Balanced truncation for model reduction of biological oscillators

Abstract

Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.

Model reduction of dominant feedback systems

“…However, there is no fundamental barrier to analyzing other biological systems with a similar feedback structure, in which the dynamics to be reduced is nonlinear. Preliminary findings suggest that balancing gramians with inertia enables the application of balanced truncation to other biological systems of interest, such as the Goldbeter model for the circadian oscillations in the expression of the per gene in Drosophila [13], see [29] for a first step in this direction.…”

“…To the best of our knowledge, the present paper and the preliminary paper [30] are the first works to explore the problem of approximating a feedback system while preserving p-dominance properties. Numerical results suggest that the problem has many potential applications in biology beyond the specific example presented here, see [29] for a first discussion in that direction.…”

From data to reduced-order models of complex dynamical systems

“…In [149], it is shown that the Kron reduction approach can be applied to open CRN. Another work on model reduction of open CRN systems uses balanced truncation to the associated variational systems obtained through a linearization, see [136].…”