• Publications
  • Influence
Separation of time-scales and model reduction for stochastic reaction networks.
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach isExpand
  • 132
  • 12
  • PDF
Central limit theorems and diffusion approximations for multiscale Markov chain models
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systemsExpand
  • 47
  • 2
  • PDF
A new method for choosing the computational cell in stochastic reaction–diffusion systems
How to choose the computational compartment or cell size for the stochastic simulation of a reaction–diffusion system is still an open problem, and a number of criteria have been suggested. AExpand
  • 28
  • 1
  • PDF
Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics
The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis–Menten enzyme kinetics. In particular, itExpand
  • 17
  • 1
  • PDF
Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast
Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to stimuli. It remains unclear how intrinsicExpand
  • 6
  • 1
Stochastic Analysis of Reaction–Diffusion Processes
TLDR
Reaction and diffusion processes are at the core of many models of biological processes, ranging from the molecular level, at which they are used to describe signaling, metabolic processes or gene control, to the population level. Expand
  • 17
  • PDF
The effect of the signalling scheme on the robustness of pattern formation in development
TLDR
We analyse both deterministic and stochastic reaction-diffusion models of pattern formation with a view towards understanding how the signalling scheme used for patterning affects the variability of boundary determination in a developing tissue. Expand
  • 15
  • PDF
Reduction for Stochastic Biochemical Reaction Networks with Multiscale Conservations
TLDR
We propose an appropriate modification of the multiscale approximation method for continuous time Markov processes to obtain more accurate approximations on the timescale of interest. Expand
  • 14
  • PDF
A multiscale approximation in a heat shock response model of E. coli
  • Hye-Won Kang
  • Mathematics, Computer Science
  • BMC Systems Biology
  • 21 November 2012
TLDR
Using the method of separation of time-scales and model reduction for stochastic reaction networks extended by Kang and Kurtz (2012), we approximate the chemical network in the heat shock response model. Expand
  • 11
  • PDF
Multiscale methods in a Heat Shock Response Model
My graduate research involves the application of stochastic analysis to biological problems. Recently, interest in mathematical biology has grown enormously and mathematicians in various areas haveExpand