Modelling biochemical systems: from Mass Action Kinetics to Linear Noise Approximation - Jesús Picó; Alejandro Vignoni; Enric Picó-Marco; Yadira Boada (Revista Iberoamericana de Automática e Informática Industrial RIAI)
In the last decade we have witnessed a growing application of engineering techniques to biology. Areas such as Systems Biology or, more recently, Synthetic Biology, get more and more attention from the engineers. Specifically, modeling in these fields makes possible the generation of new experimentally verifiable hypothesis, and new ways of biological intervention, as well as more or less mechanistic explanations of experimental results. A model-based approximation requires the consideration of the biochemical reactions dynamics and their regulation. The first part of this tutorial describes the deterministic modeling and model reduction techniques, as applied to the class of biochemical reactions specific to molecular cell biology. Noise plays a crucial role in the biological circuitry dynamics. In the field of automatic control there is a long tradition of modeling using linear stochastic differential equations, under the simplifying assumption that noise has a magnitude independent of the state. This assumption is not valid in biological circuits. The second part of the tutorial describes the most widely used methods for stochastic modeling in molecular cell biology, paying special attention to the so-called linear noise approximation.