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Modelling and analysis of gene regulatory networks

Nature Reviews Molecular Cell Biology volume 9, pages 770–780 (2008)Cite this article

Key Points

  • By combining biological knowledge and experimental data with judicious computational modelling, regulatory networks can be dissected, and analysis results can shed light on life and disease mechanisms.

  • Logical models provide a simplified, yet useful, approach that copes well with partial knowledge. They have been used successfully to identify specific regulatory interactions.

  • Continuous models can describe a wide range of phenomena and can be readily compared to experimental measurements.

  • Single-molecule level models simulate network behaviour at the resolution of individual molecular interactions. They have been successfully applied to regulatory networks that exhibit stochastic behaviour.

  • The advantages and disadvantages of the different approaches are discussed, along with future goals of computational modelling.

Abstract

Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.

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Figure 1: Logical models.
Figure 2: Ordinary differential equation model.
Figure 3: Regulated flux balance analysis model.
Figure 4: Single-molecule level model.
Figure 5: A schematic comparison of regulatory network models.

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Acknowledgements

We thank I. Ulitsky and I. Gat-Viks for their comments on the manuscript. This study was supported in part by a grant to the APO-SYS consortium from the European Community's Seventh Framework Programme, and by a grant from the Ministry of Science, Culture and Sport, Israel, and the Ministry of Research, France. G.K. was supported in part by a fellowship from the Edmond J. Safra Bioinformatics program at Tel Aviv University, Israel.

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  1. The Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Guy Karlebach & Ron Shamir

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  1. Guy Karlebach
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Correspondence to Ron Shamir.

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Glossary

Stochasticity

The property of a system whose behaviour depends on probabilities. In a model with stochasticity, a single initial state can evolve into several different trajectories, each with an associated probability.

Local state

At any time point, the value representing the status of an entity in a model is its (local) state. For example, the state of a protein may indicate whether it is phosphorylated or not (a Boolean value), or the time since its last phosphorylation (a continuous value).

Synchronous model

A model wherein the time steps at which the global state changes are discrete and (usually) equally spaced. On each step, all the states are updated simultaneously, depending on the model's regulation functions and on the global state at the previous step. In asynchronous models, system changes are not confined to specific times and global states do not progress according to 'a common clock'. Time is often continuous, and entities may change their states at different times.

Regulation function

A rule that determines the state of a specific entity in the model as a function of the states of some (other) entities. For example, several transcription factors may together regulate the expression of a gene. The set of entities whose states determine the state of entity X are entity X's regulators.

Global state

The combination of all the local states of a model at one time point.

Steady state

A global state that, once reached, always repeats itself in a trajectory. Another important dynamic behaviour in biological systems is a cycle of global states. For example, the oscillations observed in the cell cycle.

Robustness

A measure of a model's ability to withstand changes without changing its essential properties. For example, in network models, robustness can be quantified as the fraction of edge additions and/or removals that change the trajectory that emanates from some initial state.

Threshold function

A regulation function is a threshold function if it determines the state of the output entity by summing the states of its inputs and comparing the sum to some fixed value. For example, a gene upregulated if any two out of three transcription factors are active can be modelled by such a function.

Trajectory

In logical models, a trajectory is a sequence of global states that occur consecutively. In continuous models, a trajectory is the change of the level of an entity over time.

Markov chain

A stochastic process in which the next state depends only on the present state, regardless of the trajectory that led to the present state.

Heuristic

An algorithm for solving a problem that does not always provide an optimal solution to it. Heuristics are often used when it is impractical to obtain an exact optimal solution, and in many cases they provide satisfactory solutions.

Bayesian network

A probabilistic model that represents (in)dependencies between variables, taking the form of a directed acyclic graph. Often, both inference and learning can be carried out efficiently in such models. Dynamic Bayesian networks are an extension that describes dynamic behaviour.

Module

A set of genes that have identical regulation functions (and regulators). In other contexts, a module can also be a set of genes with a common function.

Inference

The selection of regulatory functions (or regulators) that best agrees with a dataset.

Discretization

A process that transforms continuous numerical values into discrete ones. For example, real-valued measurements can be discretized to 0,1 or 2, corresponding to low, medium and high levels.

Michaelis–Menten functions

Equations that describe the kinetics of an enzymatic reaction. They can be derived from ordinary differential equations that describe the concentration changes of the involved molecular species under some simplifying assumptions.

Solution space

The set of possible solutions to an optimization problem. In the context of flux balance analysis, the solution space corresponds to different combinations of fluxes that optimize the objective function and that satisfy the constraints.

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Karlebach, G., Shamir, R. Modelling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol 9, 770–780 (2008). https://doi.org/10.1038/nrm2503

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