Glycolysis in Saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations.

The glycolysis pathway in saccharomyces cerevisiae is considered, modeled by a dynamical system possessing a normally hyperbolic, exponentially attractive invariant manifold, where it exhibits limit cycle behavior. The fast dissipative action simplifies considerably the exploration of the system's robustness, since its dynamical properties are mainly determined by the slow dynamics characterizing the motion along the limit cycle on the slow manifold. This manifold expresses a number of equilibrations among components of the cellular mechanism that have a non-negligible projection in the fast subspace, while the motion along the slow manifold is due to components that have a non-negligible projection in the slow subspace. The characteristic time scale of the limit cycle can be directly altered by perturbing components whose projection in the slow subspace contributes to its generation. The same effect can be obtained indirectly by perturbing components whose projection in the fast subspace participates in the generated equilibrations, since the slow manifold will thus be displaced and the slow dynamics must adjust. Along the limit cycle, the characteristic time scale exhibits successively a dissipative and an explosive nature (leading towards or away from a fixed point, respectively). Depending on their individual contribution to the dissipative or explosive nature of the characteristic time scale, the components of the cellular mechanism can be classified as either dissipative or explosive ones. Since dissipative/explosive components tend to diminish/intensify the oscillatory behavior, one would expect that strengthening a dissipative/explosive component will diminish/intensify the oscillations. However, it is shown that strengthening dissipative (explosive) components might lead the system to amplified oscillations (fixed point). By employing the Computational Singular Perturbation method, it is demonstrated that such a behavior is due to the constraints imposed by the slow manifold.