Detailed map of a cis-regulatory input function

Fibration symmetry uncovers minimal regulatory networks for logical computation in bacteria

Symmetry principles have proven important in physics, deep learning and geometry, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems often show a high level of complexity and consist of a high number of interacting parts. Using symmetry fibrations, the relevant symmetries for biological 'message-passing' networks, we reduced the gene regulatory networks of E. coli and B. subtilis bacteria in a way that preserves information flow and highlights the computational capabilities of the network. Nodes that share isomorphic input trees are grouped into equivalence classes called fibers, whereby genes that receive signals with the same 'history' belong to one fiber and synchronize. We further reduce the networks to its computational core by removing "dangling ends" via k-core decomposition. The computational core of the network consists of a few strongly connected components in which signals can cycle while signals are transmitted between these "information vortices" in a linear feed-forward manner. These components are in charge of decision making in the bacterial cell by employing a series of genetic toggle-switch circuits that store memory, and oscillator circuits. These circuits act as the central computation machine of the network, whose output signals then spread to the rest of the network.

Soft repression and chromatin modification by conserved transcriptional corepressors

Transcriptional regulation in eukaryotic cells involves the activity of multifarious DNA-binding transcription factors and recruited corepressor complexes. Together, these complexes interact with the core transcriptional machinery, chromatin, and nuclear environment to effect complex patterns of gene regulation. Much focus has been paid to the action of master regulatory switches that are key to developmental and environmental responses, as these genetic elements have important phenotypic effects. The regulation of widely-expressed metabolic control genes has been less well studied, particularly in cases in which physically-interacting repressors and corepressors have subtle influences on steady-state expression. This latter phenomenon, termed "soft repression" is a topic of increasing interest as genomic approaches provide ever more powerful tools to uncover the significance of this level of control. This review provides an oversight of classic and current approaches to the study of transcriptional repression in eukaryotic systems, with a specific focus on opportunities and challenges that lie ahead in the study of soft repression.

Understanding the Genome-Wide Transcription Response To Various cAMP Levels in Bacteria Using Phenomenological Models

Attempts to understand gene regulation by global transcription factors have largely been limited to expression studies under binary conditions of presence and absence of the transcription factor. Studies addressing genome-wide transcriptional responses to changing transcription factor concentration at high resolution are lacking. Here, we create a data set containing the entire Escherichia coli transcriptome in Luria-Bertani (LB) broth as it responds to 10 different cAMP concentrations spanning the biological range. We use the Hill's model to accurately summarize individual gene responses into three intuitively understandable parameters, E_max, n, and k, reflecting the sensitivity, nonlinearity, and midpoint of the dynamic range. Our data show that most cAMP-regulated genes have an n of >2, with their k values centered around the wild-type concentration of cAMP. Additionally, cAMP receptor protein (CRP) affinity to a promoter is correlated with E_max but not k, hinting that a high-affinity CRP promoter need not ensure transcriptional activation at lower cAMP concentrations and instead affects the magnitude of the response. Finally, genes belonging to different functional classes are tuned to have different k, n, and E_max values. We demonstrate that phenomenological models are a better alternative for studying gene expression trends than classical clustering methods, with the phenomenological constants providing greater insights into how genes are tuned in a regulatory network. IMPORTANCE Different genes may follow different trends in response to various transcription factor concentrations. In this study, we ask two questions: (i) what are the trends that different genes follow in response to changing transcription factor concentrations and (ii) what methods can be used to extract information from the gene trends so obtained. We demonstrate a method to analyze transcription factor concentration-dependent genome-wide expression data using phenomenological models. Conventional clustering methods and principal-component analysis (PCA) can be used to summarize trends in data but have limited interpretability. The use of phenomenological models greatly enhances the interpretability and thus utility of conventional clustering. Transformation of dose-response data into phenomenological constants opens up avenues to ask and answer many different kinds of question. We show that the phenomenological constants obtained from the model fits can be used to generate insights about network topology and allows integration of other experimental data such as chromatin immunoprecipitation sequencing (ChIP-seq) to understand the system in greater detail.

Synthetic memory circuits for stable cell reprogramming in plants

Plant biotechnology predominantly relies on a restricted set of genetic parts with limited capability to customize spatiotemporal and conditional expression patterns. Synthetic gene circuits have the potential to integrate multiple customizable input signals through a processing unit constructed from biological parts to produce a predictable and programmable output. Here we present a suite of functional recombinase-based gene circuits for use in plants. We first established a range of key gene circuit components compatible with plant cell functionality. We then used these to develop a range of operational logic gates using the identify function (activation) and negation function (repression) in Arabidopsis protoplasts and in vivo, demonstrating their utility for programmable manipulation of transcriptional activity in a complex multicellular organism. Specifically, using recombinases and plant control elements, we activated transgenes in YES, OR and AND gates and repressed them in NOT, NOR and NAND gates; we also implemented the A NIMPLY B gate that combines activation and repression. Through use of genetic recombination, these circuits create stable long-term changes in expression and recording of past stimuli. This highly compact programmable gene circuit platform provides new capabilities for engineering sophisticated transcriptional programs and previously unrealized traits into plants.

Deduction of signaling mechanisms from cellular responses to multiple cues

Cell signaling networks are complex and often incompletely characterized, making it difficult to obtain a comprehensive picture of the mechanisms they encode. Mathematical modeling of these networks provides important clues, but the models themselves are often complex, and it is not always clear how to extract falsifiable predictions. Here we take an inverse approach, using experimental data at the cell level to deduce the minimal signaling network. We focus on cells' response to multiple cues, specifically on the surprising case in which the response is antagonistic: the response to multiple cues is weaker than the response to the individual cues. We systematically build candidate signaling networks one node at a time, using the ubiquitous ingredients of (i) up- or down-regulation, (ii) molecular conversion, or (iii) reversible binding. In each case, our method reveals a minimal, interpretable signaling mechanism that explains the antagonistic response. Our work provides a systematic way to deduce molecular mechanisms from cell-level 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.

Cyclic attractors of nonexpanding q-ary networks

Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However, multi-state models have also emerged as effective computational tools for the analysis of complex mechanisms underlying biological networks. Models in which variables assume more than two discrete states provide greater resolution, but this scheme introduces discontinuities. In particular, variables can increase or decrease by more than one unit in one time step. This can be corrected, without changing fixed points of the system, by applying an additional rule to each local activation function. On the other hand, if one is interested in cyclic attractors of their system, then this rule can potentially introduce new cyclic attractors that were not observed previously. This article makes some advancements in understanding the state space dynamics of multi-state network models with synchronous, sequential, or block-sequential update schedules and establishes conditions under which no new cyclic attractors are added to networks when the additional rule is applied. Our analytical results have the potential to be incorporated into modeling software and aid researchers in their analyses of biological multi-state networks.

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.

Modulating gene regulation function by chemically controlled transcription factor clustering

Recent studies have suggested that transcriptional protein condensates (or clusters) may play key roles in gene regulation and cell fate determination. However, it remains largely unclear how the gene regulation function is quantitatively tuned by transcription factor (TF) clustering and whether TF clustering may confer emergent behaviors as in cell fate control systems. Here, to address this, we construct synthetic TFs whose clustering behavior can be chemically controlled. Through single-parameter tuning of the system (i.e., TF clustering propensity), we provide lines of evidence supporting the direct transcriptional activation and amplification of target genes by TF clustering. Single-gene imaging suggests that such amplification results from the modulation of transcriptional dynamics. Importantly, TF clustering propensity modulates the gene regulation function by significantly tuning the effective TF binding affinity and to a lesser extent the ultrasensitivity, contributing to bimodality and sustained response behavior that are reminiscent of canonical cell fate control systems. Collectively, these results demonstrate that TF clustering can modulate the gene regulation function to enable emergent behaviors, and highlight the potential applications of chemically controlled protein clustering.

Transcription factor (TF) condensates appear to be pervasive, yet their roles remain debated. Here, the authors use a synthetic biology approach to show that TF clusters causally amplify transcription and can confer bimodality and “memory”.

Volumetric compression develops noise-driven single-cell heterogeneity

Recent studies have revealed that extensive heterogeneity of biological systems arises through various routes ranging from intracellular chromosome segregation to spatiotemporally varying biochemical stimulations. However, the contribution of physical microenvironments to single-cell heterogeneity remains largely unexplored. Here, we show that a homogeneous population of non-small-cell lung carcinoma develops into heterogeneous subpopulations upon application of a homogeneous physical compression, as shown by single-cell transcriptome profiling. The generated subpopulations stochastically gain the signature genes associated with epithelial-mesenchymal transition (EMT; VIM, CDH1, EPCAM, ZEB1, and ZEB2) and cancer stem cells (MKI67, BIRC5, and KLF4), respectively. Trajectory analysis revealed two bifurcated paths as cells evolving upon the physical compression, along each path the corresponding signature genes (epithelial or mesenchymal) gradually increase. Furthermore, we show that compression increases gene expression noise, which interplays with regulatory network architecture and thus generates differential cell-fate outcomes. The experimental observations of both single-cell sequencing and single-molecule fluorescent in situ hybridization agrees well with our computational modeling of regulatory network in the EMT process. These results demonstrate a paradigm of how mechanical stimulations impact cell-fate determination by altering transcription dynamics; moreover, we show a distinct path that the ecology and evolution of cancer interplay with their physical microenvironments from the view of mechanobiology and systems biology, with insight into the origin of single-cell heterogeneity.

Emergent Damped Oscillation Induced by Nutrient-Modulating Growth Feedback

Growth feedback, the inherent coupling between the synthetic gene circuit and the host cell growth, could significantly change the circuit behaviors. Previously, a diverse array of emergent behaviors, such as growth bistability, enhanced ultrasensitivity, and topology-dependent memory loss, were reported to be induced by growth feedback. However, the influence of the growth feedback on the circuit functions remains underexplored. Here, we reported an unexpected damped oscillatory behavior of a self-activation gene circuit induced by nutrient-modulating growth feedback. Specifically, after dilution of the activated self-activation switch into the fresh medium with moderate nutrients, its gene expression first decreases as the cell grows and then shows a significant overshoot before it reaches the steady state, leading to damped oscillation dynamics. Fitting the data with a coarse-grained model suggests a nonmonotonic growth-rate regulation on gene production rate. The underlying mechanism of the oscillation was demonstrated by a molecular mathematical model, which includes the ribosome allocation toward gene production, cell growth, and cell maintenance. Interestingly, the model predicted a counterintuitive dependence of oscillation amplitude on the nutrition level, where the highest peak was found in the medium with moderate nutrients, but was not observed in rich nutrients. We experimentally verified this prediction by tuning the nutrient level in the culture medium. We did not observe significant oscillatory behavior for the toggle switch, suggesting that the emergence of damped oscillatory behavior depends on circuit network topology. Our results demonstrated a new nonlinear emergent behavior mediated by growth feedback, which depends on the ribosome allocation between gene circuit and cell growth.

Extrinsic noise of the target gene governs abundance pattern of feed-forward loop motifs

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1-C4 and I1-I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

In-situ monitoring of xenobiotics using genetically engineered whole-cell-based microbial biosensors: recent advances and outlook

Industrialisation, directly or indirectly, exposes humans to various xenobiotics. The increased magnitude of chemical pesticides and toxic heavy metals in the environment, as well as their intrusion into the food chain, seriously threatens human health. Therefore, the surveillance of xenobiotics is crucial for social safety and security. Online investigation by traditional methods is not sufficient for the detection and identification of such compounds because of the high costs and their complexity. Advancement in the field of genetic engineering provides a potential opportunity to use genetically modified microorganisms. In this regard, whole-cell-based microbial biosensors (WCBMB) represent an essential tool that couples genetically engineered organisms with an operator/promoter derived from a heavy metal-resistant operon combined with a regulatory protein in the gene circuit. The plasmid controls the expression of the reporter gene, such as gfp, luc, lux and lacZ, to an inducible gene promoter and has been widely applied to assay toxicity and bioavailability. This review summarises the recent trends in the development and application of microbial biosensors and the use of mobile genes for biomedical and environmental safety concerns.

Nonlinear delay differential equations and their application to modeling biological network motifs

Biological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs.

Network motif models focus on small sub-networks in biological systems to quantitatively describe overall behavior but they often overlook time delays. Here, the authors systematically examine the most common network motifs via delay differential equations (DDE), often leading to more concise descriptions.

Soft repression: Subtle transcriptional regulation with global impact

Pleiotropically acting eukaryotic corepressors such as retinoblastoma and SIN3 have been found to physically interact with many widely expressed “housekeeping” genes. Evidence suggests that their roles at these loci are not to provide binary on/off switches, as is observed at many highly cell-type specific genes, but rather to serve as governors, directly modulating expression within certain bounds, while not shutting down gene expression. This sort of regulation is challenging to study, as the differential expression levels can be small. We hypothesize that depending on context, corepressors mediate “soft repression,” attenuating expression in a less dramatic but physiologically appropriate manner. Emerging data indicate that such regulation is a pervasive characteristic of most eukaryotic systems, and may reflect the mechanistic differences between repressor action at promoter and enhancer locations. Soft repression may represent an essential component of the cybernetic systems underlying metabolic adaptations, enabling modest but critical adjustments on a continual basis.

Unraveling the Complex Interplay of Fis and IHF Through Synthetic Promoter Engineering

Bacterial promoters are usually formed by multiple cis-regulatory elements recognized by a plethora of transcriptional factors (TFs). From those, global regulators are key elements since these TFs are responsible for the regulation of hundreds of genes in the bacterial genome. For instance, Fis and IHF are global regulators that play a major role in gene expression control in Escherichia coli, and usually, multiple cis-regulatory elements for these proteins are present at target promoters. Here, we investigated the relationship between the architecture of the cis-regulatory elements for Fis and IHF in E. coli. For this, we analyze 42 synthetic promoter variants harboring consensus cis-elements for Fis and IHF at different distances from the core -35/-10 region and in various numbers and combinations. We first demonstrated that although Fis preferentially recognizes its consensus cis-element, it can also recognize, to some extent, the consensus-binding site for IHF, and the same was true for IHF, which was also able to recognize Fis binding sites. However, changing the arrangement of the cis-elements (i.e., the position or number of sites) can completely abolish the non-specific binding of both TFs. More remarkably, we demonstrated that combining cis-elements for both TFs could result in Fis and IHF repressed or activated promoters depending on the final architecture of the promoters in an unpredictable way. Taken together, the data presented here demonstrate how small changes in the architecture of bacterial promoters could result in drastic changes in the final regulatory logic of the system, with important implications for the understanding of natural complex promoters in bacteria and their engineering for novel applications.

Decipher the complexity of cis-regulatory regions by a modified Cas9

BACKGROUND

Understanding complex mechanisms of human transcriptional regulation remains a major challenge. Classical reporter studies already enabled the discovery of cis-regulatory elements within the non-coding DNA; however, the influence of genomic context and potential interactions are still largely unknown. Using a modified Cas9 activation complex we explore the complexity of renin transcription in its native genomic context.

METHODS

With the help of genomic editing, we stably tagged the native renin on chromosome 1 with the firefly luciferase and stably integrated a programmable modified Cas9 based trans-activation complex (SAM-complex) by lentiviral transduction into human cells. By delivering five specific guide-RNA homologous to specific promoter regions of renin we were able to guide this SAM-complex to these regions of interest. We measured gene expression and generated and compared computational models.

RESULTS

SAM complexes induced activation of renin in our cells after renin specific guide-RNA had been provided. All possible combinations of the five guides were subjected to model analysis in linear models. Quantifying the prediction error and the calculation of an estimator of the relative quality of the statistical models for our given set of data revealed that a model incorporating interactions in the proximal promoter is the superior model for explanation of the data.

CONCLUSION

By applying our combined experimental and modelling approach we can show that interactions occur within the selected sequences of the proximal renin promoter region. This combined approach might potentially be useful to investigate other genomic regions. Our findings may help to better understand the transcriptional regulation of human renin.

Multiplexed Gene Expression Tuning with Orthogonal Synthetic Gene Circuits

Understanding the individual and joint contribution of multiple protein levels toward a phenotype requires precise and tunable multigene expression control. Here we introduce a pair of mammalian synthetic gene circuits that linearly and orthogonally control the expression of two reporter genes in mammalian cells with low variability in response to chemical inducers introduced into the growth medium. These gene expression systems can be used to simultaneously probe the individual and joint effects of two gene product concentrations on a cellular phenotype in basic research or biomedical applications.

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.

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.

Identification and Massively Parallel Characterization of Regulatory Elements Driving Neural Induction

Epigenomic regulation and lineage-specific gene expression act in concert to drive cellular differentiation, but the temporal interplay between these processes is largely unknown. Using neural induction from human pluripotent stem cells (hPSCs) as a paradigm, we interrogated these dynamics by performing RNA sequencing (RNA-seq), chromatin immunoprecipitation sequencing (ChIP-seq), and assay for transposase accessible chromatin using sequencing (ATAC-seq) at seven time points during early neural differentiation. We found that changes in DNA accessibility precede H3K27ac, which is followed by gene expression changes. Using massively parallel reporter assays (MPRAs) to test the activity of 2,464 candidate regulatory sequences at all seven time points, we show that many of these sequences have temporal activity patterns that correlate with their respective cell-endogenous gene expression and chromatin changes. A prioritization method incorporating all genomic and MPRA data further identified key transcription factors involved in driving neural fate. These results provide a comprehensive resource of genes and regulatory elements that orchestrate neural induction and illuminate temporal frameworks during differentiation.

Network inference performance complexity: a consequence of topological, experimental and algorithmic determinants

MOTIVATION

Network inference algorithms aim to uncover key regulatory interactions governing cellular decision-making, disease progression and therapeutic interventions. Having an accurate blueprint of this regulation is essential for understanding and controlling cell behavior. However, the utility and impact of these approaches are limited because the ways in which various factors shape inference outcomes remain largely unknown.

RESULTS

We identify and systematically evaluate determinants of performance-including network properties, experimental design choices and data processing-by developing new metrics that quantify confidence across algorithms in comparable terms. We conducted a multifactorial analysis that demonstrates how stimulus target, regulatory kinetics, induction and resolution dynamics, and noise differentially impact widely used algorithms in significant and previously unrecognized ways. The results show how even if high-quality data are paired with high-performing algorithms, inferred models are sometimes susceptible to giving misleading conclusions. Lastly, we validate these findings and the utility of the confidence metrics using realistic in silico gene regulatory networks. This new characterization approach provides a way to more rigorously interpret how algorithms infer regulation from biological datasets.

AVAILABILITY AND IMPLEMENTATION

Code is available at http://github.com/bagherilab/networkinference/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Sciences of Observation

Multiple sciences have converged, in the past two decades, on a hitherto mostly unremarked question: what is observation? Here, I examine this evolution, focusing on three sciences: physics, especially quantum information theory, developmental biology, especially its molecular and “evo-devo” branches, and cognitive science, especially perceptual psychology and robotics. I trace the history of this question to the late 19th century, and through the conceptual revolutions of the 20th century. I show how the increasing interdisciplinary focus on the process of extracting information from an environment provides an opportunity for conceptual unification, and sketch an outline of what such a unification might look like.

Interplay of synergy and redundancy in diamond motif

The formalism of partial information decomposition provides a number of independent components which altogether constitute the total information provided by the source variable(s) about the target variable(s). These non-overlapping terms are recognized as unique information, synergistic information, and redundant information. The metric of net synergy conceived as the difference between synergistic and redundant information is capable of detecting effective synergy, effective redundancy, and information independence among stochastic variables. The net synergy can be quantified using appropriate combinations of different Shannon mutual information terms. The utilization of the net synergy in network motifs with the nodes representing different biochemical species, involved in information sharing, uncovers rich store for exciting results. In the current study, we use this formalism to obtain a comprehensive understanding of the relative information processing mechanism in a diamond motif and two of its sub-motifs, namely, bifurcation and integration motif embedded within the diamond motif. The emerging patterns of effective synergy and effective redundancy and their contribution toward ensuring high fidelity information transmission are duly compared in the sub-motifs. Investigation on the metric of net synergy in independent bifurcation and integration motifs are also executed. In all of these computations, the crucial roles played by various systemic time scales, activation coefficients, and signal integration mechanisms at the output of the network topologies are especially emphasized. Following this plan of action, we become confident that the origin of effective synergy and effective redundancy can be architecturally justified by decomposing a diamond motif into bifurcation and integration motif. According to our conjecture, the presence of a common source of fluctuations creates effective redundancy. Our calculations reveal that effective redundancy empowers signal fidelity. Moreover, to achieve this, input signaling species avoids strong interaction with downstream intermediates. This strategy is capable of making the diamond motif noise-tolerant. Apart from the topological features, our study also puts forward the active contribution of additive and multiplicative signal integration mechanisms to nurture effective redundancy and effective synergy.

Modeling Procedures

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

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.

Frequency Modulation of Transcriptional Bursting Enables Sensitive and Rapid Gene Regulation

Gene regulation is a complex non-equilibrium process. Here, we show that quantitating the temporal regulation of key gene states (transcriptionally inactive, active, and refractory) provides a parsimonious framework for analyzing gene regulation. Our theory makes two non-intuitive predictions. First, for transcription factors (TFs) that regulate transcription burst frequency, as opposed to amplitude or duration, weak TF binding is sufficient to elicit strong transcriptional responses. Second, refractoriness of a gene after a transcription burst enables rapid responses to stimuli. We validate both predictions experimentally by exploiting the natural, optogenetic-like responsiveness of the Neurospora GATA-type TF White Collar Complex (WCC) to blue light. Further, we demonstrate that differential regulation of WCC target genes is caused by different gene activation rates, not different TF occupancy, and that these rates are tuned by both the core promoter and the distance between TF-binding site and core promoter. In total, our work demonstrates the relevance of a kinetic, non-equilibrium framework for understanding transcriptional regulation.

The identification of functional motifs in temporal gene expression analysis

The identification of transcription factor binding sites is essential to the understanding of the regulation of gene expression and the reconstruction of genetic regulatory networks. The in silico identification of cis-regulatory motifs is challenging due to sequence variability and lack of sufficient data to generate consensus motifs that are of quantitative or even qualitative predictive value. To determine functional motifs in gene expression, we propose a strategy to adopt false discovery rate (FDR) and estimate motif effects to evaluate combinatorial analysis of motif candidates and temporal gene expression data. The method decreases the number of predicted motifs, which can then be confirmed by genetic analysis. To assess the method we used simulated motif/expression data to evaluate parameters. We applied this approach to experimental data for a group of iron responsive genes in Salmonella typhimurium 14028S. The method identified known and potentially new ferric-uptake regulator (Fur) binding sites. In addition, we identified uncharacterized functional motif candidates that correlated with specific patterns of expression. A SAS code for the simulation and analysis gene expression data is available from the first author upon request.

Crosstalk and the Dynamical Modularity of Feed-Forward Loops in Transcriptional Regulatory Networks

Network motifs, such as the feed-forward loop (FFL), introduce a range of complex behaviors to transcriptional regulatory networks, yet such properties are typically determined from their isolated study. We characterize the effects of crosstalk on FFL dynamics by modeling the cross regulation between two different FFLs and evaluate the extent to which these patterns occur in vivo. Analytical modeling suggests that crosstalk should overwhelmingly affect individual protein-expression dynamics. Counter to this expectation we find that entire FFLs are more likely than expected to resist the effects of crosstalk (≈20% for one crosstalk interaction) and remain dynamically modular. The likelihood that cross-linked FFLs are dynamically correlated increases monotonically with additional crosstalk, but is independent of the specific regulation type or connectivity of the interactions. Just one additional regulatory interaction is sufficient to drive the FFL dynamics to a statistically different state. Despite the potential for modularity between sparsely connected network motifs, Escherichia coli (E. coli) appears to favor crosstalk wherein at least one of the cross-linked FFLs remains modular. A gene ontology analysis reveals that stress response processes are significantly overrepresented in the cross-linked motifs found within E. coli. Although the daunting complexity of biological networks affects the dynamical properties of individual network motifs, some resist and remain modular, seemingly insulated from extrinsic perturbations—an intriguing possibility for nature to consistently and reliably provide certain network functionalities wherever the need arise.

A spectrum of modularity in multi-functional gene circuits

A major challenge in systems biology is to understand the relationship between a circuit's structure and its function, but how is this relationship affected if the circuit must perform multiple distinct functions within the same organism? In particular, to what extent do multi‐functional circuits contain modules which reflect the different functions? Here, we computationally survey a range of bi‐functional circuits which show no simple structural modularity: They can switch between two qualitatively distinct functions, while both functions depend on all genes of the circuit. Our analysis reveals two distinct classes: hybrid circuits which overlay two simpler mono‐functional sub‐circuits within their circuitry, and emergent circuits, which do not. In this second class, the bi‐functionality emerges from more complex designs which are not fully decomposable into distinct modules and are consequently less intuitive to predict or understand. These non‐intuitive emergent circuits are just as robust as their hybrid counterparts, and we therefore suggest that the common bias toward studying modular systems may hinder our understanding of real biological circuits.

Molecular mechanism governing ratio-dependent transcription regulation in the ccdAB operon

Bacteria can become transiently tolerant to several classes of antibiotics. This phenomenon known as persistence is regulated by small genetic elements called toxin-antitoxin modules with intricate yet often poorly understood self-regulatory features. Here, we describe the structures of molecular complexes and interactions that drive the transcription regulation of the ccdAB toxin-antitoxin module. Low specificity and affinity of the antitoxin CcdA2 for individual binding sites on the operator are enhanced by the toxin CcdB2, which bridges the CcdA2 dimers. This results in a unique extended repressing complex that spirals around the operator and presents equally spaced DNA binding sites. The multivalency of binding sites induces a digital on-off switch for transcription, regulated by the toxin:antitoxin ratio. The ratio at which this switch occurs is modulated by non-specific interactions with the excess chromosomal DNA. Altogether, we present the molecular mechanisms underlying the ratio-dependent transcriptional regulation of the ccdAB operon.

Robust Synthetic Circuits for Two-Dimensional Control of Gene Expression in Yeast

Cellular phenotypes are the result of complex interactions between many components. Understanding and predicting the system level properties of the resulting networks requires the development of perturbation tools that can simultaneously and independently modulate multiple cellular variables. Here, we develop synthetic modules that use different arrangements of two transcriptional regulators to achieve either concurrent and independent control of the expression of two genes, or decoupled control of the mean and variance of a single gene. These modules constitute powerful tools to probe the quantitative attributes of network wiring and function.

A universal indicator of critical state transitions in noisy complex networked systems

Critical transition, a phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks. We propose an analytical framework for exactly predicting the critical transition in a complex networked system subjected to noise effects. Our prediction is based on the characteristic return time of a simple one-dimensional system derived from the original higher-dimensional system. This characteristic time, which can be easily calculated using network data, allows us to systematically separate the respective roles of dynamics, noise and topology of the underlying networked system. We find that the noise can either prevent or enhance critical transitions, playing a key role in compensating the network structural defect which suffers from either internal failures or environmental changes, or both. Our analysis of realistic or artificial examples reveals that the characteristic return time is an effective indicator for forecasting the sudden deterioration of complex networks.

Metabolomic analysis of riboswitch containing E. coli recombinant expression system

In this study we have employed metabolomics approaches to understand the metabolic effects of producing enhanced green fluorescent protein (eGFP) as a recombinant protein in Escherichia coli cells. This metabolic burden analysis was performed against a number of recombinant expression systems and control strains and included: (i) standard transcriptional recombinant expression control system BL21(DE3) with the expression plasmid pET-eGFP, (ii) the recently developed dual transcriptional-translational recombinant expression control strain BL21(IL3), with pET-eGFP, (iii) BL21(DE3) with an empty expression plasmid pET, (iv) BL21(IL3) with an empty expression plasmid, and (v) BL21(DE3) without an expression plasmid; all strains were cultured under various induction conditions. The growth profiles of all strains together with the results gathered by the analysis of the Fourier transform infrared (FT-IR) spectroscopy data, identified IPTG-dependent induction as the dominant factor hampering cellular growth and metabolism, which was in general agreement with the findings of GC-MS analysis of cell extracts and media samples. In addition, the exposure of host cells to the synthetic inducer ligand, pyrimido[4,5-d] pyrimidine-2,4-diamine (PPDA), of the orthogonal riboswitch containing expression system (BL21(IL3)) did not display any detrimental effects, and its detected levels in all the samples were at similar levels, emphasising the inability of the cells to metabolise PPDA. The overall results obtained in this study suggested that although the BL21(DE3)-EGFP and BL21(IL3)-EGFP strains produced comparable levels of recombinant eGFP, the presence of the orthogonal riboswitch seemed to be moderating the metabolic burden of eGFP production in the cells enabling higher biomass yield, whilst providing a greater level of control over protein expression.

The Local Edge Machine: inference of dynamic models of gene regulation

We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.

Inference of gene regulation functions from dynamic transcriptome data

To quantify gene regulation, a function is required that relates transcription factor binding to DNA (input) to the rate of mRNA synthesis from a target gene (output). Such a ‘gene regulation function’ (GRF) generally cannot be measured because the experimental titration of inputs and simultaneous readout of outputs is difficult. Here we show that GRFs may instead be inferred from natural changes in cellular gene expression, as exemplified for the cell cycle in the yeast S. cerevisiae. We develop this inference approach based on a time series of mRNA synthesis rates from a synchronized population of cells observed over three cell cycles. We first estimate the functional form of how input transcription factors determine mRNA output and then derive GRFs for target genes in the CLB2 gene cluster that are expressed during G2/M phase. Systematic analysis of additional GRFs suggests a network architecture that rationalizes transcriptional cell cycle oscillations. We find that a transcription factor network alone can produce oscillations in mRNA expression, but that additional input from cyclin oscillations is required to arrive at the native behaviour of the cell cycle oscillator.

DOI:http://dx.doi.org/10.7554/eLife.12188.001

Living cells rely on networks of genes to control their behavior, including how they grow, develop and respond to stress. Genes encode instructions needed to make proteins and other molecules, and much of the control is exerted at the first stage of protein production, known as transcription. During this process, a gene is copied to make molecules known as transcripts that may later be used as templates to make proteins.

Many genes encode proteins that act to regulate transcription. Therefore, an individual gene may receive inputs from other genes, and these inputs affect how much transcript the gene produces, which can be considered as the gene’s output. While these inputs and outputs can often be wired together to form a network, it is less clear exactly how all the different inputs at a gene interact to determine its output. These interactions are known as “gene regulation functions”, and knowing them would be an important step towards understanding gene networks, which would help us to predict how cells will behave in different situations.

Gene regulation functions are difficult to measure directly, so researchers would like to find other ways to assess them indirectly. A recently developed experimental technique called “dynamic transcriptome analysis” seemed promising as it measures both the inputs and outputs of all genes in a cell over time. Hillenbrand et al. used this technique to infer gene regulation functions with one or two inputs in yeast cells.

Comparing these estimates with experimental data from previous studies showed that these inferred gene regulation functions could successfully predict the output of a gene based on its inputs. Hillenbrand et al. then used these estimates to search and model a well-known genetic network that is thought to be part of the molecular clockwork that controls the timing of events that cause a cell to divide.

Currently, the approach used by Hillenbrand et al. treats gene regulation functions like “black boxes”. This means that, while an output can be predicted if the inputs are known, it cannot reveal all of the detailed mechanisms behind it. Gaining insights into the inner workings of these black boxes will require taking more data into account, such as how abundant the proteins that regulate transcription are, where they are located within cells or whether they are active or not. Therefore, the next challenge is to incorporate these kinds of data to gain a fuller picture of how gene networks operate within cells.

DOI:http://dx.doi.org/10.7554/eLife.12188.002

Rapid Discrimination Among Putative Mechanistic Models of Biochemical Systems

An overarching goal in molecular biology is to gain an understanding of the mechanistic basis underlying biochemical systems. Success is critical if we are to predict effectively the outcome of drug treatments and the development of abnormal phenotypes. However, data from most experimental studies is typically noisy and sparse. This allows multiple potential mechanisms to account for experimental observations, and often devising experiments to test each is not feasible. Here, we introduce a novel strategy that discriminates among putative models based on their repertoire of qualitatively distinct phenotypes, without relying on knowledge of specific values for rate constants and binding constants. As an illustration, we apply this strategy to two synthetic gene circuits exhibiting anomalous behaviors. Our results show that the conventional models, based on their well-characterized components, cannot account for the experimental observations. We examine a total of 40 alternative hypotheses and show that only 5 have the potential to reproduce the experimental data, and one can do so with biologically relevant parameter values.

Principles of dynamical modularity in biological regulatory networks

Intractable diseases such as cancer are associated with breakdown in multiple individual functions, which conspire to create unhealthy phenotype-combinations. An important challenge is to decipher how these functions are coordinated in health and disease. We approach this by drawing on dynamical systems theory. We posit that distinct phenotype-combinations are generated by interactions among robust regulatory switches, each in control of a discrete set of phenotypic outcomes. First, we demonstrate the advantage of characterizing multi-switch regulatory systems in terms of their constituent switches by building a multiswitch cell cycle model which points to novel, testable interactions critical for early G2/M commitment to division. Second, we define quantitative measures of dynamical modularity, namely that global cell states are discrete combinations of switch-level phenotypes. Finally, we formulate three general principles that govern the way coupled switches coordinate their function.

Designing a stochastic genetic switch by coupling chaos and bistability

In stem cell differentiation, a pluripotent stem cell becomes progressively specialized and generates specific cell types through a series of epigenetic processes. How cells can precisely determine their fate in a fluctuating environment is a currently unsolved problem. In this paper, we suggest an abstract gene regulatory network to describe mathematically the differentiation phenomenon featuring stochasticity, divergent cell fates, and robustness. The network consists of three functional motifs: an upstream chaotic motif, a buffering motif of incoherent feed forward loop capable of generating a pulse, and a downstream motif which is bistable. The dynamic behavior is typically a transient chaos with fractal basin boundaries. The trajectories take transiently chaotic journeys before divergently settling down to the bistable states. The ratio of the probability that the high state is achieved to the probability that the low state is reached can maintain a constant in a population of cells with varied molecular fluctuations. The ratio can be turned up or down when proper parameters are adjusted. The model suggests a possible mechanism for the robustness against fluctuations that is prominently featured in pluripotent cell differentiations and developmental phenomena.

Evaluating a common semi-mechanistic mathematical model of gene-regulatory networks

Modeling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern systems biology investigations into mechanisms underlying gene regulation. A key challenge in this area is the automated inference (reverse-engineering) of dynamic, mechanistic GRN models from gene expression time-course data. Common mathematical formalisms for representing such models capture two aspects simultaneously within a single parameter: (1) Whether or not a gene is regulated, and if so, the type of regulator (activator or repressor), and (2) the strength of influence of the regulator (if any) on the target or effector gene. To accommodate both roles, "generous" boundaries or limits for possible values of this parameter are commonly allowed in the reverse-engineering process. This approach has several important drawbacks. First, in the absence of good guidelines, there is no consensus on what limits are reasonable. Second, because the limits may vary greatly among different reverse-engineering experiments, the concrete values obtained for the models may differ considerably, and thus it is difficult to compare models. Third, if high values are chosen as limits, the search space of the model inference process becomes very large, adding unnecessary computational load to the already complex reverse-engineering process. In this study, we demonstrate that restricting the limits to the [−1, +1] interval is sufficient to represent the essential features of GRN systems and offers a reduction of the search space without loss of quality in the resulting models. To show this, we have carried out reverse-engineering studies on data generated from artificial and experimentally determined from real GRN systems.

Function does not follow form in gene regulatory circuits

Gene regulatory circuits are to the cell what arithmetic logic units are to the chip: fundamental components of information processing that map an input onto an output. Gene regulatory circuits come in many different forms, distinct structural configurations that determine who regulates whom. Studies that have focused on the gene expression patterns (functions) of circuits with a given structure (form) have examined just a few structures or gene expression patterns. Here, we use a computational model to exhaustively characterize the gene expression patterns of nearly 17 million three-gene circuits in order to systematically explore the relationship between circuit form and function. Three main conclusions emerge. First, function does not follow form. A circuit of any one structure can have between twelve and nearly thirty thousand distinct gene expression patterns. Second, and conversely, form does not follow function. Most gene expression patterns can be realized by more than one circuit structure. And third, multifunctionality severely constrains circuit form. The number of circuit structures able to drive multiple gene expression patterns decreases rapidly with the number of these patterns. These results indicate that it is generally not possible to infer circuit function from circuit form, or vice versa.

Controlling E. coli Gene Expression Noise

Intracellular protein copy numbers show significant cell-to-cell variability within an isogenic population due to the random nature of biological reactions. Here we show how the variability in copy number can be controlled by perturbing gene expression. Depending on the genetic network and host, different perturbations can be applied to control variability. To understand more fully how noise propagates and behaves in biochemical networks we developed stochastic control analysis (SCA) which is a sensitivity-based analysis framework for the study of noise control. Here we apply SCA to synthetic gene expression systems encoded on plasmids that are transformed into Escherichia coli. We show that (1) dual control of transcription and translation efficiencies provides the most efficient way of noise-versus-mean control. (2) The expressed proteins follow the gamma distribution function as found in chromosomal proteins. (3) One of the major sources of noise, leading to the cell-to-cell variability in protein copy numbers, is related to bursty translation. (4) By taking into account stochastic fluctuations in autofluorescence, the correct scaling relationship between the noise and mean levels of the protein copy numbers was recovered for the case of weak fluorescence signals.

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Signal integration by the CYP1A1 promoter--a quantitative study

Genes involved in detoxification of foreign compounds exhibit complex spatiotemporal expression patterns in liver. Cytochrome P450 1A1 (CYP1A1), for example, is restricted to the pericentral region of liver lobules in response to the interplay between aryl hydrocarbon receptor (AhR) and Wnt/β-catenin signaling pathways. However, the mechanisms by which the two pathways orchestrate gene expression are still poorly understood. With the help of 29 mutant constructs of the human CYP1A1 promoter and a mathematical model that combines Wnt/β-catenin and AhR signaling with the statistical mechanics of the promoter, we systematically quantified the regulatory influence of different transcription factor binding sites on gene induction within the promoter. The model unveils how different binding sites cooperate and how they establish the promoter logic; it quantitatively predicts two-dimensional stimulus-response curves. Furthermore, it shows that crosstalk between Wnt/β-catenin and AhR signaling is crucial to understand the complex zonated expression patterns found in liver lobules. This study exemplifies how statistical mechanical modeling together with combinatorial reporter assays has the capacity to disentangle the promoter logic that establishes physiological gene expression patterns.

An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays

This paper focuses on stability analysis for a class of genetic regulatory networks with interval time-varying delays. An improved integral inequality concerning on double-integral items is first established. Then, we use the improved integral inequality to deal with the resultant double-integral items in the derivative of the involved Lyapunov-Krasovskii functional. As a result, a delay-range-dependent and delay-rate-dependent asymptotical stability criterion is established for genetic regulatory networks with differential time-varying delays. Furthermore, it is theoretically proven that the stability criterion proposed here is less conservative than the corresponding one in [Neurocomputing, 2012, 93: 19-26]. Based on the obtained result, another stability criterion is given under the case that the information of the derivatives of delays is unknown. Finally, the effectiveness of the approach proposed in this paper is illustrated by a pair of numerical examples which give the comparisons of stability criteria proposed in this paper and some literature.

Trade-offs in engineering sugar utilization pathways for titratable control

Titratable systems are common tools in metabolic engineering to tune the levels of enzymes and cellular components as part of pathway optimization. For nonmodel microorganisms with limited genetic tools, inducible sugar utilization pathways offer built-in titratable systems. However, these pathways can exhibit undesirable single-cell behaviors that hamper the uniform and tunable control of gene expression. Here, we applied mathematical modeling and single-cell measurements of l-arabinose utilization in Escherichia coli to systematically explore how sugar utilization pathways can be altered to achieve desirable inducible properties. We found that different pathway alterations, such as the removal of catabolism, constitutive expression of high-affinity or low-affinity transporters, or further deletion of the other transporters, came with trade-offs specific to each alteration. For instance, sugar catabolism improved the uniformity and linearity of the response at the cost of requiring higher sugar concentrations to induce the pathway. Within these alterations, we also found that a uniform and linear response could be achieved with a single alteration: constitutively expressing the high-affinity transporter. Equivalent modifications to the d-xylose utilization pathway yielded similar responses, demonstrating the applicability of our observations. Overall, our findings indicate that there is no ideal set of typical alterations when co-opting natural utilization pathways for titratable control and suggest design rules for manipulating these pathways to advance basic genetic studies and the metabolic engineering of microorganisms for optimized chemical production.

Galactose metabolic genes in yeast respond to a ratio of galactose and glucose

Natural environments are filled with multiple, often competing, signals. In contrast, biological systems are often studied in "well-controlled" environments where only a single input is varied, potentially missing important interactions between signals. Catabolite repression of galactose by glucose is one of the best-studied eukaryotic signal integration systems. In this system, it is believed that galactose metabolic (GAL) genes are induced only when glucose levels drop below a threshold. In contrast, we show that GAL gene induction occurs at a constant external galactose:glucose ratio across a wide range of sugar concentrations. We systematically perturbed the components of the canonical galactose/glucose signaling pathways and found that these components do not account for ratio sensing. Instead we provide evidence that ratio sensing occurs upstream of the canonical signaling pathway and results from the competitive binding of the two sugars to hexose transporters. We show that a mutant that behaves as the classical model expects (i.e., cannot use galactose above a glucose threshold) has a fitness disadvantage compared with wild type. A number of common biological signaling motifs can give rise to ratio sensing, typically through negative interactions between opposing signaling molecules. We therefore suspect that this previously unidentified nutrient sensing paradigm may be common and overlooked in biology.

Hierarchy of non-glucose sugars in Escherichia coli

BACKGROUND

Understanding how cells make decisions, and why they make the decisions they make, is of fundamental interest in systems biology. To address this, we study the decisions made by E. coli on which genes to express when presented with two different sugars. It is well-known that glucose, E. coli's preferred carbon source, represses the uptake of other sugars by means of global and gene-specific mechanisms. However, less is known about the utilization of glucose-free sugar mixtures which are found in the natural environment of E. coli and in biotechnology.

RESULTS

Here, we combine experiment and theory to map the choices of E. coli among 6 different non-glucose carbon sources. We used robotic assays and fluorescence reporter strains to make precise measurements of promoter activity and growth rate in all pairs of these sugars. We find that the sugars can be ranked in a hierarchy: in a mixture of a higher and a lower sugar, the lower sugar system shows reduced promoter activity. The hierarchy corresponds to the growth rate supported by each sugar- the faster the growth rate, the higher the sugar on the hierarchy. The hierarchy is 'soft' in the sense that the lower sugar promoters are not completely repressed. Measurement of the activity of the master regulator CRP-cAMP shows that the hierarchy can be quantitatively explained based on differential activation of the promoters by CRP-cAMP. Comparing sugar system activation as a function of time in sugar pair mixtures at sub-saturating concentrations, we find cases of sequential activation, and also cases of simultaneous expression of both systems. Such simultaneous expression is not predicted by simple models of growth rate optimization, which predict only sequential activation. We extend these models by suggesting multi-objective optimization for both growing rapidly now and preparing the cell for future growth on the poorer sugar.

CONCLUSION

We find a defined hierarchy of sugar utilization, which can be quantitatively explained by differential activation by the master regulator cAMP-CRP. The present approach can be used to understand cell decisions when presented with mixtures of conditions.