Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+
Abstract
Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to “slow” and “fast” system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the “stochastic tQSSA+”. Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 06, 2018
- Source ID
- 10.1063/1.5012752
Entities
People
- Domitilla Del Vecchio
- Narmada Herath
Organizations
- Air Force Office of Scientific Research
- Massachusetts Institute of Technology