Tunability and Noise Dependence in Differentiation Dynamics

Pulsatile dynamics in the yeast proteome

The activation of transcription factors in response to environmental conditions is fundamental to cellular regulation. Recent work has revealed that some transcription factors are activated in stochastic pulses of nuclear localization, rather than at a constant level, even in a constant environment [1-12]. In such cases, signals control the mean activity of the transcription factor by modulating the frequency, duration, or amplitude of these pulses. Although specific pulsatile transcription factors have been identified in diverse cell types, it has remained unclear how prevalent pulsing is within the cell, how variable pulsing behaviors are between genes, and whether pulsing is specific to transcriptional regulators or is employed more broadly. To address these issues, we performed a proteome-wide movie-based screen to systematically identify localization-based pulsing behaviors in Saccharomyces cerevisiae. The screen examined all genes in a previously developed fluorescent protein fusion library of 4,159 strains [13] in multiple media conditions. This approach revealed stochastic pulsing in ten proteins, all transcription factors. In each case, pulse dynamics were heterogeneous and unsynchronized among cells in clonal populations. Pulsing is the only dynamic localization behavior that we observed, and it tends to occur in pairs of paralogous and redundant proteins. Taken together, these results suggest that pulsatile dynamics play a pervasive role in yeast and may be similarly prevalent in other eukaryotic species.

Temporal dynamics and transcriptional control using single-cell gene expression analysis

Background

Changes in environmental conditions lead to expression variation that manifest at the level of gene regulatory networks. Despite a strong understanding of the role noise plays in synthetic biological systems, it remains unclear how propagation of expression heterogeneity in an endogenous regulatory network is distributed and utilized by cells transitioning through a key developmental event.

Results

Here we investigate the temporal dynamics of a single-cell transcriptional network of 45 transcription factors in THP-1 human myeloid monocytic leukemia cells undergoing differentiation to macrophages. We systematically measure temporal regulation of expression and variation by profiling 120 single cells at eight distinct time points, and infer highly controlled regulatory modules through which signaling operates with stochastic effects. This reveals dynamic and specific rewiring as a cellular strategy for differentiation. The integration of both positive and negative co-expression networks further identifies the proto-oncogene MYB as a network hinge to modulate both the pro- and anti-differentiation pathways.

Conclusions

Compared to averaged cell populations, temporal single-cell expression profiling provides a much more powerful technique to probe for mechanistic insights underlying cellular differentiation. We believe that our approach will form the basis of novel strategies to study the regulation of transcription at a single-cell level.

Construction of an effective landscape for multistate genetic switches

Multistate genetic switches play a crucial role during embryonic development and tumorigenesis. An archetypical example is the three-way switch regulating epithelial-hybrid-mesenchymal transitions. We devise a special WKB-based approach to investigate white Gaussian and shot noise effects on three-way switches, and construct an effective landscape in good quantitative agreement with stochastic simulations. This approach allows efficient analytical or numerical calculation of the landscape contours, the optimal path, and the state relative stability for general multicomponent multistate switches.

Stochastic cellular fate decision making by multiple infecting lambda phage

Bacteriophage lambda is a classic system for the study of cellular decision making. Both experiments and mathematical models have demonstrated the importance of viral concentration in the lysis-lysogeny decision outcome in lambda phage. However, a recent experimental study using single cell and single phage resolution reported that cells with the same viral concentrations but different numbers of infecting phage (multiplicity of infection) can have markedly different rates of lysogeny. Thus the decision depends on not only viral concentration, but also directly on the number of infecting phage. Here, we attempt to provide a mechanistic explanation of these results using a simple stochastic model of the lambda phage genetic network. Several potential factors including intrinsic gene expression noise, spatial dynamics and cell-cycle effects are investigated. We find that interplay between the level of intrinsic noise and viral protein decision threshold is a major factor that produces dependence on multiplicity of infection. However, simulations suggest spatial segregation of phage particles does not play a significant role. Cellular image processing is used to re-analyse the original time-lapse movies from the recent study and it is found that higher numbers of infecting phage reduce the cell elongation rate. This could also contribute to the observed phenomena as cellular growth rate can affect transcription rates. Our model further predicts that rate of lysogeny is dependent on bacterial growth rate, which can be experimentally tested. Our study provides new insight on the mechanisms of individual phage decision making. More generally, our results are relevant for the understanding of gene-dosage compensation in cellular systems.

The linear interplay of intrinsic and extrinsic noises ensures a high accuracy of cell fate selection in budding yeast

To gain insights into the mechanisms of cell fate decision in a noisy environment, the effects of intrinsic and extrinsic noises on cell fate are explored at the single cell level. Specifically, we theoretically define the impulse of Cln1/2 as an indication of cell fates. The strong dependence between the impulse of Cln1/2 and cell fates is exhibited. Based on the simulation results, we illustrate that increasing intrinsic fluctuations causes the parallel shift of the separation ratio of Whi5P but that increasing extrinsic fluctuations leads to the mixture of different cell fates. Our quantitative study also suggests that the strengths of intrinsic and extrinsic noises around an approximate linear model can ensure a high accuracy of cell fate selection. Furthermore, this study demonstrates that the selection of cell fates is an entropy-decreasing process. In addition, we reveal that cell fates are significantly correlated with the range of entropy decreases.

Controlling low rates of cell differentiation through noise and ultrahigh feedback

Mammalian tissue size is maintained by slow replacement of de-differentiating and dying cells. For adipocytes, key regulators of glucose and lipid metabolism, the renewal rate is only 10% per year. We used computational modeling, quantitative mass spectrometry, and single-cell microscopy to show that cell-to-cell variability, or noise, in protein abundance acts within a network of more than six positive feedbacks to permit pre-adipocytes to differentiate at very low rates. This reconciles two fundamental opposing requirements: High cell-to-cell signal variability is needed to generate very low differentiation rates, whereas low signal variability is needed to prevent differentiated cells from de-differentiating. Higher eukaryotes can thus control low rates of near irreversible cell fate decisions through a balancing act between noise and ultrahigh feedback connectivity.

Suppression and enhancement of transcriptional noise by DNA looping

DNA looping has been observed to enhance and suppress transcriptional noise but it is uncertain which of these two opposite effects is to be expected for given conditions. Here, we derive analytical expressions for the main quantifiers of transcriptional noise in terms of the molecular parameters and elucidate the role of DNA looping. Our results rationalize paradoxical experimental observations and provide the first quantitative explanation of landmark individual-cell measurements at the single molecule level on the classical lac operon genetic system [Choi, L. Cai, K. Frieda, and X. S. Xie, Science 322, 442 (2008)].

Exact model reduction with delays: closed-form distributions and extensions to fully bi-directional monomolecular reactions

In order to systematically understand the qualitative and quantitative behaviour of chemical reaction networks, scientists must derive and analyse associated mathematical models. However, biochemical systems are often very large, with reactions occurring at multiple time scales, as evidenced by signalling pathways and gene expression kinetics. Owing to the associated computational costs, it is then many times impractical, if not impossible, to solve or simulate these systems with an appropriate level of detail. By consequence, there is a growing interest in developing techniques for the simplification or reduction of complex biochemical systems. Here, we extend our recently presented methodology on exact reduction of linear chains of reactions with delay distributions in two ways. First, we report that it is now possible to deal with fully bi-directional monomolecular systems, including degradations, synthesis and generalized bypass reactions. Second, we provide all derivations of associated delays in analytical, closed form. Both advances have a major impact on further reducing computational costs, while still retaining full accuracy. Thus, we expect our new methodology to respond to current simulation needs in pharmaceutical, chemical and biological research.

An evolutionarily conserved RNase-based mechanism for repression of transcriptional positive autoregulation

It is known that environmental context influences the degree of regulation at the transcriptional and post-transcriptional levels. However, the principles governing the differential usage and interplay of regulation at these two levels are not clear. Here, we show that the integration of transcriptional and post-transcriptional regulatory mechanisms in a characteristic network motif drives efficient environment-dependent state transitions. Through phenotypic screening, systems analysis, and rigorous experimental validation, we discovered an RNase (VNG2099C) in Halobacterium salinarum that is transcriptionally co-regulated with genes of the aerobic physiologic state but acts on transcripts of the anaerobic state. Through modelling and experimentation we show that this arrangement generates an efficient state-transition switch, within which RNase-repression of a transcriptional positive autoregulation (RPAR) loop is critical for shutting down ATP-consuming active potassium uptake to conserve energy required for salinity adaptation under aerobic, high potassium, or dark conditions. Subsequently, we discovered that many Escherichia coli operons with energy-associated functions are also putatively controlled by RPAR indicating that this network motif may have evolved independently in phylogenetically distant organisms. Thus, our data suggest that interplay of transcriptional and post-transcriptional regulation in the RPAR motif is a generalized principle for efficient environment-dependent state transitions across prokaryotes.

Noise minimisation in gene expression switches

Gene expression is subject to stochastic variation which leads to fluctuations in the rate of protein production. Recently, a study in yeast at a genomic scale showed that, in some cases, gene expression variability alters phenotypes while, in other cases, these remain unchanged despite fluctuations in the expression of other genes. These studies suggested that noise in gene expression is a physiologically relevant trait and, to prevent harmful stochastic variation in the expression levels of some genes, it can be subject to minimisation. However, the mechanisms for noise minimisation are still unclear. In the present work, we analysed how noise expression depends on the architecture of the cis-regulatory system, in particular on the number of regulatory binding sites. Using analytical calculations and stochastic simulations, we found that the fluctuation level in noise expression decreased with the number of regulatory sites when regulatory transcription factors interacted with only one other bound transcription factor. In contrast, we observed that there was an optimal number of binding sites when transcription factors interacted with many bound transcription factors. This finding suggested a new mechanism for preventing large fluctuations in the expression of genes which are sensitive to the concentration of regulators.

Functional roles of pulsing in genetic circuits

A fundamental problem in biology is to understand how genetic circuits implement core cellular functions. Time-lapse microscopy techniques are beginning to provide a direct view of circuit dynamics in individual living cells. Unexpectedly, we are discovering that key transcription and regulatory factors pulse on and off repeatedly, and often stochastically, even when cells are maintained in constant conditions. This type of spontaneous dynamic behavior is pervasive, appearing in diverse cell types from microbes to mammalian cells. Here, we review recent work showing how pulsing is generated and controlled by underlying regulatory circuits and how it provides critical capabilities to cells in stress response, signaling, and development. A major theme is the ability of pulsing to enable time-based regulation analogous to strategies used in engineered systems. Thus, pulsatile dynamics is emerging as a central, and still largely unexplored, layer of temporal organization in the cell.

Memory and modularity in cell-fate decision making

Genetically identical cells sharing an environment can display markedly different phenotypes. It is often unclear how much of this variation derives from chance, external signals, or attempts by individual cells to exert autonomous phenotypic programs. By observing thousands of cells for hundreds of consecutive generations under constant conditions, we dissect the stochastic decision between a solitary, motile state and a chained, sessile state in Bacillus subtilis. The motile state is memoryless, exhibiting no autonomous control over the time spent in the state, whereas chaining is tightly timed. Timing enforces coordination among related cells in the multicellular state. Further, we show that the three-protein regulatory circuit governing the decision is modular, as initiation and maintenance of chaining are genetically separable functions. As stimulation of the same initiating pathway triggers biofilm formation, we argue that autonomous timing allows a trial commitment to multicellularity that external signals could extend.

Phenotypic noise: effects of post-transcriptional regulatory processes affecting mRNA

The inherently stochastic nature of biomolecular processes is one of the main sources giving rise to cell-to-cell variations in protein and mRNA abundance, termed noise. Noise in isogenic populations can enhance survival under adverse conditions and stress, and has therefore played a fundamental role in evolution. On the other hand, noise may have detrimental effects and therefore cells must also display robustness to fluctuations and possess mechanisms of control in order to function properly. Noise can be introduced at every step in the cascade of intermediate events resulting in the production of functional proteins. While initial studies of noise focused on stochasticity introduced at the transcriptional level, recent years have witnessed a gradual shift of emphasis into the effects that post-transcriptional processes have on phenotypic noise. Here, we survey the insights that have been gained on the effects of processes that modify RNA transcript populations on phenotypic noise, including regulation by noncoding RNAs in prokaryotes and eukaryotes, alternative splicing and transcriptional interference.

Turning oscillations into opportunities: lessons from a bacterial decision gate

Sporulation vs. competence provides a prototypic example of collective cell fate determination. The decision is performed by the action of three modules: 1) A stochastic competence switch whose transition probability is regulated by population density, population stress and cell stress. 2) A sporulation timer whose clock rate is regulated by cell stress and population stress. 3) A decision gate that is coupled to the timer via a special repressilator-like loop. We show that the distinct circuit architecture of this gate leads to special dynamics and noise management characteristics: The gate opens a time-window of opportunity for competence transitions during which it generates oscillations that are turned into a chain of transition opportunities – each oscillation opens a short interval with high transition probability. The special architecture of the gate also leads to filtering of external noise and robustness against internal noise and variations in the circuit parameters.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

Probing cell-free gene expression noise in femtoliter volumes

Cell-free systems offer a simplified and flexible context that enables important biological reactions while removing complicating factors such as fitness, division, and mutation that are associated with living cells. However, cell-free expression in unconfined spaces is missing important elements of expression in living cells. In particular, the small volume of living cells can give rise to significant stochastic effects, which are negligible in bulk cell-free reactions. Here, we confine cell-free gene expression reactions to cell-relevant 20 fL volumes (between the volumes of Escherichia coli and Saccharomyces cerevisiae ), in polydimethylsiloxane (PDMS) containers. We demonstrate that expression efficiency varies widely among different containers, likely due to non-Poisson distribution of expression machinery at the observed scale. Previously, this phenomenon has been observed only in liposomes. In addition, we analyze gene expression noise. This analysis is facilitated by our use of cell-free systems, which allow the mapping of the measured noise properties to intrinsic noise models. In contrast, previous live cell noise analysis efforts have been complicated by multiple noise sources. Noise analysis reveals signatures of translational bursting, while noise dynamics suggest that overall cell-free expression is limited by a diminishing translation rate. In addition to offering a unique approach to understanding noise in gene circuits, our work contributes to a deeper understanding of the biophysical properties of cell-free expression systems, thus aiding efforts to harness cell-free systems for synthetic biology applications.

Synthetic biological networks

Despite their obvious relationship and overlap, the field of physics is blessed with many insightful laws, while such laws are sadly absent in biology. Here we aim to discuss how the rise of a more recent field known as synthetic biology may allow us to more directly test hypotheses regarding the possible design principles of natural biological networks and systems. In particular, this review focuses on synthetic gene regulatory networks engineered to perform specific functions or exhibit particular dynamic behaviors. Advances in synthetic biology may set the stage to uncover the relationship of potential biological principles to those developed in physics.

Inverse Gillespie for inferring stochastic reaction mechanisms from intermittent samples

Gillespie stochastic simulation is used extensively to investigate stochastic phenomena in many fields, ranging from chemistry to biology to ecology. The inverse problem, however, has remained largely unsolved: How to reconstruct the underlying reactions de novo from sparse observations. A key challenge is that often only aggregate concentrations, proportional to the population numbers, are observable intermittently. We discovered that under specific assumptions, the set of relative population updates in phase space forms a convex polytope whose vertices are indicative of the dominant underlying reactions. We demonstrate the validity of this simple principle by reconstructing stochastic models (reaction structure plus propensities) from a variety of simulated and experimental systems, where hundreds and even thousands of reactions may be occurring in between observations. In some cases, the inferred models provide mechanistic insight. This principle can lead to the understanding of a broad range of phenomena, from molecular biology to population ecology.

A structured population modeling framework for quantifying and predicting gene expression noise in flow cytometry data

We formulated a structured population model with distributed parameters to identify mechanisms that contribute to gene expression noise in time-dependent flow cytometry data. The model was validated using cell population-level gene expression data from two experiments with synthetically engineered eukaryotic cells. Our model captures the qualitative noise features of both experiments and accurately fit the data from the first experiment. Our results suggest that cellular switching between high and low expression states and transcriptional re-initiation are important factors needed to accurately describe gene expression noise with a structured population model.

Modeling gene expression in time and space

Cell populations rarely exhibit gene-expression profiles that are homogeneous in time and space. In the temporal domain, dynamical behaviors such as oscillations and pulses of protein production pervade cell biology, underlying phenomena as diverse as circadian rhythmicity, cell cycle control, stress and damage responses, and stem-cell pluripotency. In multicellular populations, spatial heterogeneities are crucial for decision making and development, among many other functions. Cells need to exquisitely coordinate this temporal and spatial variation to survive. Although the spatiotemporal character of gene expression is challenging to quantify experimentally at the level of individual cells, it is beneficial from the modeling viewpoint, because it provides strong constraints that can be probed by theoretically analyzing mathematical models of candidate gene and protein circuits. Here, we review recent examples of temporal dynamics and spatial patterning in gene expression to show how modeling such phenomenology can help us unravel the molecular mechanisms of cellular function.

A design principle of group-level decision making in cell populations

Populations of cells often switch states as a group to cope with environmental changes such as nutrient availability and cell density. Although the gene circuits that underlie the switches are well understood at the level of single cells, the ways in which such circuits work in concert among many cells to support group-level switches are not fully explored. Experimental studies of microbial quorum sensing show that group-level changes in cellular states occur in either a graded or an all-or-none fashion. Here, we show through numerical simulations and mathematical analysis that these behaviors generally originate from two distinct forms of bistability. The choice of bistability is uniquely determined by a dimensionless parameter that compares the synthesis and the transport of the inducing molecules. The role of the parameter is universal, such that it not only applies to the autoinducing circuits typically found in bacteria but also to the more complex gene circuits involved in transmembrane receptor signaling. Furthermore, in gene circuits with negative feedback, the same dimensionless parameter determines the coherence of group-level transitions from quiescence to a rhythmic state. The set of biochemical parameters in bacterial quorum-sensing circuits appear to be tuned so that the cells can use either type of transition. The design principle identified here serves as the basis for the analysis and control of cellular collective decision making.

Although the genetic circuits underlying state switching at the single-cell level are well understood, how such circuits work in concert among many cells to support the population-level switching of cellular behaviors is not fully explored. Experiments using microbial signaling systems show that group-level changes in cellular state occur in either a graded or an all-or-none fashion. We show that the type of group-level decision making used by populations is uniquely determined by a single dimensionless parameter that compares the quorum-signaling molecules accumulated within the cells with those secreted by the population. Bacterial quorum-sensing circuits appear to be tuned so that the cells can convert between the two types of decision-making in response to slight biochemical variations. Furthermore, the role of the parameter is universal such that it not only applies to the autoinducing circuits typically found in bacteria but also to the more complex gene circuits involved in transmembrane receptor signaling and negative feedback. The design principle that we describe thus serves as the basis for the analysis and control of collective cellular decision making in general.

Lessons about terminal differentiation from the specification of color-detecting photoreceptors in the Drosophila retina

Metazoans require highly diverse collections of cell types to sense, interpret, and react to the environment. Developmental programs incorporate deterministic and stochastic strategies in different contexts or different combinations to establish this multitude of cell fates. Precise genetic dissection of the processes controlling terminal photoreceptor differentiation in the Drosophila retina has revealed complex regulatory mechanisms required to generate differences in gene expression and cell fate. In this review, I discuss how a gene regulatory network interprets stochastic and regional inputs to determine the specification of color-detecting photoreceptor subtypes in the Drosophila retina. These combinatorial gene regulatory mechanisms will likely be broadly applicable to nervous system development and cell fate specification in general.

Diversity training for signal transduction: leveraging cell-to-cell variability to dissect cellular signaling, differentiation and death

Populations of 'identical' cells are rarely truly identical. Even when in the same state of differentiation, isogenic cells may vary in expression of key signaling regulators, activate signal transduction at different thresholds, and consequently respond heterogeneously to a given stimulus. Here, we review how new experimental and analytical techniques are suited to connect these different levels of variability, quantitatively mapping the effects of cell-to-cell variability on cellular decision-making. In particular, we summarize how this helps classify signaling regulators according to the impact of their variability on biological functions. We further discuss how variability can also be leveraged to shed light on the molecular mechanisms regulating cellular signaling, from the individual cell to the population of cells as a whole.

In vitro regulatory models for systems biology

The reductionist approach has revolutionized biology in the past 50 years. Yet its limits are being felt as the complexity of cellular interactions is gradually revealed by high-throughput technology. In order to make sense of the deluge of "omic data", a hypothesis-driven view is needed to understand how biomolecular interactions shape cellular networks. We review recent efforts aimed at building in vitro biochemical networks that reproduce the flow of genetic regulation. We highlight how those efforts have culminated in the rational construction of biochemical oscillators and bistable memories in test tubes. We also recapitulate the lessons learned about in vivo biochemical circuits such as the importance of delays and competition, the links between topology and kinetics, as well as the intriguing resemblance between cellular reaction networks and ecosystems.

Circuit-level input integration in bacterial gene regulation

Gene regulatory circuits can receive multiple simultaneous inputs, which can enter the system through different locations. It is thus necessary to establish how these genetic circuits integrate multiple inputs as a function of their relative entry points. Here, we use the dynamic circuit regulating competence for DNA uptake in Bacillus subtilis as a model system to investigate this issue. Specifically, we map the response of single cells in vivo to a combination of (i) a chemical signal controlling the constitutive expression of key competence genes, and (ii) a genetic perturbation in the form of copy number variation of one of these genes, which mimics the level of stress signals sensed by the bacteria. Quantitative time-lapse fluorescence microscopy shows that a variety of dynamical behaviors can be reached by the combination of the two inputs. Additionally, the integration depends strongly on the relative locations where the two perturbations enter the circuit. Specifically, when the two inputs act upon different circuit elements, their integration generates novel dynamical behavior, whereas inputs affecting the same element do not. An in silico bidimensional bifurcation analysis of a mathematical model of the circuit offers good quantitative agreement with the experimental observations, and sheds light on the dynamical mechanisms leading to the different integrated responses exhibited by the gene regulatory circuit.

Agent-based modeling of competence phenotype switching in Bacillus subtilis

Background

It is a fascinating phenomenon that in genetically identical bacteria populations of Bacillus subtilis, a distinct DNA uptake phenotype called the competence phenotype may emerge in 10–20% of the population. Many aspects of the phenomenon are believed to be due to the variable expression of critical genes: a stochastic occurrence termed “noise” which has made the phenomenon difficult to examine directly by lab experimentation.

Methods

To capture and model noise in this system and further understand the emergence of competence both at the intracellular and culture levels in B. subtilis, we developed a novel multi-scale, agent-based model. At the intracellular level, our model recreates the regulatory network involved in the competence phenotype. At the culture level, we simulated growth conditions, with our multi-scale model providing feedback between the two levels.

Results

Our model predicted three potential sources of genetic “noise”. First, the random spatial arrangement of molecules may influence the manifestation of the competence phenotype. In addition, the evidence suggests that there may be a type of epigenetic heritability to the emergence of competence, influenced by the molecular concentrations of key competence molecules inherited through cell division. Finally, the emergence of competence during the stationary phase may in part be due to the dilution effect of cell division upon protein concentrations.

Conclusions

The competence phenotype was easily translated into an agent-based model – one with the ability to illuminate complex cell behavior. Models such as the one described in this paper can simulate cell behavior that is otherwise unobservable in vivo, highlighting their potential usefulness as research tools.

Identifying dynamical systems with bifurcations from noisy partial observation

We propose a statistical machine-learning approach to derive low-dimensional models by integrating noisy time-series data from partial observation of high-dimensional systems, aiming to utilize quantitative data on biological phenomena in the cell. In particular, the method estimates a model from data at different values of a bifurcation parameter in order to characterize biological functions as bifurcation types that are insensitive to system details and experimental errors. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations and the learned systems are shown to robustly inherit the bifurcation types.

Effects of post-transcriptional regulation on phenotypic noise in Escherichia coli

Cell-to-cell variations in protein abundance, called noise, give rise to phenotypic variability between isogenic cells. Studies of noise have focused on stochasticity introduced at transcription, yet the effects of post-transcriptional regulatory processes on noise remain unknown. We study the effects of RyhB, a small-RNA of Escherichia coli produced on iron stress, on the phenotypic variability of two of its downregulated target proteins, using dual chromosomal fusions to fluorescent reporters and measurements in live individual cells. The total noise of each of the target proteins is remarkably constant over a wide range of RyhB production rates despite cells being in stress. In fact, coordinate downregulation of the two target proteins by RyhB reduces the correlation between their levels. Hence, an increase in phenotypic variability under stress is achieved by decoupling the expression of different target proteins in the same cell, rather than by an increase in the total noise of each. Extrinsic noise provides the dominant contribution to the total protein noise over the total range of RyhB production rates. Stochastic simulations reproduce qualitatively key features of our observations and show that a feed-forward loop formed by transcriptional extrinsic noise, an sRNA and its target genes exhibits strong noise filtration capabilities.

Regulation of noise in gene expression

The biochemical processes leading to the synthesis of new proteins are random, as they typically involve a small number of diffusing molecules. They lead to fluctuations in the number of proteins in a single cell as a function of time and to cell-to-cell variability of protein abundances. These in turn can lead to phenotypic heterogeneity in a population of genetically identical cells. Phenotypic heterogeneity may have important consequences for the development of multicellular organisms and the fitness of bacterial colonies, raising the question of how it is regulated. Here we review the experimental evidence that transcriptional regulation affects noise in gene expression, and discuss how the noise strength is encoded in the architecture of the promoter region. We discuss how models based on specific molecular mechanisms of gene regulation can make experimentally testable predictions for how changes to the promoter architecture are reflected in gene expression noise.

Optical systems for single cell analyses

BACKGROUND

Data extracted from a population of cells represent the average response from all cells within the population. Even when the cells are genetically identical, cell-to-cell variations and genetic noise can make the cells respond in completely different ways. To understand the mechanisms behind the behaviour of a population, the cells must also be analysed on an individual basis.

OBJECTIVE

This review highlights the use of optical manipulation, microfluidics and advanced fluorescence imaging techniques for the acquisition of single cell data.

CONCLUSION

By implementation of these three techniques, it is possible to achieve a deeper insight into the principles underlying cellular functioning and a more thorough understanding of the phenomena often observed in cell populations, thus facilitating research in drug discovery.

Cell-to-cell variability analysis dissects the plasticity of signaling of common γ chain cytokines in T cells

Natural variability in the abundance of signaling regulators can lead to divergence in cell fate, even within genetically identical cells that share a common differentiation state. We introduce cell-to-cell variability analysis (CCVA), an experimental and computational methodology that quantifies the correlation between variability in signaling regulator abundance and variation in the sensitivity of cells to stimuli. With CCVA, we investigated the unexpected effects of the interleukin 2 (IL-2) receptor α chain (IL-2Rα) on the sensitivity of primary mouse T lymphocytes to cytokines that signal through receptors that have the common γ chain (γ(c)). Our work showed that increased IL-2Rα abundance decreased the concentration of IL-2 required for a half-maximal activation (EC(50)) of the downstream effector signal transducer and activator of transcription 5 (STAT5), but reduced the responsiveness to IL-7 or IL-15, without affecting the EC(50) values of other γ(c) cytokines. To investigate the mechanism of the effect of IL-2Rα on γ(c) cytokine signaling, we introduced a Bayesian-inference computational framework that models the formation of receptor signaling complexes with data from previous biophysical measurements. With this framework, we found that a model in which IL-2Rα drives γ(c) depletion through the assembly of functional IL-2R complexes was consistent with both the CCVA data and experimental measurements. The combination of CCVA and computational modeling produced quantitative understanding of the crosstalk between γ(c) cytokine receptor signaling in T lymphocytes.

Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts

BACKGROUND

A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells.

RESULTS

For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability.

CONCLUSIONS

In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state.

Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.

OCT4/SOX2-independent Nanog autorepression modulates heterogeneous Nanog gene expression in mouse ES cells

NANOG, OCT4 and SOX2 form the core network of transcription factors supporting embryonic stem (ES) cell self-renewal. While OCT4 and SOX2 expression is relatively uniform, ES cells fluctuate between states of high NANOG expression possessing high self-renewal efficiency, and low NANOG expression exhibiting increased differentiation propensity. NANOG, OCT4 and SOX2 are currently considered to activate transcription of each of the three genes, an architecture that cannot readily account for NANOG heterogeneity. Here, we examine the architecture of the Nanog-centred network using inducible NANOG gain- and loss-of-function approaches. Rather than activating itself, Nanog activity is autorepressive and OCT4/SOX2-independent. Moreover, the influence of Nanog on Oct4 and Sox2 expression is minimal. Using Nanog:GFP reporters, we show that Nanog autorepression is a major regulator of Nanog transcription switching. We conclude that the architecture of the pluripotency gene regulatory network encodes the capacity to generate reversible states of Nanog transcription via a Nanog-centred autorepressive loop. Therefore, cellular variability in self-renewal efficiency is an emergent property of the pluripotency gene regulatory network.

Event timing at the single-cell level

The timing of a cellular event often hides critical information on the process leading to the event. Our ability to measure event times in single cells along with other quantities allow us to learn about the drivers of the timed process and its downstream effects. In this review, we cover different types of events that have been timed in single cells, methods to time such events and types of analysis that have been applied to event timings. We show how different timing distributions suggest different natures for the process. The statistical relations between the timing of different events may reveal how their respective processes are related biologically: Do they occur in sequence or in parallel? Are they independent or inter-dependent? Finally, quantifying morphological and molecular variables may help assess their contribution to the timing of an event and its related process.

Multiparameter spectral representation of noise-induced competence in Bacillus subtilis

In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis bacterium. In particular, the dependence of the competence state on rate constants of underlying reactions is investigated. We base our methodology on Polynomial Chaos (PC) spectral expansions that allow effective propagation of input parameter uncertainties to outputs of interest. Given a number of forward model training runs at sampled input parameter values, the PC modes are estimated using a Bayesian framework. As an outcome, these PC modes are described with posterior probability distributions. The resulting expansion can be regarded as an uncertain response function and can further be used as a computationally inexpensive surrogate instead of the original reaction model for subsequent analyses such as calibration or optimization studies. Furthermore, the methodology is enhanced with a classification-based mixture PC formulation that overcomes the difficulties associated with representing potentially nonsmooth input-output relationships. Finally, the global sensitivity analysis based on the multiparameter spectral representation of an observable of interest provides biological insight and reveals the most important reactions and their couplings for the competence dynamics

The importance of geometry in mathematical models of developing systems

Understanding the interaction between the spatial variation of extracellular signals and the interpretation of such signals in embryonic development is difficult without a mathematical model, but the inherent limitations of a model can have a profound impact on its utility. A central issue is the level of abstraction needed, and here we focus on the role of geometry in models and how the choice of the spatial dimension can influence the conclusions reached. A widely studied system in which the proper choice of geometry is critical is embryonic development of Drosophila melanogaster, and we discuss recent work in which 3D embryo-scale modeling is used to identify key modes of transport, analyze gap gene expression, and test BMP-mediated positive feedback mechanisms.

A synthetic biology approach to understanding cellular information processing

The survival of cells and organisms requires proper responses to environmental signals. These responses are governed by cellular networks, which serve to process diverse environmental cues. Biological networks often contain recurring network topologies called "motifs". It has been recognized that the study of such motifs allows one to predict the response of a biological network and thus cellular behavior. However, studying a single motif in complete isolation of all other network motifs in a natural setting is difficult. Synthetic biology has emerged as a powerful approach to understanding the dynamic properties of network motifs. In addition to testing existing theoretical predictions, construction and analysis of synthetic gene circuits has led to the discovery of novel motif dynamics, such as how the combination of simple motifs can lead to autonomous dynamics or how noise in transcription and translation can affect the dynamics of a motif. Here, we review developments in synthetic biology as they pertain to increasing our understanding of cellular information processing. We highlight several types of dynamic behaviors that diverse motifs can generate, including the control of input/output responses, the generation of autonomous spatial and temporal dynamics, as well as the influence of noise in motif dynamics and cellular behavior.

Fine-tuning gene networks using simple sequence repeats

The parameters in a complex synthetic gene network must be extensively tuned before the network functions as designed. Here, we introduce a simple and general approach to rapidly tune gene networks in Escherichia coli using hypermutable simple sequence repeats embedded in the spacer region of the ribosome binding site. By varying repeat length, we generated expression libraries that incrementally and predictably sample gene expression levels over a 1,000-fold range. We demonstrate the utility of the approach by creating a bistable switch library that programmatically samples the expression space to balance the two states of the switch, and we illustrate the need for tuning by showing that the switch's behavior is sensitive to host context. Further, we show that mutation rates of the repeats are controllable in vivo for stability or for targeted mutagenesis--suggesting a new approach to optimizing gene networks via directed evolution. This tuning methodology should accelerate the process of engineering functionally complex gene networks.

Bacterial survival strategies suggest rethinking cancer cooperativity

Despite decades of a much improved understanding of cancer biology, we are still baffled by questions regarding the deadliest traits of malignancy: metastatic colonization, dormancy and relapse, and the rapid evolution of multiple drug and immune resistance. New ideas are needed to resolve these critical issues. Relying on finding and demonstrating parallels between collective behavior capabilities of cancer cells and that of bacteria, we suggest communal behaviors of bacteria as a valuable model system for new perspectives and research directions. Understanding the ways in which bacteria thrive in competitive habitats and their cooperative strategies for surviving extreme stress can shed light on cooperativity in tumorigenesis and portray tumors as societies of smart communicating cells. This may translate into progress in fathoming cancer pathogenesis. We outline new experiments to test the cancer cooperativity hypothesis and reason that cancer may be outsmarted through its own 'social intelligence'.

Equation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity

Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity.

It is a surprising fact that genetically identical bacteria, living in identical conditions, can develop in completely different ways: for example, one subpopulation might grow very fast and another very slowly. These different phenotypes are thought to be one reason why bacteria that cause disease can survive antibiotic treatment or become persistent. This diversity of behaviour is usually attributed to the existence of multiple stable phenotypic states, or to the coexistence of one stable state with another unstable excited state, or finally to the possibility of the whole biochemical system that controls the phenotype being switched on and off. In this paper we describe a different scenario that leads to phenotypic diversity in two-component system signalling, a very common mechanism that bacteria use to sense external signals and control their response to changes in their environment. We use probability theory and equation-free computational analysis to calculate the average number of molecules of each chemical species present in the two-component system and hence show that sporadic production of either of two key chemical components required for signalling can delay the response to the external signal in some bacterial cells and so lead to the emergence of two distinct cell populations.

Evolutionary synthetic biology

Signaling networks process vast amounts of environmental information to generate specific cellular responses. As cellular environments change, signaling networks adapt accordingly. Here, I will discuss how the integration of synthetic biology and directed evolution approaches is shedding light on the molecular mechanisms that guide the evolution of signaling networks. In particular, I will review studies that demonstrate how different types of mutations, from the replacement of individual amino acids to the shuffling of modular domains, lead to markedly different evolutionary trajectories and consequently to diverse network rewiring. Moreover, I will argue that intrinsic evolutionary properties of signaling proteins, such as the robustness of wild type functions, the promiscuous nature of evolutionary intermediates, and the modular decoupling between binding and catalysis, play important roles in the evolution of signaling networks. Finally, I will argue that rapid advances in our ability to synthesize DNA will radically alter how we study signaling network evolution at the genome-wide level.

Noise propagation in two-step series MAPK cascade

Series MAPK enzymatic cascades, ubiquitously found in signaling networks, act as signal amplifiers and play a key role in processing information during signal transduction in cells. In activated cascades, cell-to-cell variability or noise is bound to occur and thereby strongly affects the cellular response. Commonly used linearization method (LM) applied to Langevin type stochastic model of the MAPK cascade fails to accurately predict intrinsic noise propagation in the cascade. We prove this by using extensive stochastic simulations for various ranges of biochemical parameters. This failure is due to the fact that the LM ignores the nonlinear effects on the noise. However, LM provides a good estimate of the extrinsic noise propagation. We show that the correct estimate of intrinsic noise propagation in signaling networks that contain at least one enzymatic step can be obtained only through stochastic simulations. Noise propagation in the cascade depends on the underlying biochemical parameters which are often unavailable. Based on a combination of global sensitivity analysis (GSA) and stochastic simulations, we developed a systematic methodology to characterize noise propagation in the cascade. GSA predicts that noise propagation in MAPK cascade is sensitive to the total number of upstream enzyme molecules and the total number of molecules of the two substrates involved in the cascade. We argue that the general systematic approach proposed and demonstrated on MAPK cascade must accompany noise propagation studies in biological networks.

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.