An important challenge in systems biology is the inherent complexity of biological network models, which complicates the task of relating network structure to function and of understanding the conceptual design principles by which a given network operates. Here we investigate an approach to analyze the relationship between a network structure and its function using the framework of optimization. A common feature found in a variety of biochemical networks involves the opposition of a pair of enzymatic chemical modification reactions such as phosphorylation-dephosphorylation or methylation-demethylation. The modification pair frequently adjusts biochemical properties of its target, such as activating and deactivating function. We applied optimization methodology to study a reversible modification network unit commonly found in signal transduction systems, and we explored the use of this methodology to discover design principles. The results demonstrate that different sets of rate constants used to parameterize the same network topology represent different compromises made in the resulting network operating characteristics. Moreover, the same topology can be used to encode different strategies for achieving performance goals. The ability to adopt multiple strategies may lead to significantly improved performance across a range of conditions through rate modulation or evolutionary processes. The optimization framework explored here is a practical approach to support the discovery of design principles in biological networks.