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We show how subtraction can be performed via a simple chemical reaction network that includes molecular sequestration. The network computes the difference between the production rate parameters of the two mutually sequestering species. We benefit from introducing a simple change of variables, that facilitates the derivation of an approximate solution for the differential equations modeling the chemical reaction network, under a time scale separation assumption that is valid when the sequestration rate parameter is sufficiently fast. Our main result is that we provide simple expressions confirming that temporal subtraction occurs when the inputs are constant or time varying. Through simulations, we discuss two sequestration-based architectures for feedback control in light of the subtraction operations they perform. 

A networked dynamical system is composed of subsystems interconnected via prescribed interactions. In many engineering applications, however, one subsystem can also affect others via unintended interactions that can significantly change the intended network's behavior. Although unintended interactions can be modeled as disturbance inputs to the subsystems, these disturbances depend on the network's states. Thus, a disturbance attenuation property of each subsystem is insufficient to ensure that the network is robust to unintended interactions. Here, we provide conditions on subsystem dynamics and interaction maps, such that a network is robust to unintended interactions. These conditions require that each subsystem asymptotically attenuates constant external disturbances, is monotone or near-monotone, the unintended interactions are monotone, and the prescribed interactions do not contain feedback loops. We apply this result to guide the design of resource-limited genetic circuits composed of feedback-regulated subsystems. 

Abstract Engineered signaling networks can impart cells with new functionalities useful for directing differentiation and actuating cellular therapies. For such applications, the engineered networks must be tunable, precisely regulate target gene expression, and be robust to perturbations within the complex context of mammalian cells. Here, we use bacterial two-component signaling proteins to develop synthetic phosphoregulation devices that exhibit these properties in mammalian cells. First, we engineer a synthetic covalent modification cycle based on kinase and phosphatase proteins derived from the bifunctional histidine kinase EnvZ, enabling analog tuning of gene expression via its response regulator OmpR. By regulating phosphatase expression with endogenous miRNAs, we demonstrate cell-type specific signaling responses and a new strategy for accurate cell type classification. Finally, we implement a tunable negative feedback controller via a small molecule-stabilized phosphatase, reducing output expression variance and mitigating the context-dependent effects of off-target regulation and resource competition. Our work lays the foundation for establishing tunable, precise, and robust control over cell behavior with synthetic signaling networks. 

Abstract CRISPRi-mediated gene regulation allows simultaneous control of many genes. However, highly specific sgRNA-promoter binding is, alone, insufficient to achieve independent transcriptional regulation of multiple targets. Indeed, due to competition for dCas9, the repression ability of one sgRNA changes significantly when another sgRNA becomes expressed. To solve this problem and decouple sgRNA-mediated regulatory paths, we create a dCas9 concentration regulator that implements negative feedback on dCas9 level. This allows any sgRNA to maintain an approximately constant dose-response curve, independent of other sgRNAs. We demonstrate the regulator performance on both single-stage and layered CRISPRi-based genetic circuits, zeroing competition effects of up to 15-fold changes in circuit I/O response encountered without the dCas9 regulator. The dCas9 regulator decouples sgRNA-mediated regulatory paths, enabling concurrent and independent regulation of multiple genes. This allows predictable composition of CRISPRi-based genetic modules, which is essential in the design of larger scale synthetic genetic circuits. 

Abstract Synthetic biology has the potential to bring forth advanced genetic devices for applications in healthcare and biotechnology. However, accurately predicting the behavior of engineered genetic devices remains difficult due to lack of modularity, wherein a device’s output does not depend only on its intended inputs but also on its context. One contributor to lack of modularity is loading of transcriptional and translational resources, which can induce coupling among otherwise independently-regulated genes. Here, we quantify the effects of resource loading in engineered mammalian genetic systems and develop an endoribonuclease-based feedforward controller that can adapt the expression level of a gene of interest to significant resource loading in mammalian cells. Near-perfect adaptation to resource loads is facilitated by high production and catalytic rates of the endoribonuclease. Our design is portable across cell lines and enables predictable tuning of controller function. Ultimately, our controller is a general-purpose device for predictable, robust, and context-independent control of gene expression.