Clonal populations of cells exhibit substantial phenotypic variation. Such heterogeneity can be essential for many biological processes and is conjectured to arise from stochasticity, or noise, in gene expression. We constructed strains of Escherichia coli that enable detection of noise and discrimination between the two mechanisms by which it is generated. Both stochasticity inherent in the biochemical process of gene expression (intrinsic noise) and fluctuations in other cellular components (extrinsic noise) contribute substantially to overall variation. Transcription rate, regulatory dynamics, and genetic factors control the amplitude of noise. These results establish a quantitative foundation for modeling noise in genetic networks and reveal how low intracellular copy numbers of molecules can fundamentally limit the precision of gene regulation.

Gene expression is a stochastic, or ''noisy,'' process. This noise comes about in two ways. The inherent stochasticity of biochemical processes such as transcription and translation generates ''intrinsic'' noise. In addition, fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene and thus represent ''extrinsic'' noise. Here, we show how the total variation in the level of expression of a given gene can be decomposed into its intrinsic and extrinsic components. We demonstrate theoretically that simultaneous measurement of two identical genes per cell enables discrimination of these two types of noise. Analytic expressions for intrinsic noise are given for a model that involves all the major steps in transcription and translation. These expressions give the sensitivity to various parameters, quantify the deviation from Poisson statistics, and provide a way of fitting experiment. Transcription dominates the intrinsic noise when the average number of proteins made per mRNA transcript is greater than Ӎ2. Below this number, translational effects also become important. Gene replication and cell division, included in the model, cause protein numbers to tend to a limit cycle. We calculate a general form for the extrinsic noise and illustrate it with the particular case of a single fluctuating extrinsic variable-a repressor protein, which acts on the gene of interest. All results are confirmed by stochastic simulation using plausible parameters for Escherichia coli.M olecules are discrete entities. When present in large numbers, addition or removal of any single molecule typically has little effect on the properties of a system. However, stochastic fluctuations can become significant in smaller systems. In living cells, many components are present at very low copy numbers, [e.g., of order one for DNA loci and of order tens for transcription factors (1)]. Therefore, stochastic effects are thought to be particularly important for gene expression and have been invoked to explain cell-cell variations in clonal populations (2-4). Indeed, cellular components interact with one another in complex regulatory networks. Thus, fluctuations in even a single component may potentially affect the performance of the entire system.Consider a particular gene of interest. The amount of protein it produces will vary from cell to cell in a population and over time in a single cell. These fluctuations originate in two ways: First, even if all cells were in precisely the same state, the reaction events leading to transcription and translation of the gene would still occur at different times, and in different orders, in different cells. Such stochastic effects are set locally by the gene sequence and the properties of the protein it encodes and will be referred to as ''intrinsic'' noise.In addition, one must consider that other molecular species in the cell, e.g., RNA polymerase (RNAP), are themselves gene products and therefore will also vary over time and from cell ...

Gene expression is significantly stochastic making modeling of genetic networks challenging. We present an approximation that allows the calculation of not only the mean and variance, but also the distribution of protein numbers. We assume that proteins decay substantially more slowly than their mRNA and confirm that many genes satisfy this relation by using high-throughput data from budding yeast. For a two-stage model of gene expression, with transcription and translation as first-order reactions, we calculate the protein distribution for all times greater than several mRNA lifetimes and thus qualitatively predict the distribution of times for protein levels to first cross an arbitrary threshold. If in addition the fluctuates between inactive and active states, we can find the steady-state protein distribution, which can be bimodal if fluctuations of the promoter are slow. We show that our assumptions imply that protein synthesis occurs in geometrically distributed bursts and allows mRNA to be eliminated from a master equation description. In general, we find that protein distributions are asymmetric and may be poorly characterized by their mean and variance. Through maximum likelihood methods, our expressions should therefore allow more quantitative comparisons with experimental data. More generally, we introduce a technique to derive a simpler, effective dynamics for a stochastic system by eliminating a fast variable.

Strain construction: The CI-YFP fusion protein (Fig. 1B) was constructed by PCR, and contained the entire coding sequence of the wild-type cI gene fused directly to the coding sequence of the yfp gene (from pDH5 plasmid, University of Washington Yeast Resource Center). The cI-yfp gene was expressed from the tightly regulated P LtetO-1 promoter on the pZS21 plasmid (1), which is stable and difficult to cure. Integration of CFP with the P R promoter was performed as previously described (2). Since the cfp gene is chromosomally integrated, and the repressor concentration is independently measured, the results are not affected by possible variations in plasmid copy number or plasmid loss after the end of induction of cI-yfp expression. Full induction of cI-yfp expression by anhydrotetracycline (aTc) was sufficient to repress CFP production in the λ-cascade strain to undetectable levels. When not induced, the cI-yfp plasmid had no effect on CFP expression. Thus, the strain allows exploration of the full dynamic range of CFP regulation.The O R 2*-λ-cascade strain ( Fig. S3) was constructed by site-directed mutagenesis of the P R promoter (Stratagene QuikChange Kit) with the following primers:This created a mutation which was previously designated as 'VN' (3). The underlined portion of the primers represents O R 2 and the bold nucleotide is the site of the point mutation that changes a G to a T. The 'symmetric branch' strain ( Fig. 4D) was strain MRR containing plasmid pZS21-cIYFP-Y66F. MRR contains CFP and YFP at separate, but equivalent, loci, approximately equidistant from the origin of replication, each under wild-type P R promoters (2). Plasmid pZS21-cIYFP-Y66F was identical to pZS21-cIYFP, except that site-directed mutagenesis was used to introduce a single point mutation converting the tyrosine at YFP position 66 (in the YFP chromophore) to phenyalanine, thereby eliminating repressor fluorescence.Experimental procedure and image acquisition: Cultures were grown overnight in LB + 15 µg/mL kanamycin at 37°C from single colonies, and diluted 1:100 in MSC media (M9 minimal medium + 0.6% succinate + 0.01% casamino acids + 0.15 µg/ml biotin + 1.5 µM thiamine). Cultures were grown to OD 600 ~0.1 at 32°C, and then induced if necessary. Induction consisted of adding aTc to a final concentration of 100 ng/mL for ~3 minutes at ambient temperature, followed by 2 washes with MSC to remove aTc (Fig. 1C). Cells were allowed to grow until just prior to the production of the CI-repressed gene(s), then diluted to give ~1 cell per visual field when placed between a coverslip and 1.5% low melt MSC agarose. Growth of microcolonies was observed by fluorescence microscopy at 32ºC using a Leica DMIRB/E automated fluorescence microscope (Fig. 1D and Fig. S1). Cell-cycle period (doubling time) was 45±10min for all strains. Custom Visual Basic software was written to control the microscope and related equipment (Ludl motorized stage and Hamamatsu Orca II CCD camera), via ImagePro Plus and ScopePro packages (Media Cybernetics). In most cas...

Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod's law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host-circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.systems biology | synthetic biology | mathematical cell model | host-circuit interactions | evolutionarily stable strategy I ntracellular processes rarely work in isolation but continually interact with the rest of the cell. Yet often we study cellular processes with the implicit assumption that the remainder of the cell can either be ignored or provides a constant, background environment. Work in both systems and synthetic biology is, however, showing that this assumption is weak, at best. In microbes, growth rate can affect the expression both of single genes (1, 2) and across the entire genome (3-6). Specific control by transcription factors seems to be complemented by global, unspecific regulation that reflects the physiological state of the cell (5-7). Correspondingly, progress in synthetic biology is limited by two-way interactions between synthetic circuits and the host cell that cannot be designed away (8, 9).These phenomena are thought to arise from trade-offs where commitment of a finite intracellular resource to one response necessarily reduces the commitment of that resource to another response. A trade-off in the allocation of ribosomes has been suggested to underlie global gene regulation (2, 5). Similarly, depletion of finite resources and competition for cellular processes is thought to explain the failure of some synthetic circuits (8). Such circuits "load" the host cell, which can induce physiological responses that further degrade the function of the circuit (10). Our understanding of such trade-offs, however, is mostly phenomenological.Here we take an alternative approach and ask what new insi...

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.

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are 'colored'). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high-throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.

We consider a three dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In certain limits, the Cassie and Wenzel laws, and a new equivalent rule, applicable in general, are derived. We also propose an equation in the same spirit as these results but valid on a more 'microscopic' level. Throughout we work under the presence of gravity and keep account of line tension terms.