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

Tags

Fields of Study

  • Biology
  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Breast cancer cell signaling and growth regulation.
  • Calculus or Mathematical Analysis