# Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models.

@article{Thomas2010StochasticTO, title={Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models.}, author={Philipp Thomas and Arthur V. Straube and Ramon Grima}, journal={The Journal of chemical physics}, year={2010}, volume={133 19}, pages={ 195101 } }

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic…

## 36 Citations

### Systematic approximation methods for stochastic biochemical kinetics

- Computer Science
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An asymptotic series for the moments of the Chemical Master Equation that can be computed to arbitrary precision in the system size expansion and a diagrammatic technique based on the path-integral method that allows to compute time-correlation functions are devised.

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A theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network and theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

### Model reduction for stochastic chemical systems with abundant species.

- PhysicsThe Journal of chemical physics
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It is proved that in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations.

### The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

- BiologyBMC Systems Biology
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A new general method is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions, which is expected to be of widespread utility in studying the dynamics of large noisy reaction networks.

### Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

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An introduction to basic modelling concepts as well as an overview of state of the art methods for deterministic and stochastic methods for modelling chemical networks are introduced and several approximation methods are discussed.

### Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

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An introduction to basic modelling concepts as well as an overview of state of the art methods for stochastic chemical kinetics, including the chemical Langevin equation and several approximation methods.

### Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

- PhysicsIET systems biology
- 2012

It is demonstrated that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory, in models that exhibit noise-induced oscillations.

### Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA

- Computer Science2012 IEEE International Conference on Bioinformatics and Biomedicine
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The linear noise approximation is commonly used to obtain intrinsic noise statistics for biochemical networks. These estimates are accurate for networks with large numbers of molecules. However it is…

### Intrinsic Noise Analyzer: A Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion

- Computer SciencePloS one
- 2012

The software package intrinsic Noise Analyzer (iNA) is introduced, which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen’s system size expansion of the Chemical Master Equation, and allows for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients.

### Queueing Theory-Based Perspective of the Kinetics of “Channeled” Enzyme Cascade Reactions

- BiologyACS Catalysis
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This work compares the results of a model using differential equations to describe concentration changes with a queueing model and finds that in two enzyme cascades, the queueingmodel predicts at most a 50% smaller throughput than the continuum model even if the waiting room size is smaller.

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