Incoherent merger network for robust ratiometric gene expression response.

A ratiometric response gives an output that is proportional to the ratio between the magnitudes of two inputs. Ratio computation has been observed in nature and is also needed in the development of smart probiotics and organoids. Here, we achieve ratiometric gene expression response in bacteria Escherichia coli with the incoherent merger network. In this network, one input molecule activates expression of the output protein while the other molecule activates an intermediate protein that enhances the output's degradation. When degradation rate is first order and faster than dilution, the output responds linearly to the ratio between the input molecules' levels over a wide range with R2 close to 1. Response sensitivity can be quantitatively tuned by varying the output's translation rate. Furthermore, ratiometric responses are robust to global perturbations in cellular components that influence gene expression because such perturbations affect the output through an incoherent feedforward loop. This work demonstrates a new molecular signal processing mechanism for multiplexed sense-and-respond circuits that are robust to intra-cellular context.

Creating Single-Copy Genetic Circuits.

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.

Epigenetic cell memory: The gene's inner chromatin modification circuit.

Epigenetic cell memory allows distinct gene expression patterns to persist in different cell types despite a common genotype. Although different patterns can be maintained by the concerted action of transcription factors (TFs), it was proposed that long-term persistence hinges on chromatin state. Here, we study how the dynamics of chromatin state affect memory, and focus on a biologically motivated circuit motif, among histones and DNA modifications, that mediates the action of TFs on gene expression. Memory arises from time-scale separation among three circuit's constituent processes: basal erasure, auto and cross-catalysis, and recruited erasure of modifications. When the two latter processes are sufficiently faster than the former, the circuit exhibits bistability and hysteresis, allowing active and repressed gene states to coexist and persist after TF stimulus removal. The duration of memory is stochastic with a mean value that increases as time-scale separation increases, but more so for the repressed state. This asymmetry stems from the cross-catalysis between repressive histone modifications and DNA methylation and is enhanced by the relatively slower decay rate of the latter. Nevertheless, TF-mediated positive autoregulation can rebalance this asymmetry and even confers robustness of active states to repressive stimuli. More generally, by wiring positively autoregulated chromatin modification circuits under time scale separation, long-term distinct gene expression patterns arise, which are also robust to failure in the regulatory links.

Comparison Theorems for Stochastic Chemical Reaction Networks.

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

What Is the Trait d'Union between Retroactivity and Molecular Communication Performance Limits?

Information exchange is a critical process in all communication systems, including biological ones. Retroactivity describes the load that downstream modules apply to their upstream systems in biological circuits. The motivation behind this work is that of integrating retroactivity, a concept proper of biochemical circuits, with the metrics defined in Information Theory and Digital Communications. This paper focuses on studying the impact of retroactivity on different biological signaling system models, which present analogies with well-known telecommunication systems. The mathematical analysis is performed both in the high and low molecular counts regime, by mean of the Chemical Master Equation and the Linear Noise Approximation, respectively. The main goal of this work is to provide analytical tools to maximize the reliable information exchange across different biomolecular circuit models. Results highlight how, in general, retroactivity harms communication performance. This negative effect can be mitigated by adding to the signaling circuit an independent upstream system that connects with the same pool of downstream circuits.

Effects of spatial heterogeneity on bacterial genetic circuits.

Intracellular spatial heterogeneity is frequently observed in bacteria, where the chromosome occupies part of the cell's volume and a circuit's DNA often localizes within the cell. How this heterogeneity affects core processes and genetic circuits is still poorly understood. In fact, commonly used ordinary differential equation (ODE) models of genetic circuits assume a well-mixed ensemble of molecules and, as such, do not capture spatial aspects. Reaction-diffusion partial differential equation (PDE) models have been only occasionally used since they are difficult to integrate and do not provide mechanistic understanding of the effects of spatial heterogeneity. In this paper, we derive a reduced ODE model that captures spatial effects, yet has the same dimension as commonly used well-mixed models. In particular, the only difference with respect to a well-mixed ODE model is that the association rate constant of binding reactions is multiplied by a coefficient, which we refer to as the binding correction factor (BCF). The BCF depends on the size of interacting molecules and on their location when fixed in space and it is equal to unity in a well-mixed ODE model. The BCF can be used to investigate how spatial heterogeneity affects the behavior of core processes and genetic circuits. Specifically, our reduced model indicates that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome. The extent of these effects depends on the value of the BCF, which we found to be close to unity. For translation, the value of the BCF is always greater than unity, it increases with mRNA size, and, with biologically relevant parameters, is substantially larger than unity. Our model has broad validity, has the same dimension as a well-mixed model, yet it incorporates spatial heterogeneity. This simple-to-use model can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects.

Multi-modality in gene regulatory networks with slow promoter kinetics.

Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network.

Signaling Architectures that Transmit Unidirectional Information Despite Retroactivity.

A signaling pathway transmits information from an upstream system to downstream systems, ideally in a unidirectional fashion. A key obstacle to unidirectional transmission is retroactivity, the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the fundamental question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general procedure based on mathematical analysis that provides an answer to this question. Using this procedure, we analyze the ability of a variety of signaling architectures to transmit one-way (from upstream to downstream) signals, as key biological parameters are tuned. We find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show a stringent design tradeoff that hampers their ability to overcome retroactivity. Interestingly, cascades of these architectures, which are highly represented in nature, can overcome this tradeoff and thus enable unidirectional transmission. By contrast, phosphotransfer systems, and single and double phosphorylation cycles that transmit signals from a substrate, are unable to mitigate retroactivity effects, even when cascaded, and hence are not well suited for unidirectional information transmission. These results are largely independent of the specific reaction-rate constant values, and depend on the topology of the architectures. Our results therefore identify signaling architectures that, allowing unidirectional transmission of signals, embody modular processes that conserve their input/output behavior across multiple contexts. These findings can be used to decompose natural signal transduction networks into modules, and at the same time, they establish a library of devices that can be used in synthetic biology to facilitate modular circuit design.

Isocost Lines Describe the Cellular Economy of Genetic Circuits.

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.

Modular composition of gene transcription networks.

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.

Epigenetic OCT4 regulatory network: stochastic analysis of cellular reprogramming.

Experimental studies have shown that chromatin modifiers have a critical effect on cellular reprogramming, i.e., the conversion of differentiated cells to pluripotent stem cells. Here, we develop a model of the OCT4 gene regulatory network that includes genes expressing chromatin modifiers TET1 and JMJD2, and the chromatin modification circuit on which these modifiers act. We employ this model to compare three reprogramming approaches that have been considered in the literature with respect to reprogramming efficiency and latency variability. These approaches are overexpression of OCT4 alone, overexpression of OCT4 with TET1, and overexpression of OCT4 with JMJD2. Our results show more efficient and less variable reprogramming when also JMJD2 and TET1 are overexpressed, consistent with previous experimental data. Nevertheless, TET1 overexpression can lead to more efficient reprogramming compared to JMJD2 overexpression. This is the case when the recruitment of DNA methylation by H3K9me3 is weak and the methyl-CpG-binding domain (MBD) proteins are sufficiently scarce such that they do not hamper TET1 binding to methylated DNA. The model that we developed provides a mechanistic understanding of existing experimental results and is also a tool for designing optimized reprogramming approaches that combine overexpression of cell-fate specific transcription factors (TFs) with targeted recruitment of epigenetic modifiers.

Signaling properties of a covalent modification cycle are altered by a downstream target.

We used a model system of purified components to explore the effects of a downstream target on the signaling properties of a covalent modification cycle, an example of retroactivity. In the experimental system used, a bifunctional enzyme catalyzed the modification and demodification of its substrate protein, with both activities regulated by a small molecule stimulus. Here we examined how a downstream target for one or both forms of the substrate of the covalent modification cycle affected the steady-state output of the system, the sensitivity of the response to the stimulus, and the concentration of the stimulus required to provide the half-maximal response (S(50)). When both the modified and unmodified forms of the substrate protein were sequestered by the downstream target, the sensitivity of the response was dramatically decreased, but the S(50) was only modestly affected. Conversely, when the downstream target only sequestered the unmodified form of the substrate protein, significant effects were observed on both system sensitivity and S(50). Behaviors of the experimental systems were well approximated both by simple models allowing analytical solutions and by a detailed model based on the known interactions and enzymatic activities. Modeling and experimentation indicated that retroactivity may result in subsensitive responses, even if the covalent modification cycle displays significant ultrasensitivity in the absence of retroactivity. Thus, we provide examples of how a downstream target can alter the signaling properties of an upstream signal transduction covalent modification cycle.

Synthetic genetic circuits to uncover and enforce the OCT4 trajectories of successful reprogramming of human fibroblasts.

Reprogramming human fibroblasts to induced pluripotent stem cells (iPSCs) is inefficient, with heterogeneity among transcription factor (TF) trajectories driving divergent cell states. Nevertheless, the impact of TF dynamics on reprogramming efficiency remains uncharted. Here, we identify the successful reprogramming trajectories of the core pluripotency TF, OCT4, and design a genetic controller that enforces such trajectories with high precision. By combining a genetic circuit that generates a wide range of OCT4 trajectories with live-cell imaging, we track OCT4 trajectories with clonal resolution and find that a distinct constant OCT4 trajectory is required for colony formation. We then develop a synthetic genetic circuit that yields a tight OCT4 distribution around the identified trajectory and outperforms in terms of reprogramming efficiency other circuits that less accurately regulate OCT4. Our synthetic biology approach is generalizable for identifying and enforcing TF dynamics for cell fate programming applications.

Synthetic genetic circuits to uncover the OCT4 trajectories of successful reprogramming of human fibroblasts.

Reprogramming human fibroblasts to induced pluripotent stem cells (iPSCs) is inefficient, with heterogeneity among transcription factor (TF) trajectories driving divergent cell states. Nevertheless, the impact of TF dynamics on reprogramming efficiency remains uncharted. We develop a system that accurately reports OCT4 protein levels in live cells and use it to reveal the trajectories of OCT4 in successful reprogramming. Our system comprises a synthetic genetic circuit that leverages noise to generate a wide range of OCT4 trajectories and a microRNA targeting endogenous OCT4 to set total cellular OCT4 protein levels. By fusing OCT4 to a fluorescent protein, we are able to track OCT4 trajectories with clonal resolution via live-cell imaging. We discover that a supraphysiological, stable OCT4 level is required, but not sufficient, for efficient iPSC colony formation. Our synthetic genetic circuit design and high-throughput live-imaging pipeline are generalizable for investigating TF dynamics for other cell fate programming applications.

Modularity in signaling systems.

Modularity is a property by which the behavior of a system does not change upon interconnection. It is crucial for understanding the behavior of a complex system from the behavior of the composing subsystems. Whether modularity holds in biology is an intriguing and largely debated question. In this paper, we discuss this question taking a control system theory view and focusing on signaling systems. In particular, we argue that, despite signaling systems being constituted of structural modules, such as covalent modification cycles, modularity does not hold in general. As in any engineering system, impedance-like effects, called retroactivity, appear at interconnections and alter the behavior of connected modules. We further argue that while signaling systems have evolved sophisticated ways to counter-act retroactivity and enforce modularity, retroactivity may also be exploited to finely control the information processing of signaling pathways. Testable predictions and experimental evidence are discussed with their implications.

Synthetic biology by controller design.

Natural biological systems display complex regulation and synthetic biomolecular systems have been used to understand their natural counterparts and to parse sophisticated regulations into core design principles. At the same time, the engineering of biomolecular systems has unarguable potential to transform current and to enable new, yet-to-be-imagined, biotechnology applications. In this review, we discuss the progression of control systems design in synthetic biology, from the purpose of understanding the function of naturally occurring regulatory motifs to that of creating genetic circuits whose function is sufficiently robust for biotechnology applications.

Feedforward growth rate control mitigates gene activation burden.

Heterologous gene activation causes non-physiological burden on cellular resources that cells are unable to adjust to. Here, we introduce a feedforward controller that actuates growth rate upon activation of a gene of interest (GOI) to compensate for such a burden. The controller achieves this by activating a modified SpoT enzyme (SpoTH) with sole hydrolysis activity, which lowers ppGpp level and thus increases growth rate. An inducible RelA+ expression cassette further allows to precisely set the basal level of ppGpp, and thus nominal growth rate, in any bacterial strain. Without the controller, activation of the GOI decreased growth rate by more than 50%. With the controller, we could activate the GOI to the same level without growth rate defect. A cell strain armed with the controller in co-culture enabled persistent population-level activation of a GOI, which could not be achieved by a strain devoid of the controller. The feedforward controller is a tunable, modular, and portable tool that allows dynamic gene activation without growth rate defects for bacterial synthetic biology applications.

Robust and tunable signal processing in mammalian cells via engineered covalent modification cycles.

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.

Long signaling cascades tend to attenuate retroactivity.

Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade and the parameters that affect this propagation are presently unknown. Here, we determine the downstream-to-upstream steady-state gain at each stage of the signaling cascade as a function of the cascade parameters. This gain can be made smaller than 1 (attenuation) by sufficiently fast kinase rates compared to the phosphatase rates and/or by sufficiently large Michaelis-Menten constants and sufficiently low amounts of total stage protein. Numerical studies performed on sets of biologically relevant parameters indicated that ∼50% of these parameters could give rise to amplification of the downstream perturbation at some stage in a three-stage cascade. In an n-stage cascade, the percentage of parameters that lead to an overall attenuation from the last stage to the first stage monotonically increases with the cascade length n and reaches 100% for cascades of length at least 6.