Bacteria must constantly adapt their growth to changes in nutrient availability; yet despite
large-scale changes in protein expression associated with sensing, adaptation, and processing
different environmental nutrients, simple growth laws connect the ribosome abundance and the growth
rate. Here, we investigate the origin of these growth laws by analyzing the features of ribosomal
regulation that coordinate proteome-wide expression changes with cell growth in a variety of
nutrient conditions in the model organism Escherichia coli. We identify
supply-driven feedforward activation of ribosomal protein synthesis as the key regulatory motif
maximizing amino acid flux, and autonomously guiding a cell to achieve optimal growth in different
environments. The growth laws emerge naturally from the robust regulatory strategy underlying growth
rate control, irrespective of the details of the molecular implementation. The study highlights the
interplay between phenomenological modeling and molecular mechanisms in uncovering fundamental
operating constraints, with implications for endogenous and synthetic design of microorganisms.
growth control; metabolic control; phenomenological model; resource allocation; synthetic biology
To predict the emergence of antibiotic resistance, quantitative relations must be established between the fitness of drug resistant organisms and the molecular mechanisms conferring resistance. These relations are often unknown and may depend on the state of bacterial growth. To bridge this gap, we have investigated Escherichia coli strains expressing resistance to translation-inhibiting antibiotics. We show that resistance expression and drug inhibition are linked in a positive feedback loop arising from an innate, global effect of drug-inhibited growth on gene expression. A quantitative model of bacterial growth based on this innate feedback accurately predicts the rich phenomena observed: a plateau-shaped fitness landscape, with an abrupt drop in the growth rates of cultures at a threshold drug concentration, and the coexistence of growing and non-growing populations, i.e., growth bistability, below the threshold.
We study evolution driven by spatial heterogeneity in a stochastic model of source-sink ecologies. A sink is a habitat where mortality exceeds reproduction so that a local population persists only due to immigration from a source. Immigrants can, however, adapt to conditions in the sink by mutation. To characterize the adaptation rate, we derive expressions for the first arrival time of adapted mutants. The joint effects of migration, mutation, birth and death result in two distinct parameter regimes. These results may pertain to the rapid evolution of drug-resistant pathogens and insects.
Cyclic AMP (cAMP) dependent catabolite repression effect in E. coli is among the most intensely studied regulatory processes in biology. However, the physiological function(s) of cAMP signalling and its molecular triggers remain elusive. Here we use a quantitative physiological approach to show that cAMP signalling tightly coordinates the cell’s protein expression program with its metabolic needs during exponential cell growth: The expression of carbon catabolic genes increased linearly with decreasing growth rates upon limitation of carbon influx, but decreased linearly with decreasing growth rate upon limitation of nitrogen or sulfur influx. In contrast, the expression of biosynthetic genes exhibited the opposite linear growth-rate dependence as the catabolic genes. A coarse-grained mathematical model provides a quantitative framework for understanding and predicting gene expression responses to catabolic and anabolic limitations. A scheme of integral feedback control featuring the inhibition of cAMP signalling by metabolic precursors is proposed and validated. These results reveal a key physiological role of cAMP-dependent catabolite repression: to ensure that proteomic resources are spent on distinct metabolic sectors as needed in different nutrient environments. Our finding underscores the power of quantitative physiology in unravelling the underlying functions of complex molecular signalling networks.
An important question in developmental biology is how relatively shallow gradients of morphogens can reliably establish a series of distinct transcriptional readouts. Current models emphasize interactions between transcription factors binding in distinct modes to cis-acting sequences of target genes. Another recent idea is that the cis-acting interactions may amplify preexisting biases or prepatterns to establish robust transcriptional responses. In this study, we examine the possible contribution of one such source of prepattern, namely gene length. We developed quantitative imaging tools to measure gene expression levels for several loci at a time on a single-cell basis and applied these quantitative imaging tools to dissect the establishment of a gene expression border separating the mesoderm and neuroectoderm in the early Drosophila embryo. We first characterized the formation of a transient ventral-to-dorsal gradient of the Snail (Sna) repressor and then examined the relationship between this gradient and repression of neural target genes in the mesoderm. We found that neural genes are repressed in a nested pattern within a zone of the mesoderm abutting the neuroectoderm, where Sna levels are graded. While several factors may contribute to the transient graded response to the Sna gradient, our analysis suggests that gene length may play an important, albeit transient, role in establishing these distinct transcriptional responses. One prediction of the gene-length-dependent transcriptional patterning model is that the co-regulated genes knirps (a short gene) and knirps-related (a long gene) should be transiently expressed in domains of differing widths, which we confirmed experimentally. These findings suggest that gene length may contribute to establishing graded responses to morphogen gradients by providing transient prepatterns that are subsequently amplified and stabilized by traditional cis-regulatory interactions.
Morphogen gradient; transcriptional delay; computational modeling; prepattern; multiplex in situ hybridization; Drosophila
Different codons encoding the same amino acid are not used equally in protein-coding sequences. In bacteria, there is a bias towards codons with high translation rates. This bias is most pronounced in highly expressed proteins, but a recent study of synthetic GFP-coding sequences did not find a correlation between codon usage and GFP expression, suggesting that such correlation in natural sequences is not a simple property of translational mechanisms. Here, we investigate the effect of evolutionary forces on codon usage. The relation between codon bias and protein abundance is quantitatively analyzed based on the hypothesis that codon bias evolved to ensure the efficient usage of ribosomes, a precious commodity for fast growing cells. An explicit fitness landscape is formulated based on bacterial growth laws to relate protein abundance and ribosomal load. The model leads to a quantitative relation between codon bias and protein abundance, which accounts for a substantial part of the observed bias for E. coli. Moreover, by providing an evolutionary link, the ribosome load model resolves the apparent conflict between the observed relation of protein abundance and codon bias in natural sequences and the lack of such dependence in a synthetic gfp library. Finally, we show that the relation between codon usage and protein abundance can be used to predict protein abundance from genomic sequence data alone without adjustable parameters.
The expression of genes is regularly characterized with respect to how much, how fast, when and where. Such quantitative data demands quantitative models. Thermodynamic models are based on the assumption that the level of gene expression is proportional to the equilibrium probability that RNA polymerase (RNAP) is bound to the promoter of interest. Statistical mechanics provides a framework for computing these probabilities. Within this framework, interactions of activators, repressors, helper molecules and RNAP are described by a single function, the ‘regulation factor’. This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell.
With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to their respective context. Thermodynamic models provide a useful framework for the quantitative analysis of bacterial transcription regulation. This framework can facilitate the quantification of vastly different forms of gene expression from several well-characterized bacterial promoters that are regulated by one or two species of transcription factors; it is useful because it requires only a few parameters. As such, it provides a compact description useful for higher-level studies (e.g. of genetic networks) without the need to invoke the biochemical details of every component. Moreover, it can be used to generate hypotheses on the likely mechanisms of transcriptional control.
E. coli uses an energetically costly ammonium uptake process to maintain growth in ammonium-limited conditions. Detailed analysis of this process reveals that cells employ a novel strategy to activate ammonium transport only as necessary for cell growth.
Ammonium transport by AmtB is activated abruptly upon reduction in the ammonium concentration in the medium, after the ammonium assimilation capacity is maximized.Under different growth conditions that provide cells with different growth rates even when ammonium is replete, ammonium transport by AmtB is employed only as necessary to maintain cell growth at the maximum rate.The known molecular interactions reveal an integral feedback mechanism underlying the need-based control of AmtB activity, mediated by α-ketoglutarate (aKG).The two signaling molecules, glutamine and aKG, provide seamless coordination between ammonium assimilation and ammonium transport.
The efficient sequestration of nutrients is vital for the growth and survival of microorganisms. Some nutrients, such as CO2 and NH3, are readily diffusible across the cell membrane. The large membrane permeability of these nutrients obviates the need of transporters when the ambient level is high. When the ambient level is low, however, maintaining a high intracellular nutrient level against passive back diffusion is both challenging and costly. Here, we study the delicate management of ammonium (NH4+/NH3) sequestration by E. coli cells using microfluidic chemostats. We find that as the ambient ammonium concentration is reduced, E. coli cells first maximize their ability to assimilate the gaseous NH3 diffusing into the cytoplasm and then abruptly activate ammonium transport. The onset of transport varies under different growth conditions, but always occurring just as needed to maintain growth. Quantitative modeling of known interactions reveals an integral feedback mechanism by which this need-based uptake strategy is implemented. This novel strategy ensures that the expensive cost of upholding the internal ammonium concentration against back diffusion is kept at a minimum.
active transport; futile cycle; integral feedback; metabolic coordination; microfluidics
Quantitative empirical relationships between cell composition and growth rate played an important role in the early days of microbiology. Gradually, the focus of the field began to shift from growth physiology to the ever more elaborate molecular mechanisms of regulation employed by the organisms. Advances in systems biology and biotechnology have renewed interest in the physiology of the cell as a whole. Furthermore, gene expression is known to be intimately coupled to the growth state of the cell. Here, we review recent efforts in characterizing such couplings, particularly the quantitative phenomenological approaches exploiting bacterial `growth laws.' These approaches point toward underlying design principles that can guide the predictive manipulation of cell behavior in the absence of molecular details.
2-Oxoglutarate is located at the junction between central carbon and nitrogen metabolism, serving as an intermediate for both. In nitrogen metabolism, 2-oxoglutarate acts as both a carbon skeletal carrier and an effector molecule. There have been only sporadic reports of its internal concentrations. Here we describe a sensitive and accurate method for determination of the 2-oxoglutarate pool concentration in Escherichia coli. The detection was based on fluorescence derivatization followed by reversed-phase high-pressure liquid chromatography separation. Two alternative cell sampling strategies, both of which were based on a fast filtration protocol, were sequentially developed to overcome both its fast metabolism and contamination from 2-oxoglutarate that leaks into the medium. We observed rapid changes in the 2-oxoglutarate pool concentration upon sudden depletion of nutrients: decreasing upon carbon depletion and increasing upon nitrogen depletion. The latter was studied in mutants lacking either of the two enzymes using 2-oxoglutarate as the carbon substrate for glutamate biosynthesis. The results suggest that flux restriction on either reaction greatly influences the internal 2-oxoglutarate level. Additional study indicates that KgtP, a 2-oxoglutarate proton symporter, functions to recover the leakage loss of 2-oxoglutarate. This recovery mechanism benefits the measurement of cellular 2-oxoglutarate level in practice by limiting contamination from 2-oxoglutarate leakage.
Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions.
Different times call for different measures. Therefore, cells adjust their protein levels depending on their environment. Upon the detection of certain environmental signals, transcription factors are activated, which activate or inhibit the production of specific sets of proteins. As it turns out, these transcription factors often also stimulate their own production. Indeed, such self-regulation is a common motif in signal–response systems of many organisms, including bacteria, animals, plants and viruses–but its function is not well understood. We have used mathematical models to study its benefits and drawbacks. On the one hand, calculations show that self-regulation can be a very useful tool if the cell needs to respond in a sensitive way to changes in its environment, or if it is supposed to respond only if the signal exceeds a threshold level. On the other hand, these benefits come at a cost: self-regulation severely slows down the cell's response to changes in the environment. We have analyzed how the cell can benefit from the advantages of self-regulation, while mitigating the drawbacks. This leads to strict design constraints that examples from the bacterium E. coli indeed seem to obey.
Predictive understanding of the myriads of signal transduction pathways in a cell is an outstanding challenge of systems biology. Such pathways are primarily mediated by specific but transient protein-protein interactions, which are difficult to study experimentally. In this study, we dissect the specificity of protein-protein interactions governing two-component signaling (TCS) systems ubiquitously used in bacteria. Exploiting the large number of sequenced bacterial genomes and an operon structure which packages many pairs of interacting TCS proteins together, we developed a computational approach to extract a molecular interaction code capturing the preferences of a small but critical number of directly interacting residue pairs. This code is found to reflect physical interaction mechanisms, with the strongest signal coming from charged amino acids. It is used to predict the specificity of TCS interaction: Our results compare favorably to most available experimental results, including the prediction of 7 (out of 8 known) interaction partners of orphan signaling proteins in Caulobacter crescentus. Surveying among the available bacterial genomes, our results suggest 15∼25% of the TCS proteins could participate in out-of-operon “crosstalks”. Additionally, we predict clusters of crosstalking candidates, expanding from the anecdotally known examples in model organisms. The tools and results presented here can be used to guide experimental studies towards a system-level understanding of two-component signaling.
Bacterial gene expression depends not only on specific regulations but also directly on bacterial growth, because important global parameters such as the abundance of RNA polymerases and ribosomes are all growth-rate dependent. Understanding these global effects is necessary for a quantitative understanding of gene regulation and for the robust design of synthetic genetic circuits. The observed growth-rate dependence of constitutive gene expression can be explained by a simple model using the measured growth-rate dependence of the relevant cellular parameters. More complex growth dependences for genetic circuits involving activators, repressors and feedback control were analyzed, and salient features were verified experimentally using synthetic circuits. The results suggest a novel feedback mechanism mediated by general growth-dependent effects and not requiring explicit gene regulation, if the expressed protein affects cell growth. This mechanism can lead to growth bistability and promote the acquisition of important physiological functions such as antibiotic resistance and tolerance (persistence).
growth rate; constitutive gene expression; gene regulation; genetic circuits; bistability; growth feedback; antibiotics; persister cells
Synthesis of ribosomal RNA (rRNA) is essential for fast cell growth and rRNA transcription is typically characterized by dense traffic of RNA polymerases along the rRNA genes. However, dense traffic is susceptible to traffic jams which may arise inevitably due to stochastic pausing of the polymerases. Based on recent theoretical and experimental results, we suggest that the “traffic viewpoint” provides a unique perspective towards understanding the control of ribosome synthesis in both bacterial and eukaryotic cells.
rRNA; transcription; RNA polymerase; transcript elongation; antitermination; growth rate
Short-lived protein interactions determine signal transduction specificity among genetically amplified, structurally identical two-component signaling systems. Interacting protein pairs evolve recognition precision by varying residues at specific positions in the interaction surface consistent with constraints of charge, size, and chemical properties. Such positions can be detected by covariance analyses of two-component protein databases. Here, covariance is shown to identify a cluster of co-evolving dynamic residues in two-component proteins. NMR dynamics and structural studies of both wild-type and mutant proteins in this cluster suggest that motions serve to precisely arrange the site of phosphoryl transfer within the complex.
The central role of small RNAs in regulating bacterial gene expression has been elucidated in the last years. Typically, small RNAs act via specific basepairing with target mRNAs, leading to modulation of translation initiation and mRNA stability. Quantitative studies suggest that small RNA regulation is characterized by unique features, which allow it to complement regulation at the transcriptional level. In particular, small RNAs are shown to establish a threshold for the expression of their target, providing safety mechanism against random fluctuations and transient signals. The threshold level is set by the transcription rate of the small RNA, and can thus be modulated dynamically to reflect changing environmental conditions.
The ability to learn and respond to recurrent events depends on the capacity to remember transient biological signals received in the past. Moreover, it may be desirable to remember or ignore these transient signals conditioned upon other signals that are active at specific points in time or in unique environments. Here, we propose a simple genetic circuit in bacteria that is capable of conditionally memorizing a signal in the form of a transcription factor concentration. The circuit behaves similarly to a “data latch” in an electronic circuit, i.e. it reads and stores an input signal only when conditioned to do so by a “read command.” Our circuit is of the same size as the well-known genetic toggle switch (an unconditional latch) which consists of two mutually repressing genes, but is complemented with a “regulatory front end” involving protein heterodimerization as a simple way to implement conditional control. Deterministic and stochastic analysis of the circuit dynamics indicate that an experimental implementation is feasible based on well-characterized genes and proteins. It is not known, to which extent molecular networks are able to conditionally store information in natural contexts for bacteria. However, our results suggest that such sequential logic elements may be readily implemented by cells through the combination of existing protein–protein interactions and simple transcriptional regulation.
Electronic Supplementary Material
The online version of this article (doi:10.1007/s11693-007-9006-8) contains supplementary material, which is available to authorized users.
Gene regulation; Sequential logic; Quantitative modeling; Synthetic biology
An increasing number of small RNAs (sRNAs) have been shown to regulate critical pathways in prokaryotes and eukaryotes. In bacteria, regulation by trans-encoded sRNAs is predominantly found in the coordination of intricate stress responses. The mechanisms by which sRNAs modulate expression of its targets are diverse. In common to most is the possibility that interference with the translation of mRNA targets may also alter the abundance of functional sRNAs. Aiming to understand the unique role played by sRNAs in gene regulation, we studied examples from two distinct classes of bacterial sRNAs in Escherichia coli using a quantitative approach combining experiment and theory. Our results demonstrate that sRNA provides a novel mode of gene regulation, with characteristics distinct from those of protein-mediated gene regulation. These include a threshold-linear response with a tunable threshold, a robust noise resistance characteristic, and a built-in capability for hierarchical cross-talk. Knowledge of these special features of sRNA-mediated regulation may be crucial toward understanding the subtle functions that sRNAs can play in coordinating various stress-relief pathways. Our results may also help guide the design of synthetic genetic circuits that have properties difficult to attain with protein regulators alone.
The activation of stress response programs, while crucial for the survival of a bacterial cell under stressful conditions, is costly in terms of energy and substrates and risky to the normal functions of the cell. Stress response is therefore tightly regulated. A recently discovered layer of regulation involves small RNA molecules, which bind the mRNA transcripts of their targets, inhibit their translation, and promote their cleavage. To understand the role that small RNA plays in regulation, we have studied the quantitative aspects of small RNA regulation by integrating mathematical modeling and quantitative experiments in Escherichia coli. We have demonstrated that small RNAs can tightly repress their target genes when their synthesis rate is smaller than some threshold, but have little or no effect when the synthesis rate is much larger than that threshold. Importantly, the threshold level is set by the synthesis rate of the small RNA itself and can be dynamically tuned. The effect of biochemical properties—such as the binding affinity of the two RNA molecules, which can only be altered on evolutionary time scales—is limited to setting a hierarchical order among different targets of a small RNA, facilitating in principle a global coordination of stress response.
In bacteria, small RNAs can regulate the expression of genes at the translational level. The many advantages of this type of control include a tuneable threshold response and resistance to biochemical noise.
The distribution of optimal local alignment scores of random
sequences plays a vital role in evaluating the statistical significance
of sequence alignments. These scores can be well described by an
extreme-value distribution. The distribution’s parameters depend
upon the scoring system employed and the random letter frequencies;
in general they cannot be derived analytically, but must be estimated
by curve fitting. For obtaining accurate parameter estimates, a form
of the recently described ‘island’ method has several
advantages. We describe this method in detail, and use it to investigate
the functional dependence of these parameters on finite-length edge
Cell-type specific genes were recognized by interrogating
microarrays carrying Dictyostelium gene fragments with
probes prepared from fractions enriched in prestalk and prespore
cells. Cell-type specific accumulation of mRNA from 17 newly
identified genes was confirmed by Northern analyses. DNA microarrays
carrying 690 targets were used to determine expression profiles during
development. The profiles were fit to a biologically based kinetic
equation to extract the times of transcription onset and cessation.
Although the majority of the genes that were cell-type enriched at the
slug stage were first expressed as the prespore and prestalk cells
sorted out in aggregates, some were found to be expressed earlier
before the cells had even aggregated. These early genes may have been
initially expressed in all cells and then preferentially turned over in
one or the other cell type. Alternatively, cell type divergence may
start soon after the initiation of development.