Domitilla Del Vecchio

Here, we review mathematical models of epigenetic memory, focusing on chromatin modifications as key mechanisms to achieve long-term maintenance of epigenetic states. After reviewing the main stochastic modeling frameworks, we focus on stochastic models of chromatin modifications to analyze residence time in memory states, which underpins the long-term maintenance of epigenetic information. We review these concepts through increasingly complicated chromatin modification circuits, including histone modifications, DNA methylation, and their combination.

This paper gives an overview of the use of control systems engineering in synthetic biology, motivated by applications such as cell therapy and cell fate reprogramming for regenerative medicine. A ubiquitous problem in these and other applications is the ability to control the concentration of specific regulatory factors in the cell accurately despite environmental uncertainty and perturbations. The paper describes the origin of these perturbations and how they affect the dynamics of the biomolecular ``plant'' to be controlled. A variety of biomolecular control implementations are then introduced to achieve robustness of the plant's output to perturbations and are grouped into feedback and feedforward control architectures. Although sophisticated control laws can be implemented in a computer today, they cannot be necessarily implemented inside the cell via biomolecular processes. This fact constraints the set of feasible control laws to those realizable through biomolecular processes that can be engineered with synthetic biology. After reviewing biomolecular feedback and feedforward control implementations, mostly focusing on the author's own work, the paper illustrates the application of such control strategies to cell fate reprogramming. Within this context, a master regulatory factor needs to be controlled at a specific level inside the cell in order to reprogram skin cells to pluripotent stem cells. The article closes by highlighting on-going challenges and directions of future research for biomolecular control design.

This paper gives an overview of the use of control systems engineering in synthetic biology, motivated by applications such as cell therapy and cell fate reprogramming for regenerative medicine. A ubiquitous problem in these and other applications is the ability to control the concentration of specific regulatory factors in the cell accurately despite environmental uncertainty and perturbations. The paper describes the origin of these perturbations and how they affect the dynamics of the biomolecular ``plant'' to be controlled. A variety of biomolecular control implementations are then introduced to achieve robustness of the plant's output to perturbations and are grouped into feedback and feedforward control architectures. Although sophisticated control laws can be implemented in a computer today, they cannot be necessarily implemented inside the cell via biomolecular processes. This fact constraints the set of feasible control laws to those realizable through biomolecular processes that can be engineered with synthetic biology. After reviewing biomolecular feedback and feedforward control implementations, mostly focusing on the author's own work, the paper illustrates the application of such control strategies to cell fate reprogramming. Within this context, a master regulatory factor needs to be controlled at a specific level inside the cell in order to reprogram skin cells to pluripotent stem cells. The article closes by highlighting on-going challenges and directions of future research for biomolecular control design.

The development of genetic memory devices in synthetic biology is a challenging process that requires extensive analysis and characterization. In mammalian systems, this complexity is compounded by the need for a small DNA payload for efficient delivery into the cell. Previous genetic memory devices have relied exclusively on protein-based regulation, which are limited by their large size; in this paper, we propose a microRNA-based multistable network, which effectively halves the payload size for more efficient delivery. We demonstrate that the system can be multistable, and use formal methods to characterize constraints on design parameters that guarantee multistability. Our results provide a new genetic network topology that can achieve multistability and demonstrate the use of formal methods in the design of sophisticated genetic network architectures against non-convex top-level specifications.

Understanding how opposing regulatory factors shape gene expression is essential for understanding complex biological systems. A motivating observation, drawn from cancer epigenetics, is that removing an activating factor can sometimes lead to higher, not lower, expression of a gene that is also subject to a repressing factor. Prior theoretical work explained this counterintuitive behavior by competition of repressors and activators for genomic binding sites. However, it has been difficult to test this directly in natural systems, where layers of regulation obscure causal relationships. This paper introduces a fully synthetic, tunable genetic platform in a prokaryotic model system that reconstitutes this competition mechanism in a controlled and isolated setting. The genetic platform contains a target gene with binding sites for both an activator and a repressor, together with separate overlapping decoy binding sites for the same regulators. Activator and repressor functions are implemented using CRISPRa and CRISPRi, which permit independent control of regulator expression levels, design of the binding sites, and modulation of the binding affinities. Using this minimal system, we demonstrate that increasing activator expression level can reduce expression of the target gene when both regulators are present, consistent with the hypothesis that additional activator molecules displace the repressor from decoy sites, which becomes available to repress the target. By demonstrating how competition for genomic binding sites can invert expected regulatory responses, this synthetic framework provides a system for understanding similar paradoxical behaviors in natural regulatory networks and establishes a foundation for future studies in more complex mammalian contexts. Significance Statement Gene regulation is often described in terms of activators that increase expression and repressors that decrease it, yet biological systems frequently display counterintuitive behaviors. Here we show that competition between regulators for shared genomic binding sites can invert expected responses, so that increasing an activator can reduce target gene expression. Using a minimal, fully controllable synthetic system based on CRISPR activation and interference, we isolate and experimentally validate this mechanism. Our results demonstrate that such paradoxical effects arise not from changes in intrinsic regulatory roles but from redistribution of regulators across competing sites. This work provides a general, mechanistic framework for understanding nonintuitive gene-expression patterns observed in complex systems, including those relevant to disease.

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding of how chemical reaction rate parameters impact the stochastic behavior of these systems. One property of interest is mean first passage times (MFPTs) between states. However, deriving explicit formulas for MFPTs can be highly complex. In order to address this problem, we first introduce the concept of [Formula: see text] and develop theorems to determine whether certain SCRNs have this feature by studying associated graphs. Additionally, we develop an algorithm to identify, under specific assumptions, all possible coclique level structures associated with a given SCRN. Finally, we demonstrate how the presence of such a structure in a SCRN allows us to derive closed form formulas for both upper and lower bounds for the MFPTs. Our methods can be applied to SCRNs taking values in a generic finite state space and can also be applied to models with non-mass-action kinetics. We illustrate our results with examples from the biological areas of epigenetics, neurobiology and ecology.

Mammalian cell engineering offers the opportunity to uncover biological principles and develop next-generation biotechnologies. However, epigenetic silencing of transgenes hinders the control of gene expression in mammalian cells. Here, we use chromatin editing of an integrated reporter in CHO-K1 and human induced pluripotent stem cells to study the molecular interactions driving silencing and its reversal. After transient induction of either DNA methylation or H3K9me3, stable silencing was exclusively observed with both marks. Due to the positive feedback between DNA methylation and H3K9me3 and the relative low stability of H3K9me3, our model predicts that removing DNA methylation is sufficient for transgene reactivation. Accordingly, targeted DNA demethylation reactivated the reporter irrespective of whether silencing was achieved by inducing DNA methylation, H3K9me3, or by the endogenous cellular machinery. These results shed light on molecular mechanisms at play during silencing and provide engineering tools for potent and specific transgene reactivation in mammalian cells.

Cells store information by means of chromatin modifications that persist through cell divisions and can hold gene expression silenced over generations. However, how these modifications may maintain other gene expression states has remained unclear. This study shows that chromatin modifications can maintain a wide range of gene expression levels over time, thus uncovering analog epigenetic memory. By engineering a genomic reporter and epigenetic effectors, we tracked the gene expression dynamics following targeted perturbations to the chromatin state. We found that distinct grades of DNA methylation led to corresponding, persistent gene expression levels. Altering the DNA methylation grade, in turn, resulted in permanent loss of gene expression memory. Consistent with experiments, our chromatin modification model indicates that analog memory arises when the positive feedback between DNA methylation and repressive histone modifications is lacking. This discovery will lead to a deeper understanding of epigenetic memory and to new tools for synthetic biology.

Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which diffusion is modeled using the $θ$-diffusion framework, while the reaction dynamics are spatially varying. We demonstrate that spatial heterogeneity affects the asymptotic behavior of such systems. Using contraction theory, we derive conditions that guarantee the exponential convergence of system trajectories, regardless of initial conditions. These conditions explicitly account for the influence of spatial heterogeneity in both the diffusion and reaction terms. As an application, we study a biochemical system and derive the quasi-steady-state (QSS) approximation, illustrating how spatial heterogeneity modulates the effective binding rates of biomolecular species.

Synthetic biology leverages engineering principles to program biology with new functions for applications in medicine, energy, food, and the environment. A central aspect of synthetic biology is the creation of synthetic gene circuits - engineered biological circuits capable of performing operations, detecting signals, and regulating cellular functions. Their development involves large design spaces with intricate interactions among circuit components and the host cellular machinery. Here, we discuss the emerging role of machine learning in addressing these challenges. We articulate how machine learning may enhance synthetic gene circuit engineering, from individual components to circuit-level aspects, while highlighting associated challenges. We discuss potential hybrid approaches that combine machine learning with mechanistic modeling to leverage the advantages of data-driven models with the prescriptive ability of mechanism-based models. Machine learning and its integration with mechanistic modeling are poised to advance synthetic biology, but challenges need to be overcome for such efforts to realize their potential.

Epigenetic memory allows different cells to maintain distinct gene expression patterns despite a common genetic code and plays a role in several biological processes. Chemical modifications to DNA and histones have appeared as critical mediators of epigenetic memory and much attention has gone into characterizing their dynamics. The network of positive feedback loops that these modifications form generates a rich set of dynamics that both recapitulate the traditional binary memory paradigm and also predict a new form of memory that we call analog memory. In this paper, we review models of chromatin modifications and describe how binary or analog memory hinge on the presence or lack of positive feedback loops between repressive histone modifications and DNA methylation. Future research using advanced genetic engineering tools will be able to validate the molecular interactions that dictate different forms of memory, and will thus deepen our understanding of how epigenetic memories form in different biological contexts.

Epigenetic cell memory is the property enabling multicellular organisms to keep distinct cell types despite sharing the same genotype. DNA methylation and histone modifications play a crucial role in maintaining the long-term memory of gene expression patterns specific to each cell type. Experimental results in semi-synthetic genetic systems show that these modifications silence and reactivate genes in an “all or none” manner, suggesting binary epigenetic memory (only extremal gene expression levels have long-term memory). However, in recent years, continuous and graded variations of gene expression levels have been identified across multiple cell types. Here, by introducing and analyzing a chromatin modification circuit model, we demonstrate that the experimentally observed bimodal probability distributions of gene expression level, used to support the binary memory hypothesis, are also compatible with the analog memory hypothesis, where cells can maintain any initially set gene expression level. Our study shows that intrinsic noise combined with an ultrasensitive response between the level of DNA methylation writer DNMT3A and DNA methylation grade at a gene can explain how analog epigenetic cell memory leads to a bimodal gene expression level distribution. The model can help design experiments to help distinguish between binary and analog memory, thereby offering a tool for interrogating the very essence of epigenetic cell memory.

In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits.

The identification of constraints on system parameters that will ensure that a system achieves desired requirements remains a challenge in synthetic biology, where components unintentionally affect one another by perturbing the cellular environment in which they operate. This paper shows how to solve this problem optimally for a class of input/output system-level specifications, and for unintended interactions due to resource sharing. Specifically, we show how to solve the problem based on the input/output properties of the subsystems and on the unintended interaction map. Our approach is based on the elimination of quantifiers in monotone properties of the system. We illustrate applications of this methodology to guaranteeing system-level performance of multiplexed and sequential biosensing and of bistable genetic circuits.

The design of biological systems is a challenging endeavor due to the lack of modularity caused by context effects, such multiple gene expression modules sharing a limited pool of resources. This work considers the problem of determining when specifications on the steady state system behavior can be met for suitable parameter choices, while accounting for resource sharing. We establish necessary and sufficient conditions for the feasibility of a specification for a given network of subsystems that share both production and degradation resources. This extends previous work that considered just production resource sharing and thus lays the foundation for the development of co-design techniques forgenetic networks with both production and degradation resources, where one may be able to mitigate the effects of one type of resource sharing by tuning the other.

The discovery of CRISPR-mediated gene activation (CRISPRa) has transformed the way in which we perform genetic screening, bioproduction and therapeutics through its ability to scale and multiplex. However, the emergence of loads on the key molecular resources constituting CRISPRa by the orthogonal short RNA that guide such resources to gene targets, couple theoretically independent CRISPRa modules. This coupling negates the ability of CRISPRa systems to concurrently regulate multiple genes independent of one another. In this paper, we propose to reduce this coupling by mitigating the loads on the molecular resources that constitute CRISPRa. In particular, we design a multi-variable controller that makes the concentration of these molecular resources robust to variations in the level of the short RNA loads. This work serves as a foundation to design and implement CRISPRa controllers for practical applications.

Epigenetic cell memory, the inheritance of gene expression patterns across subsequent cell divisions, is a critical property of multi-cellular organisms. In recent work [10], a subset of the authors observed in a simulation study how the stochastic dynamics and time-scale differences between establishment and erasure processes in chromatin modifications (such as histone modifications and DNA methylation) can have a critical effect on epigenetic cell memory. In this paper, we provide a mathematical framework to rigorously validate and extend beyond these computational findings. Viewing our stochastic model of a chromatin modification circuit as a singularly perturbed, finite state, continuous time Markov chain, we extend beyond existing theory in order to characterize the leading coefficients in the series expansions of stationary distributions and mean first passage times. In particular, we characterize the limiting stationary distribution in terms of a reduced Markov chain, provide an algorithm to determine the orders of the poles of mean first passage times, and determine how changing erasure rates affects system behavior. The theoretical tools developed in this paper not only allow us to set a rigorous mathematical basis for the computational findings of our prior work, highlighting the effect of chromatin modification dynamics on epigenetic cell memory, but they can also be applied to other singularly perturbed Markov chains beyond the applications in this paper, especially those associated with chemical reaction networks.

The discovery of CRISPR-mediated gene activation (CRISPRa) has transformed the way in which we perform genetic screening, bioproduction and therapeutics through its ability to scale and multiplex. However, the emergence of loads on the key molecular resources constituting CRISPRa by the orthogonal short RNA that guide such resources to gene targets, couple theoretically independent CRISPRa modules. This coupling negates the ability of CRISPRa systems to concurrently regulate multiple genes independent of one another. In this paper, we propose to reduce this coupling by mitigating the loads on the molecular resources that constitute CRISPRa. In particular, we design a multi-variable controller that makes the concentration of these molecular resources robust to variations in the level of the short RNA loads. This work serves as a foundation to design and implement CRISPRa controllers for practical applications.

Chaperones are a global resource within cellular biomolecular systems, ensuring that proteins are properly folded and preventing that aggregation leads to cell death. Introducing genetic circuits to a cell may place a load on these folding resources, resulting in unintended coupling between otherwise independent circuits' behavior. Previous analyses have considered loading effects on other cellular resources - such as gene expression resources - but have not included chaperone-enabled folding. In this paper, we model two chaperone modalities, encapsulating two important classes of chaperones as well as their potential interactions. We identify distinct responses that arise from the different architectures which can be either competitive or activating. This work indicates that native cellular chaperones may have built-in control architectures to mitigate loading by an increased demand from chaperone-reliant proteins.

ABSTRACT CRISPR-mediated gene activation (CRISPRa) allows concurrent transcriptional activation of many genes and has found widespread use in genome-wide screening, bioproduction, and therapeutics. Scaffold RNAs (scRNAs) recruit dCas9 and an activator protein (RBP-AD) to the target gene for activation with high sequence specificity. Here, we show that, despite this specificity, orthogonal scRNAs interfere with each other because they compete for dCas9 and RBP-AD. Specifically, we demonstrate that the expression of an scRNA that binds to these resources results in repression of genes targeted by different scRNAs. Intriguingly, we also discover that transcriptional gene regulation by an scRNA is biphasic, wherein increased level of the scRNA leads to gene repression instead of activation. These effects are significant even when dCas9 and RBP-AD are expressed at the maximum level tolerable by the cell. Our results demonstrate that CRISPRa systems are not as modular as previously thought and establish predictive modeling tools to assess the emergent behavior of multi-module CRISPRa networks.

Epigenetic cell memory, the inheritance of gene expression patterns across subsequent cell divisions, is a critical property of multi-cellular organisms. In recent work [10], a subset of the authors observed in a simulation study how the stochastic dynamics and time-scale differences between establishment and erasure processes in chromatin modifications (such as histone modifications and DNA methylation) can have a critical effect on epigenetic cell memory. In this paper, we provide a mathematical framework to rigorously validate and extend beyond these computational findings. Viewing our stochastic model of a chromatin modification circuit as a singularly perturbed, finite state, continuous time Markov chain, we extend beyond existing theory in order to characterize the leading coefficients in the series expansions of stationary distributions and mean first passage times. In particular, we characterize the limiting stationary distribution in terms of a reduced Markov chain, provide an algorithm to determine the orders of the poles of mean first passage times, and determine how changing erasure rates affects system behavior. The theoretical tools developed in this paper not only allow us to set a rigorous mathematical basis for the computational findings of our prior work, highlighting the effect of chromatin modification dynamics on epigenetic cell memory, but they can also be applied to other singularly perturbed Markov chains beyond the applications in this paper, especially those associated with chemical reaction networks.

Sensitive on-site virus detection is a requirement for timely action against the spread of airborne infection since ultra-low in-air viral concentrations can readily infect individuals when inhaled. Here, we consider a fieldable biosensing process that incorporates a fast RNA enrichment step in order to concentrate viral RNA in a small volume prior to RT-qPCR. The enrichment approach uses electrophoresis in an RT-qPCR-compatible buffer, and allows for concentration of RNA by nearly 5-fold within only 10 min. In order to place this performance into context, we analyzed the minimum detectable concentration of a low-cost, fieldable, biosensing process that uses electrostatic precipitation for air sampling, heating for viral RNA extraction, and then RNA enrichment, followed by RT-qPCR. With enrichment, we estimated an in-air concentration of 5,654 genome copies (gc)/m 3 with a 100% detection rate and an in-air concentration of 4,221 gc/m 3 with a 78.6% detection rate. Given that the concentrations of common viruses, such as influenza and SARS-CoV-2, in several indoor spaces are between 5,800 and 37,000 gc/m 3 , we conclude that enrichment allows a detection that is sufficiently sensitive for practical applications. • A fieldable biosensing process was demonstrated with an MDC of 5 gc/L of air. • Electrophoretic enrichment lowered the MDC at femtogram amounts of RNA. • ESP sampling, kit-free extraction and enrichment enabled cost-effective biosensing.

In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits.

Summary Chemical modifications to histones and DNA play a crucial role in the regulation of transcription and in the maintenance of chromatin states that are not permissive to gene expression [1–3]. However, the landscape of gene expression states that these modifications stably maintain remains uncharted. Here, we show that gene expression can be memorized at a wide range of levels thus implementing analog epigenetic memory. Mechanistically, we find that DNA methylation serves a primary role in maintaining memory across cell divisions while histone modifications only follow DNA methylation to regulate gene expression. Employing targeted epigenetic editing and time-course analysis, we analyzed the temporal stability of gene expression and DNA methylation post removal of epigenetic effectors. We found that the grade of DNA methylation in the gene’s promoter, defined as the mean fraction of methylated CpGs, remains stable over time and inversely correlates with gene expression level. By contrast, Histone 3 lysine 9 trimethylation (H3K9me3) could not persist after removal of its writer in the absence of DNA methylation. These experimental findings, combined with our chromatin modification model, indicate that the absence of positive feedback mechanisms around DNA methylation - unlike those found in histone modifications - enable the temporal stability of the DNA methylation grade, which leads to analog memory. These results expand current knowledge on how epigenetic memory is achieved in natural systems. Moreover, we anticipate that analog memory through graded DNA methylation will enable to program mammalian cells with fine-grained information storage. This capability will significantly enhance the sophistication of engineered cell functionality in applications including tissue engineering, organoids, and cell therapies.

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.

Modular composition of systems through defined input/output interfaces is a wide-spread engineering approach that allows to make the design of complicated systems tractable. Although this approach has percolated to the design of synthetic genetic circuits, it has proved challenging to obtain predictable design outcomes. In particular, context-dependence due to sharing a limited pool of cellular resources is a major factor that confounds modular composition of genetic modules. Here, we propose the use of a systems framework in which resource sharing among different subsystems is explicitly modeled through disturbance inputs and outputs. Within this system description, resource sharing results in undesired connectivity among subsystems, which is explicitly accounted for in design. Accordingly, we propose to use this system framework to co-design stable systems, with constant input, based on steady state specifications that each subsystem should satisfy. To this end, we provide sufficient conditions on the system parameters such that the output of each subsystem in the network remains in a small interval around a desired value, as well as an algorithmic procedure to compute the feasible region for these parameters. In general, this framework can be used to design subsystems to satisfy a specification, while explicitly accounting for context-dependence.

Hill functions are often used in stochastic models of gene regulation to approximate the dependence of gene activity on the concentration of the transcription factor (TF) that regulates the gene. However, it is generally unknown how much error one may incur from this approximation. We investigate this question in the context of transcriptional networks (TNs). Under the assumption of rapid binding and unbinding of TFs with their gene targets, we bound the approximation error (in terms of the total variation distance) between a mass-action stochastic model and a corresponding model with Hill function propensities. To do so, we use a combination of singular perturbation theory and moment analysis for stochastic chemical reaction networks. We assume throughout that TFs regulate genes in a one-to-one fashion, each regulated gene produces a single TF, TFs do not multimerize, and each gene only has a single TF binding site. These results are pertinent for the modeling of TNs and may also carry relevance for more general biological processes.

Many biomolecular systems can be described by chemical reaction networks, however, there may be several candidate networks based on the known biology for a particular system. Determining which chemical reaction network models are inconsistent with observed data can be done via model invalidation. In this work, we formulate and solve a robust version of the model invalidation problem for the case where only measurements from the stationary distribution are available. This problem corresponds to determining if an observed distribution could have been generated by the given chemical reaction network for some value of the parameters, plus a perturbation of bounded size with respect to total variation distance. The main technical tool we introduce to solve the problem is a set of generalized moments that make the problem amenable to an algorithmic solution.

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.

Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and synthetic biology, but often have a large or infinite number of states, and thus are not amenable to computation and analysis. Due to this, approximations that rely on the molecular counts and the volume being large are commonly used, with the most common being the Reaction Rate Equations and the Linear Noise Approximation. For finite time intervals, Kurtz established the validity of the Reaction Rate Equations and Linear Noise Approximation, by proving law of large numbers and central limit theorem results respectively. However, the analogous question for the stationary distribution of the Markov chain model has remained mostly unanswered, except for chemical reaction networks with special structures or bounded molecular counts. In this work, we use Stein's Method to obtain sufficient conditions for the stationary distribution of an appropriately scaled Stochastic Chemical Reaction Network to converge to the Linear Noise Approximation as the system size goes to infinity. Our results give non asymptotic bounds on the error in the Reaction Rate Equations and in the Linear Noise Approximation as applied to the stationary distribution. As a special case, we give conditions under which the global exponential stability of an equilibrium point of the Reaction Rate Equations is sufficient to obtain our error bounds, thus permitting one to obtain conclusions about the Markov chain by analyzing the deterministic Reaction Rate Equations.

Many biological systems can be modeled as a chemical reaction network with unknown parameters. Data available to identify these parameters are often in the form of a stationary distribution, such as that obtained from measurements of a cell population. In this work, we introduce a framework for analyzing the identifiability of the reaction rate coefficients of chemical reaction networks from stationary distribution data. Working with the linear noise approximation, which is a diffusive approximation to the chemical master equation, we give a computational procedure to certify global identifiability based on Hilbert's Nullstellensatz. We present a variety of examples that show the applicability of our method to chemical reaction networks of interest in systems and synthetic biology, including discrimination between possible molecular mechanisms for the interaction between biochemical species.

In the original version of this Article, the directional arrows in figure panels Fig. 2e and Fig. 2f indicating the transition between OmpR tagged with VP64 and phosphorylated OmpR tagged with VP64 were reversed. The correct figure is presented below. This has been corrected in the HTML and PDF version of the paper. In addition, the caption for Supplementary Fig. 17b “Red symbols correspond to the calculations shown in Panel (a) and Fig. 5d (threshold = 105 MEFLs Output)” was incorrectly presented as “Red symbols correspond to the calculations shown in Fig. 2c (threshold = 105 MEFLs Output – also shown drawn on plots in (a))”. The corrected Supplementary Information file is appended below.

Abstract Rapid, on-site, airborne virus detection is a requirement for timely action against the spread of air-transmissible infectious diseases. This applies both to future threats and to common viral diseases, such as influenza and COVID-19, which hit vulnerable populations yearly with severe consequences. The ultra-low concentrations of virus in the air make airborne virus detection difficult, yet readily infect individuals when breathed. Here, we propose a fieldable process that includes an enrichment step to concentrate collected genetic material in a small volume. The enrichment approach uses capillary electrophoresis and an RT-qPCR-compatible buffer, which allow enrichment of the RNA by about 5-fold within only 10 minutes of operation. Our detection process consists of air sampling through electrostatic precipitation, RNA extraction via heating, RNA enrichment, and RT-qPCR for detection. We optimized each step of the process and estimated a detection sensitivity of 3106 ± 2457 genome copies (gc) per m 3 of air. We then performed an integration experiment and confirmed a sensitivity of 5654 gc/m 3 with a detection rate of 100% and a sensitivity of 4221 gc/m 3 with a detection rate of 78.6%. When using fast RT-qPCR, the latency of the whole process is down to 61 minutes. Given that our sensitivity falls in the low range of influenza and SARS-CoV-2 concentrations reported in indoor spaces, our study shows that, with enrichment, airborne pathogen detection can be made sufficiently sensitive for practical use.

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.

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.

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.

Abstract In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation.

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.