A central focus of postgenomic research will be to understand how cellular phenomena arise from the connectivity of genes and proteins. This connectivity generates molecular network diagrams that resemble complex electrical circuits, and a systematic understanding will require the development of a mathematical framework for describing the circuitry. From an engineering perspective, the natural path towards such a framework is the construction and analysis of the underlying submodules that constitute the network. Recent experimental advances in both sequencing and genetic engineering have made this approach feasible through the design and implementation of synthetic gene networks amenable to mathematical modelling and quantitative analysis. These developments have signalled the emergence of a gene circuit discipline, which provides a framework for predicting and evaluating the dynamics of cellular processes. Synthetic gene networks will also lead to new logical forms of cellular control, which could have important applications in functional genomics, nanotechnology, and gene and cell therapy.

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.

The ability to construct synthetic gene networks enables experimental investigations of deliberately simplified systems that can be compared to qualitative and quantitative models. If simple, well-characterized modules can be coupled together into more complex networks with behaviour that can be predicted from that of the individual components, we may begin to build an understanding of cellular regulatory processes from the 'bottom up'. Here we have engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli. We studied its behaviour in synthetic gene networks under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. We develop a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and show that the model can be extended and used to accurately predict the in vivo behaviour of the network when it is expanded to include positive feedback. The model also reveals the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which we confirm experimentally. This work shows that the properties of regulatory subsystems can be used to predict the behaviour of larger, more complex regulatory networks, and that this bottom-up approach can provide insights into gene regulation.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

. We propose a synthetic gene network in Escherichia coli which combines these two features: the system acts as a relaxation oscillator and uses an intercell signaling mechanism to couple the oscillators and induce synchronous oscillations. We model the system and show that the proposed coupling scheme does lead to synchronous behavior across a population of cells. We provide an analytical treatment of the synchronization process, the dominant mechanism of which is ''fast threshold modulation.'' C ellular protein levels are determined by the interplay between the rates of gene expression and protein degradation. Because the regulation of expression occurs mainly at the level of DNA transcription (1, 2), cells often manipulate their protein levels through the modification of relevant transcription rates. Such regulation is accomplished by specific regulatory proteins called transcription factors and can occur in a positive or negative sense. Positive regulation refers to an increase in transcription rate, usually accomplished by enhancing RNA polymerase binding at a promoter site. Negative regulation, in turn, usually refers to the inhibition of polymerase binding at a promoter site. In both cases, expressed proteins act to regulate their own production and͞or that of other proteins. Such regulatory feedback can lead to complex network dynamics, and an important theme in ''postgenomic'' research will be to understand these dynamics and how they affect cellular behavior.The design and construction of de novo synthetic gene networks (3-6) provides a natural framework for reducing the complexity of gene regulation. This approach combines tools from nonlinear dynamics and statistical physics with the extensive array of techniques in traditional molecular biology (7,8). Mathematical models are utilized in the design and analysis of the various features of the network, and, to date, the qualitative agreement between model and experiment has supported the notion of such an engineeringbased approach (3-6). The power of this methodology is that it can be used to study simplified systems to gain insight into the general ''themes'' of gene regulation. These themes include subnetworks that act as switches (5, 9-13) or oscillators (3, 14-21), as well as networks that utilize feedback to dampen the effects of internal noise (6,22). In addition to the insights gleaned from the construction of small networks, such genetic modules may have important biotechnological applications in their own right. In this context, synthetic gene circuits may provide a means for controlling complex biochemical systems in much the same way that digital and analog circuits provide a means for controlling electronic and mechanical systems.Recently, a synthetic network capable of producing sustained oscillations in protein concentration was presented (3). The ''repressilator'' consisted of three genes (for simplicity, call them a, b, and c), expressing three proteins (respectively, A, B, and C). The network formed a ring: protein A repressed transcri...