Quantitative and logic modelling of molecular and gene networks

Abstract

Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms.

Figure 1. Granularity of time representation and variable values for various modelling approaches

Variables in a model can take unbounded values (for example, concentrations or the number of molecules), multiple although limited values (for example, null, low, medium or high) or Boolean values (present or absent, or active or inactive). Progression of the variables during simulations can be represented using continuous time (mirroring the real world) in a discrete manner (with updates made after specified time durations), or using iterations (which do not necessarily represent any specific duration). Green methods are updated according to logic rules, whereas purple methods compute the new values of variables using quantitative mathematics.

Figure 2. The four views of systems biology

Four different types of networks used to represent biological processes and their features are shown. a ∣ An interaction network can be used to represent physical interactions (black line) — such as that between extracellular signal-regulated kinase (ERK) and ELK1 — and functional interactions (grey lines), such as those between UBC9 (also known as UBE2I), ERK, ELK1 and c-FOS. b ∣ An activity flow can be used to show the stimulation of c-FOS activity by ELK1 activity, the stimulation of ELK1 activity by ERK activity, and its inhibition by UBC9 activity. c ∣ A detailed process description can be used to show the catalysis of ELK1 sumoylation (SUMO) and phosphorylation (P), their reversed reactions, and the trigger of c-FOS expression. The graph is simplified by the inexistence of ELK1 with both covalent modifications. d ∣ Entity relationships can be used to describe the stimulation of sumoylation and phosphorylation of ELK1 by UBC9 and ERK, respectively, and the influence of these processes on c-FOS.

Figure 3. Network inference methods

The four main approaches to infer networks from data include: correlation (part a), information theoretic (part b), Bayesian inference (part c) and differential equations (part d). The combination of several approaches seems to be the most robust method to obtain the correct network.