Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study

Area of Science:

• Systems Biology
• Computational Biology
• Mathematical Modeling

Background:

• Multiscale systems biology models benefit from stochastic and asymptotic methods, yet their comparative efficacy remains under-explored.
• Current research predominantly uses deterministic ordinary differential equations and numerical simulations, overlooking alternative frameworks like analytical and stochastic approaches.

Purpose of the Study:

• To compare the efficacy of analytical, deterministic numerical, and stochastic numerical simulation methods in modeling biological systems.
• To highlight the distinct insights and information provided by each modeling approach.

Main Methods:

• An auxin-transport model was analyzed using three distinct methodologies: analytical solutions, deterministic numerical simulations, and stochastic numerical simulations.
• Comparative analysis focused on the information content and advantages/disadvantages of each method.

Main Results:

• All three approaches generally predicted similar system behavior for the auxin-transport model.
• Analytical methods yielded explicit mathematical expressions for concentrations and transport speeds.
• Stochastic simulations effectively captured and quantified system variability.

Conclusions:

• The study provides a valuable comparison of modeling approaches, aiding researchers in selecting appropriate methods.
• Findings suggest that analytical and stochastic methods offer complementary information, enhancing understanding of biological systems.
• The work aims to bridge the gap between different modeling paradigms, paving the way for future integrative hybrid models.