Engineering of a synthetic quadrastable gene network to approach Waddington landscape and cell fate determination

Design principles of gene circuits for longevity

Aging is a dynamic process that is driven by cellular damage and disruption of homeostatic gene regulatory networks (GRNs). Traditional studies often focus on individual genes, but understanding their interplay is key to unraveling the mechanisms of aging. This review explores the gene circuits that influence longevity and highlights the role of feedback loops in maintaining cellular balance. The SIR2-HAP circuit in yeast serves as a model to explore how mutual inhibition between pathways influences aging trajectories and how engineering stable fixed points or oscillations within these circuits can extend lifespan. Feedback loops crucial for maintaining homeostasis are also reviewed, and we highlight how their destabilization accelerates aging. By leveraging systems and synthetic biology, strategies are proposed that may stabilize these loops within single cells, thereby enhancing their resilience to aging-related damage.

Modeling ncRNA-Mediated Circuits in Cell Fate Decision: From Systems Biology to Synthetic Biology

Noncoding RNAs (ncRNAs) play critical roles in essential cell fate decisions. However, the exact molecular mechanisms underlying ncRNA-mediated bistable switches remain elusive and controversial. In recent years, systematic mathematical and quantitative experimental analyses have made significant contributions to elucidating the molecular mechanisms of controlling ncRNA-mediated cell fate decision processes. In this chapter, we review and summarize the general framework of mathematical modeling of ncRNA in a pedagogical way and the application of this general framework to real biological processes. We discuss the emerging properties resulting from the reciprocal regulation between mRNA, miRNA, and competing endogenous mRNA (ceRNA). We also explore the efforts within the synthetic biology approach to understand the fundamental design principles underlying cell fate decisions. Both the positive feedback loops between ncRNAs and transcription factors and the emerging properties from the miRNA-mRNA reciprocal regulation enable bistable switches to direct cell fate decisions.

Multistability and predominant hybrid phenotypes in a four node mutually repressive network of Th1/Th2/Th17/Treg differentiation

Elucidating the emergent dynamics of cellular differentiation networks is crucial to understanding cell-fate decisions. Toggle switch - a network of mutually repressive lineage-specific transcription factors A and B - enables two phenotypes from a common progenitor: (high A, low B) and (low A, high B). However, the dynamics of networks enabling differentiation of more than two phenotypes from a progenitor cell has not been well-studied. Here, we investigate the dynamics of a four-node network A, B, C, and D inhibiting each other, forming a toggle tetrahedron. Our simulations show that this network is multistable and predominantly allows for the co-existence of six hybrid phenotypes where two of the nodes are expressed relatively high as compared to the remaining two, for instance (high A, high B, low C, low D). Finally, we apply our results to understand naïve CD4+ T cell differentiation into Th1, Th2, Th17 and Treg subsets, suggesting Th1/Th2/Th17/Treg decision-making to be a two-step process.

Enhanced cellular longevity arising from environmental fluctuations

Cellular longevity is regulated by both genetic and environmental factors. However, the interactions of these factors in the context of aging remain largely unclear. Here, we formulate a mathematical model for dynamic glucose modulation of a core gene circuit in yeast aging, which not only guided the design of pro-longevity interventions but also revealed the theoretical principles underlying these interventions. We introduce the dynamical systems theory to capture two general means for promoting longevity-the creation of a stable fixed point in the "healthy" state of the cell and the "dynamic stabilization" of the system around this healthy state through environmental oscillations. Guided by the model, we investigate how both of these can be experimentally realized by dynamically modulating environmental glucose levels. The results establish a paradigm for theoretically analyzing the trajectories and perturbations of aging that can be generalized to aging processes in diverse cell types and organisms.

Folding State within a Hysteresis Loop: Hidden Multistability in Nonlinear Physical Systems

Identifying hidden states in nonlinear physical systems that evade direct experimental detection is important as disturbances and noises can place the system in a hidden state with detrimental consequences. We study a cavity magnonic system whose main physics is photon and magnon Kerr effects. Sweeping a bifurcation parameter in numerical experiments (as would be done in actual experiments) leads to a hysteresis loop with two distinct stable steady states, but analytic calculation gives a third folded steady state "hidden" in the loop, which gives rise to the phenomenon of hidden multistability. We propose an experimentally feasible control method to drive the system into the folded hidden state. We demonstrate, through a ternary cavity magnonic system and a gene regulatory network, that such hidden multistability is in fact quite common. Our findings shed light on hidden dynamical states in nonlinear physical systems which are not directly observable but can present challenges and opportunities in applications.

Modularized Design and Construction of Tunable Microbial Consortia with Flexible Topologies

Complex and fluid bacterial community compositions are critical to diversity, stability, and function. However, quantitative and mechanistic descriptions of the dynamics of such compositions are still lacking. Here, we develop a modularized design framework that allows for bottom-up construction and the study of synthetic bacterial consortia with different topologies. We showcase the microbial consortia design and building process by constructing amensalism and competition consortia using only genetic circuit modules to engineer different strains to form the community. Functions of modules and hosting strains are validated and quantified to calibrate dynamic parameters, which are then directly fed into a full mechanistic model to accurately predict consortia composition dynamics for both amensalism and competition without further fitting. More importantly, such quantitative understanding successfully identifies the experimental conditions to achieve coexistence composition dynamics. These results illustrate the process of both computationally and experimentally building up bacteria consortia complexity and hence achieve robust control of such fluid systems.

Automated design of gene circuits with optimal mushroom-bifurcation behavior

Recent advances in synthetic biology are enabling exciting technologies, including the next generation of biosensors, the rational design of cell memory, modulated synthetic cell differentiation, and generic multifunctional biocircuits. These novel applications require the design of gene circuits leading to sophisticated behaviors and functionalities. At the same time, designs need to be kept minimal to avoid compromising cell viability. Bifurcation theory addresses such challenges by associating circuit dynamical properties with molecular details of its design. Nevertheless, incorporating bifurcation analysis into automated design processes has not been accomplished yet. This work presents an optimization-based method for the automated design of synthetic gene circuits with specified bifurcation diagrams that employ minimal network topologies. Using this approach, we designed circuits exhibiting the mushroom bifurcation, distilled the most robust topologies, and explored its multifunctional behavior. We then outline potential applications in biosensors, memory devices, and synthetic cell differentiation.

Microbial models of development: Inspiration for engineering self-assembled synthetic multicellularity

While the field of synthetic developmental biology has traditionally focused on the study of the rich developmental processes seen in metazoan systems, an attractive alternate source of inspiration comes from microbial developmental models. Microbes face unique lifestyle challenges when forming emergent multicellular collectives. As a result, the solutions they employ can inspire the design of novel multicellular systems. In this review, we dissect the strategies employed in multicellular development by two model microbial systems: the cellular slime mold Dictyostelium discoideum and the biofilm-forming bacterium Bacillus subtilis. Both microbes face similar challenges but often have different solutions, both from metazoan systems and from each other, to create emergent multicellularity. These challenges include assembling and sustaining a critical mass of participating individuals to support development, regulating entry into development, and assigning cell fates. The mechanisms these microbial systems exploit to robustly coordinate development under a wide range of conditions offer inspiration for a new toolbox of solutions to the synthetic development community. Additionally, recreating these phenomena synthetically offers a pathway to understanding the key principles underlying how these behaviors are coordinated naturally.

Engineering longevity-design of a synthetic gene oscillator to slow cellular aging

Synthetic biology enables the design of gene networks to confer specific biological functions, yet it remains a challenge to rationally engineer a biological trait as complex as longevity. A naturally occurring toggle switch underlies fate decisions toward either nucleolar or mitochondrial decline during the aging of yeast cells. We rewired this endogenous toggle to engineer an autonomous genetic clock that generates sustained oscillations between the nucleolar and mitochondrial aging processes in individual cells. These oscillations increased cellular life span through the delay of the commitment to aging that resulted from either the loss of chromatin silencing or the depletion of heme. Our results establish a connection between gene network architecture and cellular longevity that could lead to rationally designed gene circuits that slow aging.

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.

Coupled Mutual Inhibition and Mutual Activation Motifs as Tools for Cell-Fate Control

Multistability is central to biological systems. It plays a crucial role in adaptation, evolvability, and differentiation. The presence of positive feedback loops can enable multistability. The simplest of such feedback loops are (a) a mutual inhibition (MI) loop, (b) a mutual activation (MA) loop, and (c) self-activation. While it is established that all three motifs can give rise to bistability, the characteristic differences in the bistability exhibited by each of these motifs is relatively less understood. Here, we use dynamical simulations across a large ensemble of parameter sets and initial conditions to study the bistability characteristics of these motifs. Furthermore, we investigate the utility of these motifs for achieving coordinated expression through cyclic and parallel coupling amongst them. Our analysis revealed that MI-based architectures offer discrete and robust control over gene expression, multistability, and coordinated expression among multiple genes, as compared to MA-based architectures. We then devised a combination of MI and MA architectures to improve coordination and multistability. Such designs help enhance our understanding of the control structures involved in robust cell-fate decisions and provide a way to achieve controlled decision-making in synthetic systems.

An improved approach for calculating energy landscape of gene networks from moment equations

The energy landscape theory has widely been applied to study the stochastic dynamics of biological systems. Different methods have been developed to quantify the energy landscape for gene networks, e.g., using Gaussian approximation (GA) approach to calculate the landscape by solving the diffusion equation approximately from the first two moments. However, how high-order moments influence the landscape construction remains to be elucidated. Also, multistability exists extensively in biological networks. So, how to quantify the landscape for a multistable dynamical system accurately, is a paramount problem. In this work, we prove that the weighted summation from GA (WSGA), provides an effective way to calculate the landscape for multistable systems and limit cycle systems. Meanwhile, we proposed an extended Gaussian approximation (EGA) approach by considering the effects of the third moments, which provides a more accurate way to obtain probability distribution and corresponding landscape. By applying our generalized EGA approach to two specific biological systems: multistable genetic circuit and synthetic oscillatory network, we compared EGA with WSGA by calculating the KL divergence of the probability distribution between these two approaches and simulations, which demonstrated that the EGA provides a more accurate approach to calculate the energy landscape.

Multiple Gene Expression in Cell-Free Protein Synthesis Systems for Reconstructing Bacteriophages and Metabolic Pathways

As a fast and reliable technology with applications in diverse biological studies, cell-free protein synthesis has become popular in recent decades. The cell-free protein synthesis system can be considered a complex chemical reaction system that is also open to exogenous manipulation, including that which could otherwise potentially harm the cell's viability. On the other hand, since the technology depends on the cell lysates by which genetic information is transformed into active proteins, the whole system resembles the cell to some extent. These features make cell-free protein synthesis a valuable addition to synthetic biology technologies, expediting the design-build-test-learn cycle of synthetic biology routines. While the system has traditionally been used to synthesize one protein product from one gene addition, recent studies have employed multiple gene products in order to, for example, develop novel bacteriophages, viral particles, or synthetic metabolisms. Thus, we would like to review recent advancements in applying cell-free protein synthesis technology to synthetic biology, with an emphasis on multiple gene expressions.

Beyond Boolean: Ternary networks and dynamics

Boolean networks introduced by Kauffman, originally intended as a prototypical model for gaining insights into gene regulatory dynamics, have become a paradigm for understanding a variety of complex systems described by binary state variables. However, there are situations, e.g., in biology, where a binary state description of the underlying dynamical system is inadequate. We propose random ternary networks and investigate the general dynamical properties associated with the ternary discretization of the variables. We find that the ternary dynamics can be either ordered or disordered with a positive Lyapunov exponent, and the boundary between them in the parameter space can be determined analytically. A dynamical event that is key to determining the boundary is the emergence of an additional fixed point for which we provide numerical verification. We also find that the nodes playing a pivotal role in shaping the system dynamics have characteristically distinct behaviors in different regions of the parameter space, and, remarkably, the boundary between these regions coincides with that separating the ordered and disordered dynamics. Overall, our framework of ternary networks significantly broadens the classical Boolean paradigm by enabling a quantitative description of richer and more complex dynamical behaviors.

Synthetic multistability in mammalian cells

In multicellular organisms, gene regulatory circuits generate thousands of molecularly distinct, mitotically heritable states through the property of multistability. Designing synthetic multistable circuits would provide insight into natural cell fate control circuit architectures and would allow engineering of multicellular programs that require interactions among distinct cell types. We created MultiFate, a naturally inspired, synthetic circuit that supports long-term, controllable, and expandable multistability in mammalian cells. MultiFate uses engineered zinc finger transcription factors that transcriptionally self-activate as homodimers and mutually inhibit one another through heterodimerization. Using a model-based design, we engineered MultiFate circuits that generate as many as seven states, each stable for at least 18 days. MultiFate permits controlled state switching and modulation of state stability through external inputs and can be expanded with additional transcription factors. These results provide a foundation for engineering multicellular behaviors in mammalian cells.

One cell, many fates

[Figure: see text].

A Predictive Reaction-diffusion Based Model of E.coli Colony Growth Control

Bacterial colony formations exhibit diverse morphologies and dynamics. A mechanistic understanding of this process has broad implications to ecology and medicine. However, many control factors and their impacts on colony formation remain underexplored. Here we propose a reaction-diffusion based dynamic model to quantitatively describe cell division and colony expansion, where control factors of colony spreading take the form of nonlinear density-dependent function and the intercellular impacts take the form of density-dependent hill function. We validate the model using experimental E. coli colony growth data and our results show that the model is capable of predicting the whole colony expansion process in both time and space under different conditions. Furthermore, the nonlinear control factors can predict colony morphology at both center and edge of the colony.

Predictable control of RNA lifetime using engineered degradation-tuning RNAs

The ability to tune RNA and gene expression dynamics is greatly needed for biotechnological applications. Native RNA stabilizers or engineered 5' stability hairpins have been used to regulate transcript half-life to control recombinant protein expression. However, these methods have been mostly ad hoc and hence lack predictability and modularity. Here, we report a library of RNA modules called degradation-tuning RNAs (dtRNAs) that can increase or decrease transcript stability in vivo and in vitro. dtRNAs enable modulation of transcript stability over a 40-fold dynamic range in Escherichia coli with minimal influence on translation initiation. We harness dtRNAs in messenger RNAs and noncoding RNAs to tune gene circuit dynamics and enhance CRISPR interference in vivo. Use of stabilizing dtRNAs in cell-free transcription-translation reactions also tunes gene and RNA aptamer production. Finally, we combine dtRNAs with toehold switch sensors to enhance the performance of paper-based norovirus diagnostics, illustrating the potential of dtRNAs for biotechnological applications.

An in vitro model of tumor heterogeneity resolves genetic, epigenetic, and stochastic sources of cell state variability

Tumor heterogeneity is a primary cause of treatment failure and acquired resistance in cancer patients. Even in cancers driven by a single mutated oncogene, variability in response to targeted therapies is well known. The existence of additional genomic alterations among tumor cells can only partially explain this variability. As such, nongenetic factors are increasingly seen as critical contributors to tumor relapse and acquired resistance in cancer. Here, we show that both genetic and nongenetic factors contribute to targeted drug response variability in an experimental model of tumor heterogeneity. We observe significant variability to epidermal growth factor receptor (EGFR) inhibition among and within multiple versions and clonal sublines of PC9, a commonly used EGFR mutant nonsmall cell lung cancer (NSCLC) cell line. We resolve genetic, epigenetic, and stochastic components of this variability using a theoretical framework in which distinct genetic states give rise to multiple epigenetic "basins of attraction," across which cells can transition driven by stochastic noise. Using mutational impact analysis, single-cell differential gene expression, and correlations among Gene Ontology (GO) terms to connect genomics to transcriptomics, we establish a baseline for genetic differences driving drug response variability among PC9 cell line versions. Applying the same approach to clonal sublines, we conclude that drug response variability in all but one of the sublines is due to epigenetic differences; in the other, it is due to genetic alterations. Finally, using a clonal drug response assay together with stochastic simulations, we attribute subclonal drug response variability within sublines to stochastic cell fate decisions and confirm that one subline likely contains genetic resistance mutations that emerged in the absence of drug treatment.

Operating principles of circular toggle polygons

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states-(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad-three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C)-can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd-numbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

A Dimension Reduction Approach for Energy Landscape: Identifying Intermediate States in Metabolism-EMT Network

Dimension reduction is a challenging problem in complex dynamical systems. Here, a dimension reduction approach of landscape (DRL) for complex dynamical systems is proposed, by mapping a high-dimensional system on a low-dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high-dimensional systems. The consistency of barrier heights calculated from the low-dimensional landscape and transition actions calculated from the high-dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial-mesenchymal transition (EMT) and abnormal metabolism are two hallmarks of cancer. With the DRL approach, a quadrastable landscape for metabolism-EMT network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process, the cells at E state need to first change their metabolism, then enter the M state. The work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.

Memorizing environmental signals through feedback and feedforward loops

Cells in diverse organisms can store the information of previous environmental conditions for long periods of time. This form of cellular memory adjusts the cell's responses to future challenges, providing fitness advantages in fluctuating environments. Many biological functions, including cellular memory, are mediated by specific recurring patterns of interactions among proteins and genes, known as 'network motifs.' In this review, we focus on three well-characterized network motifs - negative feedback loops, positive feedback loops, and feedforward loops, which underlie different types of cellular memories. We describe the latest studies identifying these motifs in various molecular processes and discuss how the topologies and dynamics of these motifs can enable memory encoding and storage.

Winner-takes-all resource competition redirects cascading cell fate transitions

Failure of modularity remains a significant challenge for assembling synthetic gene circuits with tested modules as they often do not function as expected. Competition over shared limited gene expression resources is a crucial underlying reason. It was reported that resource competition makes two seemingly separate genes connect in a graded linear manner. Here we unveil nonlinear resource competition within synthetic gene circuits. We first build a synthetic cascading bistable switches (Syn-CBS) circuit in a single strain with two coupled self-activation modules to achieve two successive cell fate transitions. Interestingly, we find that the in vivo transition path was redirected as the activation of one switch always prevails against the other, contrary to the theoretically expected coactivation. This qualitatively different type of resource competition between the two modules follows a ‘winner-takes-all’ rule, where the winner is determined by the relative connection strength between the modules. To decouple the resource competition, we construct a two-strain circuit, which achieves successive activation and stable coactivation of the two switches. These results illustrate that a highly nonlinear hidden interaction between the circuit modules due to resource competition may cause counterintuitive consequences on circuit functions, which can be controlled with a division of labor strategy.

Synthetic gene circuits may not function as expected due to the resource competition between modules. Here the authors build cascading bistable switches to achieve two successive cell fate transitions but found a ‘winner-takes-all’ behaviour, which is overcome by a division of labour strategy.

Trajectory-based energy landscapes of gene regulatory networks

Multistability and natural biological variability can result in significant heterogeneity within a cell population, leading to challenges in understanding and modulating cell behavior. Energy landscapes can offer qualitatively intuitive visualizations of cell phenotype and facilitate a more quantitative understanding of cellular dynamics, but current methods for landscape generation are mathematically involved and often require specific system properties (e.g., ergodicity or independent gene/protein probability distributions) that do not always hold. Here, we present a simple kinetic Monte Carlo-based method for landscape generation from a system of ordinary differential equations using only simulation trajectories initialized throughout the phase space of interest. The resulting landscape produces three quantitative features relevant to understanding cell behavior: stability (reflected by the depth or potential of landscape valleys), velocity (representing average directional movement on the landscape), and variance in velocity (indicative of landscape positions with heterogeneous movements). We applied this method to a genetic toggle switch, a core decision-making network in binary cellular responses, to elucidate effects of biologically relevant intrinsic and extrinsic cues. Intrinsic noise, such as stochasticity in transcription-translation and differences in cell cycle position, manifests through changes in valley width and position, reflecting increased population heterogeneity and more probabilistic cell fate transitions. The landscapes also capture the effect of an external inducer, revealing a quantitative correlation between the rate of cell fate transition and the energy barrier above a threshold inducer concentration determined by the permissivity of the valley. Further, in tracking dynamically changing landscapes under time-varying external cues, we unexpectedly found that an oscillatory inducer input can modulate cell fate heterogeneity and lead to periodic cell fate transitions entrained to the input frequency, depending on the intrinsic degradation rate of the switch. The landscape generation approach outlined herein is generalizable to other network topologies and may provide new quantitative insights into their dynamics.

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.

A programmable fate decision landscape underlies single-cell aging in yeast

Chromatin instability and mitochondrial decline are conserved processes that contribute to cellular aging. Although both processes have been explored individually in the context of their distinct signaling pathways, the mechanism that determines which process dominates during aging of individual cells is unknown. We show that interactions between the chromatin silencing and mitochondrial pathways lead to an epigenetic landscape of yeast replicative aging with multiple equilibrium states that represent different types of terminal states of aging. The structure of the landscape drives single-cell differentiation toward one of these states during aging, whereby the fate is determined quite early and is insensitive to intracellular noise. Guided by a quantitative model of the aging landscape, we genetically engineered a long-lived equilibrium state characterized by an extended life span.

Topology-dependent interference of synthetic gene circuit function by growth feedback

Growth-mediated feedback between synthetic gene circuits and host organisms leads to diverse emerged behaviors, including growth bistability and enhanced ultrasensitivity. However, the range of possible impacts of growth feedback on gene circuits remains underexplored. Here, we mathematically and experimentally demonstrated that growth feedback affects the functions of memory circuits in a network topology-dependent way. Specifically, the memory of the self-activation switch is quickly lost due to the growth-mediated dilution of the circuit products. Decoupling of growth feedback reveals its memory, manifested by its hysteresis property across a broad range of inducer concentration. On the contrary, the toggle switch is more refractory to growth-mediated dilution and can retrieve its memory after the fast-growth phase. The underlying principle lies in the different dependence of active and repressive regulations in these circuits on the growth-mediated dilution. Our results unveil the topology-dependent mechanism on how growth-mediated feedback influences the behaviors of gene circuits.

Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape

Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.

Disentangling a complex response in cell reprogramming and probing the Waddington landscape by automatic construction of Petri nets

We analyzed the developmental switch to sporulation of a multinucleate Physarum polycephalum plasmodial cell, a complex response to phytochrome photoreceptor activation. Automatic construction of Petri nets representing finite state machines assembled from trajectories of differential gene expression in single cells revealed alternative, genotype-dependent interconnected developmental routes and identified reversible steps, metastable states, commitment points, and subsequent irreversible steps together with molecular signatures associated with cell fate decision and differentiation. Formation of cyclic transits identified by transition invariants in mutants that are locked in a proliferative state is remarkable considering the view that oncogenic alterations may cause the formation of cancer attractors. We conclude that the Petri net approach is useful to probe the Waddington landscape of cellular reprogramming, to disentangle developmental routes for the reconstruction of the gene regulatory network, and to understand how genetic alterations or physiological conditions reshape the landscape eventually creating new basins of attraction. Unraveling the complexity of pathogenesis, disease progression, drug response or the analysis of attractor landscapes in other complex systems of uncertain structure might be additional fields of application.

Intracellular Energy Variability Modulates Cellular Decision-Making Capacity

Cells generate phenotypic diversity both during development and in response to stressful and changing environments, aiding survival. Functionally vital cell fate decisions from a range of phenotypic choices are made by regulatory networks, the dynamics of which rely on gene expression and hence depend on the cellular energy budget (and particularly ATP levels). However, despite pronounced cell-to-cell ATP differences observed across biological systems, the influence of energy availability on regulatory network dynamics is often overlooked as a cellular decision-making modulator, limiting our knowledge of how energy budgets affect cell behaviour. Here, we consider a mathematical model of a highly generalisable, ATP-dependent, decision-making regulatory network, and show that cell-to-cell ATP variability changes the sets of decisions a cell can make. Our model shows that increasing intracellular energy levels can increase the number of supported stable phenotypes, corresponding to increased decision-making capacity. Model cells with sub-threshold intracellular energy are limited to a singular phenotype, forcing the adoption of a specific cell fate. We suggest that energetic differences between cells may be an important consideration to help explain observed variability in cellular decision-making across biological systems.

Intracellular Noise Level Determines Ratio Control Strategy Confined by Speed-Accuracy Trade-off

Robust and precise ratio control of heterogeneous phenotypes within an isogenic population is an essential task, especially in the development and differentiation of a large number of cells such as bacteria, sensory receptors, and blood cells. However, the mechanisms of such ratio control are poorly understood. Here, we employ experimental and mathematical techniques to understand the combined effects of signal induction and gene expression stochasticity on phenotypic multimodality. We identify two strategies to control phenotypic ratios from an initially homogeneous population, suitable roughly to high-noise and low-noise intracellular environments, and we show that both can be used to generate precise fractional differentiation. In noisy gene expression contexts, such as those found in bacteria, induction within the circuit's bistable region is enough to cause noise-induced bimodality within a feasible time frame. However, in less noisy contexts, such as tightly controlled eukaryotic systems, spontaneous state transitions are rare and hence bimodality needs to be induced with a controlled pulse of induction that falls outside the bistable region. Finally, we show that noise levels, system response time, and ratio tuning accuracy impose trade-offs and limitations on both ratio control strategies, which guide the selection of strategy alternatives.

Modeling Gene Networks to Understand Multistability in Stem Cells

Stem cells are unique in their ability to differentiate into diverse phenotypes capable of displaying radically different, yet stable, gene expression profiles. Understanding this multistable behavior is key to rationally influencing stem cell differentiation for both research and therapeutic purposes. To this end, mathematical paradigms have been adopted to simulate and explain the dynamics of complex gene networks. In this chapter, we introduce strategies for building deterministic and stochastic mathematical models of gene expression and demonstrate how analysis of these models can benefit our understanding of complex observed behaviors. Developing a mathematical understanding of biological processes is of utmost importance in understanding and controlling stem cell behavior.

A multiscale model of epigenetic heterogeneity-driven cell fate decision-making

The inherent capacity of somatic cells to switch their phenotypic status in response to damage stimuli in vivo might have a pivotal role in ageing and cancer. However, how the entry-exit mechanisms of phenotype reprogramming are established remains poorly understood. In an attempt to elucidate such mechanisms, we herein introduce a stochastic model of combined epigenetic regulation (ER)-gene regulatory network (GRN) to study the plastic phenotypic behaviours driven by ER heterogeneity. To deal with such complex system, we additionally formulate a multiscale asymptotic method for stochastic model reduction, from which we derive an efficient hybrid simulation scheme. Our analysis of the coupled system reveals a regime of tristability in which pluripotent stem-like and differentiated steady-states coexist with a third indecisive state, with ER driving transitions between these states. Crucially, ER heterogeneity of differentiation genes is for the most part responsible for conferring abnormal robustness to pluripotent stem-like states. We formulate epigenetic heterogeneity-based strategies capable of unlocking and facilitating the transit from differentiation-refractory (stem-like) to differentiation-primed epistates. The application of the hybrid numerical method validates the likelihood of such switching involving solely kinetic changes in epigenetic factors. Our results suggest that epigenetic heterogeneity regulates the mechanisms and kinetics of phenotypic robustness of cell fate reprogramming. The occurrence of tunable switches capable of modifying the nature of cell fate reprogramming might pave the way for new therapeutic strategies to regulate reparative reprogramming in ageing and cancer.

Certain modifications of the structure and functioning of the protein/DNA complex called chromatin can allow adult, fully differentiated, cells to adopt a stem cell-like pluripotent state in a purely epigenetic manner, not involving changes in the underlying DNA sequence. Such reprogramming-like phenomena may constitute an innate reparative route through which human tissues respond to injury and could also serve as a novel regenerative strategy in human pathological situations in which tissue or organ repair is impaired. However, it should be noted that in vivo reprogramming would be capable of maintaining tissue homeostasis provided the acquisition of pluripotency features is strictly transient and accompanied by an accurate replenishment of the specific cell types being lost. Crucially, an excessive reprogramming in the absence of controlled re-differentiation would impair the repair or the replacement of damaged cells, thereby promoting pathological alterations of cell fate. A mechanistic understanding of how the degree of chromatin plasticity dictates the reparative versus pathological behaviour of in vivo reprogramming to rejuvenate aged tissues while preventing tumorigenesis is urgently needed, including especially the intrinsic epigenetic heterogeneity of the tissue resident cells being reprogrammed. We here introduce a novel method that mathematically captures how epigenetic heterogeneity is actually the driving force that governs the routes and kinetics to entry into and exit from a pathological stem-like state. Moreover, our approach computationally validates the likelihood of unlocking chronic, unrestrained plastic states and drive their differentiation down the correct path by solely manipulating the intensity and direction of few epigenetic control switches. Our approach could inspire new therapeutic approaches based on in vivo cell reprogramming for efficient tissue regeneration and rejuvenation and cancer treatment.

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.

Maximum Caliber Can Build and Infer Models of Oscillation in a Three-Gene Feedback Network

Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: (i) gene expression profiles are noisy, rendering models of averages inapplicable, (ii) experiments typically measure only a few protein species while leaving other molecular actors-necessary to build traditional bottom-up models-unnoticed, and (iii) measured data are in fluorescence, not particle number. We recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species. In the present work we address scalability and broader applicability of MaxCal by extending to a three-gene (A, B, C) feedback network that exhibits oscillation, commonly known as the repressilator. We test MaxCal's inferential power by using synthetic data of noisy protein number time traces-serving as a proxy for experimental data-generated from a known underlying model. We notice that the minimal MaxCal model-accounting for production, degradation, and only one type of symmetric coupling between all three species-reasonably infers several underlying features of the circuit such as the effective production rate, degradation rate, frequency of oscillation, and protein number distribution. Next, we build models of higher complexity including different levels of coupling between A, B, and C and rigorously assess their relative performance. While the minimal model (with four parameters) performs remarkably well, we note that the most complex model (with six parameters) allowing all possible forms of crosstalk between A, B, and C slightly improves prediction of rates, but avoids ad hoc assumption of all the other models. It is also the model of choice based on Bayesian information criteria. We further analyzed time trajectories in arbitrary fluorescence (using synthetic trajectories) to mimic realistic data. We conclude that even with a three-protein system including both fluorescence noise and intrinsic gene expression fluctuations, MaxCal can faithfully infer underlying details of the network, opening future directions to model other network motifs with many species.

Towards a Quantitative Understanding of Cell Identity

Cells have traditionally been characterized using expression levels of a few proteins that are thought to specify phenotype. This requires a priori selection of proteins, which can introduce descriptor bias, and neglects the wealth of additional molecular information nested within each cell in a population, which often makes these sparse descriptors qualitative. Recently, more unbiased and quantitative cell characterization has been made possible by new high-throughput, information-dense experimental approaches and data-driven computational methods. This review discusses such quantitative descriptors in the context of three central concepts of cell identity: definition, creation, and stability. Collectively, these concepts are essential for constructing quantitative phenotypic landscapes, which will enhance our understanding of cell biology and facilitate cell engineering for research and clinical applications.

Role of noise and parametric variation in the dynamics of gene regulatory circuits

Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial-mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package.

A landscape view on the interplay between EMT and cancer metastasis

The epithelial-mesenchymal transition (EMT) is a basic developmental process that converts epithelial cells to mesenchymal cells. Although EMT might promote cancer metastasis, the molecular mechanisms for it remain to be fully clarified. To address this issue, we constructed an EMT-metastasis gene regulatory network model and quantified the potential landscape of cancer metastasis-promoting system computationally. We identified four steady-state attractors on the landscape, which separately characterize anti-metastatic (A), metastatic (M), and two other intermediate (I1 and I2) cell states. The tetrastable landscape and the existence of intermediate states are consistent with recent single-cell measurements. We identified one of the two intermediate states I1 as the EMT state. From a MAP approach, we found that for metastatic progression cells need to first undergo EMT (enter the I1 state), and then become metastatic (switch from the I1 state to the M state). Specifically, for metastatic progression, EMT genes (such as ZEB) should be activated before metastasis genes (such as BACH1). This suggests that temporal order is important for the activation of cellular programs in biological systems, and provides a possible mechanism of EMT-promoting cancer metastasis. To identify possible therapeutic targets from this landscape view, we performed sensitivity analysis for individual molecular factors, and identified optimal interventions for landscape control. We found that minimizing transition actions more effectively identifies optimal combinations of targets that induce transitions between attractors than single-factor sensitivity analysis. Overall, the landscape view not only suggests that intermediate states increase plasticity during cell fate decisions, providing a possible source for tumor heterogeneity that is critically important in metastatic progress, but also provides a way to identify therapeutic targets for preventing cancer progression.

Predicting Transcriptional Output of Synthetic Multi-input Promoters

Recent advances in synthetic biology have led to a wealth of well-characterized genetic parts. As parts libraries grow, so too does the potential to create novel multi-input promoters that integrate disparate signals to determine transcriptional output. Our ability to construct such promoters will outpace our ability to characterize promoter performance, due to the vast number of input combinations. In this study, we examine the input-output relations of recently developed synthetic multi-input promoters and describe two methods for predicting their behavior. The first method uses 1-dimensional induction data obtained from experiments on single-input systems to predict the n-dimensional induction responses of systems with n inputs. We demonstrate that this approach accurately predicts Boolean (on/off) responses of multi-input systems consisting of novel chimeric transcription factors and hybrid promoters in Escherichia coli. The second method uses only a small amount of multi-input response data to accurately predict analog system response over the entire landscape of input combinations. Taken together, these methods facilitate the design of synthetic circuits that utilize multi-input promoters.

Fluorescent Guide RNAs Facilitate Development of Layered Pol II-Driven CRISPR Circuits

Efficient clustered regularly interspaced short palindromic repeat (CRISPR) guide RNA (gRNA) expression from RNA Polymerase II (Pol II) promoters will aid in construction of complex CRISPR-based synthetic gene networks. Yet, we require tools to properly visualize gRNA directly to quantitatively study the corresponding network behavior. To address this need, we employed a fluorescent gRNA (fgRNA) to visualize synthetic CRISPR network dynamics without affecting gRNA functionality. We show that studying gRNA dynamics directly enables circuit modification and improvement of network function in Pol II-driven CRISPR circuits. This approach generates information necessary for optimizing the overall function of these networks and provides insight into the hurdles remaining in Pol II-regulated gRNA expression.

RACIPE: a computational tool for modeling gene regulatory circuits using randomization

Background

One of the major challenges in traditional mathematical modeling of gene regulatory circuits is the insufficient knowledge of kinetic parameters. These parameters are often inferred from existing experimental data and/or educated guesses, which can be time-consuming and error-prone, especially for large networks.

Results

We present a user-friendly computational tool for the community to use our newly developed method named random circuit perturbation (RACIPE), to explore the robust dynamical features of gene regulatory circuits without the requirement of detailed kinetic parameters. Taking the network topology as the only input, RACIPE generates an ensemble of circuit models with distinct randomized parameters and uniquely identifies robust dynamical properties by statistical analysis. Here, we discuss the implementation of the software and the statistical analysis methods of RACIPE-generated data to identify robust gene expression patterns and the functions of genes and regulatory links. Finally, we apply the tool on coupled toggle-switch circuits and a published circuit of B-lymphopoiesis.

Conclusions

We expect our new computational tool to contribute to a more comprehensive and unbiased understanding of mechanisms underlying gene regulatory networks. RACIPE is a free open source software distributed under (Apache 2.0) license and can be downloaded from GitHub (https://github.com/simonhb1990/RACIPE-1.0).

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0594-6) contains supplementary material, which is available to authorized users.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Computational Re-design of Synthetic Genetic Oscillators for Independent Amplitude and Frequency Modulation

To perform well in biotechnology applications, synthetic genetic oscillators must be engineered to allow independent modulation of amplitude and period. This need is currently unmet. Here, we demonstrate computationally how two classic genetic oscillators, the dual-feedback oscillator and the repressilator, can be re-designed to provide independent control of amplitude and period and improve tunability-that is, a broad dynamic range of periods and amplitudes accessible through the input "dials." Our approach decouples frequency and amplitude modulation by incorporating an orthogonal "sink module" where the key molecular species are channeled for enzymatic degradation. This sink module maintains fast oscillation cycles while alleviating the translational coupling between the oscillator's transcription factors and output. We characterize the behavior of our re-designed oscillators over a broad range of physiologically reasonable parameters, explain why this facilitates broader function and control, and provide general design principles for building synthetic genetic oscillators that are more precisely controllable.

Mean-Independent Noise Control of Cell Fates via Intermediate States

Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination.

•

Mean-independent noise control allows noise attenuation without affecting the mean

•

Intermediate states enable such control through proportional coupling

•

This controls spatial gene expression noise without shifting boundary locations

•

Specific noise levels are required for successful downstream boundary sharpening

Rational engineering of synthetic microbial systems: from single cells to consortia

One promise of synthetic biology is to provide solutions for biomedical and industrial problems by rational design of added functionality in living systems. Microbes are at the forefront of this biological engineering endeavor due to their general ease of handling and their relevance in many potential applications from fermentation to therapeutics. In recent years, the field has witnessed an explosion of novel regulatory tools, from synthetic orthogonal transcription factors to posttranslational mechanisms for increased control over the behavior of synthetic circuits. Tool development has been paralleled by the discovery of principles that enable increased modularity and the management of host-circuit interactions. Engineered cell-to-cell communication bridges the scales from intracellular to population-level coordination. These developments facilitate the translation of more than a decade of circuit design into applications.

Design of Adjacent Transcriptional Regions to Tune Gene Expression and Facilitate Circuit Construction

Polycistronic architecture is common for synthetic gene circuits, however, it remains unknown how expression of one gene is affected by the presence of other genes/noncoding regions in the operon, termed adjacent transcriptional regions (ATR). Here, we constructed synthetic operons with a reporter gene flanked by different ATRs, and we found that ATRs with high GC content, small size, and low folding energy lead to high gene expression. Based on these results, we built a model of gene expression and generated a metric that takes into account ATRs. We used the metric to design and construct logic gates with low basal expression and high sensitivity and nonlinearity. Furthermore, we rationally designed synthetic 5'ATRs with different GC content and sizes to tune protein expression levels over a 300-fold range and used these to build synthetic toggle switches with varying basal expression and degrees of bistability. Our comprehensive model and gene expression metric could facilitate the future engineering of more complex synthetic gene circuits.

Building Predictive Models of Genetic Circuits Using the Principle of Maximum Caliber

Learning the underlying details of a gene network is a major challenge in cellular and synthetic biology. We address this challenge by building a chemical kinetic model that utilizes information encoded in the stochastic protein expression trajectories typically measured in experiments. The applicability of the proposed method is demonstrated in an auto-activating genetic circuit, a common motif in natural and synthetic gene networks. Our approach is based on the principle of maximum caliber (MaxCal)-a dynamical analog of the principle of maximum entropy-and builds a minimal model using only three constraints: 1) protein synthesis, 2) protein degradation, and 3) positive feedback. The MaxCal-generated model (described with four parameters) was benchmarked against synthetic data generated using a Gillespie algorithm on a known reaction network (with seven parameters). MaxCal accurately predicts underlying rate parameters of protein synthesis and degradation as well as experimental observables such as protein number and dwell-time distributions. Furthermore, MaxCal yields an effective feedback parameter that can be useful for circuit design. We also extend our methodology and demonstrate how to analyze trajectories that are not in protein numbers but in arbitrary fluorescence units, a more typical condition in experiments. This "top-down" methodology based on minimal information-in contrast to traditional "bottom-up" approaches that require ad hoc knowledge of circuit details-provides a powerful tool to accurately infer underlying details of feedback circuits that are not otherwise visible in experiments and to help guide circuit design.