Tunability and Noise Dependence in Differentiation Dynamics

Nonheritable cellular variability accelerates the evolutionary processes of cancer

Recent cancer studies emphasize that genetic and heritable epigenetic changes drive the evolutionary rate of cancer progression and drug resistance. We discuss the ways in which nonheritable aspects of cellular variability may significantly increase evolutionary rate. Nonheritable variability arises by stochastic fluctuations in cells and by physiological responses of cells to the environment. New approaches to drug design may be required to control nonheritable variability and the evolution of resistance to chemotherapy.

Mechanisms generating bistability and oscillations in microRNA-mediated motifs

The importance of post-transcriptional regulation by microRNAs (miRNAs) has recently been recognized in almost all cellular processes. When participating in cellular processes, miRNAs mainly mediate mRNA degradation or translational repression. Recently computational and experimental studies have identified an abundance of motifs involving miRNAs and transcriptional factors (TFs). The simplest motif is a two-node miRNA-mediated feedback loop (MFL) in which a TF regulates an miRNA and the TF itself is negatively regulated by the miRNA. In this paper we present a general computational model for the MFL based on biochemical regulations and explore its dynamics by using bifurcation analysis. Our results show that the MFL can behave either as switches or as oscillators, depending on the TF as a repressor or an activator. These functional features are consistent with the widespread appearance of miRNAs in fate decisions such as proliferation, differentiation, and apoptosis during development. We found that under the interplay of a TF and an miRNA, the MFL model can behave as switches for wide ranges of parameters even without cooperative binding of the TF. In addition, oscillations induced by the miRNA in the MFL model require neither an additional positive feedback loop, nor self-activation of the gene, nor cooperative binding of the TF, nor saturated degradation. Therefore, the MFL may provide a general network structure to induce bistability or oscillations. It is hoped that the results presented here will provide a new view on how gene expression is regulated by miRNAs and further guidance for experiments. Moreover, the insight gained from this study is also expected to provide a basis for the investigation of more complex networks assembled by simple building blocks.

Spo0A~P imposes a temporal gate for the bimodal expression of competence in Bacillus subtilis

ComK transcriptionally controls competence for the uptake of transforming DNA in Bacillus subtilis. Only 10%–20% of the cells in a clonal population are randomly selected for competence. Because ComK activates its own promoter, cells exceeding a threshold amount of ComK trigger a positive feedback loop, transitioning to the competence ON state. The transition rate increases to a maximum during the approach to stationary phase and then decreases, with most cells remaining OFF. The average basal rate of comK transcription increases transiently, defining a window of opportunity for transitions and accounting for the heterogeneity of competent populations. We show that as the concentration of the response regulator Spo0A∼P increases during the entry to stationary phase it first induces comK promoter activity and then represses it by direct binding. Spo0A∼P activates by antagonizing the repressor, Rok. This amplifies an inherent increase in basal level comK promoter activity that takes place during the approach to stationary phase and is a general feature of core promoters, serving to couple the probability of competence transitions to growth rate. Competence transitions are thus regulated by growth rate and temporally controlled by the complex mechanisms that govern the formation of Spo0A∼P. On the level of individual cells, the fate-determining noise for competence is intrinsic to the comK promoter. This overall mechanism has been stochastically simulated and shown to be plausible. Thus, a deterministic mechanism modulates an inherently stochastic process.

Populations of bacterial cells sometimes bifurcate into subpopulations with different patterns of gene expression. The soil bacterium B. subtilis becomes “competent” for the uptake of environmental DNA, thus acquiring new genetic information. About 15% of the cells are chosen for expression of the competence genes by stochastic fluctuations in the transcription of comK. When the concentration of ComK exceeds a critical threshold, it activates its own expression, a molecular switch is thrown, and competence ensues in that cell. Here we ask why all of the cells do not eventually throw the switch. We show that the basal level expression of comK increases and then decreases as nutrients are exhausted, so that the number of cells exceeding the ComK threshold rises and falls, opening and closing a window of opportunity for competence. Two factors responsible for this “uptick” in comK expression are: 1) a global increase in transcription as cell division slows, and 2) a continual rise in the concentration of the master regulatory protein Spo0A-P, which activates and then represses comK as it accumulates. The global increase transmits growth rate information and the increase in Spo0A∼P encodes multiple signals, including the nutritional, replication, and population density status of the culture.

Interplay between gene expression noise and regulatory network architecture

Complex regulatory networks orchestrate most cellular processes in biological systems. Genes in such networks are subject to expression noise, resulting in isogenic cell populations exhibiting cell-to-cell variation in protein levels. Increasing evidence suggests that cells have evolved regulatory strategies to limit, tolerate or amplify expression noise. In this context, fundamental questions arise: how can the architecture of gene regulatory networks generate, make use of or be constrained by expression noise? Here, we discuss the interplay between expression noise and gene regulatory network at different levels of organization, ranging from a single regulatory interaction to entire regulatory networks. We then consider how this interplay impacts a variety of phenomena, such as pathogenicity, disease, adaptation to changing environments, differential cell-fate outcome and incomplete or partial penetrance effects. Finally, we highlight recent technological developments that permit measurements at the single-cell level, and discuss directions for future research.

Asymmetric stochastic switching driven by intrinsic molecular noise

Low-copy-number molecules are involved in many functions in cells. The intrinsic fluctuations of these numbers can enable stochastic switching between multiple steady states, inducing phenotypic variability. Herein we present a theoretical and computational study based on Master Equations and Fokker-Planck and Langevin descriptions of stochastic switching for a genetic circuit of autoactivation. We show that in this circuit the intrinsic fluctuations arising from low-copy numbers, which are inherently state-dependent, drive asymmetric switching. These theoretical results are consistent with experimental data that have been reported for the bistable system of the gallactose signaling network in yeast. Our study unravels that intrinsic fluctuations, while not required to describe bistability, are fundamental to understand stochastic switching and the dynamical relative stability of multiple states.

Pulsed feedback defers cellular differentiation

In response to sudden environmental stress, B. subtilis cells can defer sporulation for multiple cell cycles using a pulsed positive feedback loop.

Environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well-characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable “polyphasic” positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a “timer” that operates over timescales much longer than a cell cycle.

How long should a cell wait to respond to an environmental change? While many pathways such as those affecting chemotaxis respond to environmental signals quickly, in other contexts a cell may want to defer its response until long after the signal's onset—sometimes waiting multiple cell cycles. How can cells create “timers” to regulate these long deferrals? We study this question in the bacterium Bacillus subtilis, which responds to stress by transforming into a dormant spore. We show that B. subtilis can defer sporulation for extended time periods by first undergoing multiple rounds of growth and proliferation, and only then sporulating. The timer for this deferral is a pulsed positive feedback loop, which ratchets up the concentration of the sporulation master-regulator Spo0A to a critical level over multiple cell cycles. Finally, using mathematical modeling, we illustrate how a novel dynamic feedback mechanism, “polyphasic positive feedback,” lets cells defer sporulation more robustly than with other circuit strategies. Developing techniques that can access pulsing and time-delay dynamics with higher time resolution will enable us to determine if this polyphasic strategy provides a general design principle for the regulation of multi-cell-cycle deferral times seen in other systems.

A dynamical model of oocyte maturation unveils precisely orchestrated meiotic decisions

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions.

In the life cycle of sexual organisms, a specialized cell division -meiosis- reduces the number of chromosomes in gametes or spores while fertilization or mating restores the original number. The essential feature that distinguishes meiosis from mitosis (the usual division) is the succession of two rounds of division following a single DNA replication, as well as the arrest at the second division in the case of oocyte maturation. The fact that meiosis and mitosis are similar but different raises several interesting questions: What is the meiosis-specific dynamics of cell-cycle regulators? Are there mechanisms which guarantee the occurence of two and only two rounds of division despite the presence of intrinsic and extrinsic noises ? The study of a model of the molecular network that underlies the meiotic maturation process in Xenopus oocytes provides unexpected answers to these questions. On the one hand, the modular organization of this network ensures separate controls of the first and second divisions. On the other hand, regulatory synergies ensure that these two stages are precisely and reliably sequenced during meiosis. We conclude that cells have evolved a sophisticated regulatory network to achieve a robust, albeit flexible, meiotic dynamics.

Stochastic modeling of cellular networks

Noise and stochasticity are fundamental to biology because they derive from the nature of biochemical reactions. Thermal motions of molecules translate into randomness in the sequence and timing of reactions, which leads to cell-cell variability ("noise") in mRNA and protein levels even in clonal populations of genetically identical cells. This is a quantitative phenotype that has important functional repercussions, including persistence in bacterial subpopulations challenged with antibiotics, and variability in the response of cancer cells to drugs. In this chapter, we present the modeling of such stochastic cellular behaviors using the formalism of jump Markov processes, whose probability distributions evolve according to the chemical master equation (CME). We also discuss the techniques used to solve the CME. These include kinetic Monte Carlo simulations techniques such as the stochastic simulation algorithm (SSA) and method closure techniques such as the linear noise approximation (LNA).

Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy

Quantitative single-cell time-lapse microscopy is a powerful method for analyzing gene circuit dynamics and heterogeneous cell behavior. We describe the application of this method to imaging bacteria by using an automated microscopy system. This protocol has been used to analyze sporulation and competence differentiation in Bacillus subtilis, and to quantify gene regulation and its fluctuations in individual Escherichia coli cells. The protocol involves seeding and growing bacteria on small agarose pads and imaging the resulting microcolonies. Images are then reviewed and analyzed using our laboratory's custom MATLAB analysis code, which segments and tracks cells in a frame-to-frame method. This process yields quantitative expression data on cell lineages, which can illustrate dynamic expression profiles and facilitate mathematical models of gene circuits. With fast-growing bacteria, such as E. coli or B. subtilis, image acquisition can be completed in 1 d, with an additional 1-2 d for progressing through the analysis procedure.

Equivalence of on-Lattice Stochastic Chemical Kinetics with the Well-Mixed Chemical Master Equation in the Limit of Fast Diffusion

Well-mixed and lattice-based descriptions of stochastic chemical kinetics have been extensively used in the literature. Realizations of the corresponding stochastic processes are obtained by the Gillespie stochastic simulation algorithm and lattice kinetic Monte Carlo algorithms, respectively. However, the two frameworks have remained disconnected. We show the equivalence of these frameworks whereby the stochastic lattice kinetics reduces to effective well-mixed kinetics in the limit of fast diffusion. In the latter, the lattice structure appears implicitly, as the lumped rate of bimolecular reactions depends on the number of neighbors of a site on the lattice. Moreover, we propose a mapping between the stochastic propensities and the deterministic rates of the well-mixed vessel and lattice dynamics that illustrates the hierarchy of models and the key parameters that enable model reduction.

Temporal competition between differentiation programs determines cell fate choice

Multipotent differentiation, where cells adopt one of several possible fates, occurs in diverse systems ranging from bacteria to mammals. This decision-making process is driven by multiple differentiation programs that operate simultaneously in the cell. How these programs interact to govern cell fate choice is poorly understood. To investigate this issue, we simultaneously measured activities of the competing sporulation and competence programs in single Bacillus subtilis cells. This approach revealed that these competing differentiation programs progress independently without cross-regulation before the decision point. Cells seem to arrive at a fate choice through differences in the relative timing between the two programs. To test this proposed dynamic mechanism, we altered the relative timing by engineering artificial cross-regulation between the sporulation and competence circuits. Results suggest a simple model that does not require a checkpoint or intricate cross-regulation before cellular decision-making. Rather, cell fate choice appears to be the outcome of a 'molecular race' between differentiation programs that compete in time, providing a simple dynamic mechanism for decision-making.

Reversible and noisy progression towards a commitment point enables adaptable and reliable cellular decision-making

Cells must make reliable decisions under fluctuating extracellular conditions, but also be flexible enough to adapt to such changes. How cells reconcile these seemingly contradictory requirements through the dynamics of cellular decision-making is poorly understood. To study this issue we quantitatively measured gene expression and protein localization in single cells of the model organism Bacillus subtilis during the progression to spore formation. We found that sporulation proceeded through noisy and reversible steps towards an irreversible, all-or-none commitment point. Specifically, we observed cell-autonomous and spontaneous bursts of gene expression and transient protein localization events during sporulation. Based on these measurements we developed mathematical population models to investigate how the degree of reversibility affects cellular decision-making. In particular, we evaluated the effect of reversibility on the 1) reliability in the progression to sporulation, and 2) adaptability under changing extracellular stress conditions. Results show that reversible progression allows cells to remain responsive to long-term environmental fluctuations. In contrast, the irreversible commitment point supports reliable execution of cell fate choice that is robust against short-term reductions in stress. This combination of opposite dynamic behaviors (reversible and irreversible) thus maximizes both adaptable and reliable decision-making over a broad range of changes in environmental conditions. These results suggest that decision-making systems might employ a general hybrid strategy to cope with unpredictably fluctuating environmental conditions.

Cells must continuously make decisions in response to changes in their environment. These decisions must be irreversible, to prevent cells from reverting back to unfit cellular states, but also be flexible, to allow cells to go back to their previous state upon environmental changes. Using single-cell time-lapse fluorescence microscopy, we show that these seemingly contradictory properties coexist in Bacillus subtilis cells during their progression to spore formation. We suggest, on the basis of a mathematical population model, that reversible progression towards the irreversible decision to sporulate optimizes respectively adaptability and reliability of decision-making over a broad range of changes in environmental conditions.

Stochastic pulse regulation in bacterial stress response

Gene regulatory circuits can use dynamic, and even stochastic, strategies to respond to environmental conditions. We examined activation of the general stress response mediated by the alternative sigma factor, σ(B), in individual Bacillus subtilis cells. We observed that energy stress activates σ(B) in discrete stochastic pulses, with increasing levels of stress leading to higher pulse frequencies. By perturbing and rewiring the endogenous system, we found that this behavior results from three key features of the σ(B) circuit: an ultrasensitive phosphorylation switch; stochasticity ("noise"), which activates that switch; and a mixed (positive and negative) transcriptional feedback, which can both amplify a pulse and switch it off. Together, these results show how prokaryotes encode signals using stochastic pulse frequency modulation through a compact regulatory architecture.

Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells

Cancer cells within individual tumors often exist in distinct phenotypic states that differ in functional attributes. While cancer cell populations typically display distinctive equilibria in the proportion of cells in various states, the mechanisms by which this occurs are poorly understood. Here, we study the dynamics of phenotypic proportions in human breast cancer cell lines. We show that subpopulations of cells purified for a given phenotypic state return towards equilibrium proportions over time. These observations can be explained by a Markov model in which cells transition stochastically between states. A prediction of this model is that, given certain conditions, any subpopulation of cells will return to equilibrium phenotypic proportions over time. A second prediction is that breast cancer stem-like cells arise de novo from non-stem-like cells. These findings contribute to our understanding of cancer heterogeneity and reveal how stochasticity in single-cell behaviors promotes phenotypic equilibrium in populations of cancer cells.

Dynamical consequences of bandpass feedback loops in a bacterial phosphorelay

Under conditions of nutrient limitation, Bacillus subtilis cells terminally differentiate into a dormant spore state. Progression to sporulation is controlled by a genetic circuit consisting of a phosphorelay embedded in multiple transcriptional feedback loops, which is used to activate the master regulator Spo0A by phosphorylation. These transcriptional regulatory interactions are "bandpass"-like, in the sense that activation occurs within a limited band of Spo0A∼P concentrations. Additionally, recent results show that the phosphorelay activation occurs in pulses, in a cell-cycle dependent fashion. However, the impact of these pulsed bandpass interactions on the circuit dynamics preceding sporulation remains unclear. In order to address this question, we measured key features of the bandpass interactions at the single-cell level and analyzed them in the context of a simple mathematical model. The model predicted the emergence of a delayed phase shift between the pulsing activity of the different sporulation genes, as well as the existence of a stable state, with elevated Spo0A activity but no sporulation, embedded within the dynamical structure of the system. To test the model, we used time-lapse fluorescence microscopy to measure dynamics of single cells initiating sporulation. We observed the delayed phase shift emerging during the progression to sporulation, while a re-engineering of the sporulation circuit revealed behavior resembling the predicted additional state. These results show that periodically-driven bandpass feedback loops can give rise to complex dynamics in the progression towards sporulation.

A regression model approach to enable cell morphology correction in high-throughput flow cytometry

Cells exposed to stimuli exhibit a wide range of responses ensuring phenotypic variability across the population. Such single cell behavior is often examined by flow cytometry; however, gating procedures typically employed to select a small subpopulation of cells with similar morphological characteristics make it difficult, even impossible, to quantitatively compare cells across a large variety of experimental conditions because these conditions can lead to profound morphological variations. To overcome these limitations, we developed a regression approach to correct for variability in fluorescence intensity due to differences in cell size and granularity without discarding any of the cells, which gating ipso facto does. This approach enables quantitative studies of cellular heterogeneity and transcriptional noise in high-throughput experiments involving thousands of samples. We used this approach to analyze a library of yeast knockout strains and reveal genes required for the population to establish a bimodal response to oleic acid induction. We identify a group of epigenetic regulators and nucleoporins that, by maintaining an 'unresponsive population,' may provide the population with the advantage of diversified bet hedging.

Collective oscillations in developing cells: insights from simple systems

From hormonal secretion to gene expression, multicellular dynamics are rich in oscillatory regulation. When organized in space and time, periodic cell-cell signaling can give rise to long-range coordination of gene expression and cell movement in tissues. Lack of synchrony of the oscillations on the other hand can serve as a source of initial divergence of cell fate in stem cells. How properties of individual cells can account for collective rhythmic behaviors at the tissue level remains elusive in most cases. Recently, studies in chemical reactions, synthetic gene circuits, yeast and social amoeba Dictyostelium have greatly enhanced our view of collective oscillations in cell populations. From these relatively simple systems, a unified view of how excitable and oscillatory regulations could be tuned and coupled to give rise to tissue-level oscillations is emerging. The review focuses on recent progress in cyclic adenosine monophosphate oscillations in Dictyostelium and highlights similarities and differences with other systems. We will see that the autonomy of single-cell level oscillations and different ways in which cells are coupled influence how group-level information can be encoded in collective oscillations.

Adaptation by stochastic switching of a monostable genetic circuit in Escherichia coli

Stochastic switching of a bistable genetic circuit represents a potential cost-saving strategy for adaptation to environmental challenges. This study reports that stochastic switching of a monostable circuit can be sufficient to mediate reversible adaptation in E. coli.

Stochastic switching of a monostable circuit mediated the adaptation of the engineered OSU12-hisC Escherichia coli strain to histidine starvation.

The population shift of OSU12-hisC was accompanied by growth recovery and was reversible upon histidine addition. This is the first report of adaptation mediated by stochastic switching based on a monostable structure.

Weak directionality in stochastic switching initiated the population shift and the fast growth of the occasionally appearing fit cells drove the later stages of adaptation.

Adaptation of OSU12-hisC was resulted from the enhanced expression of the structural genes within the native His operon, along with the transcriptional reorganization of a large number of genes.

The fundamental mechanisms underlying adaptations can be divided into responsive switching and stochastic switching (Kussell and Leibler, 2005). Responsive switching is generally considered as resulting from evolved regulatory units, such as operons and regulons, which enable immediate adaptation (Jacob and Monod, 1961). However, as cells are subject to a wide range of both genetic and environmental perturbations that damage the specificity or efficiency of regulatory systems (Carroll, 2005; Crombach and Hogeweg, 2008), the limited number of regulatory units that can evolve and remain functional may not be sufficient to completely protect cell populations from the danger of extinction. Whether and how cells are able to survive external perturbations, when the corresponding regulatory units are absent or have been genetically disrupted, is an open question of great importance.

Recent studies showed the stochastic switching provided cells a huge potential for sustenance under severe conditions via a so-called ‘bet-hedging' strategy. The experimental evidence was generally based on a bistable genetic structure that fixed stochastically appearing fit state thus limiting further random switching (Kussell and Leibler, 2005; Acar et al, 2008). In contrast to bistable gene expression, monostable gene expression is much more common (Newman et al, 2006) and does not rely on a specific complex genetic architecture. Since a monostable structure has no fixation effect, the fit cells that would appear stochastically tend to return to the original steady state (i.e., unfit state). To achieve a population shift from a maladaptive state (but stable) to an adaptive state (but unstable), a significant increase in fitness (i.e., growth rate) of the fit cells is necessary. Otherwise, the random switching will mask occasionally occurring adaptive transitions and lead to an unchanged population at the stable but maladaptive state. Whether adaptation can be achieved by stochastic switching based on a monostable structure is however an open issue.

To address this question, we applied an engineered E. coli strain, OSU12-hisC, carrying a foreign gene circuit encompassing a physiologically functional gene, hisC, replaced from its native chromosomal locus (Figure 1A). Consequently, hisC in OSU12-hisC is no longer responsive to the native regulation (His operon) that senses histidine depletion. Instead, the foreign gene circuit provided a monostable structure for hisC's stochastic switching. The green fluorescent protein (gfpuv5) was co-expressed with hisC for the quantitative evaluation of HisC in single cells. The upstream regulation of TetR, whose expression level was reported by the red fluorescent protein (dsred.T4), was introduced to achieve the inducible GFP (HisC) level. The full induction of TetR by IPTG was applied to avoid any possible upstream noise that caused by the abundance of endogenous LacI.

Microscopic observation revealed that the OSU12-hisC cells showed stronger green fluorescence after histidine depletion (Figure 1B), which suggested an increased expression level of hisC. Population analysis using flow cytometry showed that the distributions of both GFP concentration and GFP bias (GFP/RFP ratio) in OSU12-hisC shifted towards a higher level in histidine-free conditions (Figure 1C and D), whereas, the depletion caused only a slight change in distributions of OSU11, a control strain carrying both the same engineered genetic circuit and an intact His operon, including the hisC gene in its native context. Repeated experiments revealed that the increases in both GFP concentration (∼2.1 folds) and GFP bias (∼1.5 folds) due to histidine depletion were highly significant (P<0.005, N=6) in OSU12-hisC. In particular, the increased GFP bias strongly suggested that the change in gene expression occurred specifically in the rewired hisC (i.e., GFP) but not in all genes (e.g., RFP). Furthermore, both the growth recovery accompanied population shift and the stress relaxation triggered restoration were clearly observed. It strongly indicated that the adaptation was mediated by stochastic switching of hisC under the monostable control.

Analysis on microcolonies' formation (Figure 4A) showed stochastic behaviour and directionality in individual cells. Variation in cellular GFP level was clearly observed in individual cells. Stochastic switching of hisC was verified according to the random changes in GFP bias along with the cell division under histidine-rich conditions (Figure 4B). On the other hand, the microcolonies formed under the histidine-free conditions tended to the higher level of GFP bias were observed (Figure 4B). The directional tendency favoured the high GFP (HisC) level was evidently detected in the first 2 h after histidine depletion, which resulted in a population shift (Figure 4C). In contrast, the distributions of microcolonies grown in histidine-rich conditions kept steady, due to the randomized directions of stochastic switching (Figure 4C). Further analysis showed that the stochastic fluctuations in the initial state had an important role not only in fate decision (i.e., whether to grow) but also in the directionality of the stochastic switch.

Microarray analysis showed the adaptation of OSU12-hisC was resulted from the enhanced expression of the structural genes within the native His operon, along with the transcriptional reorganization of a large number of genes. In summary, in contrast to bistable structures, the monostable structure used here did not fix the phenotype but allowed the cells to decide where to go. Taken together, the findings suggest that bacteria do not necessarily need to evolve signalling mechanisms to control gene expression appropriately, even for essential genes.

Stochastic switching is considered as a cost-saving strategy for adaptation to environmental challenges. We show here that stochastic switching of a monostable circuit can mediate the adaptation of the engineered OSU12-hisC Escherichia coli strain to histidine starvation. In this strain, the hisC gene was deleted from the His operon and placed under the control of a monostable foreign promoter. In response to histidine depletion, the OSU12-hisC population shifted to a higher HisC expression level, which is beneficial under starving conditions but is not favoured by the monostable circuit. The population shift was accompanied by growth recovery and was reversible upon histidine addition. A weak directionality in stochastic switching of hisC was observed in growing microcolonies under histidine-free conditions. Directionality and fate decision were in part dependent on the initial cellular status. Finally, microarray analysis indicated that OSU12-hisC reorganized its transcriptome to reach the appropriate physiological state upon starvation. These findings suggest that bacteria do not necessarily need to evolve signalling mechanisms to control gene expression appropriately, even for essential genes.

An incoherent regulatory network architecture that orchestrates B cell diversification in response to antigen signaling

B cell receptor signaling controls the expression of IRF-4, a transcription factor required for B cell differentiation. This study shows that IRF-4 regulates divergent B cell fates via a ‘kinetic-control' mechanism that determines the duration of a transient developmental state.

The intensity of signaling through the B cell receptor controls the level of expression of IRF-4, a transcription factor required for B cell differentiation. The rate of IRF-4 production dictates the extent of antibody gene diversification that B cells undergo upon antigen encounter before differentiating into antibody-secreting plasma cells.

Computational modeling and experimental analyses substantiate a model, whereby IRF-4 regulates B cell fate trajectories via a ‘kinetic-control' mechanism.

Kinetic control is a process by which B cells pass through an obligate state of variable duration that sets the degree of cellular diversification prior to their terminal differentiation.

An incoherent regulatory network architecture, within which IRF-4 is embedded, is the basis for realization of kinetic control.

The generation of a diverse set of pathogen-specific antibodies, with differing affinities and effector functions, by B lymphocytes is essential for efficient protection from many microorganisms. Antibody gene diversification in B cells is mediated by two molecular processes termed class-switch recombination and somatic hypermutation (CSR/SHM) (F1A). The former enables the generation of antibodies with the same antigen-binding specificity, but different effector domains, whereas the latter results in a repertoire of antibodies with a range of affinities for a given antigen containing the same effector domain. CSR/SHM occurs in antigen-activated B cells before their terminal differentiation into plasma cells. The transcription factor IRF-4 is required for CSR/SHM as well as plasma-cell differentiation, with its highest levels of expression being necessary for the latter. IRF-4 acts in the context of a network of regulators that include Blimp-1, Pax5, Bach2 and Bcl-6 (F1B). Despite extensive characterization of these individual factors, how the network responds to sensing of antigen by the B cell antigen receptor (BCR, antibody molecule expressed on cell surface) to regulate the extent of antibody gene diversification and plasma-cell differentiation remains to be addressed.

To address this issue, we assemble a computational model. The model reveals two contrasting scenarios that can underlie B cell fate dynamics. In one case, the initial rate of IRF-4 production controls a binary cell fate choice that involves either going to the CSR/SHM state or to the plasma-cell state; the time spent in the CSR state is relatively insensitive to the initial rate of IRF-4 production (herein called ‘basic bistability'). In the other case, IRF-4 drives all cells through a transient CSR/SHM state, but the initial rate of IRF-4 production sets its duration (‘kinetic control'). Both scenarios predict that increasing the initial rate of IRF-4 production favors the generation of plasma cells at the expense of CSR/SHM, but they differ fundamentally with respect to the underlying gene expression patterns.

To distinguish between these two scenarios experimentally, we utilize two different genetic models. The first involves the B1-8i transgenic mouse whose B cells express a rearranged V187.2 VDJ Ig heavy chain gene segment that is specific for the hapten nitrophenol (NP). The second is a newly developed mouse model that allows exogenous control of IRF-4 expression in naive primary B cells using a tet-inducible allele. Using these models, we show that (i) BCR signal strength sets the initial rate of IRF-4 accumulation and (ii) the concentration of IRF-4 is sensed by an incoherent gene regulatory network architecture to regulate the extent of CSR/SHM prior to plasma-cell differentiation. Our results are consistent with the ‘kinetic-control model' in which the levels of BCR-induced IRF-4 expression control the duration of an obligate CSR/SHM state that enables B cell diversification before terminal differentiation into plasma cells. Evidence for the transient CSR/SHM state is corroborated by both patterns of gene expression and the presence of AID-dependent mutations in individual non-switched plasmablasts.

Our results provide a molecular framework for understanding how B cells balance the competing demands for Ig CSR and SHM with the secretion of antibodies during humoral immune responses. The key feature of the network architecture that allows IRF-4 to coordinate the two competing states of gene expression in a temporal manner is that it simultaneously but asymmetrically activates both sides of a bistable mutual repression circuit. Because the two effects of the primary regulator antagonize each other, we describe the circuit as being based on an ‘incoherent' regulatory motif. Other incoherent regulatory motifs in varied biological systems are also associated with the acquisition of transient cell states, and we consider how the kinetic-control mechanism proposed by us could more generally serve to translate developmental cues into elaborate morphogenetic patterns.

The B-lymphocyte lineage is a leading system for analyzing gene regulatory networks (GRNs) that orchestrate distinct cell fate transitions. Upon antigen recognition, B cells can diversify their immunoglobulin (Ig) repertoire via somatic hypermutation (SHM) and/or class switch DNA recombination (CSR) before differentiating into antibody-secreting plasma cells. We construct a mathematical model for a GRN underlying this developmental dynamic. The intensity of signaling through the Ig receptor is shown to control the bimodal expression of a pivotal transcription factor, IRF-4, which dictates B cell fate outcomes. Computational modeling coupled with experimental analysis supports a model of ‘kinetic control', in which B cell developmental trajectories pass through an obligate transient state of variable duration that promotes diversification of the antibody repertoire by SHM/CSR in direct response to antigens. More generally, this network motif could be used to translate a morphogen gradient into developmental inductive events of varying time, thereby enabling the specification of distinct cell fates.

Decision making in living cells: lessons from a simple system

The life cycle of bacteriophage lambda serves as a simplified paradigm for cell-fate decisions. The ongoing quantitative, high-resolution experimental investigation of this life cycle has produced some important insights in recent years. These insights have to do with the way cells choose among alternative fates, how they maintain long-term memory of their gene-expression state, and how they switch from one stable state to another. The recent studies have highlighted the role of spatiotemporal effects in cellular processes and the importance of distinguishing chemical stochasticity from possible hidden variables in cellular decision making.

Phenotype switching and mutations in random environments

Cell populations can benefit from changing phenotype when the environment changes. One mechanism for generating these changes is stochastic phenotype switching, whereby cells switch stochastically from one phenotype to another according to genetically determined rates, irrespective of the current environment, with the matching of phenotype to environment then determined by selective pressure. This mechanism has been observed in numerous contexts, but identifying the precise connection between switching rates and environmental changes remains an open problem. Here, we introduce a simple model to study the evolution of phenotype switching in a finite population subject to random environmental shocks. We compare the successes of competing genotypes with different switching rates, and analyze how the optimal switching rates depend on the frequency of environmental changes. If environmental changes are as rare as mutations, then the optimal switching rates mimic the rates of environmental changes. If the environment changes more frequently, then the optimal genotype either maximally favors fitness in the more common environment or has the maximal switching rate to each phenotype. Our results also explain why the optimum is relatively insensitive to fitness in each environment.

Effective theories for circuits and automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational, and social systems makes the problem harder. Here, we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.

Activated membrane patches guide chemotactic cell motility

Many eukaryotic cells are able to crawl on surfaces and guide their motility based on environmental cues. These cues are interpreted by signaling systems which couple to cell mechanics; indeed membrane protrusions in crawling cells are often accompanied by activated membrane patches, which are localized areas of increased concentration of one or more signaling components. To determine how these patches are related to cell motion, we examine the spatial localization of RasGTP in chemotaxing Dictyostelium discoideum cells under conditions where the vertical extent of the cell was restricted. Quantitative analyses of the data reveal a high degree of spatial correlation between patches of activated Ras and membrane protrusions. Based on these findings, we formulate a model for amoeboid cell motion that consists of two coupled modules. The first module utilizes a recently developed two-component reaction diffusion model that generates transient and localized areas of elevated concentration of one of the components along the membrane. The activated patches determine the location of membrane protrusions (and overall cell motion) that are computed in the second module, which also takes into account the cortical tension and the availability of protrusion resources. We show that our model is able to produce realistic amoeboid-like motion and that our numerical results are consistent with experimentally observed pseudopod dynamics. Specifically, we show that the commonly observed splitting of pseudopods can result directly from the dynamics of the signaling patches.

Different types of cells are able to directionally migrate, responding to spatially-varying environmental cues. To do so, the cell needs to sense its environment, decide on the correct direction, and finally implement the needed mechanical changes in order to actually move. In this work we study the relation between the sensing-signaling system and the mechanical motion. We first show that membrane protrusions which drive the overall translocation occur exactly at the same locations at which membrane-bound signal-transduction effectors accumulate. These high concentration areas, also termed “patches”, exhibit interesting dynamics of disappearing and reappearing. Based on these findings, we develop a mathematical-computational model, in which membrane protrusions are driven by these membrane “patches”. These protrusions are then coupled to other cellular forces and the overall model predicts motion and its relationship to shape changes. Using our approach, we show that several observed features of cellular motility, for example the splitting of the cell tip, can be explained by the upstream signaling dynamics.

The importance of structured noise in the generation of self-organizing tissue patterns through contact-mediated cell-cell signalling

Lateral inhibition provides the basis for a self-organizing patterning system in which distinct cell states emerge from an otherwise uniform field of cells. The development of the microchaete bristle pattern on the notum of the fruitfly, Drosophila melanogaster, has long served as a popular model of this process. We recently showed that this bristle pattern depends upon a population of dynamic, basal actin-based filopodia, which span multiple cell diameters. These protrusions establish transient signalling contacts between non-neighbouring cells, generating a type of structured noise that helps to yield a well-ordered and spaced pattern of bristles. Here, we develop a general model of protrusion-based patterning to analyse the role of noise in this process. Using a simple asynchronous cellular automata rule-based model we show that this type of structured noise drives the gradual refinement of lateral inhibition-mediated patterning, as the system moves towards a stable configuration in which cells expressing the inhibitory signal are near-optimally packed. By analysing the effects of introducing thresholds required for signal detection in this model of lateral inhibition, our study shows how filopodia-mediated cell-cell communication can generate complex patterns of spots and stripes, which, in the presence of signalling noise, align themselves across a patterning field. Thus, intermittent protrusion-based signalling has the potential to yield robust self-organizing tissue-wide patterns without the need to invoke diffusion-mediated signalling.

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.

MecA dampens transitions to spore, biofilm exopolysaccharide and competence expression by two different mechanisms

The adapter protein MecA targets the transcription factor ComK for degradation by the ClpC/ClpP proteolytic complex, thereby negatively regulating competence in Bacillus subtilis. Here we show that MecA also decreases the frequency of transitions to the sporulation pathway as well as the expression of eps, which encodes synthesis of the biofilm matrix exopolysaccharide. We present genetic and biophysical evidence that MecA downregulates eps expression and spore formation by directly interacting with Spo0A. MecA does not target Spo0A for degradation, and apparently does not prevent the phosphorylation of Spo0A. We propose that it inhibits the transcriptional activity of Spo0A∼P by direct binding. Thus, in its interaction with Spo0A, MecA differs from its role in the regulation of competence where it targets ComK for degradation. MecA acts as a general buffering protein for development, acting by two distinct mechanisms to regulate inappropriate transitions to energy-intensive pathways.

Fluctuations in spo0A transcription control rare developmental transitions in Bacillus subtilis

Phosphorylated Spo0A is a master regulator of stationary phase development in the model bacterium Bacillus subtilis, controlling the formation of spores, biofilms, and cells competent for transformation. We have monitored the rate of transcription of the spo0A gene during growth in sporulation medium using promoter fusions to firefly luciferase. This rate increases sharply during transient diauxie-like pauses in growth rate and then declines as growth resumes. In contrast, the rate of transcription of an rRNA gene decreases and increases in parallel with the growth rate, as expected for stable RNA synthesis. The growth pause-dependent bursts of spo0A transcription, which reflect the activity of the spo0A vegetative promoter, are largely independent of all known regulators of spo0A transcription. Evidence is offered in support of a “passive regulation” model in which RNA polymerase stops transcribing rRNA genes during growth pauses, thus becoming available for the transcription of spo0A. We show that the bursts are followed by the production of phosphorylated Spo0A, and we propose that they represent initial responses to stress that bring the average cell closer to the thresholds for transition to bimodally expressed developmental responses. Measurement of the numbers of cells expressing a competence marker before and after the bursts supports this hypothesis. In the absence of ppGpp, the increase in spo0A transcription that accompanies the entrance to stationary phase is delayed and sporulation is markedly diminished. In spite of this, our data contradicts the hypothesis that sporulation is initiated when a ppGpp-induced depression of the GTP pool relieves repression by CodY. We suggest that, while the programmed induction of sporulation that occurs in stationary phase is apparently provoked by increased flux through the phosphorelay, bet-hedging stochastic transitions to at least competence are induced by bursts in transcription.

A hallmark of the intensively studied model organism Bacillus subtilis is its ability to enter developmental pathways: forming spores, acquiring the ability to take up environmental DNA, and the formation of biofilms. These pathways are dependent on the transcription factor Spo0A. All are expressed heterogeneously across populations of cells and exhibit characteristic rates of transition to the developmental pathways depending on environmental signals. We have monitored the rate of transcription of spo0A during growth and have detected unexpected fluctuations that correlate with pauses in the growth rate. We present support for a model in which the release of RNA polymerase from transcription of ribosomal RNA genes during the growth pauses permits increased transcription of spo0A. We show that these bursts in transcription increase the still-rare probability of transition to the transformable state, suggesting that this transition is limited by the transcription rate of spo0A. In contrast, it has been shown that the programmed development of spores is determined by the rate of phosphorylation of Spo0A. Thus there are two modes of developmental transition. We also show that a popular hypothesis for the initiation of spore formation by release of repression by the protein CodY is incorrect.

Gene circuit designs for noisy excitable dynamics

Certain cellular processes take the form of activity pulses that can be interpreted in terms of noise-driven excitable dynamics. Here we present an overview of different gene circuit architectures that exhibit excitable pulses of protein expression, when subject to molecular noise. Different types of excitable dynamics can occur depending on the bifurcation structure leading to the specific excitable phase-space topology. The bifurcation structure is not, however, linked to a particular circuit architecture. Thus a given gene circuit design can sustain different classes of excitable dynamics depending on the system parameters.

Cellular decision making and biological noise: from microbes to mammals

Cellular decision making is the process whereby cells assume different, functionally important and heritable fates without an associated genetic or environmental difference. Such stochastic cell fate decisions generate nongenetic cellular diversity, which may be critical for metazoan development as well as optimized microbial resource utilization and survival in a fluctuating, frequently stressful environment. Here, we review several examples of cellular decision making from viruses, bacteria, yeast, lower metazoans, and mammals, highlighting the role of regulatory network structure and molecular noise. We propose that cellular decision making is one of at least three key processes underlying development at various scales of biological organization.

How mathematical modelling elucidates signalling in Bacillus subtilis

Appropriate stimulus perception, signal processing and transduction ensure optimal adaptation of bacteria to environmental challenges. In the Gram-positive model bacterium Bacillus subtilis signalling networks and molecular interactions therein are well-studied, making this species a suitable candidate for the application of mathematical modelling. Here, we review systems biology approaches, focusing on chemotaxis, sporulation, σ(B) -dependent general stress response and competence. Processes like chemotaxis and Z-ring assembly depend critically on the subcellular localization of proteins. Environmental response strategies, including sporulation and competence, are characterized by phenotypic heterogeneity in isogenic cultures. The examples of mathematical modelling also include investigations that have demonstrated how operon structure and signalling dynamics are intricately interwoven to establish optimal responses. Our review illustrates that these interdisciplinary approaches offer new insights into the response of B. subtilis to environmental challenges. These case studies reveal modelling as a tool to increase the understanding of complex systems, to help formulating hypotheses and to guide the design of more directed experiments that test predictions.

High-throughput tracking of single yeast cells in a microfluidic imaging matrix

Time-lapse live cell imaging is a powerful tool for studying signaling network dynamics and complexity and is uniquely suited to single cell studies of response dynamics, noise, and heritable differences. Although conventional imaging formats have the temporal and spatial resolution needed for such studies, they do not provide the simultaneous advantages of cell tracking, experimental throughput, and precise chemical control. This is particularly problematic for system-level studies using non-adherent model organisms such as yeast, where the motion of cells complicates tracking and where large-scale analysis under a variety of genetic and chemical perturbations is desired. We present here a high-throughput microfluidic imaging system capable of tracking single cells over multiple generations in 128 simultaneous experiments with programmable and precise chemical control. High-resolution imaging and robust cell tracking are achieved through immobilization of yeast cells using a combination of mechanical clamping and polymerization in an agarose gel. The channel and valve architecture of our device allows for the formation of a matrix of 128 integrated agarose gel pads, each allowing for an independent imaging experiment with fully programmable medium exchange via diffusion. We demonstrate our system in the combinatorial and quantitative analysis of the yeast pheromone signaling response across 8 genotypes and 16 conditions, and show that lineage-dependent effects contribute to observed variability at stimulation conditions near the critical threshold for cellular decision making.

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Counterintuitive dynamics of various biological phenomena occur when composite system dynamics differ qualitatively from that of their component systems. Such composite systems typically arise when modelling situations with time-varying biotic or abiotic conditions, and examples range from metapopulation dynamics to population genetic models. These biological, and related physical, phenomena can often be modelled as simple financial games, wherein capital is gained and lost through gambling. Such games have been developed and used as heuristic devices to elucidate the processes at work in generating seemingly paradoxical outcomes across a spectrum of disciplines, albeit in a field-specific, ad hoc fashion. Here, we propose that studying these simple games can provide a much deeper understanding of the fundamental principles governing paradoxical behaviours in models from a diversity of topics in evolution and ecology in which fluctuating environmental effects, whether deterministic or stochastic, are an essential aspect of the phenomenon of interest. Of particular note, we find that, for a broad class of models, the ecological concept of equilibrium reactivity provides an intuitive necessary condition that must be satisfied in order for environmental variability to promote population persistence. We contend that further investigations along these lines promise to unify aspects of the study of a range of topics, bringing questions from genetics, species persistence and coexistence and the evolution of bet-hedging strategies, under a common theoretical purview.

Programmable ligand detection system in plants through a synthetic signal transduction pathway

Background

There is an unmet need to monitor human and natural environments for substances that are intentionally or unintentionally introduced. A long-sought goal is to adapt plants to sense and respond to specific substances for use as environmental monitors. Computationally re-designed periplasmic binding proteins (PBPs) provide a means to design highly sensitive and specific ligand sensing capabilities in receptors. Input from these proteins can be linked to gene expression through histidine kinase (HK) mediated signaling. Components of HK signaling systems are evolutionarily conserved between bacteria and plants. We previously reported that in response to cytokinin-mediated HK activation in plants, the bacterial response regulator PhoB translocates to the nucleus and activates transcription. Also, we previously described a plant visual response system, the de-greening circuit, a threshold sensitive reporter system that produces a visual response which is remotely detectable and quantifiable.

Methodology/Principal Findings

We describe assembly and function of a complete synthetic signal transduction pathway in plants that links input from computationally re-designed PBPs to a visual response. To sense extracellular ligands, we targeted the computational re-designed PBPs to the apoplast. PBPs bind the ligand and develop affinity for the extracellular domain of a chemotactic protein, Trg. We experimentally developed Trg fusions proteins, which bind the ligand-PBP complex, and activate intracellular PhoR, the HK cognate of PhoB. We then adapted Trg-PhoR fusions for function in plants showing that in the presence of an external ligand PhoB translocates to the nucleus and activates transcription. We linked this input to the de-greening circuit creating a detector plant.

Conclusions/Significance

Our system is modular and PBPs can theoretically be designed to bind most small molecules. Hence our system, with improvements, may allow plants to serve as a simple and inexpensive means to monitor human surroundings for substances such as pollutants, explosives, or chemical agents.

Origins of regulated cell-to-cell variability

Single-cell measurements and lineage-tracing experiments are revealing that phenotypic cell-to-cell variability is often the result of deterministic processes, despite the existence of intrinsic noise in molecular networks. In most cases, this determinism represents largely uncharacterized molecular regulatory mechanisms, which places the study of cell-to-cell variability in the realm of molecular cell biology. Further research in the field will be important to advance quantitative cell biology because it will provide new insights into the mechanisms by which cells coordinate their intracellular activities in the spatiotemporal context of the multicellular environment.

Mathematical modelling of the sporulation-initiation network in Bacillus subtilis revealing the dual role of the putative quorum-sensing signal molecule PhrA

Bacillus subtilis cells may opt to forgo normal cell division and instead form spores if subjected to certain environmental stimuli, for example nutrient deficiency or extreme temperature. The resulting spores are extremely resilient and can survive for extensive periods of time, importantly under particularly harsh conditions such as those mentioned above. The sporulation process is highly time and energy consuming and essentially irreversible. The bacteria must therefore ensure that this route is only undertaken under appropriate circumstances. The gene regulation network governing sporulation initiation accordingly incorporates a variety of signals and is of significant complexity. We present a model of this network that includes four of these signals: nutrient levels, DNA damage, the products of the competence genes, and cell population size. Our results can be summarised as follows: (i) the model displays the correct phenotypic behaviour in response to these signals; (ii) a basal level of sda expression may prevent sporulation in the presence of nutrients; (iii) sporulation is more likely to occur in a large population of cells than in a small one; (iv) finally, and of most interest, PhrA can act simultaneously as a quorum-sensing signal and as a timing mechanism, delaying sporulation when the cell has damaged DNA, possibly thereby allowing the cell time to repair its DNA before forming a spore.

Origins of stochastic intracellular processes and consequences for cell-to-cell variability and cellular survival strategies

Quantitative analyses of the dynamics of single cells have become a powerful approach in current cell biology. They give us an unprecedented opportunity to study dynamics of molecular networks at a high level of accuracy in living single cells. Genetically identical cells, growing in the same environment and sharing the same growth history, can differ remarkably in their molecular makeup and physiological behaviors. The origins of this cell-to-cell variability have in many cases been traced to the inevitable stochasticity of molecular reactions. Those mechanisms can cause isogenic cells to have qualitatively different life histories. Many studies indicate that molecular noise can be exploited by cell populations to enhance survival prospects in uncertain environments. On the other hand, cells have evolved noise-suppression mechanisms to cope with the inevitable noise in their functioning so as to reduce the hazardous effects of noise. In this chapter, we discuss key experiments, theoretical results, and physiological consequences of molecular stochasticity to introduce this exciting field to a broader community of (systems) biologists.

Approaching the molecular origins of collective dynamics in oscillating cell populations

From flocking birds, to organ generation, to swarming bacterial colonies, biological systems often exhibit collective behaviors. Here, we review recent advances in our understanding of collective dynamics in cell populations. We argue that understanding population-level oscillations requires examining the system under consideration at three different levels of complexity: at the level of isolated cells, homogenous populations, and spatially structured populations. We discuss the experimental and theoretical challenges this poses and highlight how new experimental techniques, when combined with conceptual tools adapted from physics, may help us overcome these challenges.

Emergence of noise-induced oscillations in the central circadian pacemaker

Bmal1 is an essential transcriptional activator within the mammalian circadian clock. We report here that the suprachiasmatic nucleus (SCN) of Bmal1-null mutant mice, unexpectedly, generates stochastic oscillations with periods that overlap the circadian range. Dissociated SCN neurons expressed fluctuating levels of PER2 detected by bioluminescence imaging but could not generate circadian oscillations intrinsically. Inhibition of intercellular communication or cyclic-AMP signaling in SCN slices, which provide a positive feed-forward signal to drive the intracellular negative feedback loop, abolished the stochastic oscillations. Propagation of this feed-forward signal between SCN neurons then promotes quasi-circadian oscillations that arise as an emergent property of the SCN network. Experimental analysis and mathematical modeling argue that both intercellular coupling and molecular noise are required for the stochastic rhythms, providing a novel biological example of noise-induced oscillations. The emergence of stochastic circadian oscillations from the SCN network in the absence of cell-autonomous circadian oscillatory function highlights a previously unrecognized level of circadian organization.

Functional roles for noise in genetic circuits

The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or 'noise', in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward.

Early Career Research Award Lecture. Structure, evolution and dynamics of transcriptional regulatory networks

The availability of entire genome sequences and the wealth of literature on gene regulation have enabled researchers to model an organism's transcriptional regulation system in the form of a network. In such a network, TFs (transcription factors) and TGs (target genes) are represented as nodes and regulatory interactions between TFs and TGs are represented as directed links. In the present review, I address the following topics pertaining to transcriptional regulatory networks. (i) Structure and organization: first, I introduce the concept of networks and discuss our understanding of the structure and organization of transcriptional networks. (ii) Evolution: I then describe the different mechanisms and forces that influence network evolution and shape network structure. (iii) Dynamics: I discuss studies that have integrated information on dynamics such as mRNA abundance or half-life, with data on transcriptional network in order to elucidate general principles of regulatory network dynamics. In particular, I discuss how cell-to-cell variability in the expression level of TFs could permit differential utilization of the same underlying network by distinct members of a genetically identical cell population. Finally, I conclude by discussing open questions for future research and highlighting the implications for evolution, development, disease and applications such as genetic engineering.

Patterns of basal signaling heterogeneity can distinguish cellular populations with different drug sensitivities

Phenotypic heterogeneity has been widely observed in cellular populations. However, the extent to which heterogeneity contains biologically or clinically important information is not well understood. Here, we investigated whether patterns of basal signaling heterogeneity, in untreated cancer cell populations, could distinguish cellular populations with different drug sensitivities. We modeled cellular heterogeneity as a mixture of stereotyped signaling states, identified based on colocalization patterns of activated signaling molecules from microscopy images. We found that patterns of heterogeneity could be used to separate the most sensitive and resistant populations to paclitaxel within a set of H460 lung cancer clones and within the NCI-60 panel of cancer cell lines, but not for a set of less heterogeneous, immortalized noncancer human bronchial epithelial cell (HBEC) clones. Our results suggest that patterns of signaling heterogeneity, characterized as ensembles of a small number of distinct phenotypic states, can reveal functional differences among cellular populations.

Optimal strategy for competence differentiation in bacteria

A phylogenetically diverse subset of bacterial species are naturally competent for transformation by DNA. Transformation entails recombination of genes between different lineages, representing a form of bacterial sex that increases standing genetic variation. We first assess whether homologous recombination by transformation is favored by evolution. Using stochastic population genetic computer simulations in which beneficial and deleterious mutations occur at many loci throughout the whole genome, we find that transformation can increase both the rate of adaptive evolution and the equilibrium level of fitness. Secondly, motivated by experimental observations of Bacillus subtilis, we assume that competence additionally entails a weak persister phenotype, i.e., the rates of birth and death are reduced for these cells. Consequently, persisters evolve more slowly than non-persisters. We show via simulation that strains which stochastically switch into and out of the competent phenotype are evolutionarily favored over strains that express only a single phenotype. Our model's simplicity enables us to derive and numerically solve a system of finite- deterministic equations that describe the evolutionary dynamics. The observed tradeoff between the benefit of recombination and the cost of persistence may explain the previously mysterious observation that only a fractional subpopulation of B. subtilis cells express competence. More generally, this work demonstrates that population genetic forces can give rise to phenotypic diversity even in an unchanging and homogeneous environment.

In certain environmental conditions, populations of the bacterium Bacillus subtilis split into two physiologically distinct phenotypes. While some cells continue to grow and divide, a minority become “competent” for transformation by extracellular DNA. This differentiation process is driven not by genetic differences among cells, but rather by noisy molecular fluctuations. Although the differentiation process is thought to confer an evolutionary advantage, the basis of this advantage has remained elusive until now. We developed computer simulations of the joint dynamics of cell replication, cell death, mutation, and the quasi-sexual transfer of genes through the extracellular DNA pool. We find that bacterial sex via DNA transformation is indirectly favored by evolutionary forces. However, the indirect benefits of sex are counterbalanced by a reduced replication rate. We find that these opposing forces present an evolutionary dilemma best solved when the population splits into the two experimentally observed phenotypes. These results present a mechanism that selects for phenotypic diversity, even in an unchanging and homogeneous environment.

Interplay between intrinsic noise and the stochasticity of the cell cycle in bacterial colonies

Herein we report on the effects that different stochastic contributions induce in bacterial colonies in terms of protein concentration and production. In particular, we consider for what we believe to be the first time cell-to-cell diversity due to the unavoidable randomness of the cell-cycle duration and its interplay with other noise sources. To that end, we model a recent experimental setup that implements a protein dilution protocol by means of division events to characterize the gene regulatory function at the single cell level. This approach allows us to investigate the effect of different stochastic terms upon the total randomness experimentally reported for the gene regulatory function. In addition, we show that the interplay between intrinsic fluctuations and the stochasticity of the cell-cycle duration leads to different constructive roles. On the one hand, we show that there is an optimal value of protein concentration (alternatively an optimal value of the cell cycle phase) such that the noise in protein concentration attains a minimum. On the other hand, we reveal that there is an optimal value of the stochasticity of the cell cycle duration such that the coherence of the protein production with respect to the colony average production is maximized. The latter can be considered as a novel example of the recently reported phenomenon of diversity induced resonance.

Distribution and regulation of stochasticity and plasticity in Saccharomyces cerevisiae

Stochasticity is an inherent feature of complex systems with nanoscale structure. In such systems information is represented by small collections of elements (e.g., a few electrons on a quantum dot), and small variations in the populations of these elements may lead to big uncertainties in the information. Unfortunately, little is known about how to work within this inherently noisy environment to design robust functionality into complex nanoscale systems. Here, we look to the biological cell as an intriguing model system where evolution has mediated the trade-offs between fluctuations and function, and in particular we look at the relationships and trade-offs between stochastic and deterministic responses in the gene expression of budding yeast (Saccharomyces cerevisiae). We find gene regulatory arrangements that control the stochastic and deterministic components of expression, and show that genes that have evolved to respond to stimuli (stress) in the most strongly deterministic way exhibit the most noise in the absence of the stimuli. We show that this relationship is consistent with a bursty two-state model of gene expression, and demonstrate that this regulatory motif generates the most uncertainty in gene expression when there is the greatest uncertainty in the optimal level of gene expression.

Calcium signals driven by single channel noise

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular Ca2+ oscillations are sequences of random spikes despite the involvement of many molecules in spike generation. This randomness arises from the stochastic state transitions of individual Ca2+ release channels and does not average out due to the existence of steep concentration gradients. The system is hierarchical due to the structural levels channel--channel cluster--cell and a corresponding strength of coupling. Concentration gradients introduce microdomains which couple channels of a cluster strongly. But they couple clusters only weakly; too weak to establish deterministic behavior on cell level. Here, we present a multi-scale modelling concept for stochastic hierarchical systems. It simulates active molecules individually as Markov chains and their coupling by deterministic diffusion. Thus, we are able to follow the consequences of random single molecule state changes up to the signal on cell level. To demonstrate the potential of the method, we simulate a variety of experiments. Comparisons of simulated and experimental data of spontaneous oscillations in astrocytes emphasize the role of spatial concentration gradients in Ca2+ signalling. Analysis of extensive simulations indicates that frequency encoding described by the relation between average and standard deviation of interspike intervals is surprisingly robust. This robustness is a property of the random spiking mechanism and not a result of control.