Systems biology approaches are extensively used to model and reverse engineer gene regulatory networks from experimental data. Conversely, synthetic biology allows "de novo" construction of a regulatory network to seed new functions in the cell. At present, the usefulness and predictive ability of modeling and reverse engineering cannot be assessed and compared rigorously. We built in the yeast Saccharomyces cerevisiae a synthetic network, IRMA, for in vivo "benchmarking" of reverse-engineering and modeling approaches. The network is composed of five genes regulating each other through a variety of regulatory interactions; it is negligibly affected by endogenous genes, and it is responsive to small molecules. We measured time series and steady-state expression data after multiple perturbations. These data were used to assess state-of-the-art modeling and reverse-engineering techniques. A semiquantitative model was able to capture and predict the behavior of the network. Reverse engineering based on differential equations and Bayesian networks correctly inferred regulatory interactions from the experimental data.

We describe an innovative experimental and computational approach to control the expression of a protein in a population of yeast cells. We designed a simple control algorithm to automatically regulate the administration of inducer molecules to the cells by comparing the actual protein expression level in the cell population with the desired expression level. We then built an automated platform based on a microfluidic device, a time-lapse microscopy apparatus, and a set of motorized syringes, all controlled by a computer. We tested the platform to force yeast cells to express a desired fixed, or time-varying, amount of a reporter protein over thousands of minutes. The computer automatically switched the type of sugar administered to the cells, its concentration and its duration, according to the control algorithm. Our approach can be used to control expression of any protein, fused to a fluorescent reporter, provided that an external molecule known to (indirectly) affect its promoter activity is available.

Real-time automatic regulation of gene expression is a key technology for synthetic biology enabling, for example, synthetic circuit's components to operate in an optimal range. Computer-guided control of gene expression from a variety of inducible promoters has been only recently successfully demonstrated. Here we compared, in silico and in vivo, three different control algorithms: the Proportional-Integral (PI) and Model Predictive Control (MPC) controllers, which have already been used to control gene expression, and the Zero Average Dynamics (ZAD), a control technique used to regulate electrical power systems. We chose as an experimental testbed the most commonly used inducible promoter in yeast: the galactose-responsive GAL1 promoter. We set two control tasks: either force cells to express a desired constant fluorescence level of a reporter protein downstream of the GAL1 promoter (set-point) or a time-varying fluorescence (tracking). Using a microfluidics-based experimental platform, in which either glucose or galactose can be provided to the cells, we demonstrated that both the MPC and ZAD control strategies can successfully regulate gene expression from the GAL1 promoter in living cells for thousands of minutes. The MPC controller can track fast reference signals better than ZAD but with a higher actuation effort due to the large number of input switches it requires. Conversely, the PI controller's performance is comparable to that achieved by the MPC and the ZAD controllers only for the set-point regulation

Complex networked systems abound in Nature and Technology. They consist of a multitude of interacting agents communicating with each other over a web of complex interconnections. Flocks of birds, platoon of cooperating robots, swirling fishes in the Ocean are all examples whose intricate dynamics can be modeled in terms of three essential ingredients: (i) a mathematical description of the dynamical behavior of each of the agents in the network; (ii) an interaction (or coupling) protocol used by agents to communicate with each other and (iii) a graph describing the network of interconnections between neighboring agents. These three elements are actually mapped onto the mathematical model usually considered in the literature to describe a complex network which uses appropriate equations to describe the node dynamics, the coupling protocol and the network topology

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BackgroundRNA interference (RNAi) is a regulatory cellular process that controls post-transcriptional gene silencing. During RNAi double-stranded RNA (dsRNA) induces sequence-specific degradation of homologous mRNA via the generation of smaller dsRNA oligomers of length between 21-23nt (siRNAs). siRNAs are then loaded onto the RNA-Induced Silencing multiprotein Complex (RISC), which uses the siRNA antisense strand to specifically recognize mRNA species which exhibit a complementary sequence. Once the siRNA loaded-RISC binds the target mRNA, the mRNA is cleaved and degraded, and the siRNA loaded-RISC can degrade additional mRNA molecules. Despite the widespread use of siRNAs for gene silencing, and the importance of dosage for its efficiency and to avoid off target effects, none of the numerous mathematical models proposed in literature was validated to quantitatively capture the effects of RNAi on the target mRNA degradation for different concentrations of siRNAs. Here, we address this pressing open problem performing in vitro experiments of RNAi in mammalian cells and testing and comparing different mathematical models fitting experimental data to in-silico generated data. We performed in vitro experiments in human and hamster cell lines constitutively expressing respectively EGFP protein or tTA protein, measuring both mRNA levels, by quantitative Real-Time PCR, and protein levels, by FACS analysis, for a large range of concentrations of siRNA oligomers.ResultsWe tested and validated four different mathematical models of RNA interference by quantitatively fitting models' parameters to best capture the in vitro experimental data. We show that a simple Hill kinetic model is the most efficient way to model RNA interference. Our experimental and modeling findings clearly show that the RNAi-mediated degradation of mRNA is subject to saturation effects.ConclusionsOur model has a simple mathematical form, amenable to analytical investigations and a small set of parameters with an intuitive physical meaning, that makes it a unique and reliable mathematical tool. The findings here presented will be a useful instrument for better understanding RNAi biology and as modelling tool in Systems and Synthetic Biology.

Power electronics is rich in nonlinear dynamics. Its operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This chapter provides an overview of the chaotic dynamics and bifurcation scenarios observed in power electronics circuits, emphasizing the salient features of the circuit operation and the modelling strategies. This chapter covers the modelling approaches, analysis methods, and a classification of the common types of bifurcations observed in power electronics.

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