# Long-time analytic approximation of large stochastic oscillators: simulation, analysis and inference

BioRxiv : the Preprint Server for Biology
Giorgos Minas, David A Rand

## Abstract

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-$\kappa$B system are used to illustrate our results.

## Related Concepts

Simulation
Correct brand of docusate-phenolphthalein
Analysis
Anhydrous Dextrose
Protein Expression
Inebriated protein, Drosophila
CLOCK gene
Cancer Models Database
Fisher's Exact Test

## Related Feeds

### BioRxiv & MedRxiv Preprints

BioRxiv and MedRxiv are the preprint servers for biology and health sciences respectively, operated by Cold Spring Harbor Laboratory. Here are the latest preprint articles (which are not peer-reviewed) from BioRxiv and MedRxiv.