Stochastic mechanisms are ubiquitous in biological systems. Biochemical reactions that involve small numbers of molecules are intrinsically noisy, being dominated by large concentration fluctuations 1-3 . This intrinsic noise has been implicated in the random lysis/lysogeny decision of bacteriophage-λ 4 , in the loss of synchrony of circadian clocks 5,6 and in the decrease of precision of cell signals 7 . We sought to quantitatively investigate the extent to which the occurrence of molecular fluctuations within single cells (biochemical noise) could explain the variation of gene expression levels between cells in a genetically identical population (phenotypic noise). We have isolated the biochemical contribution to phenotypic noise from that of other noise sources by carrying out a series of differential measurements. We varied independently the rates of transcription and translation of a single fluorescent reporter gene in the chromosome of Bacillus subtilis, and we quantitatively measured the resulting changes in the phenotypic noise characteristics. We report that of these two parameters, increased translational efficiency is the predominant source of increased phenotypic noise. This effect is consistent with a stochastic model of gene expression in which proteins are produced in random and sharp bursts. Our results thus provide the first direct experimental evidence of the biochemical origin of phenotypic noise, demonstrating that the level of phenotypic variation in an isogenic population can be regulated by genetic parameters.We selected as our reporter system a single-copy chromosomal gene with an inducible promoter. As an estimated 50-80% of bacterial genes are transcriptionally regulated 8 , this system typifies the majority of naturally occurring genes, allowing our results to be extended to natural systems. We incorporated a single copy of our reporter, the green fluorescent protein gene (gfp), into the chromosome of B. subtilis. We chose to integrate gfp into the chromosome itself, rather than in the form of plasmids, as variation in plasmid copy number 9,10 can act as an additional and unwanted source of noise. Transcriptional efficiency was regulated by using an isopropyl-β-D-thiogalactopyranoside (IPTG)-inducible promoter, P spac , upstream of gfp, and varying the concentration of IPTG in the growth medium. Translational efficiency was regulated by constructing a series of B. subtilis strains ( Table 1) that contained point mutations in the ribosome binding site (RBS) and initiation codon of gfp 11 . The use of two different strategies to regulate transcriptional and translational processes introduces a potential bias in the relative contributions of these processes to biochemical noise. As a control, we constructed four additional strains (Table 2) whose transcription rates were altered by mutations in the promoter region of the reporter gene. As described below, both strategies of transcriptional regulation produced similar results.We measured expression of green fluorescent protein (GFP) for si...
Multistability, the capacity to achieve multiple internal states in response to a single set of external inputs, is the defining characteristic of a switch. Biological switches are essential for the determination of cell fate in multicellular organisms, the regulation of cell-cycle oscillations during mitosis and the maintenance of epigenetic traits in microbes. The multistability of several natural and synthetic systems has been attributed to positive feedback loops in their regulatory networks. However, feedback alone does not guarantee multistability. The phase diagram of a multistable system, a concise description of internal states as key parameters are varied, reveals the conditions required to produce a functional switch. Here we present the phase diagram of the bistable lactose utilization network of Escherichia coli. We use this phase diagram, coupled with a mathematical model of the network, to quantitatively investigate processes such as sugar uptake and transcriptional regulation in vivo. We then show how the hysteretic response of the wild-type system can be converted to an ultrasensitive graded response. The phase diagram thus serves as a sensitive probe of molecular interactions and as a powerful tool for rational network design.
The vertebrate body axis is subdivided into repeated segments, best exemplified by the vertebrae that derive from embryonic somites. The number of somites is precisely defined for any given species but varies widely from one species to another. To determine the mechanism controlling somite number, we have compared somitogenesis in zebrafish, chicken, mouse and corn snake embryos. Here we present evidence that in all of these species a similar 'clock-and-wavefront' mechanism operates to control somitogenesis; in all of them, somitogenesis is brought to an end through a process in which the presomitic mesoderm, having first increased in size, gradually shrinks until it is exhausted, terminating somite formation. In snake embryos, however, the segmentation clock rate is much faster relative to developmental rate than in other amniotes, leading to a greatly increased number of smaller-sized somites.
The somites of the vertebrate embryo are clocked out sequentially from the presomitic mesoderm (PSM) at the tail end of the embryo. Formation of each somite corresponds to one cycle of oscillation of the somite segmentation clock—a system of genes whose expression switches on and off periodically in the cells of the PSM. We have previously proposed a simple mathematical model explaining how the oscillations, in zebrafish at least, may be generated by a delayed negative feedback loop in which the products of two Notch target genes, her1 and her7, directly inhibit their own transcription, as well as that of the gene for the Notch ligand DeltaC; Notch signalling via DeltaC keeps the oscillations of neighbouring cells in synchrony. Here we subject the model to quantitative tests. We show how to read temporal information from the spatial pattern of stripes of gene expression in the anterior PSM and in this way obtain values for the biosynthetic delays and molecular lifetimes on which the model critically depends. Using transgenic lines of zebrafish expressing her1 or her7 under heat-shock control, we confirm the regulatory relationships postulated by the model. From the timing of somite segmentation disturbances following a pulse of her7 misexpression, we deduce that although her7 continues to oscillate in the anterior half of the PSM, it governs the future somite segmentation behaviour of the cells only while they are in the posterior half. In general, the findings strongly support the mathematical model of how the somite clock works, but they do not exclude the possibility that other oscillator mechanisms may operate upstream from the her7/her1 oscillator or in parallel with it.
Somite segmentation depends on a gene expression oscillator or clock in the posterior presomitic mesoderm (PSM) and on read-out machinery in the anterior PSM to convert the pattern of clock phases into a somite pattern. Notch pathway mutations disrupt somitogenesis, and previous studies have suggested that Notch signalling is required both for the oscillations and for the read-out mechanism. By blocking or overactivating the Notch pathway abruptly at different times, we show that Notch signalling has no essential function in the anterior PSM and is required only in the posterior PSM, where it keeps the oscillations of neighbouring cells synchronized. Using a GFP reporter for the oscillator gene her1, we measure the influence of Notch signalling on her1 expression and show by mathematical modelling that this is sufficient for synchronization. Our model, in which intracellular oscillations are generated by delayed autoinhibition of her1 and her7 and synchronized by Notch signalling, explains the observations fully, showing that there are no grounds to invoke any additional role for the Notch pathway in the patterning of somite boundaries in zebrafish.
Cellular polarization is often a response to distinct extracellular or intracellular cues, such as nutrient gradients or cortical landmarks. However, in the absence of such cues, some cells can still select a polarization axis at random. Positive feedback loops promoting localized activation of the GTPase Cdc42p are central to this process in budding yeast. Here, we explore spontaneous polarization during bud site selection in mutant yeast cells that lack functional landmarks. We find that these cells do not select a single random polarization axis, but continuously change this axis during the G1 phase of the cell cycle. This is reflected in traveling waves of activated Cdc42p which randomly explore the cell periphery. Our integrated computational and in vivo analyses of these waves reveal a negative feedback loop that competes with the aforementioned positive feedback loops to regulate Cdc42p activity and confer dynamic responsiveness on the robust initiation of cell polarization.
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, presteadystate 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.gene networks ͉ systems biology O ne of the central goals of systems biology is to predict the dynamic behavior of a cell's genetic and metabolic networks. These predictions traditionally stem from models in which discrete molecular events, such as transcription and translation, are represented by continuous and deterministic differential equations. Such equations are valid when behavior of individual cells is very similar to the average behavior of the population. However, in many cases, the inherently stochastic nature of biological systems leads to significant cell-to-cell variability (1-3), and previous studies indicate that individual cells often behave very differently from the population average in response to external stimuli. For example, studies of bacterial persistence indicate that the population survival rate can be fundamentally different from the average cell's survival rate in response to environmental stress (4, 5). The impact of noise-induced population heterogeneity is also relevant when studying cellular memory, where fluctuations in protein numbers can cause the stability of epigenetic memory to degrade by effectively causing cells to forget their original states (6, 7). In these cases, stochastic modeling techniques must be used to describe the large cell-tocell variability. Although deterministic models can describe dynamic network behavior and analytical stochastic models can faithfully predict steady-state population distributions (8), little work has been done to connect dynamic cellular behavior with noise models. It is important that stochastic models of biological systems...
SUMMARYOscillations are prevalent in natural systems. A gene expression oscillator, called the segmentation clock, controls segmentation of precursors of the vertebral column. Genes belonging to the Hes/her family encode the only conserved oscillating genes in all analyzed vertebrate species. Hes/Her proteins form dimers and negatively autoregulate their own transcription. Here, we developed a stochastic two-dimensional multicellular computational model to elucidate how the dynamics, i.e. period, amplitude and synchronization, of the segmentation clock are regulated. We performed parameter searches to demonstrate that autoregulatory negative-feedback loops of the redundant repressor Her dimers can generate synchronized gene expression oscillations in wild-type embryos and reproduce the dynamics of the segmentation oscillator in different mutant conditions. Our model also predicts that synchronized oscillations can be robustly generated as long as the half-lives of the repressor dimers are shorter than 6 minutes. We validated this prediction by measuring, for the first time, the half-life of Her7 protein as 3.5 minutes. These results demonstrate the importance of building biologically realistic stochastic models to test biological models more stringently and make predictions for future experimental studies.
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