Abstract
To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This ‘global’ analysis is then supplemented by a ‘local’ analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our ‘glocal’ combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets.
Highlights
Biologists’ qualitative reasoning about outcomes of experiments show inherent limitations
The second, local aspect of our method evaluates the robustness of model behavior – for each of the previously generated parameter sets – to five different kinds of perturbations, including concentration perturbations and molecular noise
To illustrate the application of our method, we focus on two recent models of the cyanobacterial circadian oscillator [31,32]
Summary
Biologists’ qualitative reasoning about outcomes of experiments show inherent limitations. Mathematical models of cellular processes, such as signaling, cell-cycle regulation, or circadian rhythmicity [1,2] can compensate for these limitations. Such models are often systems of ordinary differential equations, whose state variables represent the molecules that take part in a process. A model is judged superior if there exist parameters (in its usually high-dimensional parameter space) that allow the model to mimic biologically observed behavior more closely than other models This approach fails in the common situation where parameters are underdetermined by model behavior and many parameter sets exist that match the behavior well [5]. Global methods characterize properties of a model’s parameter space, such as
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