Combinatorial transcriptional control of the lactose operon of Escherichia coli

The unreasonable effectiveness of equilibrium gene regulation through the cell cycle

Systems like the prototypical lac operon can reliably hold repression of transcription upon DNA replication across cell cycles with just 10 repressor molecules per cell and behave as if they were at equilibrium. The origin of this phenomenology is still an unresolved question. Here, we develop a general theory to analyze strong perturbations in quasi-equilibrium systems and use it to quantify the effects of DNA replication in gene regulation. We find a scaling law linking actual with predicted equilibrium transcription via a single kinetic parameter. We show that even the lac operon functions beyond the physical limits of naive regulation through compensatory mechanisms that suppress non-equilibrium effects. Synthetic systems without adjuvant activators, such as the cAMP receptor protein (CRP), lack this reliability. Our results provide a rationale for the function of CRP, beyond just being a tunable activator, as a mitigator of cell cycle perturbations.

Broccoli aptamer allows quantitative transcription regulation studies in vitro

Quantitative transcription regulation studies in vivo and in vitro often make use of reporter proteins. Here we show that using Broccoli aptamers, quantitative study of transcription in various regulatory scenarios is possible without a translational step. To explore the method we studied several regulatory scenarios that we analyzed using thermodynamic occupancy-based models, and found excellent agreement with previous studies. In the next step we show that non-coding DNA can have a dramatic effect on the level of transcription, similar to the influence of the lac repressor with a strong affinity to operator sites. Finally, we point out the limitations of the method in terms of delay times coupled to the folding of the aptamer. We conclude that the Broccoli aptamer is suitable for quantitative transcription measurements.

A parameterized two-domain thermodynamic model explains diverse mutational effects on protein allostery

New experimental findings continue to challenge our understanding of protein allostery. Recent deep mutational scanning study showed that allosteric hotspots in the tetracycline repressor (TetR) and its homologous transcriptional factors are broadly distributed rather than spanning well-defined structural pathways as often assumed. Moreover, hotspot mutation-induced allostery loss was rescued by distributed additional mutations in a degenerate fashion. Here, we develop a two-domain thermodynamic model for TetR, which readily rationalizes these intriguing observations. The model accurately captures the in vivo activities of various mutants with changes in physically transparent parameters, allowing the data-based quantification of mutational effects using statistical inference. Our analysis reveals the intrinsic connection of intra- and inter-domain properties for allosteric regulation and illustrate epistatic interactions that are consistent with structural features of the protein. The insights gained from this study into the nature of two-domain allostery are expected to have broader implications for other multi-domain allosteric proteins.

Regulatory properties of transcription factors with diverse mechanistic function

Transcription factors (TFs) regulate the process of transcription through the modulation of different kinetic steps. Although models can often describe the observed transcriptional output of a measured gene, predicting a TFs role on a given promoter requires an understanding of how the TF alters each step of the transcription process. In this work, we use a simple model of transcription to assess the role of promoter identity, and the degree to which TFs alter binding of RNAP (stabilization) and initiation of transcription (acceleration) on three primary characteristics: the range of steady-state regulation, cell-to-cell variability in expression, and the dynamic response time of a regulated gene. We find that steady state regulation and the response time of a gene behave uniquely for TFs that regulate incoherently, i.e that speed up one step but slow the other. We also find that incoherent TFs have dynamic implications, with one type of incoherent mode configuring the promoter to respond more slowly at intermediate TF concentrations. We also demonstrate that the noise of gene expression for these TFs is sensitive to promoter strength, with a distinct non-monotonic profile that is apparent under stronger promoters. Taken together, our work uncovers the coupling between promoters and TF regulatory modes with implications for understanding natural promoters and engineering synthetic gene circuits with desired expression properties.

Predictive Biophysical Neural Network Modeling of a Compendium of in vivo Transcription Factor DNA Binding Profiles for Escherichia coli

The DNA binding of most Escherichia coli Transcription Factors (TFs) has not been comprehensively mapped, and few have models that can quantitatively predict binding affinity. We report the global mapping of in vivo DNA binding for 139 E. coli TFs using ChIP-Seq. We used these data to train BoltzNet, a novel neural network that predicts TF binding energy from DNA sequence. BoltzNet mirrors a quantitative biophysical model and provides directly interpretable predictions genome-wide at nucleotide resolution. We used BoltzNet to quantitatively design novel binding sites, which we validated with biophysical experiments on purified protein. We have generated models for 125 TFs that provide insight into global features of TF binding, including clustering of sites, the role of accessory bases, the relevance of weak sites, and the background affinity of the genome. Our paper provides new paradigms for studying TF-DNA binding and for the development of biophysically motivated neural networks.

Governing principles of transcriptional logic out of equilibrium

To survive, adapt, and develop, cells respond to external and internal stimuli by tightly regulating transcription. Transcriptional regulation involves the combinatorial binding of a repertoire of transcription factors to DNA, which often results in switch-like binary outputs akin to Boolean logic gates. Recent experimental studies have demonstrated that in eukaryotes, transcription factor binding to DNA often involves energy expenditure, thereby driving the system out of equilibrium. The governing principles of transcriptional logic operations out of equilibrium remain unexplored. Here, we employ a simple two-input, single-locus model of transcription that can accommodate both equilibrium and nonequilibrium mechanisms. Using this model, we find that nonequilibrium regimes can give rise to all the logic operations accessible in equilibrium. Strikingly, energy expenditure alters the regulatory function of the two transcription factors in a mutually exclusive manner. This allows for the emergence of new logic operations that are inaccessible in equilibrium. Overall, our results show that energy expenditure can expand the range of cellular decision-making without the need for more complex promoter architectures.

Specificity, synergy, and mechanisms of splice-modifying drugs

Drugs that target pre-mRNA splicing hold great therapeutic potential, but the quantitative understanding of how these drugs work is limited. Here we introduce mechanistically interpretable quantitative models for the sequence-specific and concentration-dependent behavior of splice-modifying drugs. Using massively parallel splicing assays, RNA-seq experiments, and precision dose-response curves, we obtain quantitative models for two small-molecule drugs, risdiplam and branaplam, developed for treating spinal muscular atrophy. The results quantitatively characterize the specificities of risdiplam and branaplam for 5' splice site sequences, suggest that branaplam recognizes 5' splice sites via two distinct interaction modes, and contradict the prevailing two-site hypothesis for risdiplam activity at SMN2 exon 7. The results also show that anomalous single-drug cooperativity, as well as multi-drug synergy, are widespread among small-molecule drugs and antisense-oligonucleotide drugs that promote exon inclusion. Our quantitative models thus clarify the mechanisms of existing treatments and provide a basis for the rational development of new therapies.

A multiplexed bacterial two-hybrid for rapid characterization of protein-protein interactions and iterative protein design

Protein-protein interactions (PPIs) are crucial for biological functions and have applications ranging from drug design to synthetic cell circuits. Coiled-coils have been used as a model to study the sequence determinants of specificity. However, building well-behaved sets of orthogonal pairs of coiled-coils remains challenging due to inaccurate predictions of orthogonality and difficulties in testing at scale. To address this, we develop the next-generation bacterial two-hybrid (NGB2H) method, which allows for the rapid exploration of interactions of programmed protein libraries in a quantitative and scalable way using next-generation sequencing readout. We design, build, and test large sets of orthogonal synthetic coiled-coils, assayed over 8,000 PPIs, and used the dataset to train a more accurate coiled-coil scoring algorithm (iCipa). After characterizing nearly 18,000 new PPIs, we identify to the best of our knowledge the largest set of orthogonal coiled-coils to date, with fifteen on-target interactions. Our approach provides a powerful tool for the design of orthogonal PPIs.

A stimulus-contingent positive feedback loop enables IFN-β dose-dependent activation of pro-inflammatory genes

Type I interferons (IFN) induce powerful antiviral and innate immune responses via the transcription factor, IFN-stimulated gene factor (ISGF3). However, in some pathological contexts, type I IFNs are responsible for exacerbating inflammation. Here, we show that a high dose of IFN-β also activates an inflammatory gene expression program in contrast to IFN-λ3, a type III IFN, which elicits only the common antiviral gene program. We show that the inflammatory gene program depends on a second, potentiated phase in ISGF3 activation. Iterating between mathematical modeling and experimental analysis, we show that the ISGF3 activation network may engage a positive feedback loop with its subunits IRF9 and STAT2. This network motif mediates stimulus-specific ISGF3 dynamics that are dependent on ligand, dose, and duration of exposure, and when engaged activates the inflammatory gene expression program. Our results reveal a previously underappreciated dynamical control of the JAK-STAT/IRF signaling network that may produce distinct biological responses and suggest that studies of type I IFN dysregulation, and in turn therapeutic remedies, may focus on feedback regulators within it.

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Significance Statement

Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

Principles of gene regulation quantitatively connect DNA to RNA and proteins in bacteria

Protein concentrations are set by a complex interplay between gene-specific regulatory processes and systemic factors, including cell volume and shared gene expression machineries. Elucidating this interplay is crucial for discerning and designing gene regulatory systems. We quantitatively characterized gene-specific and systemic factors that affect transcription and translation genome-wide for Escherichia coli across many conditions. The results revealed two design principles that make regulation of gene expression insulated from concentrations of shared machineries: RNA polymerase activity is fine-tuned to match translational output, and translational characteristics are similar across most messenger RNAs (mRNAs). Consequently, in bacteria, protein concentration is set primarily at the promoter level. A simple mathematical formula relates promoter activities and protein concentrations across growth conditions, enabling quantitative inference of gene regulation from omics data.

Shared cis-regulatory modules control expression of the tandem paralogs midline and H15 in the follicular epithelium

The posterior end of the follicular epithelium is patterned by midline (MID) and its paralog H15, the Drosophila homologs of the mammalian Tbx20 transcription factor. We have previously identified two cis-regulatory modules (CRMs) that recapitulate the endogenous pattern of mid in the follicular epithelium. Here, using CRISPR/Cas9 genome editing, we demonstrate redundant activity of these mid CRMs. Although the deletion of either CRM alone generated marginal change in mid expression, the deletion of both CRMs reduced expression by 60%. Unexpectedly, the deletion of the 5' proximal CRM of mid eliminated H15 expression. Interestingly, expression of these paralogs in other tissues remained unaffected in the CRM deletion backgrounds. These results suggest that the paralogs are regulated by a shared CRM that coordinates gene expression during posterior fate determination. The consistent overlapping expression of mid and H15 in various tissues may indicate that the paralogs could also be under shared regulation by other CRMs in these tissues.

Optimal transcriptional regulation of dynamic bacterial responses to sudden drug exposures

Cellular responses to the presence of toxic compounds in their environment require prompt expression of the correct levels of the appropriate enzymes, which are typically regulated by transcription factors that control gene expression for the duration of the response. The characteristics of each response dictate the choice of regulatory parameters such as the affinity of the transcription factor to its binding sites and the strength of the promoters it regulates. Although much is known about the dynamics of cellular responses, we still lack a framework to understand how different regulatory strategies evolved in natural systems relate to the selective pressures acting in each particular case. Here, we analyze a dynamical model of a typical antibiotic response in bacteria, where a transcriptionally repressed enzyme is induced by a sudden exposure to the drug that it processes. We identify strategies of gene regulation that optimize this response for different types of selective pressures, which we define as a set of costs associated with the drug, enzyme, and repressor concentrations during the response. We find that regulation happens in a limited region of the regulatory parameter space. While responses to more costly (toxic) drugs favor the usage of strongly self-regulated repressors, responses where expression of enzyme is more costly favor the usage of constitutively expressed repressors. Only a very narrow range of selective pressures favor weakly self-regulated repressors. We use this framework to determine which costs and benefits are most critical for the evolution of a variety of natural cellular responses that satisfy the approximations in our model and to analyze how regulation is optimized in new environments with different demands.

Indirect optimization of staphylokinase expression level in dicistronic auto-inducible system

Design of experiment (DOE) is a statistical approach for designing, performing, and interpreting a large set of data with the minimum number of tests. In our previous study, we developed a novel Hsp27 SILEX system for production of recombinant proteins. In the present study, we optimized indirectly the most effective factors including inoculation load, self-induction temperature, and culture media on autoinduction of staphylokinase (SAK) expression using RSM methodology and fluorometry. The expression level of SAK was assayed at different runs after 6 h incubation at 90 rpm. The results indicated all parameters significantly affect the SAK expression level (p < 0.05). The optimum expression condition was obtained with an inoculation load of 0.05, a temperature of 25 °C, and TB culture medium. The analysis of variance with a R² value of 0.91 showed that a quadratic model well described this prediction (p < 0.05). Applying the optimized condition led to an approximately fourfold increase in the SAK expression level (from 1.3 to 5.2 µg/ml). Moreover, the recombinant protein was purified using immobilized metal affinity chromatography and the activity was also confirmed by semi-quantitative caseinolytic method.

Robustness of DNA looping across multiple cell divisions in individual bacteria

DNA looping has emerged as a central paradigm of transcriptional regulation, as it is shared across many living systems. One core property of DNA looping-based regulation is its ability to greatly enhance repression or activation of genes with only a few copies of transcriptional regulators. However, this property based on a small number of proteins raises the question of the robustness of such a mechanism with respect to the large intracellular perturbations taking place during growth and division of the cell. Here we address the issue of sensitivity to variations of intracellular parameters of gene regulation by DNA looping. We use the lac system as a prototype to experimentally identify the key features of the robustness of DNA looping in growing Escherichia coli cells. Surprisingly, we observe time intervals of tight repression spanning across division events, which can sometimes exceed 10 generations. Remarkably, the distribution of such long time intervals exhibits memoryless statistics that is mostly insensitive to repressor concentration, cell division events, and the number of distinct loops accessible to the system. By contrast, gene regulation becomes highly sensitive to these perturbations when DNA looping is absent. Using stochastic simulations, we propose that the observed robustness to division emerges from the competition between fast, multiple rebinding events of repressors and slow initiation rate of the RNA polymerase. We argue that fast rebinding events are a direct consequence of DNA looping that ensures robust gene repression across a range of intracellular perturbations.

Stochastic gene transcription with non-competitive transcription regulatory architecture

The transcription factors, such as activators and repressors, can interact with the promoter of gene either in a competitive or non-competitive way. In this paper, we construct a stochastic model with non-competitive transcriptional regulatory architecture and develop an analytical theory that re-establishes the experimental results with an improved data fitting. The analytical expressions in the theory allow us to study the nature of the system corresponding to any of its parameters and hence, enable us to find out the factors that govern the regulation of gene expression for that architecture. We notice that, along with transcriptional reinitiation and repressors, there are other parameters that can control the noisiness of this network. We also observe that, the Fano factor (at mRNA level) varies from sub-Poissonian regime to super-Poissonian regime. In addition to the aforementioned properties, we observe some anomalous characteristics of the Fano factor (at mRNA level) and that of the variance of protein at lower activator concentrations in the presence of repressor molecules. This model is useful to understand the architecture of interactions which may buffer the stochasticity inherent to gene transcription.

Intermittent induction of LEA peptide by lactose enhances the expression of insecticidal proteins in Bacillus thuringiensis

Cry toxins from Bacillus thuringiensis (Bt) have been extensively applied in agriculture to substitute the use of chemical insecticides. We have previously reported the use of a coexpression system in which late embryogenesis abundant (LEA) peptides under the control of the lac promoter increase the expression of insecticidal proteins in Bt. The use of lactose to induce the expression of LEA peptides may be a desirable alternative to isopropyl β‐D‐thiogalactopyranoside, the most frequently used inducer for recombinant protein expression. In this study we investigated the use of lactose as an inducer for optimal protein expression. We observed enhanced insecticidal Cry protein expression by applying a simple technique based on intermittent induction, and then optimized concentration and the point of induction time from the 11^th h to the 15^th h. Our data suggest that intermittent induction of lactose might be a new technique for the enhancement of bacterial protein expression.

Inducer exclusion, by itself, cannot account for the glucose-mediated lac repression of Escherichia coli

The lac operon of Escherichia coli is repressed several 100-fold in the presence of glucose. This repression has been attributed to cAMP receptor protein-mediated inhibition of lac transcription and EIIA^Glc-mediated inhibition of lactose transport (inducer exclusion). The growing evidence against the first mechanism has led to the postulate that the repression is driven by inducer exclusion. Although inducer exclusion reduces the permease activity only 2-fold in fully induced cells, it could be more potent in partially induced cells. Here, we show that even in partially induced cells, inducer exclusion reduces the permease activity no more than 6-fold. Moreover, the repression is so small because these experiments are performed in the presence of chloramphenicol. Indeed, when glucose is added to a culture growing on glycerol and TMG, but no chloramphenicol, lac expression is repressed 900-fold. This repression is primarily due to reversal of the positive feedback loop, i.e., the decline of the intracellular TMG level leads to a lower permease level, which reduces the intracellular TMG level even further. The repression in the absence of chloramphenicol is therefore primarily due to positive feedback, which does not exist during measurements of inducer exclusion.

Quantifying the regulatory role of individual transcription factors in Escherichia coli

Gene regulation often results from the action of multiple transcription factors (TFs) acting at a promoter, obscuring the individual regulatory effect of each TF on RNA polymerase (RNAP). Here we measure the fundamental regulatory interactions of TFs in E. coli by designing synthetic target genes that isolate individual TFs' regulatory effects. Using a thermodynamic model, each TF's regulatory interactions are decoupled from TF occupancy and interpreted as acting through (de)stabilization of RNAP and (de)acceleration of transcription initiation. We find that the contribution of each mechanism depends on TF identity and binding location; regulation immediately downstream of the promoter is insensitive to TF identity, but the same TFs regulate by distinct mechanisms upstream of the promoter. These two mechanisms are uncoupled and can act coherently, to reinforce the observed regulatory role (activation/repression), or incoherently, wherein the TF regulates two distinct steps with opposing effects.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

Gene transcriptional process is random. It occurs in bursts and follows single-molecular kinetics. Intermittent bursts are measured based on their frequency and size. They influence temporal fluctuations in the abundance of total mRNA and proteins by generating distinct transcriptional variations referred to as “noise”. Noisy expression induces uncertainty because the association between transcriptional variation and the extent of gene expression fluctuation is ambiguous. The promoter architecture and remote interference of different cis-regulatory elements are the crucial determinants of noise, which is reflected in phenotypic heterogeneity. An alternative perspective considers that cellular parameters dictating genome-wide transcriptional kinetics follow a universal pattern. Research on noise and systematic perturbations of promoter sequences reinforces that both gene-specific and genome-wide regulation occur across species ranging from bacteria and yeast to animal cells. Thus, deciphering gene-expression noise is essential across different genomics applications. Amidst the mounting conflict, it is imperative to reconsider the scope, progression, and rational construction of diversified viewpoints underlying the origin of the noise. Here, we have established an indication connecting noise, gene expression variations, and bacterial phenotypic variability. This review will enhance the understanding of gene-expression noise in various scientific contexts and applications.

Integrated Strategies for Enhancing the Expression of the AqCoA Chitosanase in Pichia pastoris by Combined Optimization of Molecular Chaperones Combinations and Copy Numbers via a Novel Plasmid pMC-GAP

In our previous study, the chitosanase AqCoA and the chitooligosaccharides it produced were found to exhibit significant protective effects against fungal diseases. In this study, we enhanced the expression of AqCoA using the novel pMC-GAP that enables stable transformation of Escherichia coli, and built an integrated model based on the gene copy number, molecular chaperones, and protein production of AqCoA. In terms of gene dosage, the highest hydrolase activity was 0.32 U/ml in the strain with four copies, which was 1.78-fold higher than that of the strain with only one copy (0.18 U/ml). In addition, we found the chaperones such as PDI, ERO1, HAC1, YDJ1, SSE1, SSA4, and SSO2 improved protein expression. Furthermore, the PDI/ERO1, SSA4/SSE1, and YDJ1/SSO2 pairs synergistically increased the expression levels by 61%, 31%, and 42%, respectively. Finally, we investigated the combined effects of gene copy numbers and molecular chaperones on protein expression. The highest activity reached 2.32 U/ml in the strain with six integrated molecular chaperone expression cassettes and sixteen copies of the target gene, which was 13-fold higher than that of the control strain with only one copy (GAP-1AqCoA). Combined optimization of gene dosage and molecular chaperone combinations significantly increased the expression level of AqCoA, providing a powerful strategy to improve the expression of other heterologous proteins in P. pastoris.

Global coordination of metabolic pathways in Escherichia coli by active and passive regulation

Microorganisms adjust metabolic activity to cope with diverse environments. While many studies have provided insights into how individual pathways are regulated, the mechanisms that give rise to coordinated metabolic responses are poorly understood. Here, we identify the regulatory mechanisms that coordinate catabolism and anabolism in Escherichia coli. Integrating protein, metabolite, and flux changes in genetically implemented catabolic or anabolic limitations, we show that combined global and local mechanisms coordinate the response to metabolic limitations. To allocate proteomic resources between catabolism and anabolism, E. coli uses a simple global gene regulatory program. Surprisingly, this program is largely implemented by a single transcription factor, Crp, which directly activates the expression of catabolic enzymes and indirectly reduces the expression of anabolic enzymes by passively sequestering cellular resources needed for their synthesis. However, metabolic fluxes are not controlled by this regulatory program alone; instead, fluxes are adjusted mostly through passive changes in the local metabolite concentrations. These mechanisms constitute a simple but effective global regulatory program that coarsely partitions resources between different parts of metabolism while ensuring robust coordination of individual metabolic reactions.

Prebiotic properties of Bacillus coagulans MA-13: production of galactoside hydrolyzing enzymes and characterization of the transglycosylation properties of a GH42 β-galactosidase

Background

The spore-forming lactic acid bacterium Bacillus coagulans MA-13 has been isolated from canned beans manufacturing and successfully employed for the sustainable production of lactic acid from lignocellulosic biomass. Among lactic acid bacteria, B. coagulans strains are generally recognized as safe (GRAS) for human consumption. Low-cost microbial production of industrially valuable products such as lactic acid and various enzymes devoted to the hydrolysis of oligosaccharides and lactose, is of great importance to the food industry. Specifically, α- and β-galactosidases are attractive for their ability to hydrolyze not-digestible galactosides present in the food matrix as well as in the human gastrointestinal tract.

Results

In this work we have explored the potential of B. coagulans MA-13 as a source of metabolites and enzymes to improve the digestibility and the nutritional value of food. A combination of mass spectrometry analysis with conventional biochemical approaches has been employed to unveil the intra- and extra- cellular glycosyl hydrolase (GH) repertoire of B. coagulans MA-13 under diverse growth conditions. The highest enzymatic activity was detected on β-1,4 and α-1,6-glycosidic linkages and the enzymes responsible for these activities were unambiguously identified as β-galactosidase (GH42) and α-galactosidase (GH36), respectively. Whilst the former has been found only in the cytosol, the latter is localized also extracellularly. The export of this enzyme may occur through a not yet identified secretion mechanism, since a typical signal peptide is missing in the α-galactosidase sequence. A full biochemical characterization of the recombinant β-galactosidase has been carried out and the ability of this enzyme to perform homo- and hetero-condensation reactions to produce galacto-oligosaccharides, has been demonstrated.

Conclusions

Probiotics which are safe for human use and are capable of producing high levels of both α-galactosidase and β-galactosidase are of great importance to the food industry. In this work we have proven the ability of B. coagulans MA-13 to over-produce these two enzymes thus paving the way for its potential use in treatment of gastrointestinal diseases.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12934-021-01553-y.

Reconciling kinetic and thermodynamic models of bacterial transcription

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.

Exploring the effect of network topology, mRNA and protein dynamics on gene regulatory network stability

Homeostasis of protein concentrations in cells is crucial for their proper functioning, requiring steady-state concentrations to be stable to fluctuations. Since gene expression is regulated by proteins such as transcription factors (TFs), the full set of proteins within the cell constitutes a large system of interacting components, which can become unstable. We explore factors affecting stability by coupling the dynamics of mRNAs and proteins in a growing cell. We find that mRNA degradation rate does not affect stability, contrary to previous claims. However, global structural features of the network can dramatically enhance stability. Importantly, a network resembling a bipartite graph with a lower fraction of interactions that target TFs has a higher chance of being stable. Scrambling the E. coli transcription network, we find that the biological network is significantly more stable than its randomized counterpart, suggesting that stability constraints may have shaped network structure during the course of evolution.

Nonequilibrium models of optimal enhancer function

Simple biophysical models successfully describe bacterial regulatory code, by predicting gene expression from DNA sequences that bind specialized regulatory proteins. Analogous simple models fail in multicellular organisms, where regulatory proteins bind DNA very transiently, yet, nevertheless, effect precise control over gene expression. To date, the more general, “nonequilibrium” models have proven difficult to analyze and connect to data. Here, we reduce this complexity theoretically, by constructing simple nonequilibrium models which perform optimal gene regulation within known experimental constraints.

In prokaryotes, thermodynamic models of gene regulation provide a highly quantitative mapping from promoter sequences to gene-expression levels that is compatible with in vivo and in vitro biophysical measurements. Such concordance has not been achieved for models of enhancer function in eukaryotes. In equilibrium models, it is difficult to reconcile the reported short transcription factor (TF) residence times on the DNA with the high specificity of regulation. In nonequilibrium models, progress is difficult due to an explosion in the number of parameters. Here, we navigate this complexity by looking for minimal nonequilibrium enhancer models that yield desired regulatory phenotypes: low TF residence time, high specificity, and tunable cooperativity. We find that a single extra parameter, interpretable as the “linking rate,” by which bound TFs interact with Mediator components, enables our models to escape equilibrium bounds and access optimal regulatory phenotypes, while remaining consistent with the reported phenomenology and simple enough to be inferred from upcoming experiments. We further find that high specificity in nonequilibrium models is in a trade-off with gene-expression noise, predicting bursty dynamics—an experimentally observed hallmark of eukaryotic transcription. By drastically reducing the vast parameter space of nonequilibrium enhancer models to a much smaller subspace that optimally realizes biological function, we deliver a rich class of models that could be tractably inferred from data in the near future.

Inherent regulatory asymmetry emanating from network architecture in a prevalent autoregulatory motif

Predicting gene expression from DNA sequence remains a major goal in the field of gene regulation. A challenge to this goal is the connectivity of the network, whose role in altering gene expression remains unclear. Here, we study a common autoregulatory network motif, the negative single-input module, to explore the regulatory properties inherited from the motif. Using stochastic simulations and a synthetic biology approach in E. coli, we find that the TF gene and its target genes have inherent asymmetry in regulation, even when their promoters are identical; the TF gene being more repressed than its targets. The magnitude of asymmetry depends on network features such as network size and TF-binding affinities. Intriguingly, asymmetry disappears when the growth rate is too fast or too slow and is most significant for typical growth conditions. These results highlight the importance of accounting for network architecture in quantitative models of gene expression.

Kinetic control of stationary flux ratios for a wide range of biochemical processes

One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi-first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5'-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes.

Figure 1 Theory Meets Figure 2 Experiments in the Study of Gene Expression

It is tempting to believe that we now own the genome. The ability to read and rewrite it at will has ushered in a stunning period in the history of science. Nonetheless, there is an Achilles' heel exposed by all of the genomic data that has accrued: We still do not know how to interpret them. Many genes are subject to sophisticated programs of transcriptional regulation, mediated by DNA sequences that harbor binding sites for transcription factors, which can up- or down-regulate gene expression depending upon environmental conditions. This gives rise to an input-output function describing how the level of expression depends upon the parameters of the regulated gene-for instance, on the number and type of binding sites in its regulatory sequence. In recent years, the ability to make precision measurements of expression, coupled with the ability to make increasingly sophisticated theoretical predictions, has enabled an explicit dialogue between theory and experiment that holds the promise of covering this genomic Achilles' heel. The goal is to reach a predictive understanding of transcriptional regulation that makes it possible to calculate gene expression levels from DNA regulatory sequence. This review focuses on the canonical simple repression motif to ask how well the models that have been used to characterize it actually work. We consider a hierarchy of increasingly sophisticated experiments in which the minimal parameter set learned at one level is applied to make quantitative predictions at the next. We show that these careful quantitative dissections provide a template for a predictive understanding of the many more complex regulatory arrangements found across all domains of life.

Dissipation in Non-Steady State Regulatory Circuits

In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

High-order interactions distort the functional landscape of microbial consortia

Understanding the link between community composition and function is a major challenge in microbial population biology, with implications for the management of natural microbiomes and the design of synthetic consortia. Specifically, it is poorly understood whether community functions can be quantitatively predicted from traits of species in monoculture. Inspired by the study of complex genetic interactions, we have examined how the amylolytic rate of combinatorial assemblages of six starch-degrading soil bacteria depend on the separate functional contributions from each species and their interactions. Filtering our results through the theory of biochemical kinetics, we show that this simple function is additive in the absence of interactions among community members. For about half of the combinatorially assembled consortia, the amylolytic function is dominated by pairwise and higher-order interactions. For the other half, the function is additive despite the presence of strong competitive interactions. We explain the mechanistic basis of these findings and propose a quantitative framework that allows us to separate the effect of behavioral and population dynamics interactions. Our results suggest that the functional robustness of a consortium to pairwise and higher-order interactions critically affects our ability to predict and bottom-up engineer ecosystem function in complex communities.

Diversity in lac Operon Regulation among Diverse Escherichia coli Isolates Depends on the Broader Genetic Background but Is Not Explained by Genetic Relatedness

The lac operon of Escherichia coli is a classic model for studying gene regulation. This study has uncovered features such as the environmental input logic controlling gene expression, as well as gene expression bistability and hysteresis. Most lac operon studies have focused on a few lab strains, and it is not known how generally those findings apply to the diversity of E. coli strains. We examined the environmental dependence of lac gene regulation in 20 natural isolates of E. coli and found a wide range of regulatory responses. By transferring lac genes from natural isolate strains into a common reference strain, we found that regulation depends on both the lac genes themselves and on the broader genetic background, indicating potential for still-greater regulatory diversity following horizontal gene transfer. Our results reveal that there is substantial natural variation in the regulation of the lac operon and indicate that this variation can be ecologically meaningful.

Transcription of bacterial genes is controlled by the coordinated action of cis- and trans-acting regulators. The activity and mode of action of these regulators can reflect different requirements for gene products in different environments. A well-studied example is the regulatory function that integrates the environmental availability of glucose and lactose to control the Escherichia colilac operon. Most studies of lac operon regulation have focused on a few closely related strains. To determine the range of natural variation in lac regulatory function, we introduced a reporter construct into 23 diverse E. coli strains and measured expression with combinations of inducer concentrations. We found a wide range of regulatory functions. Several functions were similar to the one observed in a reference lab strain, whereas others depended weakly on the presence of cAMP. Some characteristics of the regulatory function were explained by the genetic relatedness of strains, indicating that differences varied on relatively short time scales. The regulatory characteristics explained by genetic relatedness were among those that best predicted the initial growth of strains following transition to a lactose environment, suggesting a role for selection. Finally, we transferred the lac operon, with the lacI regulatory gene, from five natural isolate strains into a reference lab strain. The regulatory function of these hybrid strains revealed the effect of local and global regulatory elements in controlling expression. Together, this work demonstrates that regulatory functions can be varied within a species and that there is variation within a species to best match a function to particular environments.

Measuring transcription at a single gene copy reveals hidden drivers of bacterial individuality

Single-cell measurements of mRNA copy-number inform our understanding of stochastic gene expression [1-3], but these measurements coarse-grain over the individual copies of the gene, where transcription and its regulation stochastically take plasce [4, 5]. Here we combine single-molecule quantification of mRNA and gene loci to measure the transcriptional activity of an endogenous gene in individual Escherichia coli bacteria. Interpreted using a theoretical model for mRNA dynamics, the single-cell data allows us to obtain the probabilistic rates of promoter switching, transcription initiation and elongation, mRNA release and degradation. Unexpectedly, we find that gene activity can be strongly coupled to the transcriptional state of another copy of the same gene present in the cell, and to the event of gene replication during the bacterial cell cycle. These gene-copy and cell-cycle correlations demonstrate the limits of mapping whole-cell mRNA numbers to the underlying stochastic gene activity, and instead highlight the contribution of previously hidden variables to the observed population heterogeneity.

Predictive shifts in free energy couple mutations to their phenotypic consequences

Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level responses. Here, we present a framework centered on measuring changes in the free energy of the system to link individual mutations in an allosteric transcriptional repressor to the parameters which govern its response. We find that the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor of Escherichia coli, probing several mutations in the DNA binding and inducer binding domains. We find that the change in gene expression due to a point mutation can be captured by modifying only the model parameters that describe the respective domain of the wild-type protein. These parameters appear to be insulated, with mutations in the DNA binding domain altering only the DNA affinity and those in the inducer binding domain altering only the allosteric parameters. Changing these subsets of parameters tunes the free energy of the system in a way that is concordant with theoretical expectations. Finally, we show that the induction profiles and resulting free energies associated with pairwise double mutants can be predicted with quantitative accuracy given knowledge of the single mutants, providing an avenue for identifying and quantifying epistatic interactions.

How the avidity of polymerase binding to the -35/-10 promoter sites affects gene expression

Although the key promoter elements necessary to drive transcription in Escherichia coli have long been understood, we still cannot predict the behavior of arbitrary novel promoters, hampering our ability to characterize the myriad sequenced regulatory architectures as well as to design new synthetic circuits. This work builds upon a beautiful recent experiment by Urtecho et al. [G. Urtecho, et al, Biochemistry, 68, 1539-1551 (2019)] who measured the gene expression of over 10,000 promoters spanning all possible combinations of a small set of regulatory elements. Using these data, we demonstrate that a central claim in energy matrix models of gene expression-that each promoter element contributes independently and additively to gene expression-contradicts experimental measurements. We propose that a key missing ingredient from such models is the avidity between the -35 and -10 RNA polymerase binding sites and develop what we call a multivalent model that incorporates this effect and can successfully characterize the full suite of gene expression data. We explore several applications of this framework, namely, how multivalent binding at the -35 and -10 sites can buffer RNA polymerase (RNAP) kinetics against mutations and how promoters that bind overly tightly to RNA polymerase can inhibit gene expression. The success of our approach suggests that avidity represents a key physical principle governing the interaction of RNA polymerase to its promoter.

Simulating Genetic Circuits in Bacterial Populations with Growth Heterogeneity

We computationally study genetic circuits in bacterial populations with heterogeneities in the growth rate. To that end, we present a stochastic simulation method for gene circuits in populations of cells and propose an efficient implementation that we call the "Next Family Method". Within this approach, we implement different population setups, specifically Chemostat-type growth and growth in an ideal Mother Machine and show that the population structure and its statistics are different for the different setups whenever there is growth heterogeneity. Such dependence on the population setup is demonstrated, in the case of bistable systems with different growth rates in the stable states, to have distinctive signatures on quantities including the distributions of protein concentration and growth rates, and hysteresis curves. Applying this method to a bistable antibiotic resistance circuit, we find that as a result of the different statistics in different population setups, the estimated minimal inhibitory concentration of the antibiotic becomes dependent on the population setup in which it is measured.

Measuring cis-regulatory energetics in living cells using allelic manifolds

Gene expression in all organisms is controlled by cooperative interactions between DNA-bound transcription factors (TFs), but quantitatively measuring TF-DNA and TF-TF interactions remains difficult. Here we introduce a strategy for precisely measuring the Gibbs free energy of such interactions in living cells. This strategy centers on the measurement and modeling of ‘allelic manifolds’, a multidimensional generalization of the classical genetics concept of allelic series. Allelic manifolds are measured using reporter assays performed on strategically designed cis-regulatory sequences. Quantitative biophysical models are then fit to the resulting data. We used this strategy to study regulation by two Escherichia coli TFs, CRP and σ70 RNA polymerase. Doing so, we consistently obtained energetic measurements precise to ∼0.1 kcal/mol. We also obtained multiple results that deviate from the prior literature. Our strategy is compatible with massively parallel reporter assays in both prokaryotes and eukaryotes, and should therefore be highly scalable and broadly applicable.

Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that minor issues remain unresolved (see decision letter).

Testing the retroelement invasion hypothesis for the emergence of the ancestral eukaryotic cell

Phylogenetic evidence suggests that the invasion and proliferation of retroelements, selfish mobile genetic elements that copy and paste themselves within a host genome, was one of the early evolutionary events in the emergence of eukaryotes. Here we test the effects of this event by determining the pressures retroelements exert on simple genomes. We transferred two retroelements, human LINE-1 and the bacterial group II intron Ll.LtrB, into bacteria, and find that both are functional and detrimental to growth. We find, surprisingly, that retroelement lethality and proliferation are enhanced by the ability to perform eukaryotic-like nonhomologous end-joining (NHEJ) DNA repair. We show that the only stable evolutionary consequence in simple cells is maintenance of retroelements in low numbers, suggesting how retrotransposition rates and costs in early eukaryotes could have been constrained to allow proliferation. Our results suggest that the interplay between NHEJ and retroelements may have played a fundamental and previously unappreciated role in facilitating the proliferation of retroelements, elements of which became the ancestors of the spliceosome components in eukaryotes.

Theoretical analysis of inducer and operator binding for cyclic-AMP receptor protein mutants

Allosteric transcription factors undergo binding events at inducer binding sites as well as at distinct DNA binding domains, and it is difficult to disentangle the structural and functional consequences of these two classes of interactions. We compare the ability of two statistical mechanical models—the Monod-Wyman-Changeux (MWC) and the Koshland-Némethy-Filmer (KNF) models of protein conformational change—to characterize the multi-step activation mechanism of the broadly acting cyclic-AMP receptor protein (CRP). We first consider the allosteric transition resulting from cyclic-AMP binding to CRP, then analyze how CRP binds to its operator, and finally investigate the ability of CRP to activate gene expression. We use these models to examine a beautiful recent experiment that created a single-chain version of the CRP homodimer, creating six mutants using all possible combinations of the wild type, D53H, and S62F subunits. We demonstrate that the MWC model can explain the behavior of all six mutants using a small, self-consistent set of parameters whose complexity scales with the number of subunits, providing a significant benefit over previous models. In comparison, the KNF model not only leads to a poorer characterization of the available data but also fails to generate parameter values in line with the available structural knowledge of CRP. In addition, we discuss how the conceptual framework developed here for CRP enables us to not merely analyze data retrospectively, but has the predictive power to determine how combinations of mutations will interact, how double mutants will behave, and how each construct would regulate gene expression.

Post-transcriptional bursting in genes regulated by small RNA molecules

Gene expression programs in living cells are highly dynamic due to spatiotemporal molecular signaling and inherent biochemical stochasticity. Here we study a mechanism based on molecule-to-molecule variability at the RNA level for the generation of bursts of protein production, which can lead to heterogeneity in a cell population. We develop a mathematical framework to show numerically and analytically that genes regulated post transcriptionally by small RNA molecules can exhibit such bursts due to different states of translation activity (on or off), mostly revealed in a regime of few molecules. We exploit this framework to compare transcriptional and post-transcriptional bursting and also to illustrate how to tune the resulting protein distribution with additional post-transcriptional regulations. Moreover, because RNA-RNA interactions are predictable with an energy model, we define the kinetic constants of on-off switching as functions of the two characteristic free-energy differences of the system, activation and formation, with a nonequilibrium scheme. Overall, post-transcriptional bursting represents a distinctive principle linking gene regulation to gene expression noise, which highlights the importance of the RNA layer beyond the simple information transfer paradigm and significantly contributes to the understanding of the intracellular processes from a first-principles perspective.

Distinct mechanisms coordinate transcription and translation under carbon and nitrogen starvation in Escherichia coli

Bacteria adapt to environmental stress by producing proteins that provide stress protection. However, stress can severely perturb the kinetics of gene expression, disrupting protein production. Here, we characterized how Escherichia coli mitigates such perturbations under nutrient stress through the kinetic coordination of transcription and translation. We observed that, when translation became limiting under nitrogen starvation, transcription elongation slowed accordingly. This slowdown was mediated by (p)ppGpp, the alarmone whose primary role is thought to be promoter regulation. This kinetic coordination by (p)ppGpp was critical for the robust synthesis of gene products. Surprisingly, under carbon starvation, (p)ppGpp was dispensable for robust synthesis. Characterization of the underlying kinetics revealed that under carbon starvation, transcription became limiting, and translation aided transcription elongation. This mechanism naturally coordinated transcription with translation, alleviating the need for (p)ppGpp as a mediator. These contrasting mechanisms for coordination resulted in the condition-dependent effects of (p)ppGpp on global protein synthesis and starvation survival. Our findings reveal a kinetic aspect of gene expression plasticity, establishing (p)ppGpp as a condition-dependent global effector of gene expression.

Systematic approach for dissecting the molecular mechanisms of transcriptional regulation in bacteria

Organisms must constantly make regulatory decisions in response to a change in cellular state or environment. However, while the catalog of genomes expands rapidly, we remain ignorant about how the genes in these genomes are regulated. Here, we show how a massively parallel reporter assay, Sort-Seq, and information-theoretic modeling can be used to identify regulatory sequences. We then use chromatography and mass spectrometry to identify the regulatory proteins that bind these sequences. The approach results in quantitative base pair-resolution models of promoter mechanism and was shown in both well-characterized and unannotated promoters in Escherichia coli. Given the generality of the approach, it opens up the possibility of quantitatively dissecting the mechanisms of promoter function in a wide range of bacteria.

Gene regulation is one of the most ubiquitous processes in biology. However, while the catalog of bacterial genomes continues to expand rapidly, we remain ignorant about how almost all of the genes in these genomes are regulated. At present, characterizing the molecular mechanisms by which individual regulatory sequences operate requires focused efforts using low-throughput methods. Here, we take a first step toward multipromoter dissection and show how a combination of massively parallel reporter assays, mass spectrometry, and information-theoretic modeling can be used to dissect multiple bacterial promoters in a systematic way. We show this approach on both well-studied and previously uncharacterized promoters in the enteric bacterium Escherichia coli. In all cases, we recover nucleotide-resolution models of promoter mechanism. For some promoters, including previously unannotated ones, the approach allowed us to further extract quantitative biophysical models describing input–output relationships. Given the generality of the approach presented here, it opens up the possibility of quantitatively dissecting the mechanisms of promoter function in E. coli and a wide range of other bacteria.

Tuning Transcriptional Regulation through Signaling: A Predictive Theory of Allosteric Induction

Allosteric regulation is found across all domains of life, yet we still lack simple, predictive theories that directly link the experimentally tunable parameters of a system to its input-output response. To that end, we present a general theory of allosteric transcriptional regulation using the Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous simple repression motif in bacteria by first predicting the behavior of strains that span a large range of repressor copy numbers and DNA binding strengths and then constructing and measuring their response. Our model not only accurately captures the induction profiles of these strains, but also enables us to derive analytic expressions for key properties such as the dynamic range and [EC₅₀]. Finally, we derive an expression for the free energy of allosteric repressors that enables us to collapse our experimental data onto a single master curve that captures the diverse phenomenology of the induction profiles.

Intrinsic adaptive value and early fate of gene duplication revealed by a bottom-up approach

The population genetic mechanisms governing the preservation of gene duplicates, especially in the critical very initial phase, have remained largely unknown. Here, we demonstrate that gene duplication confers per se a weak selective advantage in scenarios of fitness trade-offs. Through a precise quantitative description of a model system, we show that a second gene copy serves to reduce gene expression inaccuracies derived from pervasive molecular noise and suboptimal gene regulation. We then reveal that such an accuracy in the phenotype yields a selective advantage in the order of 0.1% on average, which would allow the positive selection of gene duplication in populations with moderate/large sizes. This advantage is greater at higher noise levels and intermediate concentrations of the environmental molecule, when fitness trade-offs become more evident. Moreover, we discuss how the genome rearrangement rates greatly condition the eventual fixation of duplicates. Overall, our theoretical results highlight an original adaptive value for cells carrying new-born duplicates, broadly analyze the selective conditions that determine their early fates in different organisms, and reconcile population genetics with evolution by gene duplication.

The genetic basis for the adaptation of E. coli to sugar synthesis from CO2

Understanding the evolution of a new metabolic capability in full mechanistic detail is challenging, as causative mutations may be masked by non-essential "hitchhiking" mutations accumulated during the evolutionary trajectory. We have previously used adaptive laboratory evolution of a rationally engineered ancestor to generate an Escherichia coli strain able to utilize CO₂ fixation for sugar synthesis. Here, we reveal the genetic basis underlying this metabolic transition. Five mutations are sufficient to enable robust growth when a non-native Calvin-Benson-Bassham cycle provides all the sugar-derived metabolic building blocks. These mutations are found either in enzymes that affect the efflux of intermediates from the autocatalytic CO₂ fixation cycle toward biomass (prs, serA, and pgi), or in key regulators of carbon metabolism (crp and ppsR). Using suppressor analysis, we show that a decrease in catalytic capacity is a common feature of all mutations found in enzymes. These findings highlight the enzymatic constraints that are essential to the metabolic stability of autocatalytic cycles and are relevant to future efforts in constructing non-native carbon fixation pathways.