Effect of Phenotypic Selection on Stochastic Gene Expression

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

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.

"Bet hedging" against climate change in developing and adult animals: roles for stochastic gene expression, phenotypic plasticity, epigenetic inheritance and adaptation

Animals from embryos to adults experiencing stress from climate change have numerous mechanisms available for enhancing their long-term survival. In this review we consider these options, and how viable they are in a world increasingly experiencing extreme weather associated with climate change. A deeply understood mechanism involves natural selection, leading to evolution of new adaptations that help cope with extreme and stochastic weather events associated with climate change. While potentially effective at staving off environmental challenges, such adaptations typically occur very slowly and incrementally over evolutionary time. Consequently, adaptation through natural selection is in most instances regarded as too slow to aid survival in rapidly changing environments, especially when considering the stochastic nature of extreme weather events associated with climate change. Alternative mechanisms operating in a much shorter time frame than adaptation involve the rapid creation of alternate phenotypes within a life cycle or a few generations. Stochastic gene expression creates multiple phenotypes from the same genotype even in the absence of environmental cues. In contrast, other mechanisms for phenotype change that are externally driven by environmental clues include well-understood developmental phenotypic plasticity (variation, flexibility), which can enable rapid, within-generation changes. Increasingly appreciated are epigenetic influences during development leading to rapid phenotypic changes that can also immediately be very widespread throughout a population, rather than confined to a few individuals as in the case of favorable gene mutations. Such epigenetically-induced phenotypic plasticity can arise rapidly in response to stressors within a generation or across a few generations and just as rapidly be "sunsetted" when the stressor dissipates, providing some capability to withstand environmental stressors emerging from climate change. Importantly, survival mechanisms resulting from adaptations and developmental phenotypic plasticity are not necessarily mutually exclusive, allowing for classic "bet hedging". Thus, the appearance of multiple phenotypes within a single population provides for a phenotype potentially optimal for some future environment. This enhances survival during stochastic extreme weather events associated with climate change. Finally, we end with recommendations for future physiological experiments, recommending in particular that experiments investigating phenotypic flexibility adopt more realistic protocols that reflect the stochastic nature of weather.

Benchmarking imputation methods for network inference using a novel method of synthetic scRNA-seq data generation

Background

Single cell RNA-sequencing (scRNA-seq) has very rapidly become the new workhorse of modern biology providing an unprecedented global view on cellular diversity and heterogeneity. In particular, the structure of gene-gene expression correlation contains information on the underlying gene regulatory networks. However, interpretation of scRNA-seq data is challenging due to specific experimental error and biases that are unique to this kind of data including drop-out (or technical zeros).

Methods

To deal with this problem several methods for imputation of zeros for scRNA-seq have been developed. However, it is not clear how these processing steps affect inference of genetic networks from single cell data. Here, we introduce Biomodelling.jl, a tool for generation of synthetic scRNA-seq data using multiscale modelling of stochastic gene regulatory networks in growing and dividing cells.

Results

Our tool produces realistic transcription data with a known ground truth network topology that can be used to benchmark different approaches for gene regulatory network inference. Using this tool we investigate the impact of different imputation methods on the performance of several network inference algorithms.

Conclusions

Biomodelling.jl provides a versatile and useful tool for future development and benchmarking of network inference approaches using scRNA-seq data.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04778-9

Emergent expression of fitness-conferring genes by phenotypic selection

Genotypic and phenotypic adaptation is the consequence of ongoing natural selection in populations and is key to predicting and preventing drug resistance. Whereas classic antibiotic persistence is all-or-nothing, here we demonstrate that an antibiotic resistance gene displays linear dose-responsive selection for increased expression in proportion to rising antibiotic concentration in growing Escherichia coli populations. Furthermore, we report the potentially wide-spread nature of this form of emergent gene expression (EGE) by instantaneous phenotypic selection process under bactericidal and bacteriostatic antibiotic treatment, as well as an amino acid synthesis pathway enzyme under a range of auxotrophic conditions. We propose an analogy to Ohm's law in electricity (V = IR), where selection pressure acts similarly to voltage (V), gene expression to current (I), and resistance (R) to cellular machinery constraints and costs. Lastly, mathematical modeling using agent-based models of stochastic gene expression in growing populations and Bayesian model selection reveal that the EGE mechanism requires variability in gene expression within an isogenic population, and a cellular "memory" from positive feedbacks between growth and expression of any fitness-conferring gene. Finally, we discuss the connection of the observed phenomenon to a previously described general fluctuation-response relationship in biology.

Phenotypic-dependent variability and the emergence of tolerance in bacterial populations

Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well-documented to intersperse much more tightly than traditionally assumed, especially in communities of microorganisms. Advancing the development of mathematical and computational approaches to shed novel light onto eco-evolutionary problems is a challenge of utmost relevance. With this motivation in mind, here we scrutinize recent experimental results showing evidence of rapid evolution of tolerance by lag in bacterial populations that are periodically exposed to antibiotic stress in laboratory conditions. In particular, the distribution of single-cell lag times-i.e., the times that individual bacteria from the community remain in a dormant state to cope with stress-evolves its average value to approximately fit the antibiotic-exposure time. Moreover, the distribution develops right-skewed heavy tails, revealing the presence of individuals with anomalously large lag times. Here, we develop a parsimonious individual-based model mimicking the actual demographic processes of the experimental setup. Individuals are characterized by a single phenotypic trait: their intrinsic lag time, which is transmitted with variation to the progeny. The model-in a version in which the amplitude of phenotypic variations grows with the parent's lag time-is able to reproduce quite well the key empirical observations. Furthermore, we develop a general mathematical framework allowing us to describe with good accuracy the properties of the stochastic model by means of a macroscopic equation, which generalizes the Crow-Kimura equation in population genetics. Even if the model does not account for all the biological mechanisms (e.g., genetic changes) in a detailed way-i.e., it is a phenomenological one-it sheds light onto the eco-evolutionary dynamics of the problem and can be helpful to design strategies to hinder the emergence of tolerance in bacterial communities. From a broader perspective, this work represents a benchmark for the mathematical framework designed to tackle much more general eco-evolutionary problems, thus paving the road to further research avenues.

Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

Populations of genetically identical cells tend to exhibit remarkable variability. This seemingly counter-intuitive observation has broad and fascinating implications, and has thus been a focal point of biological modeling. Many important processes act on this cellular heterogeneity at the population level, leading to an intricate coupling between the single-cell and the population-level dynamics. For example, selection pressures or growth rates may depend crucially on the expression of a particular gene (or gene family). Classical single-cell modeling approaches, such as the chemical master equation, can accurately describe the mechanisms driving cellular noise, however, they cannot encapsulate how the aforementioned auxiliary processes affect the population composition. In this work, we propose a unifying framework that extends the classical chemical master equation to faithfully capture the single-cell variability alongside the population-level evolution. We develop, analyse, and showcase an open-source numerical tool to simulate the dynamics of such populations in time. The tool is designed for straightforward use by a non-technical audience: a high-level description of the underlying chemical and population-level processes suffices to simulate complex system dynamics. Simultaneously, we retain high customisability of the underlying mathematical representation for the more advanced user. Ultimately, the unifying framework and the associated computational tool open new horizons in the study of how fundamental microscopic dynamics give rise to complex macroscopic phenomena.

The influence of methylation status on a stochastic model of MGMT dynamics in glioblastoma: Phenotypic selection can occur with and without a downshift in promoter methylation status

Glioblastoma originates in the brain and is one of the most aggressive cancer types. Glioblastoma represents 15% of all brain tumours, with a median survival of 15 months. Although the current standard of care for such a tumour (the Stupp protocol) has shown positive results for the prognosis of patients, O-6-methylguanine-DNA methyltransferase (MGMT) driven drug resistance has been an issue of increasing concern and hence requires innovative approaches. In addition to the well established drug resistance factors such as tumour location and blood brain barriers, it is also important to understand how the genetic and epigenetic dynamics of the glioblastoma cells can play a role. One important aspect of this is the study of methylation status of MGMT following administration of temozolomide. In this paper, we extend our previously published model that simulated MGMT expression in glioblastoma cells to incorporate the promoter methylation status of MGMT. This methylation status has clinical significance and is used as a marker for patient outcomes. Using this model, we investigate the causative relationship between temozolomide treatment and the methylation status of the MGMT promoter in a population of cells. In addition by constraining the model to relevant biological data using Approximate Bayesian Computation, we were able to identify parameter regimes that yield different possible modes of resistances, namely, phenotypic selection of MGMT, a downshift in the methylation status of the MGMT promoter or both simultaneously. We analysed each of the parameter sets associated with the different modes of resistance, presenting representative solutions as well as discovering some similarities between them as well as unique requirements for each of them. Finally, we used them to devise optimal strategies for inhibiting MGMT expression with the aim of minimising live glioblastoma cell numbers.

Phenotypic selection through cell death: stochastic modelling of O-6-methylguanine-DNA methyltransferase dynamics

Glioblastoma (GBM) is the most aggressive malignant primary brain tumour with a median overall survival of 15 months. To treat GBM, patients currently undergo a surgical resection followed by exposure to radiotherapy and concurrent and adjuvant temozolomide (TMZ) chemotherapy. However, this protocol often leads to treatment failure, with drug resistance being the main reason behind this. To date, many studies highlight the role of O-6-methylguanine-DNA methyltransferase (MGMT) in conferring drug resistance. The mechanism through which MGMT confers resistance is not well studied-particularly in terms of computational models. With only a few reasonable biological assumptions, we were able to show that even a minimal model of MGMT expression could robustly explain TMZ-mediated drug resistance. In particular, we showed that for a wide range of parameter values constrained by novel cell growth and viability assays, a model accounting for only stochastic gene expression of MGMT coupled with cell growth, division, partitioning and death was able to exhibit phenotypic selection of GBM cells expressing MGMT in response to TMZ. Furthermore, we found this selection allowed the cells to pass their acquired phenotypic resistance onto daughter cells in a stable manner (as long as TMZ is provided). This suggests that stochastic gene expression alone is enough to explain the development of chemotherapeutic resistance.

Inferring fitness landscapes and selection on phenotypic states from single-cell genealogical data

Recent advances in single-cell time-lapse microscopy have revealed non-genetic heterogeneity and temporal fluctuations of cellular phenotypes. While different phenotypic traits such as abundance of growth-related proteins in single cells may have differential effects on the reproductive success of cells, rigorous experimental quantification of this process has remained elusive due to the complexity of single cell physiology within the context of a proliferating population. We introduce and apply a practical empirical method to quantify the fitness landscapes of arbitrary phenotypic traits, using genealogical data in the form of population lineage trees which can include phenotypic data of various kinds. Our inference methodology for fitness landscapes determines how reproductivity is correlated to cellular phenotypes, and provides a natural generalization of bulk growth rate measures for single-cell histories. Using this technique, we quantify the strength of selection acting on different cellular phenotypic traits within populations, which allows us to determine whether a change in population growth is caused by individual cells’ response, selection within a population, or by a mixture of these two processes. By applying these methods to single-cell time-lapse data of growing bacterial populations that express a resistance-conferring protein under antibiotic stress, we show how the distributions, fitness landscapes, and selection strength of single-cell phenotypes are affected by the drug. Our work provides a unified and practical framework for quantitative measurements of fitness landscapes and selection strength for any statistical quantities definable on lineages, and thus elucidates the adaptive significance of phenotypic states in time series data. The method is applicable in diverse fields, from single cell biology to stem cell differentiation and viral evolution.

Selection is a ubiquitous process in biological populations in which individuals are endowed with heterogeneous reproductive abilities, and it occurs even among genetically homogeneous cells due to the existence of phenotypic noise. Unlike genotypes, which can remain stable for many generations, phenotypic fluctuations at the single cell level are often comparable to cellular generation times. For this reason, quantifying the contribution of specific phenotypic states to cellular fitness remains a major challenge. Here, we develop a method to measure the fitness landscape and selection strength acting on diverse cellular phenotypes by employing a novel conceptual framework in which cellular histories are regarded as a basic unit of selection. With this framework, one can tell quantitatively whether a population adapts to environmental changes by selection or through individual responses. This new analytical approach to genetics reveals the roles of heterogeneous expression patterns and dynamics without directly perturbing genes. Applications in diverse fields including stem cell differentiation and viral evolution are discussed.

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

Fluctuations, or “noise”, in the response of a system is usually thought to be harmful. However, it is becoming increasingly clear that in single-celled organisms, noise can sometimes help cells survive. This is because noise can enhance the diversity of responses within a cell population. In this study, we identify a novel benefit of noise in the competence response of a population of Bacillus subtilis bacteria, where competence is the ability of bacteria to take in DNA from their environment when under stress. We use computational modeling and experiments to show that noise increases the range of stress levels for which these bacteria exhibit a highly dynamic response, meaning that they are neither unresponsive, nor permanently in the competent state. Since a dynamic response is thought to be optimal for survival, this study suggests that noise is exploited to increase the fitness of the bacterial population.

Intrinsic phenotypic stability of a bi-stable auto regulatory gene

Even under homogenous conditions clonal cells can assume different distinct states for generations to follow, also known as epigenetic inheritance. Such long periods of different phenotypic states can be formed due to the existence of more than one stable state in the molecule concentration, where the different states are explored through molecular fluctuations. By formulating a single reaction variable representing the birth and death of molecules, including transcription, translation and decay, we calculate the escape time from the phenotypic states attained from autocatalytic synthesis through a Fokker- Planck formulation and integration of an effective pseudo-potential. We calculate the stability of the phenotypic states both for cooperative binding feedback and dimer binding feedback, resulting in non-linear decay.

Generation and filtering of gene expression noise by the bacterial cell cycle

Background

Gene expression within cells is known to fluctuate stochastically in time. However, the origins of gene expression noise remain incompletely understood. The bacterial cell cycle has been suggested as one source, involving chromosome replication, exponential volume growth, and various other changes in cellular composition. Elucidating how these factors give rise to expression variations is important to models of cellular homeostasis, fidelity of signal transmission, and cell-fate decisions.

Results

Using single-cell time-lapse microscopy, we measured cellular growth as well as fluctuations in the expression rate of a fluorescent protein and its concentration. We found that, within the population, the mean expression rate doubles throughout the cell cycle with a characteristic cell cycle phase dependent shape which is different for slow and fast growth rates. At low growth rate, we find the mean expression rate was initially flat, and then rose approximately linearly by a factor two until the end of the cell cycle. The mean concentration fluctuated at low amplitude with sinusoidal-like dependence on cell cycle phase. Traces of individual cells were consistent with a sudden two-fold increase in expression rate, together with other non-cell cycle noise. A model was used to relate the findings and to explain the cell cycle-induced variations for different chromosomal positions.

Conclusions

We found that the bacterial cell cycle contribution to expression noise consists of two parts: a deterministic oscillation in synchrony with the cell cycle and a stochastic component caused by variable timing of gene replication. Together, they cause half of the expression rate noise. Concentration fluctuations are partially suppressed by a noise cancelling mechanism that involves the exponential growth of cellular volume. A model explains how the functional form of the concentration oscillations depends on chromosome position.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-016-0231-z) contains supplementary material, which is available to authorized users.

Adaptability of non-genetic diversity in bacterial chemotaxis

Bacterial chemotaxis systems are as diverse as the environments that bacteria inhabit, but how much environmental variation can cells tolerate with a single system? Diversification of a single chemotaxis system could serve as an alternative, or even evolutionary stepping-stone, to switching between multiple systems. We hypothesized that mutations in gene regulation could lead to heritable control of chemotactic diversity. By simulating foraging and colonization of E. coli using a single-cell chemotaxis model, we found that different environments selected for different behaviors. The resulting trade-offs show that populations facing diverse environments would ideally diversify behaviors when time for navigation is limited. We show that advantageous diversity can arise from changes in the distribution of protein levels among individuals, which could occur through mutations in gene regulation. We propose experiments to test our prediction that chemotactic diversity in a clonal population could be a selectable trait that enables adaptation to environmental variability.

DOI:http://dx.doi.org/10.7554/eLife.03526.001

Bacterial colonies are generally made up of genetically identical cells. Despite this, a closer look at the members of a bacterial colony shows that these cells can have very different behaviors. For example, some cells may grow more quickly than others, or be more resistant to antibiotics. The mechanisms driving this diversity are only beginning to be identified and understood.

Escherichia coli bacteria can move towards, or away from, certain chemicals in their surrounding environment to help them navigate toward favorable conditions. This behavior is known as chemotaxis. The signals from all of these chemicals are processed in E. coli by just one set of proteins, which control the different behaviors that are needed for the bacteria to follow them. Different numbers of these proteins are found in different—but genetically identical—bacteria, and the number of proteins is linked to how the bacteria perform these behaviors.

It has been suggested that diversity can be beneficial to the overall bacterial population, as it helps the population survive environmental changes. This suggests that the level of diversity in the population should adapt to the level of diversity in the environment. However, it remains unknown how this adaptation occurs.

Frankel et al. developed and combined several models and simulations to investigate whether differences in chemotaxis protein production help an E. coli colony to survive. The models show that in different environments, it can be beneficial for the population as a whole if different cells have different responses to the chemicals present. For example, if a lot of a useful chemical is present, bacteria are more likely to survive by heading straight to the source. If not much chemical is detected, the bacteria may need to move in a more exploratory manner.

Frankel et al. find that different amounts of chemotaxis proteins produce these different behaviors. To survive in a changing environment, it is therefore best for the E. coli colony to contain cells that have different amounts of these proteins. Frankel et al. propose that the variability of chemotaxis protein levels between genetically identical cells can change through mutations in the genes that control how many of the proteins are produced, and predict that such mutations allow populations to adapt to environmental changes.

The environments simulated in the model were much simpler than would be found in the real world, and Frankel et al. describe experiments that are now being performed to confirm and expand on their results. The model could be used in the future to shed light on the behavior of other cells that are genetically identical but exhibit diverse behaviors, from other bacterial species to more complex cancer cells.

DOI:http://dx.doi.org/10.7554/eLife.03526.002