David R. McMillen

Engineered gene circuits.

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.

COMPUTATIONAL STUDIES OF GENE REGULATORY NETWORKS: IN NUMERO MOLECULAR BIOLOGY

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.

A bottom-up approach to gene regulation.

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.

Designer gene networks: Towards fundamental cellular control

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.

Synchronizing genetic relaxation oscillators by intercell signaling

The ability to design and construct synthetic gene regulatory networks offers the prospect of studying issues related to cellular function in a simplified context; such networks also have many potential applications in biotechnology. A synthetic network exhibiting oscillatory behavior has recently been constructed [Elowitz, M. B. & Leibler, S. (2000) Nature (London) 403, 335–338]. It has also been shown that a natural bacterial quorum-sensing mechanism can be used in a synthetic system to communicate a signal between two populations of cells, such that receipt of the signal causes expression of a target gene [Weiss, R. & Knight, T. F. (2000) in DNA6: Sixth International Meeting on DNA-Based Computers, June 13–17, 2000, Leiden, The Netherlands]. 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.”

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks

BackgroundIntrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks.ResultsWe have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS.ConclusionsWe have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Tuning Response Curves for Synthetic Biology

Synthetic biology may be viewed as an effort to establish, formalize, and develop an engineering discipline in the context of biological systems. The ability to tune the properties of individual components is central to the process of system design in all fields of engineering, and synthetic biology is no exception. A large and growing number of approaches have been developed for tuning the responses of cellular systems, and here we address specifically the issue of tuning the rate of response of a system: given a system where an input affects the rate of change of an output, how can the shape of the response curve be altered experimentally? This affects a system’s dynamics as well as its steady-state properties, both of which are critical in the design of systems in synthetic biology, particularly those with multiple components. We begin by reviewing a mathematical formulation that captures a broad class of biological response curves and use this to define a standard set of varieties of tuning: vertical shifting, horizontal scaling, and the like. We then survey the experimental literature, classifying the results into our defined categories, and organizing them by regulatory level: transcriptional, post-transcriptional, and post-translational.

Physical Constraints on Biological Integral Control Design for Homeostasis and Sensory Adaptation

Synthetic biology includes an effort to use design-based approaches to create novel controllers, biological systems aimed at regulating the output of other biological processes. The design of such controllers can be guided by results from control theory, including the strategy of integral feedback control, which is central to regulation, sensory adaptation, and long-term robustness. Realization of integral control in a synthetic network is an attractive prospect, but the nature of biochemical networks can make the implementation of even basic control structures challenging. Here we present a study of the general challenges and important constraints that will arise in efforts to engineer biological integral feedback controllers or to analyze existing natural systems. Constraints arise from the need to identify target output values that the combined process-plus-controller system can reach, and to ensure that the controller implements a good approximation of integral feedback control. These constraints depend on mild assumptions about the shape of input-output relationships in the biological components, and thus will apply to a variety of biochemical systems. We summarize our results as a set of variable constraints intended to provide guidance for the design or analysis of a working biological integral feedback controller.

Dark proteins: Effect of inclusion body formation on quantification of protein expression

Plasmid‐borne gene expression systems have found wide application in the emerging fields of systems biology and synthetic biology, where plasmids are used to implement simple network architectures, either to test systems biology hypotheses about issues such as gene expression noise or as a means of exerting artificial control over a cells dynamics. In both these cases, fluorescent proteins are commonly applied as a means of monitoring the expression of genes in the living cell, and efforts have been made to quantify protein expression levels through fluorescence intensity calibration and by monitoring the partitioning of proteins among the two daughter cells after division; such quantification is important in formulating the predictive models desired in systems and synthetic biology research. A potential pitfall of using plasmid‐based gene expression systems is that the high protein levels associated with expression from plasmids can lead to the formation of inclusion bodies, insoluble aggregates of misfolded, nonfunctional proteins that will not generate fluorescence output; proteins caught in these inclusion bodies are thus “dark” to fluorescence‐based detection methods. If significant numbers of proteins are incorporated into inclusion bodies rather than becoming biologically active, quantitative results obtained by fluorescent measurements will be skewed; we investigate this phenomenon here. We have created two plasmid constructs with differing average copy numbers, both incorporating an unregulated promoter (PLtetO‐1 in the absence of TetR) expressing the GFP derivative enhanced green fluorescent protein (EGFP), and inserted them into Escherichia coli bacterial cells (a common model organism for work on the dynamics of prokaryotic gene expression). We extracted the inclusion bodies, denatured them, and refolded them to render them active, obtaining a measurement of the average number of EGFP per cell locked into these aggregates; at the same time, we used calibrated fluorescent intensity measurements to determine the average number of active EGFP present per cell. Both measurements were carried out as a function of cellular doubling time, over a range of 45–75 min. We found that the ratio of inclusion body EGFP to active EGFP varied strongly as a function of the cellular growth rate, and that the number of “dark” proteins in the aggregates could in fact be substantial, reaching ratios as high as approximately five proteins locked into inclusion bodies for every active protein (at the fastest growth rate), and dropping to ratios well below 1 (for the slowest growth rate). Our results suggest that efforts to compare computational models to protein numbers derived from fluorescence measurements should take inclusion body loss into account, especially when working with rapidly growing cells. Proteins 2008.

Simplification of Stochastic Chemical Reaction Models with Fast and Slow Dynamics

Biological systems often involve chemical reactions occurring in low-molecule-number regimes, where fluctuations are not negligible and thus stochastic models are required to capture the system behaviour. The resulting models are generally quite large and complex, involving many reactions and species. For clarity and computational tractability, it is important to be able to simplify these systems to equivalent ones involving fewer elements. While many model simplification approaches have been developed for deterministic systems, there has been limited work on applying these approaches to stochastic modelling. Here, we describe a method that reduces the complexity of stochastic biochemical network models, and apply this method to the reduction of a mammalian signalling cascade and a detailed model of the process of bacterial gene expression. Our results indicate that the simplified model gives an accurate representation for not only the average numbers of all species, but also for the associated fluctuations and statistical parameters.