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Computational Studies of Gene Regulatory Networks: in Numero Molecular Biology REVIEWS COMPUTATIONAL STUDIES OF GENE REGULATORY NETWORKS: IN NUMERO MOLECULAR BIOLOGY Jeff Hasty, David McMillen, Farren Isaacs and James J. Collins Remarkable progress in genomic research is leading to a complete map of the building blocks of biology. Knowledge of this map is, in turn, setting the stage for a fundamental description of cellular function at the DNA level. Such a description will entail an understanding of gene regulation, in which proteins often regulate their own production or that of other proteins in a complex web of interactions. The implications of the underlying logic of genetic networks are difficult to deduce through experimental techniques alone, and successful approaches will probably involve the union of new experiments and computational modelling techniques. NONLINEAR DYNAMICS An important theme in post-genomic research will description of gene regulation. If this were a complex In a system governed by probably be the dissection and analysis of the complex electrical circuit, there would be an accompanying set nonlinear dynamics, the rate dynamical interactions involved in gene regulation. of equations that would faithfully describe its func- of change of any variable Although the concepts of protein–DNA feedback loops tionality. This description would be built from a cannot be written as a linear function of the other variables. and network complexity are not new, experimental knowledge of the properties of the individual compo- Most real systems are nonlinear advances are inducing a resurgence of interest in the nents (resistors, capacitors, inductors and so on) and and show interesting quantitative description of gene regulation. These provide a framework for predicting behaviour that behaviours not seen in advances are beginning to allow a ‘modular’ description results from modification of the circuit. An acceptable linear systems (for example, of the regulatory processes that underlie basic cellular model that describes the p53 activation network (FIG. 1) only nonlinear systems can 1–5 be multistable). function . In the light of nearly three decades of paral- would thus be built from knowledge of the basic regu- lel progress in the study of complex NONLINEAR and STO- latory themes and could predict the effects of genetic STOCHASTIC CHASTIC processes, the project of quantitatively describ- perturbations to the system. Probabilistic; governed ing gene regulatory networks is timely. In this article, we review recent advances in the by chance. Pioneering theoretical work on gene regulatory mathematical modelling of genetic regulation. Most networks has anticipated the emergence of post- of this work has focused on networks that involve genomic research, and has provided a mathematical transcription factors and we restrict ourselves to work framework for the current description and analysis of in this class. We begin with the modelling of specific complex regulatory mechanisms6–18. Although these genetic networks and discuss representative models studies have identified the need for a quantitative that have been used for several relatively simple net- description of gene regulation, their true significance works. We then turn to the recent progress in design- Centre for BioDynamics and Department of has only recently emerged with experimental tech- ing and testing synthetic gene networks. Although Biomedical Engineering, niques that can determine their validity. The diagram these networks have important biotechnological Boston University, 44 in FIG. 1 depicts some of the known components of the implications in their own right22,23, we highlight their Cummington Street, regulatory network that involve the tumour-suppres- use in determining the primary themes of gene regu- Boston, Massachusetts 02215, USA. sor protein p53 (REFS 19–20). These types of schematic latory networks. In this regard, the accurate mathe- 2,21 Correspondence to J.H. resemble circuit diagrams and in many regards this matical description of synthetic networks provides e-mail: [email protected] analogy highlights the motivation for a quantitative the foundation for describing complex, naturally 268 | APRIL 2001 | VOLUME 2 www.nature.com/reviews/genetics © 2001 Macmillan Magazines Ltd REVIEWS DNA breaks Ultraviolet light, stress Oncogenes remain even after the perturbation is removed. Understanding how MULTISTABILITY arises is thus relevant to understanding the operation of natural biological DNA- ATM dependent ATR Casein p14ARF switches (such as the lysogeny/lysis switches that occur kinase kinase kinase kinase II in viruses, for example λ-bacteriophage), as well as to the design of synthetic switching networks. A recent analysis29 considered a generic rate-equation model to determine the precise conditions required for the exis- p53 MDM2 tence of multiple stable fixed points in a two-gene sys- tem. Another study28 used a model (derived from REF. 17) to determine the relationship between the num- ber of OPERATOR sites that constitute a given promoter p21 and the number of stable steady states that the system could support (see below). In addition to considering the existence of stable GADD45 Scotin PERP NOXA fixed points, their degree of stability can be considered. KILLER/DR5 P53AIP1 States vary in how quickly they recover from perturba- 14-3-3σ TSP1 BAI1 tions, the size of perturbation they can withstand Fas Bax PIIDD before being forced into another state and, in noisy sys- Reprimo Reactive oxygen species Maspin GD-AIF tems, the expected length of time it will take for noise to induce a transition to another state. NEGATIVE FEEDBACK Growth arrest Apoptosis Prevention of new increases stability in generic gene regulatory systems, blood vessel formation whereas POSITIVE FEEDBACK decreases stability7. It has often Figure 1 | Regulatory diagram for the activation of the tumour-suppressor protein p53. been assumed that switches based on the action of The complexity of the p53 network highlights the need for a quantitative description of genetic small numbers of individual molecules could not be circuitry. (ATM, ataxia telangiectasia mutated; ATR, AT and Rad3-related; MDM2, mouse double minute 2; GADD45, growth arrest and DNA-damage inducible; PERP, p53 apoptosis- very stable, because small numbers of molecules gener- associated target; KILLER/DR5, death receptor 5; P53AIP1, p53-regulated apoptosis- ally imply that the system will be subjected to larger inducing protein 1; Bax, Bcl2-associated X protein; PIDD, p53 protein induced, with death fluctuations than systems with greater numbers of domain; TSP1, tumour-suppressor region 1; BAI1, brain-specific angiogenesis inhibitor 1; GD- molecules. However, a recent analysis, using a general AIF, glioma-derived angiogenesis inhibitory factor.)(Redrawn with permission from REF. 19 © formulation applicable to any biological switch30, indi- (2000) Macmillan Magazines Ltd.) cates that switches based on only tens of molecules could flip states in milliseconds and remain stable for occurring networks. Throughout this review, we years. This degree of stability is an upper bound and ground our discussion through the use of illustrative thus does not necessarily indicate how stable any par- examples and primarily focus on modelling efforts ticular biochemical switch will be; however, it does that are directly connected to experiments. point out the possibility of achieving the required sta- FIXED POINT bility. With larger numbers of molecules (hundreds A point at which the rates of Modelling genetic networks rather than tens), even greater degrees of stability change of all variables in a Several traditional approaches to analysing gene regula- should be achievable. system are exactly zero. A system tion have been based on modelling specific natural sys- Many cellular processes are characterized by oscil- precisely at its fixed point (or (BOX 1) steady state) will remain there tems . By contrast, some researchers have concen- lations that are generated at the genetic level and sev- permanently. Small trated on analysing abstract models to obtain general eral investigations have focused on the general condi- perturbations to a system that is results. The power of the latter approach is that it can tions under which oscillations are to be expected initially poised at a ‘stable’ fixed offer insight into the behaviour of entire classes of bio- from a given gene network27,31–33. One of these33 con- point will be accompanied by a logical system. This approach has recently been cludes that oscillatory behaviour cannot exist in sys- return to the stable fixed point. reviewed in some detail24 and here we discuss several tems with only positive-feedback interactions; this MULTISTABILITY representative examples. result applies to systems with and without time The property of having more In a typical experimental situation, regulatory net- delays. Additionally, systems with only negative feed- than one stable fixed point. works are quantified by the concentrations of the con- back can generate oscillations in the presence of time stitutive gene products. When a gene product is in an delays34, and mixed positive and negative feedback OPERATOR 32,33 A prokaryotic DNA regulatory equilibrium state (that is, its rate of production is bal- can also generate oscillatory behaviour . element that interacts with a anced by its rate of degradation), small perturbations repressor to control the to this steady state will be accompanied by an exponen- Naturally occurring gene networks transcription of adjacent genes.
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