Module-Based Analysis of Robustness Tradeoffs in the Heat Shock Response System

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Abstract
Biological systems have evolved complex regulatory mechanisms, even in situations where much simpler designs seem to be sufficient for generating nominal functionality. Using module-based analysis coupled with rigorous mathematical comparisons, we propose that in analogy to control engineering architectures, the complexity of cellular systems and the presence of hierarchical modular structures can be attributed to the necessity of achieving robustness. We employ the Escherichia coli heat shock response system, a strongly conserved cellular mechanism, as an example to explore the design principles of such modular architectures. In the heat shock response system, the sigma-factor σ32 is a central regulator that integrates multiple feedforward and feedback modules. Each of these modules provides a different type of robustness with its inherent tradeoffs in terms of transient response and efficiency. We demonstrate how the overall architecture of the system balances such tradeoffs. An extensive mathematical exploration nevertheless points to the existence of an array of alternative strategies for the existing heat shock response that could exhibit similar behavior. We therefore deduce that the evolutionary constraints facing the system might have steered its architecture toward one of many robustly functional solutions. Biological systems maintain phenotypic stability in the face of various perturbations arising from environmental changes, stochastic fluctuations, and genetic variations. This robustness, which seems to be an inherent property of such systems, is still poorly understood at the molecular level. At the same time, systems approaches that were used with great success in the study and design of complex engineered systems provide a unique opportunity for investigating the basic tenants of robustness in cellular mechanisms. This is motivated by the fact that at the system level, biology and engineering seem to have a large number of common features despite their extremely different physical implementations. The heat shock response is one such robust cellular system, which interestingly achieves its seemingly simple objective of refolding or eliminating heat-denatured proteins through a complicated set of interactions. In analogy to engineering control architectures, the complex regulation strategies seem to be a specifically designed solution to generate robustness against different types of perturbations.