Biological network design strategies: discovery through dynamic optimization Bambang S. Adiwijaya, ab Paul I. Barton* c and Bruce Tidor* abd Received 14th July 2006, Accepted 16th October 2006 First published as an Advance Article on the web 27th October 2006 DOI: 10.1039/b610090b 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. Introduction The development of quantitative models describing biological networks for a number of interesting systems is being undertaken. 1–23 These models aim to capture the underlying structure, dynamics, and detailed mechanisms of their experi- mental counterparts in a manner that recapitulates known behaviors, provides a means for understanding that behavior, and also predicts previously unmeasured or new behavior. The detail, accuracy, and number of systems for which models are available are all expected to grow for the foreseeable future. These models may potentially be used to generate hypotheses, understand design principles, create synthetic components, and produce effective therapeutic strategies. An important chal- lenge 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 one class of approaches for analyzing the relationship between network structure and functional behavior. We are concerned with dynamic properties, which may be particularly important for biological systems, although the same framework can address questions of steady-state behavior, which are generally simpler. The overall approach involves applying optimization techniques to identify the best combinations of model parameter values to achieve canonical functional character- istics. In this manner, we study the relationship between model parameters (such as rate constants) and function. This complements, but differs fundamentally from, approaches in which systematic variation is applied to the parameters and the resultant change to behavior is monitored (sensitivity analysis and other variational approaches). 9,24–27 Here, essentially by manipulating the desired functional behavior (generally pro- perties of the network output) and by monitoring the resultant required parameter values—i.e., the inverse of more standard variational approaches—we can learn about the relationship between function and parameterization and may be in a position to discover new design principles. This approach works synergistically with variational analysis, which we then apply to dissect the roles of individual parameters. The fundamental network unit examined here consists of the enzyme catalyzed chemical modification of a protein molecule and the reverse reaction catalyzed by a different enzyme. This basic unit is found repeatedly in multiple configurations throughout a wide variety of biological pathways, including methylation–demethylation reactions integral to bacterial chemotaxis 28 and phosphorylation–dephosphorylation a Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA b Biological Engineering Division, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA c Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA. E-mail: pib@mit.edu d Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA. E-mail: tidor@mit.edu; Fax: +1 (617) 252-1816; Tel: +1 (617) 253-7258 PAPER www.rsc.org/molecularbiosystems | Molecular BioSystems 650 | Mol. BioSyst., 2006, 2, 650–659 This journal is ß The Royal Society of Chemistry 2006