Mapping the environmental fitness landscape of a synthetic gene circuit

Synthetic gene circuit evolution: Insights and opportunities at the mid-scale

Directed evolution focuses on optimizing single genetic components for predefined engineering goals by artificial mutagenesis and selection. In contrast, experimental evolution studies the adaptation of entire genomes in serially propagated cell populations, to provide an experimental basis for evolutionary theory. There is a relatively unexplored gap at the middle ground between these two techniques, to evolve in vivo entire synthetic gene circuits with nontrivial dynamic function instead of single parts or whole genomes. We discuss the requirements for such mid-scale evolution, with hypothetical examples for evolving synthetic gene circuits by appropriate selection and targeted shuffling of a seed set of genetic components in vivo. Implementing similar methods should aid the rapid generation, functionalization, and optimization of synthetic gene circuits in various organisms and environments, accelerating both the development of biomedical and technological applications and the understanding of principles guiding regulatory network evolution.

Nonlethal deleterious mutation-induced stress accelerates bacterial aging

Random mutagenesis, including when it leads to loss of gene function, is a key mechanism enabling microorganisms' long-term adaptation to new environments. However, loss-of-function mutations are often deleterious, triggering, in turn, cellular stress and complex homeostatic stress responses, called "allostasis," to promote cell survival. Here, we characterize the differential impacts of 65 nonlethal, deleterious single-gene deletions on Escherichia coli growth in three different growth environments. Further assessments of select mutants, namely, those bearing single adenosine triphosphate (ATP) synthase subunit deletions, reveal that mutants display reorganized transcriptome profiles that reflect both the environment and the specific gene deletion. We also find that ATP synthase α-subunit deleted (ΔatpA) cells exhibit elevated metabolic rates while having slower growth compared to wild-type (wt) E. coli cells. At the single-cell level, compared to wt cells, individual ΔatpA cells display near normal proliferation profiles but enter a postreplicative state earlier and exhibit a distinct senescence phenotype. These results highlight the complex interplay between genomic diversity, adaptation, and stress response and uncover an "aging cost" to individual bacterial cells for maintaining population-level resilience to environmental and genetic stress; they also suggest potential bacteriostatic antibiotic targets and -as select human genetic diseases display highly similar phenotypes, - a bacterial origin of some human diseases.

Dynamical model of antibiotic responses linking expression of resistance genes to metabolism explains emergence of heterogeneity during drug exposures

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistancetetoperon inE. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

A synthetic differentiation circuit in Escherichia coli for suppressing mutant takeover

Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels-gene expression and cell division-are intricately convoluted? We show the principle of maximum caliber (MaxCal)-integrated within a Bayesian framework-can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors-gene expression noise, cell division noise, and fluorescence distortion-all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.

Nonmonotone invasion landscape by noise-aware control of metastasis activator levels

A major pharmacological assumption is that lowering disease-promoting protein levels is generally beneficial. For example, inhibiting metastasis activator BACH1 is proposed to decrease cancer metastases. Testing such assumptions requires approaches to measure disease phenotypes while precisely adjusting disease-promoting protein levels. Here we developed a two-step strategy to integrate protein-level tuning, noise-aware synthetic gene circuits into a well-defined human genomic safe harbor locus. Unexpectedly, engineered MDA-MB-231 metastatic human breast cancer cells become more, then less and then more invasive as we tune BACH1 levels up, irrespective of the native BACH1. BACH1 expression shifts in invading cells, and expression of BACH1's transcriptional targets confirm BACH1's nonmonotone phenotypic and regulatory effects. Thus, chemical inhibition of BACH1 could have unwanted effects on invasion. Additionally, BACH1's expression variability aids invasion at high BACH1 expression. Overall, precisely engineered, noise-aware protein-level control is necessary and important to unravel disease effects of genes to improve clinical drug efficacy.

Effects of growth feedback on gene circuits: A dynamical understanding

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are crucial for both fundamental and applied research. Utilizing transcriptional regulation circuits with adaptation as a paradigm, we systematically study 435 distinct topological structures and uncover six categories of failures. Three dynamical mechanisms of circuit failures are identified: continuous deformation of the response curve, strengthened or induced oscillations, and sudden switching to coexisting attractors. Our extensive computations also uncover a scaling law between a circuit robustness measure and the strength of growth feedback. Despite the negative effects of growth feedback on the majority of circuit topologies, we identify a few circuits that maintain optimal performance as designed, a feature important for applications.

Cell Decision Making through the Lens of Bayesian Learning

Cell decision making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this process. Our hypothesis is that cell decision-making regulation is dictated by Bayesian learning. In this article, we explore the implications of this hypothesis for internal state temporal evolution. By using a timescale separation between internal and external variables on the mesoscopic scale, we derive a hierarchical Fokker-Planck equation for cell-microenvironment dynamics. By combining this with the Bayesian learning hypothesis, we find that changes in microenvironmental entropy dominate the cell state probability distribution. Finally, we use these ideas to understand how cell sensing impacts cell decision making. Notably, our formalism allows us to understand cell state dynamics even without exact biochemical information about cell sensing processes by considering a few key parameters.

Unraveling non-genetic heterogeneity in cancer with dynamical models and computational tools

Individual cells within an otherwise genetically homogenous population constantly undergo fluctuations in their molecular state, giving rise to non-genetic heterogeneity. Such diversity is being increasingly implicated in cancer therapy resistance and metastasis. Identifying the origins of non-genetic heterogeneity is therefore crucial for making clinical breakthroughs. We discuss with examples how dynamical models and computational tools have provided critical multiscale insights into the nature and consequences of non-genetic heterogeneity in cancer. We demonstrate how mechanistic modeling has been pivotal in establishing key concepts underlying non-genetic diversity at various biological scales, from population dynamics to gene regulatory networks. We discuss advances in single-cell longitudinal profiling techniques to reveal patterns of non-genetic heterogeneity, highlighting the ongoing efforts and challenges in statistical frameworks to robustly interpret such multimodal datasets. Moving forward, we stress the need for data-driven statistical and mechanistically motivated dynamical frameworks to come together to develop predictive cancer models and inform therapeutic strategies.

Horizontal gene transfer enables programmable gene stability in synthetic microbiota

The functions of many microbial communities exhibit remarkable stability despite fluctuations in the compositions of these communities. To date, a mechanistic understanding of this function-composition decoupling is lacking. Statistical mechanisms have been commonly hypothesized to explain such decoupling. Here, we proposed that dynamic mechanisms, mediated by horizontal gene transfer (HGT), also enable the independence of functions from the compositions of microbial communities. We combined theoretical analysis with numerical simulations to illustrate that HGT rates can determine the stability of gene abundance in microbial communities. We further validated these predictions using engineered microbial consortia of different complexities transferring one or more than a dozen clinically isolated plasmids, as well as through the reanalysis of data from the literature. Our results demonstrate a generalizable strategy to program the gene stability of microbial communities.

Non-genetic resistance facilitates survival while hindering the evolution of drug resistance due to intraspecific competition

Rising rates of resistance to antimicrobial drugs threaten the effective treatment of infections across the globe. Drug resistance has been established to emerge from non-genetic mechanisms as well as from genetic mechanisms. However, it is still unclear how non-genetic resistance affects the evolution of genetic drug resistance. We develop deterministic and stochastic population models that incorporate resource competition to quantitatively investigate the transition from non-genetic to genetic resistance during the exposure to static and cidal drugs. We find that non-genetic resistance facilitates the survival of cell populations during drug treatment while hindering the development of genetic resistance due to competition between the non-genetically and genetically resistant subpopulations. Non-genetic resistance in the presence of subpopulation competition increases the fixation times of drug resistance mutations, while increasing the probability of mutation before population extinction during cidal drug treatment. Intense intraspecific competition during drug treatment leads to extinction of susceptible and non-genetically resistant subpopulations. Alternating between drug and no drug conditions results in oscillatory population dynamics, increased resistance mutation fixation timescales, and reduced population survival. These findings advance our fundamental understanding of the evolution of resistance and may guide novel treatment strategies for patients with drug-resistant infections.

Revisiting moment-closure methods with heterogeneous multiscale population models

Stochastic chemical kinetics at the single-cell level give rise to heterogeneous populations of cells even when all individuals are genetically identical. This heterogeneity can lead to nonuniform behaviour within populations, including different growth characteristics, cell-fate dynamics, and response to stimuli. Ultimately, these diverse behaviours lead to intricate population dynamics that are inherently multiscale: the population composition evolves based on population-level processes that interact with stochastically distributed single-cell states. Therefore, descriptions that account for this heterogeneity are essential to accurately model and control chemical processes. However, for real-world systems such models are computationally expensive to simulate, which can make optimisation problems, such as optimal control or parameter inference, prohibitively challenging. Here, we consider a class of multiscale population models that incorporate population-level mechanisms while remaining faithful to the underlying stochasticity at the single-cell level and the interplay between these two scales. To address the complexity, we study an order-reduction approximations based on the distribution moments. Since previous moment-closure work has focused on the single-cell kinetics, extending these techniques to populations models prompts us to revisit old observations as well as tackle new challenges. In this extended multiscale context, we encounter the previously established observation that the simplest closure techniques can lead to non-physical system trajectories. Despite their poor performance in some systems, we provide an example where these simple closures outperform more sophisticated closure methods in accurately, efficiently, and robustly solving the problem of optimal control of bioproduction in a microbial consortium model.

Using single-cell models to predict the functionality of synthetic circuits at the population scale

SignificanceAt the single-cell level, biochemical processes are inherently stochastic. For many natural systems, the resulting cell-to-cell variability is exploited by microbial populations. In synthetic biology, however, the interplay of cell-to-cell variability and population processes such as selection or growth often leads to circuits not functioning as predicted by simple models. Here we show how multiscale stochastic kinetic models that simultaneously track single-cell and population processes can be obtained based on an augmentation of the chemical master equation. These models enable us to quantitatively predict complex population dynamics of a yeast optogenetic differentiation system from a specification of the circuit's components and to demonstrate how cell-to-cell variability can be exploited to purposefully create unintuitive circuit functionality.

Tipping the Balance: A Criticality Perspective

Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP). Under steady state conditions, the model has similarities with a well-known model of population genetics which exhibits a purely noise-induced transition from unimodality to bimodality at a critical value of the noise intensity σ2. The noise is associated with the parameter λ representing the system-environment coupling. In the case of the tumour model, λ has a natural interpretation in terms of the tissue microenvironment which has considerable influence on the phenotypic composition of the tumour. Oncogenic transformations give rise to considerable fluctuations in the parameter. We compute the λ−σ2 phase diagram in a stochastic setting, drawing analogies between bifurcations and phase transitions. In the region of bimodality, a transition from a state of balance to a state of dominance, in terms of the competing subpopulations, occurs at λ = 0. Away from this point, the NCP (CP) subpopulation becomes dominant as λ changes towards positive (negative) values. The variance of the steady state probability density function as well as two entropic measures provide characteristic signatures at the transition point.

Mechanism of life-long maintenance of neuron identity despite molecular fluctuations

Cell fate is maintained over long timescales, yet molecular fluctuations can lead to spontaneous loss of this differentiated state. Our simulations identified a possible mechanism that explains life-long maintenance of ASE neuron fate in Caenorhabditis elegans by the terminal selector transcription factor CHE-1. Here, fluctuations in CHE-1 level are buffered by the reservoir of CHE-1 bound at its target promoters, which ensures continued che-1 expression by preferentially binding the che-1 promoter. We provide experimental evidence for this mechanism by showing that che-1 expression was resilient to induced transient CHE-1 depletion, while both expression of CHE-1 targets and ASE function were lost. We identified a 130 bp che-1 promoter fragment responsible for this resilience, with deletion of a homeodomain binding site in this fragment causing stochastic loss of ASE identity long after its determination. Because network architectures that support this mechanism are highly conserved in cell differentiation, it may explain stable cell fate maintenance in many systems.

Potentiating antibiotic efficacy via perturbation of non-essential gene expression

Proliferation of multidrug-resistant (MDR) bacteria poses a threat to human health, requiring new strategies. Here we propose using fitness neutral gene expression perturbations to potentiate antibiotics. We systematically explored 270 gene knockout-antibiotic combinations in Escherichia coli, identifying 90 synergistic interactions. Identified gene targets were subsequently tested for antibiotic synergy on the transcriptomic level via multiplexed CRISPR-dCas9 and showed successful sensitization of E. coli without a separate fitness cost. These fitness neutral gene perturbations worked as co-therapies in reducing a Salmonella enterica intracellular infection in HeLa. Finally, these results informed the design of four antisense peptide nucleic acid (PNA) co-therapies, csgD, fnr, recA and acrA, against four MDR, clinically isolated bacteria. PNA combined with sub-minimal inhibitory concentrations of trimethoprim against two isolates of Klebsiella pneumoniae and E. coli showed three cases of re-sensitization with minimal fitness impacts. Our results highlight a promising approach for extending the utility of current antibiotics.

Stochastic response of bacterial cells to antibiotics: its mechanisms and implications for population and evolutionary dynamics

The effectiveness of antibiotics against bacterial infections has been declining due to the emergence of resistance. Precisely understanding the response of bacteria to antibiotics is critical to maximizing antibiotic-induced bacterial eradication while minimizing the emergence of antibiotic resistance. Cell-to-cell heterogeneity in antibiotic susceptibility is observed across various bacterial species for a wide range of antibiotics. Heterogeneity in antibiotic susceptibility is not always due to the genetic differences. Rather, it can be caused by non-genetic mechanisms such as stochastic gene expression and biased partitioning upon cell division. Heterogeneous susceptibility leads to the stochastic growth and death of individual cells and stochastic fluctuations in population size. These fluctuations have important implications for the eradication of bacterial populations and the emergence of genotypic resistance.

Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case

The way that progenitor cell fate decisions and the associated environmental sensing are regulated to ensure the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue still remains elusive. Here, we investigate how cells regulate their sensing intensity and radius to guarantee the required thermodynamic robustness of a differentiated tissue. In particular, we are interested in finding the conditions where dedifferentiation at cell level is possible (microscopic reversibility), but tissue maintains its spatial order and differentiation integrity (macroscopic irreversibility). In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation. To assess the predictive and explanatory power of our theory, we challenge it against the avian photoreceptor mosaic data. By calibrating a single parameter, the LEUP can predict the cone color spatial distribution in the avian retina and, at the same time, suggest that such a spatial pattern is associated with quasi-optimal cell sensing. By means of the stochastic thermodynamics formalism, we find out that thermodynamic robustness of differentiated tissues depends on cell metabolism and cell sensing properties. In turn, we calculate the limits of the cell sensing radius that ensure the robustness of differentiated tissue spatial order. Finally, we further constrain our model predictions to the avian photoreceptor mosaic.

Does transcriptional heterogeneity facilitate the development of genetic drug resistance?

Non-genetic forms of antimicrobial (drug) resistance can result from cell-to-cell variability that is not encoded in the genetic material. Data from recent studies also suggest that non-genetic mechanisms can facilitate the development of genetic drug resistance. We speculate on how the interplay between non-genetic and genetic mechanisms may affect microbial adaptation and evolution during drug treatment. We argue that cellular heterogeneity arising from fluctuations in gene expression, epigenetic modifications, as well as genetic changes contribute to drug resistance at different timescales, and that the interplay between these mechanisms enhance pathogen resistance. Accordingly, developing a better understanding of the role of non-genetic mechanisms in drug resistance and how they interact with genetic mechanisms will enhance our ability to combat antimicrobial resistance. Also see the video abstract here: https://youtu.be/aefGpdh-bgU.

Dependence of bacterial growth rate on dynamic temperature changes

Temperature is an important determinant of bacterial growth. While the dependence of bacterial growth on different temperatures has been well studied for many bacterial species, prediction of bacterial growth rate for dynamic temperature changes is relatively unclear. Here, the authors address this issue using a combination of experimental measurements of the growth, at the resolution of 5 min, of Escherichia coli and mathematical models. They measure growth curves at different temperatures and estimate model parameters to predict bacterial growth profiles subject to dynamic temperature changes. They compared these predicted growth profiles for various step‐like temperature changes with experimental measurements using the coefficient of determination and mean square error and based on this comparison, ranked the different growth models, finding that the generalised logistic growth model gave the smallest error. They note that as the maximum specific growth increases the duration of this growth predominantly decreases. These results provide a basis to compute the dependence of the growth rate parameter in biomolecular circuits on dynamic temperatures and may be useful for designing biomolecular circuits that are robust to temperature.

Towards an engineering theory of evolution

Biological technologies are fundamentally unlike any other because biology evolves. Bioengineering therefore requires novel design methodologies with evolution at their core. Knowledge about evolution is currently applied to the design of biosystems ad hoc. Unless we have an engineering theory of evolution, we will neither be able to meet evolution's potential as an engineering tool, nor understand or limit its unintended consequences for our biological designs. Here, we propose the evotype as a helpful concept for engineering the evolutionary potential of biosystems, or other self-adaptive technologies, potentially beyond the realm of biology.

Control of synthetic microbial consortia in time, space, and composition

While synthetic microbial systems are becoming increasingly complicated, single-strain systems cannot match the complexity of their multicellular counterparts. Such complexity, however, is much more difficult to control. Recent advances have increased our ability to control temporal, spatial, and community compositional organization, including modular adhesive systems, strain growth relationships, and asymmetric cell division. While these systems generally work independently, combining them into unified systems has proven difficult. Once such unification is proven successful we will unlock a new frontier of synthetic biology and open the door to the creation of synthetic biological systems with true multicellularity.

Interplay between genetic, epigenetic, and gene expression variability: Considering complexity in evolvability

Genetic variability, epigenetic variability, and gene expression variability (noise) are generally considered independently in their relationship with phenotypic variation. However, they appear to be intrinsically interconnected and influence it in combination. The study of the interplay between genetic and epigenetic variability has the longest history. This article rather considers the introduction of gene expression variability in its relationships with the two others and reviews for the first time experimental evidences over the four relationships connected to gene expression noise. They show how introducing this third source of variability complicates the way of thinking evolvability and the emergence of biological novelty. Finally, cancer cells are proposed to be an ideal model to decipher the dynamic interplay between genetic, epigenetic, and gene expression variability when one of them is either experimentally increased or therapeutically targeted. This interplay is also discussed in an evolutionary perspective in the context of cancer cell drug resistance.

Critical Comparison of MaxCal and Other Stochastic Modeling Approaches in Analysis of Gene Networks

Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of the circuit must be inferred. One potentially useful avenue is to harness hidden information from single-cell stochastic gene expression time trajectories measured for long periods of time—recorded at frequent intervals—over multiple cells. This raises the feasibility vs. accuracy dilemma while deciding between different models of mining these stochastic trajectories. We demonstrate that inference based on the Maximum Caliber (MaxCal) principle is the method of choice by critically evaluating its computational efficiency and accuracy against two other typical modeling approaches: (i) a detailed model (DM) with explicit consideration of multiple molecules including protein-promoter interaction, and (ii) a coarse-grain model (CGM) using Hill type functions to model feedback. MaxCal provides a reasonably accurate model while being significantly more computationally efficient than DM and CGM. Furthermore, MaxCal requires minimal assumptions since it is a top-down approach and allows systematic model improvement by including constraints of higher order, in contrast to traditional bottom-up approaches that require more parameters or ad hoc assumptions. Thus, based on efficiency, accuracy, and ability to build minimal models, we propose MaxCal as a superior alternative to traditional approaches (DM, CGM) when inferring underlying details of gene circuits with feedback from limited data.

Optimal transition paths of phenotypic switching in a non-Markovian self-regulation gene expression

Gene expression is a complex biochemical process involving multiple reaction steps, creating molecular memory because the probability of waiting time between consecutive reaction steps no longer follows exponential distributions. What effect the molecular memory has on metastable states in gene expression remains not fully understood. Here, we study transition paths of switching between bistable states for a non-Markovian model of gene expression equipped with a self-regulation. Employing the large deviation theory for this model, we analyze the optimal transition paths of switching between bistable states in gene expression, interestingly finding that dynamic behaviors in gene expression along the optimal transition paths significantly depend on the molecular memory. Moreover, we discover that the molecular memory can prolong the time of switching between bistable states in gene expression along the optimal transition paths. Our results imply that the molecular memory may be an unneglectable factor to affect switching between metastable states in gene expression.

Stable maintenance of hidden switches as a strategy to increase the gene expression stability

In response to severe genetic and environmental perturbations, wild-type organisms can express hidden alternative phenotypes adaptive to such adverse conditions. While our theoretical understanding of the population-level fitness advantage and evolution of phenotypic switching under variable environments has grown, the mechanism by which these organisms maintain phenotypic switching capabilities under static environments remains to be elucidated. Here, using computational simulations, we analyzed the evolution of gene circuits under natural selection and found that different strategies evolved to increase the gene expression stability near the optimum level. In a population comprising bistable individuals, a strategy of maintaining bistability and raising the potential barrier separating the bistable regimes was consistently taken. Our results serve as evidence that hidden bistable switches can be stably maintained during environmental stasis-an essential property enabling the timely release of adaptive alternatives with small genetic changes in the event of substantial perturbations.

Use and Abuse of Entropy in Biology: A Case for Caliber

Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon's diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information.

Inferring a network from dynamical signals at its nodes

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.

Advancing Antimicrobial Resistance Research Through Quantitative Modeling and Synthetic Biology

Antimicrobial resistance (AMR) is an emerging global health crisis that is undermining advances in modern medicine and, if unmitigated, threatens to kill 10 million people per year worldwide by 2050. Research over the last decade has demonstrated that the differences between genetically identical cells in the same environment can lead to drug resistance. Fluctuations in gene expression, modulated by gene regulatory networks, can lead to non-genetic heterogeneity that results in the fractional killing of microbial populations causing drug therapies to fail; this non-genetic drug resistance can enhance the probability of acquiring genetic drug resistance mutations. Mathematical models of gene networks can elucidate general principles underlying drug resistance, predict the evolution of resistance, and guide drug resistance experiments in the laboratory. Cells genetically engineered to carry synthetic gene networks regulating drug resistance genes allow for controlled, quantitative experiments on the role of non-genetic heterogeneity in the development of drug resistance. In this perspective article, we emphasize the contributions that mathematical, computational, and synthetic gene network models play in advancing our understanding of AMR to discover effective therapies against drug-resistant infections.

How Do Cells Adapt? Stories Told in Landscapes

Cells adapt to changing environments. Perturb a cell and it returns to a point of homeostasis. Perturb a population and it evolves toward a fitness peak. We review quantitative models of the forces of adaptation and their visualizations on landscapes. While some adaptations result from single mutations or few-gene effects, others are more cooperative, more delocalized in the genome, and more universal and physical. For example, homeostasis and evolution depend on protein folding and aggregation, energy and protein production, protein diffusion, molecular motor speeds and efficiencies, and protein expression levels. Models provide a way to learn about the fitness of cells and cell populations by making and testing hypotheses.

A protein kinase A-regulated network encodes short- and long-lived cellular memories

Cells can store memories of prior experiences to modulate their responses to subsequent stresses, as seen for the protein kinase A (PKA)-mediated general stress response in yeast, which is required for resistance against future stressful conditions. Using microfluidics and time-lapse microscopy, we quantitatively analyzed how the cellular memory of stress adaptation is encoded in single yeast cells. We found that cellular memory was biphasic. Short-lived memory was mediated by trehalose synthase and trehalose metabolism. Long-lived memory was mediated by PKA-regulated stress-responsive transcription factors and cytoplasmic messenger ribonucleoprotein granules. Short- and long-lived memory could be selectively induced by different priming input dynamics. Computational modeling revealed how the PKA-mediated regulatory network could encode previous stimuli into memories with distinct dynamics. This biphasic memory-encoding scheme might represent a general strategy to prepare for future challenges in rapidly changing environments.

The Maximum Caliber Variational Principle for Nonequilibria

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

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.

Evolutionary regain of lost gene circuit function

Natural or synthetic genetic modules can lose their function over long-term evolution if the function is costly. How populations can evolve to restore such broken function is poorly understood. To test the reversibility of evolutionary breakdown, we use yeast cell populations with a chromosomally integrated synthetic gene circuit. In previous evolution experiments the gene circuit lost its costly function through various mutations. By exposing such mutant populations to conditions where regaining gene circuit function would be beneficial, we find adaptation scenarios with or without repairing lost gene circuit function. These results are important for drug resistance or future synthetic biology applications where evolutionary loss and regain of function play a significant role.

Evolutionary reversibility—the ability to regain a lost function—is an important problem both in evolutionary and synthetic biology, where repairing natural or synthetic systems broken by evolutionary processes may be valuable. Here, we use a synthetic positive-feedback (PF) gene circuit integrated into haploid Saccharomyces cerevisiae cells to test if the population can restore lost PF function. In previous evolution experiments, mutations in a gene eliminated the fitness costs of PF activation. Since PF activation also provides drug resistance, exposing such compromised or broken mutants to both drug and inducer should create selection pressure to regain drug resistance and possibly PF function. Indeed, evolving 7 PF mutant strains in the presence of drug revealed 3 adaptation scenarios through genomic, PF-external mutations that elevate PF basal expression, possibly by affecting transcription, translation, degradation, and other fundamental cellular processes. Nonfunctional mutants gained drug resistance without ever developing high expression, while quasifunctional and dysfunctional PF mutants developed high expression nongenetically, which then diminished, although more slowly for dysfunctional mutants where revertant clones arose. These results highlight how intracellular context, such as the growth rate, can affect regulatory network dynamics and evolutionary dynamics, which has important consequences for understanding the evolution of drug resistance and developing future synthetic biology applications.

Role of network-mediated stochasticity in mammalian drug resistance

A major challenge in biology is that genetically identical cells in the same environment can display gene expression stochasticity (noise), which contributes to bet-hedging, drug tolerance, and cell-fate switching. The magnitude and timescales of stochastic fluctuations can depend on the gene regulatory network. Currently, it is unclear how gene expression noise of specific networks impacts the evolution of drug resistance in mammalian cells. Answering this question requires adjusting network noise independently from mean expression. Here, we develop positive and negative feedback-based synthetic gene circuits to decouple noise from the mean for Puromycin resistance gene expression in Chinese Hamster Ovary cells. In low Puromycin concentrations, the high-noise, positive-feedback network delays long-term adaptation, whereas it facilitates adaptation under high Puromycin concentration. Accordingly, the low-noise, negative-feedback circuit can maintain resistance by acquiring mutations while the positive-feedback circuit remains mutation-free and regains drug sensitivity. These findings may have profound implications for chemotherapeutic inefficiency and cancer relapse.

The role of gene expression noise in the evolution of drug resistance in mammalian cells is unclear. Here, by uncoupling noise from mean expression of a drug resistance gene in CHO cells the authors show that noisy expression aids adaptation to high drug levels, but delays it at low drug levels.

Simulating Genetic Circuits in Bacterial Populations with Growth Heterogeneity

We computationally study genetic circuits in bacterial populations with heterogeneities in the growth rate. To that end, we present a stochastic simulation method for gene circuits in populations of cells and propose an efficient implementation that we call the "Next Family Method". Within this approach, we implement different population setups, specifically Chemostat-type growth and growth in an ideal Mother Machine and show that the population structure and its statistics are different for the different setups whenever there is growth heterogeneity. Such dependence on the population setup is demonstrated, in the case of bistable systems with different growth rates in the stable states, to have distinctive signatures on quantities including the distributions of protein concentration and growth rates, and hysteresis curves. Applying this method to a bistable antibiotic resistance circuit, we find that as a result of the different statistics in different population setups, the estimated minimal inhibitory concentration of the antibiotic becomes dependent on the population setup in which it is measured.

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.

Modeling cell population dynamics

 Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.

Modeling cell population dynamics

 Quantitative modeling is quickly becoming an integral part of biology, due to the ability of mathematical models and computer simulations to generate insights and predict the behavior of living systems. Single-cell models can be incapable or misleading for inferring population dynamics, as they do not consider the interactions between cells via metabolites or physical contact, nor do they consider competition for limited resources such as nutrients or space. Here we examine methods that are commonly used to model and simulate cell populations. First, we cover simple models where analytic solutions are available, and then move on to more complex scenarios where computational methods are required. Overall, we present a summary of mathematical models used to describe cell population dynamics, which may aid future model development and highlights the importance of population modeling in biology.

Applying ecological resistance and resilience to dissect bacterial antibiotic responses

An essential property of microbial communities is the ability to survive a disturbance. Survival can be achieved through resistance, the ability to absorb effects of a disturbance without a notable change, or resilience, the ability to recover after being perturbed by a disturbance. These concepts have long been applied to the analysis of ecological systems, although their interpretations are often subject to debate. Here, we show that this framework readily lends itself to the dissection of the bacterial response to antibiotic treatment, where both terms can be unambiguously defined. The ability to tolerate the antibiotic treatment in the short term corresponds to resistance, which primarily depends on traits associated with individual cells. In contrast, the ability to recover after being perturbed by an antibiotic corresponds to resilience, which primarily depends on traits associated with the population. This framework effectively reveals the phenotypic signatures of bacterial pathogens expressing extended-spectrum β-lactamases (ESBLs) when treated by a β-lactam antibiotic. Our analysis has implications for optimizing treatment of these pathogens using a combination of a β-lactam and a β-lactamase (Bla) inhibitor. In particular, our results underscore the need to dynamically optimize combination treatments based on the quantitative features of the bacterial response to the antibiotic or the Bla inhibitor.

Multiscale effects of heating and cooling on genes and gene networks

Fluctuating environments such as changes in ambient temperature represent a fundamental challenge to life. Cells must protect gene networks that protect them from such stresses, making it difficult to understand how temperature affects gene network function in general. Here, we focus on single genes and small synthetic network modules to reveal four key effects of nonoptimal temperatures at different biological scales: (i) a cell fate choice between arrest and resistance, (ii) slower growth rates, (iii) Arrhenius reaction rates, and (iv) protein structure changes. We develop a multiscale computational modeling framework that captures and predicts all of these effects. These findings promote our understanding of how temperature affects living systems and enables more robust cellular engineering for real-world applications.

Most organisms must cope with temperature changes. This involves genes and gene networks both as subjects and agents of cellular protection, creating difficulties in understanding. Here, we study how heating and cooling affect expression of single genes and synthetic gene circuits in Saccharomyces cerevisiae. We discovered that nonoptimal temperatures induce a cell fate choice between stress resistance and growth arrest. This creates dramatic gene expression bimodality in isogenic cell populations, as arrest abolishes gene expression. Multiscale models incorporating population dynamics, temperature-dependent growth rates, and Arrhenius scaling of reaction rates captured the effects of cooling, but not those of heating in resistant cells. Molecular-dynamics simulations revealed how heating alters the conformational dynamics of the TetR repressor, fully explaining the experimental observations. Overall, nonoptimal temperatures induce a cell fate decision and corrupt gene and gene network function in computationally predictable ways, which may aid future applications of engineered microbes in nonstandard temperatures.

Multiplexed deactivated CRISPR-Cas9 gene expression perturbations deter bacterial adaptation by inducing negative epistasis

The ever-increasing threat of multi-drug resistant bacteria, a shrinking antibiotic pipeline, and the innate ability of microorganisms to adapt necessitates long-term strategies to slow the evolution of antibiotic resistance. Here we develop an approach, dubbed Controlled Hindrance of Adaptation of OrganismS or CHAOS, involving induction of epistasis between gene perturbations to deter adaption. We construct a combinatorial library of multiplexed, deactivated CRISPR-Cas9 devices to systematically perturb gene expression in Escherichia coli. While individual perturbations improved fitness during antibiotic exposure, multiplexed perturbations caused large fitness loss in a significant epistatic fashion. Strains exhibiting epistasis adapted significantly more slowly over three to fourteen days, and loss in adaptive potential was shown to be sustainable. Finally, we show that multiplexed peptide nucleic acids increase the antibiotic susceptibility of clinically isolated Carbapenem-resistant E. coli in an epistatic fashion. Together, these results suggest a new therapeutic strategy for restricting the evolution of antibiotic resistance.

Peter Otoupal et al. present CHAOS, an approach for preventing the development of antibiotic resistance in E. coli through CRISPR-Cas9-based perturbation of gene expression. They show that multiplexed perturbations decrease fitness of clinically-isolated Carbapenem-resistant E. coli upon antibiotic exposure.

Lineage space and the propensity of bacterial cells to undergo growth transitions

The molecular makeup of the offspring of a dividing cell gradually becomes phenotypically decorrelated from the parent cell by noise and regulatory mechanisms that amplify phenotypic heterogeneity. Such regulatory mechanisms form networks that contain thresholds between phenotypes. Populations of cells can be poised near the threshold so that a subset of the population probabilistically undergoes the phenotypic transition. We sought to characterize the diversity of bacterial populations around a growth-modulating threshold via analysis of the effect of non-genetic inheritance, similar to conditions that create antibiotic-tolerant persister cells and other examples of bet hedging. Using simulations and experimental lineage data in Escherichia coli, we present evidence that regulation of growth amplifies the dependence of growth arrest on cellular lineage, causing clusters of related cells undergo growth arrest in certain conditions. Our simulations predict that lineage correlations and the sensitivity of growth to changes in toxin levels coincide in a critical regime. Below the critical regime, the sizes of related growth arrested clusters are distributed exponentially, while in the critical regime clusters sizes are more likely to become large. Furthermore, phenotypic diversity can be nearly as high as possible near the critical regime, but for most parameter values it falls far below the theoretical limit. We conclude that lineage information is indispensable for understanding regulation of cellular growth.

An Artificial Yeast Genetic Circuit Enables Deep Mutational Scanning of an Antimicrobial Resistance Protein

Understanding the molecular mechanisms underlying antibiotic resistance requires concerted efforts in enzymology and medicinal chemistry. Here we describe a new synthetic biology approach to antibiotic development, where the presence of tetracycline antibiotics is linked to a life-death selection in Saccharomyces cerevisiae. This artificial genetic circuit allowed the deep mutational scanning of the tetracycline inactivating enzyme TetX, revealing key functional residues. We used both positive and negative selections to confirm the importance of different residues for TetX activity, and profiled activity hotspots for different tetracyclines to reveal substrate-specific activity determinants. We found that precise positioning of FAD and hydrophobic shielding of the tetracycline are critical for enzymatic inactivation of doxycycline. However, positioning of FAD is suboptimal in the case of anhydrotetracycline, potentially explaining its comparatively poor degradation and potential as an inhibitor for this family of enzymes. By combining artificial genetic circuits whose function can be modulated by antimicrobial resistance determinants, we establish a framework to select for the next generation of antibiotics.

Distribution shapes govern the discovery of predictive models for gene regulation

Systems biology seeks to combine experiments with computation to predict biological behaviors. However, despite tremendous data and knowledge, biological models make less-accurate predictions compared with other fields. By analyzing single-cell, single-molecule measurements of mRNA during yeast stress response, we explore why and how the shapes of experimental distributions control prediction accuracy. We show how asymmetric data distributions with long tails cause standard modeling approaches to yield excellent fits but make meaningless predictions. We show how these biases arise from the violation of fundamental assumptions in standard modeling approaches. We demonstrate how advanced computational tools solve this dilemma and achieve predictive understanding of spatiotemporal mechanisms of transcription control including RNA polymerase initiation and elongation and mRNA accumulation, transport, and decay.

Despite substantial experimental and computational efforts, mechanistic modeling remains more predictive in engineering than in systems biology. The reason for this discrepancy is not fully understood. One might argue that the randomness and complexity of biological systems are the main barriers to predictive understanding, but these issues are not unique to biology. Instead, we hypothesize that the specific shapes of rare single-molecule event distributions produce substantial yet overlooked challenges for biological models. We demonstrate why modern statistical tools to disentangle complexity and stochasticity, which assume normally distributed fluctuations or enormous datasets, do not apply to the discrete, positive, and nonsymmetric distributions that characterize mRNA fluctuations in single cells. As an example, we integrate single-molecule measurements and advanced computational analyses to explore mitogen-activated protein kinase induction of multiple stress response genes. Through systematic analyses of different metrics to compare the same model to the same data, we elucidate why standard modeling approaches yield nonpredictive models for single-cell gene regulation. We further explain how advanced tools recover precise, reproducible, and predictive understanding of transcription regulation mechanisms, including gene activation, polymerase initiation, elongation, mRNA accumulation, spatial transport, and decay.