Showing papers by "Marc Hafner published in 2011"

Efficient characterization of high-dimensional parameter spaces for systems biology

Abstract: A 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. We 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. Our 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.

Deterministic characterization of phase noise in biomolecular oscillators.

Abstract: On top of the many external perturbations, cellular oscillators also face intrinsic perturbations due the randomness of chemical kinetics. Biomolecular oscillators, distinct in their parameter sets or distinct in their architecture, show different resilience with respect to such intrinsic perturbations. Assessing this resilience can be done by ensemble stochastic simulations. These are computationally costly and do not permit further insights into the mechanistic cause of the observed resilience. For reaction systems operating at a steady state, the linear noise approximation (LNA) can be used to determine the effect of molecular noise. Here we show that methods based on LNA fail for oscillatory systems and we propose an alternative ansatz. It yields an asymptotic expression for the phase diffusion coefficient of stochastic oscillators. Moreover, it allows us to single out the noise contribution of every reaction in an oscillatory system. We test the approach on the one-loop model of the Drosophila circadian clock. Our results are consistent with those obtained through stochastic simulations with a gain in computational efficiency of about three orders of magnitude.

Rational design of robust biomolecular circuits: from specification to parameters

Abstract: Despite the early success stories synthetic biology, the development of larger, more complex synthetic systems necessitates the use of appropriate design methodologies. In particular, the integration of smaller circuits in order to perform complex tasks remains one of the most important challenges faced in synthetic biology. We propose here a methodology to determine the region in the parameter space where a given dynamical model works as desired. It is based on the inverse problem of finding parameter sets that exhibit the specified behavior for a defined topology. The main issue we face is that such inverse mapping is highly expansive and suffers from instability: small changes in the specified dynamic property could lead to large deviations in the parameters for the identified models. To solve this issue, we discuss regularized maps complemented by local analysis. With a stabilized inversion map, small neighborhoods in the property space are mapped to small neighborhoods in the parameter space, thereby finding parameter vectors that are robust to the problem specification. To specify dynamic circuit properties we discuss Linear Temporal Logic (LTL). We apply these concepts to two models of the cyanobacterial circadian oscillation.