrate information from statistical and explicit models. Model‐based predictions of effective perturbations can be combined with closed‐loop iterative experimental search to refine the drug combination.

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Scheme of different types of landscapes. The structure of the control landscape can inform the choice of the search strategy. Left: Rugged, found, for example, in spin glasses as a result of competition between ferromagnetic and antiferromagnetic interactions. Center: Funnel, found, for example, in protein folding fitness landscapes. Right: Robust, found, for example, in quantum control problems in which often control parameters give perfect control or no control at all.

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Diagram of the iterative search framework. At each iteration, a high‐throughput assay measures cellular (or organism) phenotype in response to a drug combination, which is fed into the algorithm. The algorithm then generates new candidate combinations to test based on the previous results. Conceptually, this is equivalent to a search through the phenotype landscape in the space of possible drugs and doses.

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Using the biological search algorithm (‘Stack Sequential‐Top Down’ or SS‐TD) to optimize combinations for cancer cell selectivity. The colors indicate the selectivity of the drug interventions and the aim is to find treatments with high selectivity for one of the cell lines. This desired selectivity is shown as dark blue. The red shades are partially selective for the other cell line. Iterations of the algorithm apply different sizes of combinations, starting with individual drugs. A statistically significant enrichment of the desired selective combinations (dark blue) is shown. (Adapted with permission from Ref 46. Copyright 2009 PLoS).

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Biological search algorithm. In this model‐free approach to combination design, drugs are iteratively combined and measured, in effect searching through the vast space of possibilities.

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Model‐based approach to designing combinations. Explicit models of biochemical interactions, usually fitted to measured biological data (including genome‐wide or ‘omic’ data such as microarrays), are used to predict optimal combinations via simulation.

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Statistical association models. This approach attempts to design combinations based on the desired phenotype and linear combinations of input/output relationships of single drugs.

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The brute force approach. Brute force is a term meaning exhaustive testing of all possible combinations. High‐throughput screening technology allows the testing of pairs of drugs over a range of doses, but combinatorial explosion usually prevents exhaustive measurement of combinations of more than two drugs except when exploring combinations from very limited sets of compounds.

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