Genetic circuits in living cells share transcriptional and translational resources that are available in limited amounts. This leads to unexpected couplings among seemingly unconnected modules, which result in poorly predictable circuit behavior. In this study, we determine these interdependencies between products of different genes by characterizing the economy of how transcriptional and translational resources are allocated to the production of proteins in genetic circuits. We discover that, when expressed from the same plasmid, the combinations of attainable protein concentrations are constrained by a linear relationship, which can be interpreted as an isocost line, a concept used in microeconomics. We created a library of circuits with two reporter genes, one constitutive and the other inducible in the same plasmid, without a regulatory path between them. In agreement with the model predictions, experiments reveal that the isocost line rotates when changing the ribosome binding site strength of the inducible gene and shifts when modifying the plasmid copy number. These results demonstrate that isocost lines can be employed to predict how genetic circuits become coupled when sharing resources and provide design guidelines for minimizing the effects of such couplings.

Predicting the dynamic behavior of a large network from that of the composing modules is a central problem in systems and synthetic biology. Yet, this predictive ability is still largely missing because modules display context-dependent behavior. One cause of context-dependence is retroactivity, a phenomenon similar to loading that influences in non-trivial ways the dynamic performance of a module upon connection to other modules. Here, we establish an analysis framework for gene transcription networks that explicitly accounts for retroactivity. Specifically, a module's key properties are encoded by three retroactivity matrices: internal, scaling, and mixing retroactivity. All of them have a physical interpretation and can be computed from macroscopic parameters (dissociation constants and promoter concentrations) and from the modules' topology. The internal retroactivity quantifies the effect of intramodular connections on an isolated module's dynamics. The scaling and mixing retroactivity establish how intermodular connections change the dynamics of connected modules. Based on these matrices and on the dynamics of modules in isolation, we can accurately predict how loading will affect the behavior of an arbitrary interconnection of modules. We illustrate implications of internal, scaling, and mixing retroactivity on the performance of recurrent network motifs, including negative autoregulation, combinatorial regulation, two-gene clocks, the toggle switch, and the single-input motif. We further provide a quantitative metric that determines how robust the dynamic behavior of a module is to interconnection with other modules. This metric can be employed both to evaluate the extent of modularity of natural networks and to establish concrete design guidelines to minimize retroactivity between modules in synthetic systems.

SUMMARY Synthetic biology is increasingly used to develop sophisticated living devices for basic and applied research. Many of these genetic devices are engineered using multi-copy plasmids, but as the field progresses from proof-of-principle demonstrations to practical applications, it is important to develop single-copy synthetic modules that minimize consumption of cellular resources and can be stably maintained as genomic integrants. Here we use empirical design, mathematical modeling and iterative construction and testing to build single-copy, bistable toggle switches with improved performance and reduced metabolic load that can be stably integrated into the host genome. Deterministic and stochastic models led us to focus on basal transcription to optimize circuit performance and helped to explain the resulting circuit robustness across a large range of component expression levels. The design parameters developed here provide important guidance for future efforts to convert functional multi-copy gene circuits into optimized single-copy circuits for practical, real-world use.

Abstract-Gene circuits share transcriptional and translational resources in the cell. The fact that these common resources are available only in limited amounts leads to unexpected couplings in protein expressions. As a result, our predictive ability of describing the behavior of gene circuits is limited. In this paper, we consider the simultaneous expression of proteins and describe the coupling among protein concentrations due to competition for RNA polymerase and ribosomes. In particular, we identify the limitations and trade-offs in gene expression by characterizing the attainable combinations of protein concentrations. We further present two application examples of our results: we show that even in the absence of regulatory linkages, genes can seemingly behave as repressors, and surprisingly, as activators to each other, purely due to the limited availability of shared cellular resources.

Without accounting for the limited availability of shared cellular resources, the standard model of gene expression fails to reliably predict experimental data obtained in vitro. To overcome this limitation, we develop a dynamical model of gene expression explicitly modeling competition for scarce resources. In addition to accurately describing the experimental data, this model only depends on a handful of easily identifiable parameters with clear physical interpretation. Based on this model, we then characterize the combinations of protein concentrations that are simultaneously realizable with shared resources. As application examples, we demonstrate how the results can be used to explain similarities/differences among different in vitro extracts, furthermore, we illustrate that accounting for resource usage is essential in circuit design considering the toggle switch. I. INTRODUCTION One of the fundamental goals of synthetic biology is to engineer complex behaviors both at the cellular and population levels. Unfortunately, parts designed separately often fail to function once interconnected due to context-dependence. Sources of context-dependence include interactions among parts due to spatial co-localization [1], dependence on the host organism and strain [2], growth-dependence [3], enviromental dependence [4], and unwanted couplings due to the composition of modules [5], [6], [7]. As a result, while there are great successes in creating more and more complex circuits, these efforts often involve numerous iterative cycles of building and testing components. While these steps are slow and expensive in vivo, they are significantly faster and cheaper in vitro. As a result, cell-free transcription-translation (TX-TL) systems offer a promising avenue for synthetic biology [8]. Additionally, these systems do not suffer from unwanted coupling between the synthetic parts and the behavior of the host organism, for instance, issues related to cell growth. Unfortunately, however, protein expression requires the availability of resources (RNAP, nucleotides, tRNAs, ribosomes, ATP, etc.) that are shared among genes, and as a result, protein expression levels are coupled even in the absence of regulatory linkages in vitro [9], just as in vivo [10], [11]. To reliably analyze and predict circuit behavior, these couplings need to be accounted for, otherwise circuits need to be continuously redesigned and re-tuned. According to the most commonly used model of gene expression, mRNA m i is transcribed and degraded with rate