Long-time analytic approximation of large stochastic oscillators: Simulation, analysis and inference.

Area of Science:

• Computational Biology
• Systems Biology
• Stochastic Dynamical Systems

Background:

• Analyzing large, complex stochastic dynamical models in systems biology requires advanced analytical tools and efficient simulation/estimation algorithms.
• Existing methods like the standard Linear Noise Approximation (LNA) have limitations in long-term accuracy for biological oscillators.

Purpose of the Study:

• To develop a new stochastic approximation for biological oscillators that enhances accuracy and speed for analysis.
• To overcome the limitations of the standard LNA, providing uniform accuracy over extended time scales while retaining analytical tractability.

Main Methods:

• Introduced the phase-corrected LNA (pcLNA), a novel stochastic approximation method.
• Developed analytical expressions for probability distributions, Fisher Information Matrix, and Kullback-Leibler divergence.
• Presented new algorithms for system-global sensitivity analysis, statistical inference, and long-term simulation of oscillating systems.

Main Results:

• The pcLNA method maintains the speed and analytical tractability of the LNA while achieving uniform accuracy for long simulation times.
• New algorithms for statistical inference and simulation are significantly faster than existing leaping and diffusion integration algorithms, with comparable accuracy.
• Demonstrated the efficacy of pcLNA using stochastic models of the circadian clock and NF-κB system.

Conclusions:

• The phase-corrected LNA (pcLNA) provides a powerful and efficient tool for analyzing complex stochastic dynamical systems in biology.
• This method addresses the critical need for accurate, fast simulation and estimation in systems biology research.
• pcLNA facilitates deeper insights into biological oscillators through improved analytical capabilities and computational efficiency.