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.

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.

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.

The epigenetic Oct4 gene regulatory network: stochastic analysis of different cellular reprogramming approaches

In the last decade, several experimental studies have shown how chromatin modifications (histone modifications and DNA methylation) and their effect on DNA compaction have a critical effect on cellular reprogramming, i.e., the conversion of differentiated cells to a pluripotent state. In this paper, we compare three reprogramming approaches that have been considered in the literature: (a) prefixed overexpression of transcription factors (TFs) alone (Oct4), (b) prefixed overexpression of Oct4 and DNA methylation "eraser" TET, and (c) prefixed overexpression of Oct4 and H3K9me3 eraser JMJD2. To this end, we develop a model of the pluritpotency gene regulatory network, that includes, for each gene, a circuit recently published encapsulating the main interactions among chromatin modifications and their effect on gene expression. We then conduct a computational study to evaluate, for each reprogramming approach, latency and variability. Our results show a faster and less stochastic reprogramming process when also eraser enzymes are overexpressed, consistent with previous experimental data. However, TET overexpression leads to a faster and more efficient reprogramming compared to JMJD2 overexpression when the recruitment of DNA methylation by H3K9me3 is weak and the MBD protein level is sufficiently low such that it does not hamper TET binding to methylated DNA. The model developed here provides a mechanistic understanding of the outcomes of former experimental studies and is also a tool for the development of optimized reprogramming approaches that combine TF overexpression with modifiers of chromatin state.

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.

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 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.

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.

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.

Epigenetic cell memory ensures that cells are locked into specialized functions for the life-time of an organism. Phenotype loss is often associated with disease, such as cancer, and also required for artificially reprogramming cells from one type to another. Chromatin state, determined by histone modifications and DNA methylation, has recently appeared as a key mediator of epigenetic cell memory. However, a mechanistic understanding of how the dynamics of chromatin state affect the temporal duration of this memory is lacking. Here, we developed and analyzed a theoretical framework that includes these dynamics in gene regulation. Our results show that when both recruited erasure and auto/cross-catalysis among histone modifications and DNA methylation are sufficiently slower than basal erasure of all modifications, loss of cell memory will occur. Our mathematical formulas show how the parameters capturing these time scales depend on the abundance of methyl-DNA-binding proteins, on writers, erasers, and readers of nucleosome modifications, and on cell division time. With this information, one may design experimental interventions to either enforce phenotypic plasticity or re-lock phenotypes in aberrant cells.

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.

Predicting Composition of Genetic Circuits with Resource Competition: Demand and Sensitivity

The design of genetic circuits typically relies on characterization of constituent modules in isolation to predict the behavior of modules' composition. However, it has been shown that the behavior of a genetic module changes when other modules are in the cell due to competition for shared resources. In order to engineer multimodule circuits that behave as intended, it is thus necessary to predict changes in the behavior of a genetic module when other modules load cellular resources. Here, we introduce two characteristics of circuit modules: the demand for cellular resources and the sensitivity to resource loading. When both are known for every genetic module in a circuit library, they can be used to predict any module's behavior upon addition of any other module to the cell. We develop an experimental approach to measure both characteristics for any circuit module using a resource sensor module. Using the measured resource demand and sensitivity for each module in a library, the outputs of the modules can be accurately predicted when they are inserted in the cell in arbitrary combinations. These resource competition characteristics may be used to inform the design of genetic circuits that perform as predicted despite resource competition.

Context-aware synthetic biology by controller design: Engineering the mammalian cell

The rise of systems biology has ushered a new paradigm: the view of the cell as a system that processes environmental inputs to drive phenotypic outputs. Synthetic biology provides a complementary approach, allowing us to program cell behavior through the addition of synthetic genetic devices into the cellular processor. These devices, and the complex genetic circuits they compose, are engineered using a design-prototype-test cycle, allowing for predictable device performance to be achieved in a context-dependent manner. Within mammalian cells, context effects impact device performance at multiple scales, including the genetic, cellular, and extracellular levels. In order for synthetic genetic devices to achieve predictable behaviors, approaches to overcome context dependence are necessary. Here, we describe control systems approaches for achieving context-aware devices that are robust to context effects. We then consider cell fate programing as a case study to explore the potential impact of context-aware devices for regenerative medicine applications.

dCas9 regulator to neutralize competition in CRISPRi circuits

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.

An endoribonuclease-based feedforward controller for decoupling resource-limited genetic modules in mammalian cells

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.

Reprogramming multistable monotone systems with application to cell fate control

Multistability is a key property of dynamical systems modeling cellular regulatory networks implicated in cell fate decisions, where, different stable steady states usually represent distinct cell phenotypes. Monotone network motifs are highly represented in these regulatory networks. In this paper, we leverage the properties of monotone dynamical systems to provide theoretical results that guide the selection of inputs that trigger a transition, i.e., reprogram the network, to a desired stable steady state. We first show that monotone dynamical systems with bounded trajectories admit a minimum and a maximum stable steady state. Then, we provide input choices that are guaranteed to reprogram the system to these extreme steady states. For intermediate states, we provide an input space that is guaranteed to contain an input that reprograms the system to the desired state. We then provide implementation guidelines for finite-time procedures that search this space for such an input, along with rules to prune parts of the space during search. We demonstrate these results on simulations of two recurrent regulatory network motifs: self-activation within mutual antagonism and self-activation within mutual cooperation. Our results depend uniquely on the structure of the network and are independent of specific parameter values.

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.

Realizing 'integral control' in living cells: how to overcome leaky integration due to dilution?

A major problem in the design of synthetic genetic circuits is robustness to perturbations and uncertainty. Because of this, there have been significant efforts in recent years in finding approaches to implement integral control in genetic circuits. Integral controllers have the unique ability to make the output of a process adapt perfectly to disturbances. However, implementing an integral controller is challenging in living cells. This is because a key aspect of any integral controller is a 'memory' element that stores the accumulation (integral) of the error between the output and its desired set-point. The ability to realize such a memory element in living cells is fundamentally challenged by the fact that all biomolecules dilute as cells grow, resulting in a 'leaky' memory that gradually fades away. As a consequence, the adaptation property is lost. Here, we propose a general principle for designing integral controllers such that the performance is practically unaffected by dilution. In particular, we mathematically prove that if the reactions implementing the integral controller are all much faster than dilution, then the adaptation error due to integration leakiness becomes negligible. We exemplify this design principle with two synthetic genetic circuits aimed at reaching adaptation of gene expression to fluctuations in cellular resources. Our results provide concrete guidance on the biomolecular processes that are most appropriate for implementing integral controllers in living cells.

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.

Stochastic multistationarity in a model of the hematopoietic stem cell differentiation network

A central issue in the analysis of multi-stable systems is that of controlling the relative size of the basins of attraction of alternative states through suitable choices of system parameters. We are interested here mainly in the stochastic version of this problem, that of shaping the stationary probability distribution of a Markov chain so that various alternative modes become more likely than others. Although many of our results are more general, we were motivated by an important biological question, that of cell differentiation. In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining the different cell types. Specifically, we study here the "PU.1/GATA-1 circuit" which is involved in the control of the development of mature blood cells from hematopoietic stem cells (HSCs). All mature, specialized blood cells have been shown to be derived from multipotent HSCs. Our first contribution is to introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge. We then find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.

Reprogramming cooperative monotone dynamical systems

Multistable dynamical systems are ubiquitous in nature, especially in the context of regulatory networks controlling cell fate decisions, wherein stable steady states correspond to different cell phenotypes. In the past decade, it has become experimentally possible to "reprogram" the fate of a cell by suitable externally imposed input stimulations. In several of these reprogramming instances, the underlying regulatory network has a known structure and often it falls in the class of cooperative monotone dynamical systems. In this paper, we therefore leverage this structure to provide concrete guidance on the choice of inputs that reprogram a cooperative dynamical system to a desired target steady state. Our results are parameter-independent and therefore can serve as a practical guidance to cell-fate reprogramming experiments.

Computational Analysis of Altering Cell Fate

The notion of reprogramming cell fate is a direct challenge to the traditional view in developmental biology that a cell's phenotypic identity is sealed after undergoing differentiation. Direct experimental evidence, beginning with the somatic cell nuclear transfer experiments of the twentieth century and culminating in the more recent breakthroughs in transdifferentiation and induced pluripotent stem cell (iPSC) reprogramming, have rewritten the rules for what is possible with cell fate transformation. Research is ongoing in the manipulation of cell fate for basic research in disease modeling, drug discovery, and clinical therapeutics. In many of these cell fate reprogramming experiments, there is often little known about the genetic and molecular changes accompanying the reprogramming process. However, gene regulatory networks (GRNs) can in some cases be implicated in the switching of phenotypes, providing a starting point for understanding the dynamic changes that accompany a given cell fate reprogramming process. In this chapter, we present a framework for computationally analyzing cell fate changes by mathematically modeling these GRNs. We provide a user guide with several tutorials of a set of techniques from dynamical systems theory that can be used to probe the intrinsic properties of GRNs as well as study their responses to external perturbations.

Realizing 'integral control' in living cells: how to overcome leaky integration due to dilution?

A major problem in the design of synthetic genetic circuits is robustness to perturbations and uncertainty. Because of this, there have been significant efforts in recent years in finding approaches to implement integral control in genetic circuits. Integral controllers have the unique ability to make the output of a process adapt perfectly to disturbances. However, implementing an integral controller is challenging in living cells. This is because a key aspect of any integral controller is a 'memory' element that stores the accumulation (integral) of the error between the output and its desired set-point. The ability to realize such a memory element in living cells is fundamentally challenged by the fact that all biomolecules dilute as cells grow, resulting in a 'leaky' memory that gradually fades away. As a consequence, the adaptation property is lost. Here, we propose a general principle for designing integral controllers such that the performance is practically unaffected by dilution. In particular, we mathematically prove that if the reactions implementing the integral controller are all much faster than dilution, then the adaptation error due to integration leakiness becomes negligible. We exemplify this design principle with two synthetic genetic circuits aimed at reaching adaptation of gene expression to fluctuations in cellular resources. Our results provide concrete guidance on the biomolecular processes that are most appropriate for implementing integral controllers in living cells.

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.

Resource Competition Shapes the Response of Genetic Circuits

A common approach to design genetic circuits is to compose gene expression cassettes together. While appealing, this modular approach is challenged by the fact that expression of each gene depends on the availability of transcriptional/translational resources, which is in turn determined by the presence of other genes in the circuit. This raises the question of how competition for resources by different genes affects a circuit's behavior. Here, we create a library of genetic activation cascades in E. coli bacteria, where we explicitly tune the resource demand by each gene. We develop a general Hill-function-based model that incorporates resource competition effects through resource demand coefficients. These coefficients lead to nonregulatory interactions among genes that reshape the circuit's behavior. For the activation cascade, such interactions result in surprising biphasic or monotonically decreasing responses. Finally, we use resource demand coefficients to guide the choice of ribosome binding site and DNA copy number to restore the cascade's intended monotonically increasing response. Our results demonstrate how unintended circuit's behavior arises from resource competition and provide a model-guided methodology to minimize the resulting effects.

A Blueprint for a Synthetic Genetic Feedback Controller to Reprogram Cell Fate

To artificially reprogram cell fate, experimentalists manipulate the gene regulatory networks (GRNs) that maintain a cell's phenotype. In practice, reprogramming is often performed by constant overexpression of specific transcription factors (TFs). This process can be unreliable and inefficient. Here, we address this problem by introducing a new approach to reprogramming based on mathematical analysis. We demonstrate that reprogramming GRNs using constant overexpression may not succeed in general. Instead, we propose an alternative reprogramming strategy: a synthetic genetic feedback controller that dynamically steers the concentration of a GRN's key TFs to any desired value. The controller works by adjusting TF expression based on the discrepancy between desired and actual TF concentrations. Theory predicts that this reprogramming strategy is guaranteed to succeed, and its performance is independent of the GRN's structure and parameters, provided that feedback gain is sufficiently high. As a case study, we apply the controller to a model of induced pluripotency in stem cells.

Control theory meets synthetic biology

The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology.

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.

Synthetic tunable amplifying buffer circuit in E. coli

While predictable design of a genetic circuit's output is a major goal of synthetic biology, it remains a significant challenge because DNA binding sites in the cell affect the concentration of available transcription factors (TF). To mitigate this problem, we propose to use a TF that results from the (reversible) phosphorylation of protein substrate as a circuit's output. We demonstrate that by comparatively increasing the amounts of substrate and phosphatase, the TF concentration becomes robust to the presence of DNA binding sites and can be kept at a desired value. The circuit's input/output gain can, in turn, be tuned by changing the relative amounts of the substrate and phosphatase, realizing an amplifying buffer circuit with tunable gain. In our experiments in E. coli, we employ phospho-NRI as the output TF, phosphorylated by the NRII kinase, and dephosphorylated by the NRII phosphatase. Amplifying buffer circuits such as ours could be used to insulate a circuit's output from the context, bringing synthetic biology one step closer to modular design.

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.

Biological modules are inherently context-dependent as the input/output behavior of a module often changes upon connection with other modules. One source of context-dependence is retroactivity, a loading phenomenon by which a downstream system affects the behavior of an upstream system upon interconnection. This fact renders it difficult to predict how modules will behave once connected to each other. In this paper, we propose a general modeling framework for gene transcription networks to accurately predict how retroactivity affects the dynamic behavior of interconnected modules, based on salient physical properties of the same modules in isolation. We illustrate how our framework predicts surprising and counter-intuitive dynamic properties of naturally occurring network structures, which cannot be captured by existing models of the same dimension. We describe implications of our findings on the bottom-up approach to designing synthetic circuits, and on the top-down approach to identifying functional modules in natural networks, revealing trade-offs between robustness to interconnection and dynamic performance. Our framework carries substantial conceptual analogies with electrical network theory based on equivalent representations. We believe that the framework we have proposed, also based on equivalent network representations, can be similarly useful for the analysis and design of biological networks.

Retroactivity controls the temporal dynamics of gene transcription

Just like in many engineering systems, impedance-like effects, called retroactivity, arise at the interconnection of biomolecular circuits, leading to unexpected changes in a circuit's behavior. In this paper, we provide a combined experimental and theoretical study to characterize the effects of retroactivity on the temporal dynamics of a gene transcription module in vivo. The response of the module to an inducer was measured both in isolation and when the module was connected to downstream clients. The connected module, when compared to the isolated module, responded selectively to the introduction of the inducer versus its withdrawal. Specifically, a "sign-sensitive delay" appeared, in which the connected module displayed a time delay in the response to induction and anticipation in the response to de-induction. The extent of these effects can be made larger by increasing the amounts of downstream clients and/or their binding affinity to the output protein of the module. Our experimental results and mathematical formulas make it possible to predict the extent of the change in the dynamic behavior of a module after interconnection. They can be employed to both recover the predictive power of a modular approach to understand systems or as an additional design tool to shape the temporal behavior of gene transcription.

Tuning genetic clocks employing DNA binding sites

Periodic oscillations play a key role in cell physiology from the cell cycle to circadian clocks. The interplay of positive and negative feedback loops among genes and proteins is ubiquitous in these networks. Often, delays in a negative feedback loop and/or degradation rates are a crucial mechanism to obtain sustained oscillations. How does nature control delays and kinetic rates in feedback networks? Known mechanisms include proper selection of the number of steps composing a feedback loop and alteration of protease activity, respectively. Here, we show that a remarkably simple means to control both delays and effective kinetic rates is the employment of DNA binding sites. We illustrate this design principle on a widely studied activator-repressor clock motif, which is ubiquitous in natural systems. By suitably employing DNA target sites for the activator and/or the repressor, one can switch the clock “on” and “off” and precisely tune its period to a desired value. Our study reveals a design principle to engineer dynamic behavior in biomolecular networks, which may be largely exploited by natural systems and employed for the rational design of synthetic circuits.

Response to Comment on “‘Load-Induced Modulation of Signal Transduction Networks’: Reconciling Ultrasensitivity with Bifunctionality?”

Complex biochemical and regulatory properties of a bifunctional enzyme mean that its activity cannot be modeled as a simple bifunctional system with distinct and reciprocally regulated states.

Load-induced modulation of signal transduction networks

Biological signal transduction networks are commonly viewed as circuits that pass along information--in the process amplifying signals, enhancing sensitivity, or performing other signal-processing tasks--to transcriptional and other components. Here, we report on a "reverse-causality" phenomenon, which we call load-induced modulation. Through a combination of analytical and experimental tools, we discovered that signaling was modulated, in a surprising way, by downstream targets that receive the signal and, in doing so, apply what in physics is called a load. Specifically, we found that non-intuitive changes in response dynamics occurred for a covalent modification cycle when load was present. Loading altered the response time of a system, depending on whether the activity of one of the enzymes was maximal and the other was operating at its minimal rate or whether both enzymes were operating at submaximal rates. These two conditions, which we call "limit regime" and "intermediate regime," were associated with increased or decreased response times, respectively. The bandwidth, the range of frequency in which the system can process information, decreased in the presence of load, suggesting that downstream targets participate in establishing a balance between noise-filtering capabilities and a circuit's ability to process high-frequency stimulation. Nodes in a signaling network are not independent relay devices, but rather are modulated by their downstream targets.

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.

A method for determining the robustness of bio-molecular oscillator models

Background

Quantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations.

Results

A novel method for quantifying the robustness of oscillatory behavior to parameter perturbations is presented in this paper. This method relies on the combination of Hopf bifurcation and Routh-Hurwitz stability criterion, which is widely applied in control system design. The proposed method is employed to calculate the robustness of two oscillating biochemical network models previously analyzed in the literature. The robustness bounds here obtained are tighter than what was previously obtained in the literature for both models.

Conclusion

The method here proposed for quantifying the robustness of biochemical oscillator models is computationally less demanding than similar multiparamter variation techniques available in the literature. It also provides tighter bounds on two models previously analyzed in the literature.

Modular cell biology: retroactivity and insulation

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input-output dynamic characteristics of transcriptional components, focusing on a property, which we call 'retroactivity', that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter-binding sites, or when the affinity of such binding sites is high. To attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation-dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast timescales of the phosphorylation and dephosphorylation reactions.