Contributions of low molecule number and chromosomal positioning to stochastic gene expression

Coupling and coordination in gene expression processes: a systems biology view

Genome-scale analyses have allowed us to progress beyond studying gene expression at the level of individual components of a given process by providing global information about functional connections between genes, mRNAs and their regulatory proteins. Such analyses have greatly increased our understanding of the interplay between different events in gene regulation and have highlighted previously unappreciated functional connections, including coupling between nuclear and cytoplasmic processes. Genome-wide approaches have also revealed extensive coordination within regulatory levels, such as the organization of transcription factors into regulatory motifs. Overall, these studies enhance our understanding of how the many components of the eukaryotic cell function as a system to allow both coordination and versatility in gene expression.

Heritable stochastic switching revealed by single-cell genealogy

The partitioning and subsequent inheritance of cellular factors like proteins and RNAs is a ubiquitous feature of cell division. However, direct quantitative measures of how such nongenetic inheritance affects subsequent changes in gene expression have been lacking. We tracked families of the yeast Saccharomyces cerevisiae as they switch between two semi-stable epigenetic states. We found that long after two cells have divided, they continued to switch in a synchronized manner, whereas individual cells have exponentially distributed switching times. By comparing these results to a Poisson process, we show that the time evolution of an epigenetic state depends initially on inherited factors, with stochastic processes requiring several generations to decorrelate closely related cells. Finally, a simple stochastic model demonstrates that a single fluctuating regulatory protein that is synthesized in large bursts can explain the bulk of our results.

When cells divide, not only DNA but an entire pattern of gene expression can be passed from mother to daughter cell. Once cell division is complete, random processes cause this pattern to change, with closely related cells growing less similar over time. We measured inheritance of a dynamic gene-expression state in single yeast cells. We used an engineered network where individual cells switch between two semi-stable states (ON and OFF), even in a constant environment. Several generations after cells have physically separated, many pairs of closely related cells switch in near synchrony. We quantified this effect by measuring how likely a mother cell is to have switched given that the daughter cell has already switched. This yields a conditional probability distribution that is very different from the exponential one found in the entire population of switching cells. We measured the extent to which this correlation between switching cells persists by comparing our results with a model Poisson process. Together, these findings demonstrate the inheritance of a dynamic gene expression state whose post-division changes include both random factors arising from noise as well as correlated factors that originate in two related cells' shared history. Finally, we constructed a model that demonstrates that our major findings can be explained by burst-like fluctuations in the levels of a single regulatory protein.

When cells divide, each daughter cell inherits a share of the contents of the mother. If the contents include a regulatory system with a feedback loop, sister cells switch states in synchrony.

Master equation simulation analysis of immunostained Bicoid morphogen gradient

Background

The concentration gradient of Bicoid protein which determines the developmental pathways in early Drosophila embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.

Results

We compared quantitative observations of Bicoid levels in immunostained Drosophila embryos with a spatially extended Master Equation model which represents diffusion, decay, and anterior synthesis. We show that the intrinsic noise of an autonomous reaction-diffusion gradient is Poisson distributed. We demonstrate how experimental noise can be identified in the logarithm domain from single embryo analysis, and then separated from intrinsic noise in the normalized variance domain of an ensemble statistical analysis. We show how measurement sensitivity affects our observations, and how small amounts of rescaling noise can perturb the noise strength (Fano factor) observed. We demonstrate that the biological noise level in data can serve as a physical constraint for restricting the model's parameter space, and for predicting the Bicoid molecular number and variation range. An estimate based on a low variance ensemble of embryos suggests that the steady-state Bicoid molecular number in a nucleus should be larger than 300 in the middle of the embryo, and hence the gradient should extend to the posterior end of the embryo, beyond the previously assumed background limit. We exhibit the predicted molecular number gradient together with measurement effects, and make a comparison between conditions of higher and lower variance respectively.

Conclusion

Quantitative comparison of Master Equation simulations with immunostained data enabled us to determine narrow ranges for key biophysical parameters, which for this system can be independently validated. Intrinsic noise is clearly detectable as well, although the staining process introduces certain limits in resolution.

Contribution of IL-12R mediated feedback loop to Th1 cell differentiation

T helper 1 (Th1) cell fate is induced by overlapping signaling pathways, whose kinetic principles and regulatory motifs are largely unknown. We identified a simple positive feedback loop in the STAT4 signaling pathway, whereby activation by IL-12 leads to the increased expression in IL-12 receptor. A computational analysis shows that this feedback loop synergizes with the one mediated by the IFN-gamma secreted by differentiating cells, when the induction of Th1 cell fate is weak. Positive feedback loops are often utilized to enhance phenotypic differentiation. This effect was confirmed by experiments showing that stochastic fluctuations in the expression of IL-12 receptor gene were amplified, leading to two discrete levels of expression in a cell population.

Analysis of fluctuation in protein abundance without promoter regulation based on Escherichia coli continuous culture

Fluctuation of protein abundance of isogenic Escherichia coli cells in uniform environment was studied. Based on a continuous culture system, which provides homogeneous culture environment, we investigated the fluctuation in GlnA protein abundance regardless of known glnALG promoter regulation. As results by flow cytometer, we found that the GlnA protein abundance in the cells exhibit a large fluctuation, even though GlnA protein is an essential factor for cell growth and the environment is homogeneous. Furthermore, among several steady states, transient processes of such heterogeneous cell population were investigated, by changing the environmental conditions. The results showed that the expression of GlnA protein can be controlled, depending on its necessity, even though there is no known regulatory machinery. These results may provide a clue to understand the nature of regulation of protein expression dynamics with the stochastic fluctuation.

An engineered L-arginine sensor of Chlamydia pneumoniae enables arginine-adjustable transcription control in mammalian cells and mice

For optimal compatibility with biopharmaceutical manufacturing and gene therapy, heterologous transgene control systems must be responsive to side-effect-free physiologic inducer molecules. The arginine-inducible interaction of the ArgR repressor and the ArgR-specific ARG box, which synchronize arginine import and synthesis in the intracellular human pathogen Chlamydia pneumoniae, was engineered for arginine-regulated transgene (ART) expression in mammalian cells. A synthetic arginine-responsive transactivator (ARG), consisting of ArgR fused to the Herpes simplex VP16 transactivation domain, reversibly adjusted transgene transcription of chimeric ARG box-containing mammalian minimal promoters (P_ART) in an arginine-inducible manner. Arginine-controlled transgene expression showed rapid induction kinetics in a variety of mammalian cell lines and was adjustable and reversible at concentrations which were compatible with host cell physiology. ART variants containing different transactivation domains, variable spacing between ARG box and minimal promoter and several tandem ARG boxes showed modified regulation performance tailored for specific expression scenarios and cell types. Mice implanted with microencapsulated cells engineered for ART-inducible expression of the human placental secreted alkaline phosphatase (SEAP) exhibited adjustable serum phosphatase levels after treatment with different arginine doses. Using a physiologic inducer, such as the amino acid l-arginine, to control heterologous transgenes in a seamless manner which is devoid of noticeable metabolic interference will foster novel opportunities for precise expression dosing in future gene therapy scenarios as well as the manufacturing of difficult-to-produce protein pharmaceuticals.

Evolution of chromosome organization driven by selection for reduced gene expression noise

The distribution of genes on eukaryotic chromosomes is nonrandom, but the reasons behind this are not well understood. The commonly observed clustering of essential genes is a case in point. Here we model and test a new hypothesis. Essential proteins are unusual in that random fluctuations in abundance (noise) can be highly deleterious. We hypothesize that persistently open chromatin domains are sinks for essential genes, as they enable reduced noise by avoidance of transcriptional bursting associated with chromatin remodeling. Simulation of the model captures clustering and correctly predicts that (i) essential gene clusters are associated with low nucleosome occupancy (ii) noise-sensitive nonessential genes cluster with essential genes (iii) nonessential genes of similar knockout fitness are physically linked (iv) genes in domains rich in essential genes have low noise (v) essential genes are rare subtelomerically and (vi) essential gene clusters are preferentially conserved. We conclude that different noise characteristics of different genomic domains favors nonrandom gene positioning. This has implications for gene therapy and understanding transgenic phenotypes.

Epigenetic gene expression noise and phenotypic diversification of clonal cell populations

Spontaneous emergence of phenotypic heterogeneity in cultures of genetically identical cells is a frequently observed phenomenon that provides a simple in vitro experimental system to model the problems of in vivo differentiation. In the present study, we have investigated whether stochastic variation of gene expression levels could contribute to phenotypic change in human cells. We have applied the two fluorescence-coding gene method and the expression variability of the two reporter genes to human cells in culture. We have quantified the portion of gene expression variation determined by global, promoter-specific, or by epigenetic sources. These two types of variation appear to contribute, in different ways, to the phenotypic diversification of clonal cell populations. Global, or promoter-specific, gene expression noise increases with cellular stress and contributes to the emergence of cellular diversity by diversifying the gene-expression levels. Epigenetic mechanisms act to increase the robustness of the cellular state by stabilizing gene transcription levels or by reinforcing the silenced state.

Target protectors reveal dampening and balancing of Nodal agonist and antagonist by miR-430

MicroRNAs (miRNAs) repress hundreds of target messenger RNAs (mRNAs), but the physiological roles of specific miRNA-mRNA interactions remain largely elusive. We report that zebrafish microRNA-430 (miR-430) dampens and balances the expression of the transforming growth factor-beta (TGF-beta) Nodal agonist squint and the TGF-beta Nodal antagonist lefty. To disrupt the interaction of specific miRNA-mRNA pairs, we developed target protector morpholinos complementary to miRNA binding sites in target mRNAs. Protection of squint or lefty mRNAs from miR-430 resulted in enhanced or reduced Nodal signaling, respectively. Simultaneous protection of squint and lefty or absence of miR-430 caused an imbalance and reduction in Nodal signaling. These findings establish an approach to analyze the in vivo roles of specific miRNA-mRNA pairs and reveal a requirement for miRNAs in dampening and balancing agonist/antagonist pairs.

Three-dimensional genome organization in interphase and its relation to genome function

Higher order chromatin structure, i.e. the three-dimensional (3D) organization of the genome in the interphase nucleus, is an important component in the orchestration of gene expression in the mammalian genome. In this review we describe principles of higher order chromatin structure discussing three organizational parameters, i.e. chromatin folding, chromatin compaction and the nuclear position of the chromatin fibre. We argue that principles of 3D genome organization are probabilistic traits, reflected in a considerable cell-to-cell variation in 3D genome structure. It will be essential to understand how such higher order organizational aspects contribute to genome function to unveil global genome regulation.

Living with noisy genes: how cells function reliably with inherent variability in gene expression

Within a population of genetically identical cells there can be significant variation, or noise, in gene expression. Yet even with this inherent variability, cells function reliably. This review focuses on our understanding of noise at the level of both single genes and genetic regulatory networks, emphasizing comparisons between theoretical models and experimental results whenever possible. To highlight the importance of noise, we particularly emphasize examples in which a stochastic description of gene expression leads to a qualitatively different outcome than a deterministic one.

Combinatorial promoter design for engineering noisy gene expression

Understanding the behavior of basic biomolecular components as parts of larger systems is one of the goals of the developing field of synthetic biology. A multidisciplinary approach, involving mathematical and computational modeling in parallel with experimentation, is often crucial for gaining such insights and improving the efficiency of artificial gene network design. Here we used such an approach and developed a combinatorial promoter design strategy to characterize how the position and multiplicity of tetO(2) operator sites within the GAL1 promoter affect gene expression levels and gene expression noise in Saccharomyces cerevisiae. We observed stronger transcriptional repression and higher gene expression noise as a single operator site was moved closer to the TATA box, whereas for multiple operator-containing promoters, we found that the position and number of operator sites together determined the dose-response curve and gene expression noise. We developed a generic computational model that captured the experimentally observed differences for each of the promoters, and more detailed models to successively predict the behavior of multiple operator-containing promoters from single operator-containing promoters. Our results suggest that the independent binding of single repressors is not sufficient to explain the more complex behavior of the multiple operator-containing promoters. Taken together, our findings highlight the importance of joint experimental-computational efforts and some of the challenges of using a bottom-up approach based on well characterized, isolated biomolecular components for predicting the behavior of complex, synthetic gene networks, e.g., the whole can be different from the sum of its parts.

Cell-to-cell heterogeneity in growth rate and gene expression in Methylobacterium extorquens AM1

Cell-to-cell heterogeneity in gene expression and growth parameters was assessed in the facultative methylotroph Methylobacterium extorquens AM1. A transcriptional fusion between a well-characterized methylotrophy promoter (P(mxaF)) and gfp(uv) (encoding a variant of green fluorescent protein [GFPuv]) was used to assess single-cell gene expression. Using a flowthrough culture system and laser scanning microscopy, data on fluorescence and cell size were obtained over time through several growth cycles for cells grown on succinate or methanol. Cells were grown continuously with no discernible lag between divisions, and high cell-to-cell variability was observed for cell size at division (2.5-fold range), division time, and growth rate. When individual cells were followed over multiple division cycles, no direct correlation was observed between the growth rate before a division and the subsequent growth rate or between the cell size at division and the subsequent growth rate. The cell-to-cell variability for GFPuv fluorescence from the P(mxaF) promoter was less, with a range on the order of 1.5-fold. Fluorescence and growth rate were also followed during a carbon shift experiment, in which cells growing on succinate were shifted to methanol. Variability of the response was observed, and the growth rate at the time of the shift from succinate to methanol was a predictor of the response. Higher growth rates at the time of the substrate shift resulted in greater decreases in growth rates immediately after the shift, but full induction of P(mxaF)-gfp(uv) was achieved faster. These results demonstrate that in M. extorquens, physiological heterogeneity at the single-cell level plays an important role in determining the population response to the metabolic shift examined.

Hypothesis testing via integrated computer modeling and digital fluorescence microscopy

Computational modeling has the potential to add an entirely new approach to hypothesis testing in yeast cell biology. Here, we present a method for seamless integration of computational modeling with quantitative digital fluorescence microscopy. This integration is accomplished by developing computational models based on hypotheses for underlying cellular processes that may give rise to experimentally observed fluorescent protein localization patterns. Simulated fluorescence images are generated from the computational models of underlying cellular processes via a "model-convolution" process. These simulated images can then be directly compared to experimental fluorescence images in order to test the model. This method provides a framework for rigorous hypothesis testing in yeast cell biology via integrated mathematical modeling and digital fluorescence microscopy.

Computational methods for diffusion-influenced biochemical reactions

MOTIVATION

We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli.

RESULTS

In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems.

AVAILABILITY

Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/

From functional genomics to systems biology

This review discusses the talks presented at the third EMBL Biennial Symposium, From functional genomics to systems biology, held in Heidelberg, Germany, 14-17 October 2006. Current issues and trends in various subfields of functional genomics and systems biology are considered, including analysis of regulatory elements, signalling networks, transcription networks, protein-protein interaction networks, genetic interaction networks, medical applications of DNA microarrays, and metagenomics. Several technological advances in the fields of DNA microarrays, identification of regulatory elements in the genomes of higher eukaryotes, and MS for detection of protein interactions are introduced. Major directions of future systems biology research are also discussed.

Propagation of extrinsic perturbation in a negatively auto-regulated pathway

The apparent precision of the output in multi-step biochemical pathways in the face of external and intrinsic perturbations is non-obvious and conceptually difficult. Using a simple three-step negatively auto-regulated model pathway, we show that the effect of perturbation at different steps of the pathway and its transmission through the network is dependent on the context (i.e., the position) of the particular reaction step in relation to the topology of the regulatory network, stoichiometry of reactions, type of nonlinearity involved in the reactions and also on the intrinsic dynamical state of the pathway variables. We delineate the qualitative and quantitative changes in the pathway dynamics for constant ('bias') and random external perturbations acting on the pathway steps locally or globally to all steps. We show that constant perturbation induces qualitative change in dynamics, whereas random fluctuations cause significant quantitative variations in the concentrations of the different variables. Thus, the dynamic response of multi-step biochemical pathways to external perturbation depends on their biochemical, topological and dynamical features.

Stochastic gene expression: from single molecules to the proteome

Protein production involves a series of stochastic chemical steps. One consequence of this fact is that the copy number of any given protein varies substantially from cell to cell, even within isogenic populations. Recent experiments have measured this variation for thousands of different proteins, revealing a linear relationship between variance and mean level of expression for much of the proteome. This simple relationship is frequently thought to arise from the random production and degradation of mRNAs, but several lines of evidence suggest that infrequent gene activation events also bear responsibility. In support of the latter hypothesis, single-molecule experiments have demonstrated that mRNA transcripts are often produced in large bursts. Moreover, the temporal pattern of these bursts appears to be correlated for chromosomally proximal genes, suggesting the existence of an upstream player.

Noise in timing and precision of gene activities in a genetic cascade

The timing of events along the induction cascade of bacteriophage lambda is independent of UV dose and displays increased relative temporal precision with cascade progression.

This behavior is reproduced by a model of a cascade consisting of independent steps that shows that higher temporal precision can be attained by a cascade consisting of a large number of fast steps.

The observed cell-cell variability in cascade timing is not due to differences in uniform dilation of intervals between events among cells, but rather to the independent distribution of interval durations within the cascade, consistently with the modular architecture of the lambda genome.

The single-cell time lapse study reveals a bistable regime at low UV doses in which some cells are induced while others are not, evidence for a commitment point beyond which lysis will occur, and an unexpected shutoff of the lambda pR promoter.

Stochasticity or noise, an inherent property of all biological networks, is often manifested by different phenotypic behaviors in clonal populations of cells (Raser and O'Shea, 2005). Noise can arise, for instance, from sources such as cell–cell variations in small numbers of regulatory molecules or from the stochastic nature of molecular interactions (Paulsson, 2005). Besides affecting the number of molecules in a cell, noise may also lead to variability in timing of particular events along a given pathway. In this work, we studied temporal noise in the induction cascade of phage lambda.

Infection of a bacterial cell by bacteriophage lambda can lead to two different fates (Ptashne, 2004; Dodd et al, 2005; Oppenheim et al, 2005): the phage can either multiply inside the host leading to its eventual lysis and the generation of progeny virions (the lytic pathway) or, alternatively, it can integrate its genome into the host's genome (prophage state), replicating passively with the latter (the lysogenic pathway). The prophage state is highly stable, being maintained by a phage-encoded repressor, which shuts off phage genes leading to lytic growth. However, the lytic pathway can be induced in a lysogenic cell, through the activation of the bacterial SOS response to DNA damage (Little, 1996), for example by UV irradiation. Once activated, the SOS response results in cleavage of the lambda repressor, leading to expression of the phage early and late genes, and culminating in the lysis of the host cell.

The lambda induction cascade has been extensively characterized over the years. We built upon this knowledge to tap the cascade at different points and quantitatively analyze the progressive loss of temporal coherence between cells, as different stages along the cascade are executed, following synchronous induction. Using time-lapse microscopy, we monitored the time of activation of early and late genes in individual cells using lambda pR and pR′-tR′ promoter-GFP fusions, respectively, by means of reporter plasmids, and finally the time of lysis. Sample results are shown in Figure 2.

At low UV levels (5 J/m²), the network exhibits bistability: only approximately 40% of the bacteria lyse, whereas the others continue to divide, following a lag period. At high UV levels (20 J/m²), almost all bacteria lyse. We found that the timing of events in cells that lyse is independent of UV dose. This is in contrast to the known behavior of the SOS network (Friedman et al, 2005), indicating that these two networks proceed independently. Following induction, a surprising shutoff in the activity of the pR promoter is observed in all cells (see Figure 2). Furthermore, the data show that whereas early genes are expressed in all cells irrespective of cell fate, late genes are expressed only in the lysing cells, indicating that similar to infection, a specific commitment checkpoint is operating.

To characterize the temporal variability in a cell population, we used the coefficient of variation, defined as the non-dimensional ratio of the standard deviation and the mean time of occurrence of a particular event. We studied the changes in both standard deviation and coefficient of variation in timing of various events along the lambda induction cascade, from the expression of the early genes to the ultimate lysis of the cells. As shown in Figure 6, the absolute noise as measured by the standard deviation increases as the cascade progresses. In contrast, the coefficient of variation, which measures variability relative to the time of occurrence, decreases. Simple theoretical considerations described in the text yield a necessary and sufficient condition for a monotonic decrease in the coefficient of variation. Higher temporal precision can be achieved when the cascade is composed of a large number of fast steps.

Further support for the independence of network modules is furnished by a correlation analysis of the times of occurrence of different steps along the lytic cascade. This analysis also indicates that the variability in lysis time is not due to differences in the global rate of cascade progression, but probably to random fluctuations in the execution time of the various cascade stages. Indeed, phage lambda gene expression architecture is well known to have evolved from a number of independent regulatory modules (Hendrix, 2003).

Biological developmental pathways require proper timing of gene expression. We investigated timing variations of defined steps along the lytic cascade of bacteriophage λ. Gene expression was followed in individual lysogenic cells, after induction with a pulse of UV irradiation. At low UV doses, some cells undergo partial induction and eventually divide, whereas others follow the lytic pathway. The timing of events in cells committed to lysis is independent of the level of activation of the SOS response, suggesting that the lambda network proceeds autonomously after induction. An increased loss of temporal coherence of specific events from prophage induction to lysis is observed, even though the coefficient of variation of timing fluctuations decreases. The observed temporal variations are not due to cell factors uniformly dilating the timing of execution of the cascade. This behavior is reproduced by a simple model composed of independent stages, which for a given mean duration predicts higher temporal precision, when a cascade consists of a large number of steps. Evidence for the independence of regulatory modules in the network is presented.

Phenotypic consequences of promoter-mediated transcriptional noise

A more complete understanding of the causes and effects of cell-cell variability in gene expression is needed to elucidate whether the resulting phenotypes are disadvantageous or confer some adaptive advantage. Here we show that increased variability in gene expression, affected by the sequence of the TATA box, can be beneficial after an acute change in environmental conditions. We rationally introduce mutations within the TATA region of an engineered Saccharomyces cerevisiae GAL1 promoter and measure promoter responses that can be characterized as being either highly variable and rapid or steady and slow. We computationally illustrate how a stable transcription scaffold can result in "bursts" of gene expression, enabling rapid individual cell responses in the transient and increased cell-cell variability at steady state. We experimentally verify computational predictions that the rapid response and increased cell-cell variability enabled by TATA-containing promoters confer a clear benefit in the face of an acute environmental stress.

Stochastic mRNA synthesis in mammalian cells

Individual cells in genetically homogeneous populations have been found to express different numbers of molecules of specific proteins. We investigated the origins of these variations in mammalian cells by counting individual molecules of mRNA produced from a reporter gene that was stably integrated into the cell's genome. We found that there are massive variations in the number of mRNA molecules present in each cell. These variations occur because mRNAs are synthesized in short but intense bursts of transcription beginning when the gene transitions from an inactive to an active state and ending when they transition back to the inactive state. We show that these transitions are intrinsically random and not due to global, extrinsic factors such as the levels of transcriptional activators. Moreover, the gene activation causes burst-like expression of all genes within a wider genomic locus. We further found that bursts are also exhibited in the synthesis of natural genes. The bursts of mRNA expression can be buffered at the protein level by slow protein degradation rates. A stochastic model of gene activation and inactivation was developed to explain the statistical properties of the bursts. The model showed that increasing the level of transcription factors increases the average size of the bursts rather than their frequency. These results demonstrate that gene expression in mammalian cells is subject to large, intrinsically random fluctuations and raise questions about how cells are able to function in the face of such noise.

Dose response relationship in anti-stress gene regulatory networks

To maintain a stable intracellular environment, cells utilize complex and specialized defense systems against a variety of external perturbations, such as electrophilic stress, heat shock, and hypoxia, etc. Irrespective of the type of stress, many adaptive mechanisms contributing to cellular homeostasis appear to operate through gene regulatory networks that are organized into negative feedback loops. In general, the degree of deviation of the controlled variables, such as electrophiles, misfolded proteins, and O₂, is first detected by specialized sensor molecules, then the signal is transduced to specific transcription factors. Transcription factors can regulate the expression of a suite of anti-stress genes, many of which encode enzymes functioning to counteract the perturbed variables. The objective of this study was to explore, using control theory and computational approaches, the theoretical basis that underlies the steady-state dose response relationship between cellular stressors and intracellular biochemical species (controlled variables, transcription factors, and gene products) in these gene regulatory networks. Our work indicated that the shape of dose response curves (linear, superlinear, or sublinear) depends on changes in the specific values of local response coefficients (gains) distributed in the feedback loop. Multimerization of anti-stress enzymes and transcription factors into homodimers, homotrimers, or even higher-order multimers, play a significant role in maintaining robust homeostasis. Moreover, our simulation noted that dose response curves for the controlled variables can transition sequentially through four distinct phases as stressor level increases: initial superlinear with lesser control, superlinear more highly controlled, linear uncontrolled, and sublinear catastrophic. Each phase relies on specific gain-changing events that come into play as stressor level increases. The low-dose region is intrinsically nonlinear, and depending on the level of local gains, presence of gain-changing events, and degree of feedforward gene activation, this region can appear as superlinear, sublinear, or even J-shaped. The general dose response transition proposed here was further examined in a complex anti-electrophilic stress pathway, which involves multiple genes, enzymes, and metabolic reactions. This work would help biologists and especially toxicologists to better assess and predict the cellular impact brought about by biological stressors.

To maintain a stable intracellular environment, cells are equipped with multiple specialized defense programs that are launched in response to various external chemical and physical stressors. These anti-stress mechanisms comprise primarily gene regulatory networks, and like many manmade control devices, such as thermostats and automobile cruise controls, they are often organized into negative feedback circuits. A quantitative understanding of how these control circuits operate in the cell can help us to assess and predict more accurately the cellular impacts brought about by perturbing stressors, such as environmental toxicants. Using control theory and computer simulations, we explored nature's design principle for anti-stress gene regulatory networks, and the manner in which cells respond and adapt to perturbations. We showed that cells can exploit multiple mechanisms, such as protein homodimerization, cooperative binding, and auto-regulation, to enhance the feedback loop gain, which, according to control theory, is a basic principle for effective perturbation resistance. We also illustrated that the steady-state dose response curve is likely to transition through multiple phases as stressor level increases, and that the low-dose region is inherently nonlinear. Our results challenge the common practice of linear extrapolation for evaluating the low-dose effect, and would lead to improved human health risk assessment for exposures to environmental toxicants.

Genome dynamics and transcriptional deregulation in aging

Genome instability has been implicated as a major cause of both cancer and aging. Using a lacZ-plasmid transgenic mouse model we have shown that mutations accumulate with age in a tissue-specific manner. Genome rearrangements, including translocations and large deletions, are a major component of the mutation spectrum in some tissues at old age such as heart. Such large mutations were also induced by hydrogen peroxide (H2O2) in lacZ-plasmid mouse embryonic fibroblasts (MEFs) and demonstrated to be replication-independent. This was in contrast to ultraviolet light-induced point mutations, which were much more abundant in proliferating than in quiescent MEFs. To test if large rearrangements could adversely affect patterns of gene expression we PCR-amplified global mRNA content of single MEFs treated with H2O2. Such treatment resulted in a significant increase in cell-to-cell variation in gene expression, which was found to parallel the induction and persistence of genome rearrangement mutations at the lacZ reporter locus. Increased transcriptional noise was also found among single cardiomyocytes from old mice as compared with similar cells from young mice. While these results do not directly indicate a cause and effect relationship between genome rearrangement mutations and transcriptional deregulation, they do underscore the stochastic nature of genotoxic effects on cells and tissues and could provide a mechanism for age-related cellular degeneration in postmitotic tissue, such as heart or brain.

Combined multicolor-FISH and immunostaining

The combination of multicolor-FISH and immunostaining produces a powerful visual method to analyze in situ DNA-protein interactions and dynamics. Representing one of the major technical improvements of FISH technology, this method has been used extensively in the field of chromosome and genome research, as well as in clinical studies, and serves as an important tool to bridge molecular analysis and cytological description. In this short review, the development and significance of this method will be briefly summarized using a limited number of examples to illustrate the large body of literature. In addition to descriptions of technical considerations, future applications and perspectives have also been discussed focusing specifically on the areas of genome organization, gene expression and medical research. We anticipate that this versatile method will play an important role in the study of the structure and function of the dynamic genome and for the development of potential applications for medical research.

Clonal and non-clonal chromosome aberrations and genome variation and aberration

The theoretical view that genome aberrations rather than gene mutations cause a majority of cancers has gained increasing support from recent experimental data. Genetic aberration at the chromosome level is a key aspect of genome aberration and the systematic definition of chromosomal aberrations with their impact on genome variation and cancer genome evolution is of great importance. However, traditionally, efforts have focused on recurrent clonal chromosome aberrations (CCAs). The significance of stochastic non-clonal chromosome aberrations (NCCAs) is discussed in this paper with emphasis on the simple types of NCCAs that have until recently been considered "non-significant background". Comparison of various subtypes of transitional and late-stage CCAs with simple and complex types of NCCAs has uncovered a dynamic relationship among NCCAs, CCAs, overall genomic instability, and karyotypic evolution, as well as the stochastic nature of cancer evolution. Here, we review concepts and methodologies to measure NCCAs and discuss the possible causative mechanism and consequences of NCCAs. This study raises challenging questions regarding the concept of cancer evolution driven by stochastic chromosomal aberration mediated genome irregularities that could have repercussions reaching far beyond cancer and organismal genomes.

Increased cell-to-cell variation in gene expression in ageing mouse heart

The accumulation of somatic DNA damage has been implicated as a cause of ageing in metazoa. One possible mechanism by which increased DNA damage could lead to cellular degeneration and death is by stochastic deregulation of gene expression. Here we directly test for increased transcriptional noise in aged tissue by dissociating single cardiomyocytes from fresh heart samples of both young and old mice, followed by global mRNA amplification and quantification of mRNA levels in a panel of housekeeping and heart-specific genes. Although gene expression levels already varied among cardiomyocytes from young heart, this heterogeneity was significantly elevated at old age. We had demonstrated previously an increased load of genome rearrangements and other mutations in the heart of aged mice. To confirm that increased stochasticity of gene expression could be a result of increased genome damage, we treated mouse embryonic fibroblasts in culture with hydrogen peroxide. Such treatment resulted in a significant increase in cell-to-cell variation in gene expression, which was found to parallel the induction and persistence of genome rearrangement mutations at a lacZ reporter locus. These results underscore the stochastic nature of the ageing process, and could provide a mechanism for age-related cellular degeneration and death in tissues of multicellular organisms.

Oscillations and variability in the p53 system

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.

External noise and feedback regulation: steady-state statistics of auto-regulatory genetic network

The steady-state statistics of a single gene auto-regulatory genetic network with the additive external Gaussian white noises is investigated. The main result shows that the negative feedback will result in that the mRNA noise has a positive contribution to the protein noise, but the positive feedback will result in that the mRNA noise has a negative contribution to the protein noise. If there is no feed back, then the contribution of mRNA noise to protein noise is always positive. On the other hand, the analysis and numerical simulations of linear and nonlinear feedback show that it is possible that the negative feedback increases, but the positive feedback decreases, the protein noise.

Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks

We discuss two methods that can be used to estimate the impact of internal and external variability on nonlinear systems, and demonstrate their utility by comparing two experimentally implemented oscillatory genetic networks with different designs. The methods allow for rapid estimations of intrinsic and extrinsic noise and should prove useful in the analysis of natural genetic networks and when constructing synthetic gene regulatory systems.

Stochastic Transcriptional Regulatory Systems with Time Delays: A Mean-Field Approximation

Modeling transcriptional regulation with time delays is an important problem of computational cell biology. In this paper, we propose a computational tool for studying transcriptional regulation in single cells based on a mean-field approximation method. The main idea is to replace the occurrence probabilities of the underlying transcriptional events by their mean values and use appropriately chosen additive noise terms to model statistical variations not accounted by this approximation. The proposed methodology allows us to characterize the transient and steady-state behavior of transcriptional regulation. Moreover, it provides a rather simple and computationally attractive tool for rapid statistical characterization of the dynamic behavior of a nonlinear transcriptional regulatory system with time delays.

Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in Escherichia coli

MOTIVATION

Many biochemical networks involve reactions localized on the cell membrane. This can give rise to spatial gradients of the concentration of cytosolic species. Moreover, the number of membrane molecules can be small and stochastic effects can become relevant. Pathways usually consist of a complex interaction network and are characterized by a large set of parameters. The inclusion of spatial and stochastic effects is a major challenge in developing quantitative and dynamic models of pathways.

RESULTS

We have developed a particle-based spatial stochastic method (GMP) to simulate biochemical networks in space, including fluctuations from the diffusion of particles and reactions. Gradients emerging from membrane reactions can be resolved. As case studies for the GMP method we used a simple gene expression system and the phosphoenolpyruvate:glucose phosphotransferase system pathway.

AVAILABILITY

The source code for the GMP method is available at http://www.science.uva.nl/research/scs/CellMath/GMP.

Noise in protein expression scales with natural protein abundance

Noise in gene expression is generated at multiple levels, such as transcription and translation, chromatin remodeling and pathway-specific regulation. Studies of individual promoters have suggested different dominating noise sources, raising the question of whether a general trend exists across a large number of genes and conditions. We examined the variation in the expression levels of 43 Saccharomyces cerevisiae proteins, in cells grown under 11 experimental conditions. For all classes of genes and under all conditions, the expression variance was approximately proportional to the mean; the same scaling was observed at steady state and during the transient responses to the perturbations. Theoretical analysis suggests that this scaling behavior reflects variability in mRNA copy number, resulting from random 'birth and death' of mRNA molecules or from promoter fluctuations. Deviation of coexpressed genes from this general trend, including high noise in stress-related genes and low noise in proteasomal genes, may indicate fluctuations in pathway-specific regulators or a differential activation pattern of the underlying gene promoters.

Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise

A major goal of biology is to provide a quantitative description of cellular behaviour. This task, however, has been hampered by the difficulty in measuring protein abundances and their variation. Here we present a strategy that pairs high-throughput flow cytometry and a library of GFP-tagged yeast strains to monitor rapidly and precisely protein levels at single-cell resolution. Bulk protein abundance measurements of >2,500 proteins in rich and minimal media provide a detailed view of the cellular response to these conditions, and capture many changes not observed by DNA microarray analyses. Our single-cell data argue that noise in protein expression is dominated by the stochastic production/destruction of messenger RNAs. Beyond this global trend, there are dramatic protein-specific differences in noise that are strongly correlated with a protein's mode of transcription and its function. For example, proteins that respond to environmental changes are noisy whereas those involved in protein synthesis are quiet. Thus, these studies reveal a remarkable structure to biological noise and suggest that protein noise levels have been selected to reflect the costs and potential benefits of this variation.

Search for an association between the human CYP1A2 genotype and CYP1A2 metabolic phenotype

The genotype responsible for more than 60-fold interindividual differences in human hepatic CYP1A2 constitutive expression is not understood. Resequencing the human CYP1A1_CYP1A2 locus (39.6 kb) in five major geographically isolated subgroups recently led to the identification of 85 single nucleotide polymorphisms (SNPs), 57 of which were double-hit SNPs. Here, we attempted to correlate the CYP1A2 genotype with a metabolic phenotype. We chose 16 SNPs (all having a minor allele frequency > or =0.05 in Caucasians) to genotype 32 DNA samples (26 Caucasians, six Ethiopians) in which CYP1A2 metabolism had previously been determined. From 280 subjects (five locations worldwide) that had been CYP1A2-phenotyped, we genotyped the 10 highest, 14 lowest and eight intermediate DNA samples. Although no SNP was significant (P<0.05), possibly due to the small sample size, we found a trend for several of the six SNPs across the CYP1A2 linkage disequilibrium block associated with the trait. Five CYP1A2 haplotypes were inferred, two of which had not previously been reported; haplotype 1A2H10 showed the greatest association with CYP1A2 activity. Regulatory sequences responsible for the large interindividual differences in hepatic CYP1A2 gene basal expression might reside, in part, with some of these CYP1A2 SNPS but, in large part, might be located either cis (in nearby sequences not yet haplotyped) or trans in that they are not linked to the gene. We conclude that no SNP or haplotype in the CYP1A2 gene has yet been identified that can unequivocally be used to predict the metabolic phenotype in any individual patient.

Predicting stochastic gene expression dynamics in single cells

Fluctuations in protein numbers (noise) due to inherent stochastic effects in single cells can have large effects on the dynamic behavior of gene regulatory networks. Although deterministic models can predict the average network behavior, they fail to incorporate the stochasticity characteristic of gene expression, thereby limiting their relevance when single cell behaviors deviate from the population average. Recently, stochastic models have been used to predict distributions of steady-state protein levels within a population but not to predict the dynamic, presteady-state distributions. In the present work, we experimentally examine a system whose dynamics are heavily influenced by stochastic effects. We measure population distributions of protein numbers as a function of time in the Escherichia coli lactose uptake network (lac operon). We then introduce a dynamic stochastic model and show that prediction of dynamic distributions requires only a few noise parameters in addition to the rates that characterize a deterministic model. Whereas the deterministic model cannot fully capture the observed behavior, our stochastic model correctly predicts the experimental dynamics without any fit parameters. Our results provide a proof of principle for the possibility of faithfully predicting dynamic population distributions from deterministic models supplemented by a stochastic component that captures the major noise sources.

Coherence and Timing of Cell Cycle Start Examined at Single-Cell Resolution

Cell cycle "Start" in budding yeast involves induction of a large battery of G1/S-regulated genes, coordinated with bud morphogenesis. It is unknown how intra-Start coherence of these events and inter-Start timing regularity are achieved. We developed quantitative time-lapse fluorescence microscopy on a multicell-cycle timescale, for following expression of unstable GFP under control of the G1 cyclin CLN2 promoter. Swi4, a major activator of the G1/S regulon, was required for a robustly coherent Start, as swi4 cells exhibited highly variable loss of cooccurrence of regular levels of CLN2pr-GFP expression with budding. In contrast, other known Start regulators Mbp1 and Cln3 are not needed for coherence but ensure regular timing of Start onset. The interval of nuclear retention of Whi5, a Swi4 repressor, largely accounts for wild-type mother-daughter asymmetry and for variable Start timing in cln3 mbp1 cells. Thus, multiple pathways may independently suppress qualitatively different kinds of noise at Start.