BackgroundA biological system's robustness to mutations and its evolution are influenced by the structure of its viable space, the region of its space of biochemical parameters where it can exert its function. In systems with a large number of biochemical parameters, viable regions with potentially complex geometries fill a tiny fraction of the whole parameter space. This hampers explorations of the viable space based on "brute force" or Gaussian sampling.ResultsWe here propose a novel algorithm to characterize viable spaces efficiently. The algorithm combines global and local explorations of a parameter space. The global exploration involves an out-of-equilibrium adaptive Metropolis Monte Carlo method aimed at identifying poorly connected viable regions. The local exploration then samples these regions in detail by a method we call multiple ellipsoid-based sampling. Our algorithm explores efficiently nonconvex and poorly connected viable regions of different test-problems. Most importantly, its computational effort scales linearly with the number of dimensions, in contrast to "brute force" sampling that shows an exponential dependence on the number of dimensions. We also apply this algorithm to a simplified model of a biochemical oscillator with positive and negative feedback loops. A detailed characterization of the model's viable space captures well known structural properties of circadian oscillators. Concretely, we find that model topologies with an essential negative feedback loop and a nonessential positive feedback loop provide the most robust fixed period oscillations. Moreover, the connectedness of the model's viable space suggests that biochemical oscillators with varying topologies can evolve from one another.ConclusionsOur algorithm permits an efficient analysis of high-dimensional, nonconvex, and poorly connected viable spaces characteristic of complex biological circuitry. It allows a systematic use of robustness as a tool for model discrimination.

Predictive dynamical models are critical for the analysis of complex biological systems. However, methods to systematically develop and discriminate among systems biology models are still lacking. We describe a computational method that incorporates all hypothetical mechanisms about the architecture of a biological system into a single model and automatically generates a set of simpler models compatible with observational data. As a proof of principle, we analyzed the dynamic control of the transcription factor Msn2 in Saccharomyces cerevisiae, specifically the short-term mechanisms mediating the cells' recovery after release from starvation stress. Our method determined that 12 of 192 possible models were compatible with available Msn2 localization data. Iterations between model predictions and rationally designed phosphoproteomics and imaging experiments identified a single-circuit topology with a relative probability of 99% among the 192 models. Model analysis revealed that the coupling of dynamic phenomena in Msn2 phosphorylation and transport could lead to efficient stress response signaling by establishing a rate-of-change sensor. Similar principles could apply to mammalian stress response pathways. Systematic construction of dynamic models may yield detailed insight into nonobvious molecular mechanisms.