A growth-rate composition formula for the growth of E.coli on co-utilized carbon substrates

When bacteria are cultured in medium with multiple carbon substrates, they frequently consume these substrates simultaneously. Building on recent advances in the understanding of metabolic coordination exhibited by Escherichia coli cells through cAMP-Crp signaling, we show that this signaling system responds to the total carbon-uptake flux when substrates are co-utilized and derive a mathematical formula that accurately predicts the resulting growth rate, based only on the growth rates on individual substrates.

Quantitative proteomic analysis reveals a simple strategy of global resource allocation in bacteria

A central aim of cell biology was to understand the strategy of gene expression in response to the environment. Here, we study gene expression response to metabolic challenges in exponentially growing Escherichia coli using mass spectrometry. Despite enormous complexity in the details of the underlying regulatory network, we find that the proteome partitions into several coarse-grained sectors, with each sector's total mass abundance exhibiting positive or negative linear relations with the growth rate. The growth rate-dependent components of the proteome fractions comprise about half of the proteome by mass, and their mutual dependencies can be characterized by a simple flux model involving only two effective parameters. The success and apparent generality of this model arises from tight coordination between proteome partition and metabolism, suggesting a principle for resource allocation in proteome economy of the cell. This strategy of global gene regulation should serve as a basis for future studies on gene expression and constructing synthetic biological circuits. Coarse graining may be an effective approach to derive predictive phenomenological models for other ‘omics’ studies.

Emergence of robust growth laws from optimal regulation of ribosome synthesis

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.

Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse

Reaction-diffusion models have been used as a paradigm for describing the de novo emergence of biological patterns such as stripes and spots. In many organisms, these initial patterns are typically refined and elaborated over the subsequent course of development. Here we study the formation of secondary hair follicle patterns in the skin of developing mouse embryos. We used the expression of sex-determining region Y box 2 to identify and distinguish the primary and secondary hair follicles and to infer the spatiotemporal dynamics of the follicle formation process. Quantitative analysis of the specific follicle patterns observed reveals a simple geometrical rule governing the formation of secondary follicles, and motivates an expansion-induction (EI) model in which new follicle formation is driven by the physical growth of the embryo. The EI model requires only one diffusible morphogen and provides quantitative, accurate predictions on the relative positions and timing of secondary follicle formation, using only the observed configuration of primary follicles as input. The same model accurately describes the positions of additional follicles that emerge from skin explants treated with an activator. Thus, the EI model provides a simple and robust mechanism for predicting secondary space-filling patterns in growing embryos.

Bacterial growth: global effects on gene expression, growth feedback and proteome partition

The function of endogenous as well as synthetic genetic circuits is generically coupled to the physiological state of the cell. For exponentially growing bacteria, a key characteristic of the state of the cell is the growth rate and thus gene expression is often growth-rate dependent. Here we review recent results on growth-rate dependent gene expression. We distinguish different types of growth-rate dependencies by the mechanisms of regulation involved and the presence or absence of an effect of the gene product on growth. The latter can lead to growth feedback, feedback mediated by changes of the global state of the cell. Moreover, we discuss how growth rate dependence can be used as a guide to study the molecular implementation of physiological regulation.

Direct coupling analysis for protein contact prediction

During evolution, structure, and function of proteins are remarkably conserved, whereas amino-acid sequences vary strongly between homologous proteins. Structural conservation constrains sequence variability and forces different residues to coevolve, i.e., to show correlated patterns of amino-acid occurrences. However, residue correlation may result from direct coupling, e.g., by a contact in the folded protein, or be induced indirectly via intermediate residues. To use empirically observed correlations for predicting residue-residue contacts, direct and indirect effects have to be disentangled. Here we present mechanistic details on how to achieve this using a methodology called Direct Coupling Analysis (DCA). DCA has been shown to produce highly accurate estimates of amino-acid pairs that have direct reciprocal constraints in evolution. Specifically, we provide instructions and protocols on how to use the algorithmic implementations of DCA starting from data extraction to predicted-contact visualization in contact maps or representative protein structures.

The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria

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 nongrowing populations, that is, growth bistability, below the threshold.

Stripe formation in bacterial systems with density-suppressed motility

Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that includes growth and density-suppressed motility of the cells. The spreading of a region of immotile cells into an initially cell-free region is analyzed. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

Stripe formation in bacterial systems with density-suppressed motility

Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that includes growth and density-suppressed motility of the cells. The spreading of a region of immotile cells into an initially cell-free region is analyzed. From the calculated front profile we provide an analytic ansatz to determine the phase boundary between the stripe and the no-stripe phases. The influence of various parameters on the phase boundary is discussed.

Need-based activation of ammonium uptake in Escherichia coli

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.

Speed, sensitivity, and bistability in auto-activating signaling circuits

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.

Bacterial growth laws and their applications

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.

Dissecting the specificity of protein-protein interaction in bacterial two-component signaling: orphans and crosstalks

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.

Interdependence of cell growth and gene expression: origins and consequences

In bacteria, the rate of cell proliferation and the level of gene expression are intimately intertwined. Elucidating these relations is important both for understanding the physiological functions of endogenous genetic circuits and for designing robust synthetic systems. We describe a phenomenological study that reveals intrinsic constraints governing the allocation of resources toward protein synthesis and other aspects of cell growth. A theory incorporating these constraints can accurately predict how cell proliferation and gene expression affect one another, quantitatively accounting for the effect of translation-inhibiting antibiotics on gene expression and the effect of gratuitous protein expression on cell growth. The use of such empirical relations, analogous to phenomenological laws, may facilitate our understanding and manipulation of complex biological systems before underlying regulatory circuits are elucidated.

Sources and sinks: a stochastic model of evolution in heterogeneous environments

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.

Reversible adenylylation of glutamine synthetase is dynamically counterbalanced during steady-state growth of Escherichia coli

Glutamine synthetase (GS) is the central enzyme for nitrogen assimilation in Escherichia coli and is subject to reversible adenylylation (inactivation) by a bifunctional GS adenylyltransferase/adenylyl-removing enzyme (ATase). In vitro, both of the opposing activities of ATase are regulated by small effectors, most notably glutamine and 2-oxoglutarate. In vivo, adenylyltransferase (AT) activity is critical for growth adaptation when cells are shifted from nitrogen-limiting to nitrogen-excess conditions and a rapid decrease of GS activity by adenylylation is needed. Here, we show that the adenylyl-removing (AR) activity of ATase is required to counterbalance its AT activity during steady-state growth under both nitrogen-excess and nitrogen-limiting conditions. This conclusion was established by studying AR(-)/AT(+) mutants, which surprisingly displayed steady-state growth defects in nitrogen-excess conditions due to excessive GS adenylylation. Moreover, GS was abnormally adenylylated in the AR(-) mutants even under nitrogen-limiting conditions, whereas there was little GS adenylylation in wild-type strains. Despite the importance of AR activity, we establish that AT activity is significantly regulated in vivo, mainly by the cellular glutamine concentration. There is good general agreement between quantitative estimates of AT regulation in vivo and results derived from previous in vitro studies except at very low AT activities. We propose additional mechanisms for the low AT activities in vivo. The results suggest that dynamic counterbalance by reversible covalent modification may be a general strategy for controlling the activity of enzymes such as GS, whose physiological output allows adaptation to environmental fluctuations.

Computational modeling of phosphotransfer complexes in two-component signaling

Two-component signal transduction systems enable cells in bacteria, fungi, and plants to react to extracellular stimuli. A sensor histidine kinase (SK) detects such stimuli with its sensor domains and transduces the input signals to a response regulator (RR) by trans-phosphorylation. This trans-phosphorylation reaction requires the formation of a complex formed by the two interacting proteins. The complex is stabilized by transient interactions. The nature of the transient interactions makes it challenging for experimental techniques to gain structural information. X-ray crystallography requires stable crystals, which are difficult to grow and stabilize. Similarly, the mere size of these systems proves problematic for NMR. Theoretical methods can, however, complement existing data. The statistical direct coupling analysis presented in the previous chapter reveals the interacting residues at the contact interface of the SK/RR pair. This information can be combined with the structures of the individual proteins in molecular dynamical simulation to generate structural models of the complex. The general approach, referred to as MAGMA, was tested on the sporulation phosphorelay phosphotransfer complex, the Spo0B/Spo0F pair, delivering crystal resolution accuracy. The MAGMA method is described here in a step-by-step explanation. The developed parameters are transferrable to other SK/RR systems.

Growth rate-dependent global effects on gene expression in bacteria

Bacterial gene expression depends not only on specific regulatory mechanisms, but also on bacterial growth, because important global parameters such as the abundance of RNA polymerases and ribosomes are all growth-rate dependent. Understanding of these global effects is necessary for a quantitative understanding of gene regulation and for the design of synthetic genetic circuits. We find that 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 dependencies for genetic circuits involving activators, repressors, and feedback control were analyzed and verified experimentally with synthetic circuits. Additional results suggest a feedback mechanism mediated by general growth-dependent effects that does not require 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).

Traffic patrol in the transcription of ribosomal RNA

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.

Small RNAs establish gene expression thresholds

The central role of small RNAs in regulating bacterial gene expression has been elucidated in the past 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.

An integrated mechanobiochemical feedback mechanism describes chromosome motility from prometaphase to anaphase in mitosis

During mitosis, chromosomes undergo a series of movements while being end-on attached to the kinetochore microtubules (KMTs) from spindle poles. The mechanism underlying such movements and their physiological functions remains elusive. We describe a mechanobiochemical feedback model of chromosome motility. The key ingredient is a feedback mechanism between the local chemical reactions that control the dynamics of KMTs and the mechanical state of the chromosome via tension-sensitive proteins localized at the kinetochores. This model can recapitulate all of the essential and distinct features of chromosome motilities from prometaphase to anaphase in a coherent manner. We further show that this feedback mechanism provides robust and precise means of guiding the chromosome to the cell equator regardless of the initial conditions and uncertainty in velocity. Predictions of our model can be tested experimentally.

Co-evolving motions at protein-protein interfaces of two-component signaling systems identified by covariance analysis

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.