Modeling the dynamic behavior of biochemical regulatory networks

•Mathematical models are vital tools for understanding molecular regulatory networks.•Logical models give qualitative insights but lack quantitative details.•Piecewise-linear ODE models can be improved by smoothing the step function.•A ‘standard component’ approach is both flexible and accurate.•Stochastic differential equations can capture mRNA noise accurately and efficiently. Strategies for modeling the complex dynamical behavior of gene/protein regulatory networks have evolved over the last 50 years as both the knowledge of these molecular control systems and the power of computing resources have increased. Here, we review a number of common modeling approaches, including Boolean (logical) models, systems of piecewise-linear or fully non-linear ordinary differential equations, and stochastic models (including hybrid deterministic/stochastic approaches). We discuss the pro's and con's of each approach, to help novice modelers choose a modeling strategy suitable to their problem, based on the type and bounty of available experimental information. We illustrate different modeling strategies in terms of some abstract network motifs, and in the specific context of cell cycle regulation.