The expression of genes is regularly characterized with respect to how much, how fast, when and where. Such quantitative data demands quantitative models. Thermodynamic models are based on the assumption that the level of gene expression is proportional to the equilibrium probability that RNA polymerase (RNAP) is bound to the promoter of interest. Statistical mechanics provides a framework for computing these probabilities. Within this framework, interactions of activators, repressors, helper molecules and RNAP are described by a single function, the 'regulation factor'. This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell.

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cisregulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a ''programmable'' computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed. Biological organisms ranging from bacteria to humans possess an enormous repertoire of genetic responses to ever-changing combinations of cellular and environmental signals. To a large extent, this repertoire is encoded in complex networks of genes closely regulating the activities of each other. Characterizing and decoding the connectivity of gene regulatory networks has been an outstanding challenge of post-genome molecular biology (1-4). However, unlike integrated circuits, which process information through synchronized cascades of many simple and fast nodes and for which connectivity is the primary source of network complexity, a gene-regulatory network typically consists of only a few tens to hundreds of genes, the expression of which is slow and asynchronous (5). Yet these ''nodes'' are very sophisticated in their capacity to integrate signals: In eukaryotes, each node can be regulated combinatorially, often by four to five other nodes (1, 6), and the regulatory control function can be extremely complex (7). Here we focus primarily on one node of a gene-regulatory network and investigate quantitatively the power and limitations of combinatorial gene regulation in the context of bacterial transcription. We find that the bacterial transcription system is already capable of im...

With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to their respective context. Thermodynamic models provide a useful framework for the quantitative analysis of bacterial transcription regulation. This framework can facilitate the quantification of vastly different forms of gene expression from several well-characterized bacterial promoters that are regulated by one or two species of transcription factors; it is useful because it requires only a few parameters. As such, it provides a compact description useful for higher-level studies (e.g. of genetic networks) without the need to invoke the biochemical details of every component. Moreover, it can be used to generate hypotheses on the likely mechanisms of transcriptional control.

A grand challenge of systems biology is to predict the kinetic responses of living systems to perturbations starting from the underlying molecular interactions. Changes in the nutrient environment have long been used to study regulation and adaptation phenomena in microorganisms1–3 and they remain a topic of active investigation4–11. Although much is known about the molecular interactions that govern the regulation of key metabolic processes in response to applied perturbations12–17, they are insufficiently quantified for predictive bottom-up modelling. Here we develop a top-down approach, expanding the recently established coarse-grained proteome allocation models15,18–20 from steady-state growth into the kinetic regime. Using only qualitative knowledge of the underlying regulatory processes and imposing the condition of flux balance, we derive a quantitative model of bacterial growth transitions that is independent of inaccessible kinetic parameters. The resulting flux-controlled regulation model accurately predicts the time course of gene expression and biomass accumulation in response to carbon upshifts and downshifts (for example, diauxic shifts) without adjustable parameters. As predicted by the model and validated by quantitative proteomics, cells exhibit suboptimal recovery kinetics in response to nutrient shifts owing to a rigid strategy of protein synthesis allocation, which is not directed towards alleviating specific metabolic bottlenecks. Our approach does not rely on kinetic parameters, and therefore points to a theoretical framework for describing a broad range of such kinetic processes without detailed knowledge of the underlying biochemical reactions.

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