Translational cross talk in gene networks

Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

Solving stochastic gene-expression models using queueing theory: A tutorial review

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite-server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and nonstationary distributions and/or moments of mRNA/protein numbers and bounds on the Fano factor. This approach may enable the solution of complex models that have hitherto evaded analytical solution.

Noisy Delay Denoises Biochemical Oscillators

Genetic oscillations are generated by delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay is distributed because it arises from a sequence of noisy processes, including transcription, translocation, translation, and folding. Because the delay determines repression timing and, therefore, oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. Here, we demonstrate that noisy delay can surprisingly denoise genetic oscillators. Specifically, moderate delay noise improves the signal-to-noise ratio and sharpens oscillation peaks, all without impacting period and amplitude. We show that this denoising phenomenon occurs in a variety of well-studied genetic oscillators, and we use queueing theory to uncover the universal mechanisms that produce it.

The effect of microRNA on protein variability and gene expression fidelity

Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such posttranscriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here, we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA posttranscriptionally will always increase, rather than decrease, gene expression noise when the silencing of mRNA also increases its degradation, as is expected for microRNA interactions with mRNA. In that regime, we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression.

Bacterial degrons in synthetic circuits

Bacterial proteases are a promising post-translational regulation strategy in synthetic circuits because they recognize specific amino acid degradation tags (degrons) that can be fine-tuned to modulate the degradation levels of tagged proteins. For this reason, recent efforts have been made in the search for new degrons. Here we review the up-to-date applications of degradation tags for circuit engineering in bacteria. In particular, we pay special attention to the effects of degradation bottlenecks in synthetic oscillators and introduce mathematical approaches to study queueing that enable the quantitative modelling of proteolytic queues.

Accelerating Whole-Cell Simulations of mRNA Translation Using a Dedicated Hardware

In recent years, intracellular biophysical simulations have been used with increasing frequency not only for answering basic scientific questions but also in the field of synthetic biology. However, since these models include networks of interaction between millions of components, they are extremely time-consuming and cannot run easily on parallel computers. In this study, we demonstrate for the first time a novel approach addressing this challenge by using a dedicated hardware designed specifically to simulate such processes. As a proof of concept, we specifically focus on mRNA translation, which is the process consuming most of the energy in the cell. We design a hardware that simulates translation in Escherichia coli and Saccharomyces cerevisiae for thousands of mRNAs and ribosomes, which is in orders of magnitude faster than a similar software solution. With the sharp increase in the amount of genomic data available today and the complexity of the corresponding models inferred from them, we believe that the strategy suggested here will become common and can be used among others for simulating entire cells with all gene expression steps.

Picking the right metaphors for addressing microbial systems: economic theory helps understanding biological complexity

Any descriptive language is necessarily metaphoric and interpretative. Two somewhat overlapping-but not identical-languages have been thoroughly employed in the last decade to address the issue of regulatory complexity in biological systems: the terminology of network theory and the jargon of electric circuitry. These approaches have found many formal equivalences between the layout of extant genetic circuits and the architecture of man-made counterparts. However, these languages still fail to describe accurately key features of biological objects, in particular the diversity of signal-transfer molecules and the diffusion that is inherent to any biochemical system. Furthermore, current formalisms associated with networks and circuits can hardly face the problem of multi-scale regulatory complexity-from single molecules to entire ecosystems. We argue that the language of economic theory might be instrumental not only to portray accurately many features of regulatory networks, but also to unveil aspects of the biological complexity problem that remain opaque to other types of analyses. The main perspective opened by the economic metaphor when applied to control of microbiological activities is a focus on metabolism, not gene selfishness, as the necessary background to make sense of regulatory phenomena. As an example, we analyse and reinterpret the widespread phenomenon of catabolite repression with the formal frame of the consumer's choice theory.

Prediction of Cellular Burden with Host-Circuit Models

Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognized bottleneck in the design of robust circuits. In this tutorial we discuss the use of computational models that integrate gene circuits and the physiology of host cells. Through various use cases, we illustrate the power of host-circuit models to predict the impact of design parameters on both burden and circuit functionality. Our approach relies on a new generation of computational models for microbial growth that can flexibly accommodate resource bottlenecks encountered in gene circuit design. Adoption of this modeling paradigm can facilitate fast and robust design cycles in synthetic biology.

Whole cell biophysical modeling of codon-tRNA competition reveals novel insights related to translation dynamics

The importance of mRNA translation models has been demonstrated across many fields of science and biotechnology. However, a whole cell model with codon resolution and biophysical dynamics is still lacking. We describe a whole cell model of translation for E. coli. The model simulates all major translation components in the cell: ribosomes, mRNAs and tRNAs. It also includes, for the first time, fundamental aspects of translation, such as competition for ribosomes and tRNAs at a codon resolution while considering tRNAs wobble interactions and tRNA recycling. The model uses parameters that are tightly inferred from large scale measurements of translation. Furthermore, we demonstrate a robust modelling approach which relies on state-of-the-art practices of translation modelling and also provides a framework for easy generalizations. This novel approach allows simulation of thousands of mRNAs that undergo translation in the same cell with common resources such as ribosomes and tRNAs in feasible time. Based on this model, we demonstrate, for the first time, the direct importance of competition for resources on translation and its accurate modelling. An effective supply-demand ratio (ESDR) measure, which is related to translation factors such as tRNAs, has been devised and utilized to show superior predictive power in complex scenarios of heterologous gene expression. The devised model is not only more accurate than the existing models, but, more importantly, provides a framework for analyzing complex whole cell translation problems and variables that haven't been explored before, making it important in various biomedical fields.

mRNA translation is a fundamental process in all living organisms and the importance of its modeling has been demonstrated across many fields of science and biotechnology. Specifically, modeling a whole cell context with a high resolution has been a great challenge in the field, making many important problems un-addressable. In this study we devised a novel model, which allows, for the first time, simultaneous simulation of thousands of mRNAs, along with various bio-physical aspects that affect translation (such as codon-resolution dynamics and shared resources pool of both ribosomes and tRNAs). We demonstrated (using experimental data) that this model is more accurate than existing ones, and, more importantly, provides a framework for addressing complex translation problems (such as heterologous expression) at whole cell scale and in reasonable time. We demonstrated the model using E. coli data, but the model can be easily tailored to other organisms as well. Our model addresses an urgent unmet need for biophysically accurate whole cell translation model with resources coupling and has potential applications in many fields, including medicine and biotechnology.

Modelling and measuring intracellular competition for finite resources during gene expression

Dissecting the competition between genes for shared expressional resources is of fundamental importance for understanding the interplay between cellular components. Owing to the relationship between gene expression and cellular fitness, genomes are shaped by evolution to improve resource allocation. Whereas experimental approaches to investigate intracellular competition require technical resources and human expertise, computational models and in silico simulations allow vast numbers of experiments to be carried out and controlled easily, and with significantly reduced costs. Thus, modelling competition has a pivotal role in understanding the effects of competition on the biophysics of the cell. In this article, we review various computational models proposed to describe the different types of competition during gene expression. We also present relevant synthetic biology experiments and their biotechnological implications, and discuss the open questions in the field.

Heterogeneity coordinates bacterial multi-gene expression in single cells

For a genetically identical microbial population, multi-gene expression in various environments requires effective allocation of limited resources and precise control of heterogeneity among individual cells. However, it is unclear how resource allocation and cell-to-cell variation jointly shape the overall performance. Here we demonstrate a Simpson’s paradox during overexpression of multiple genes: two competing proteins in single cells correlated positively for every induction condition, but the overall correlation was negative. Yet this phenomenon was not observed between two competing mRNAs in single cells. Our analytical framework shows that the phenomenon arises from competition for translational resource, with the correlation modulated by both mRNA and ribosome variability. Thus, heterogeneity plays a key role in single-cell multi-gene expression and provides the population with an evolutionary advantage, as demonstrated in this study.

Microbes perform multitasking for a wide range of purposes, including survival, adaptation, colonization, and evolution. Both modelling and experimental results at the ensemble level reveal trade-offs between different tasks due to resource competition, but it is unclear how single cells allocate limited intracellular resources to perform multitasking, and how does a population coordinate single cell performances during multitasking to maximize population efficiencies. In this study, we address this question by using bacterial multi-gene overexpression as the basic form of multitasking. We discovered and analyzed a statistical phenomenon called Simpson’s paradox, where competing proteins in single cells correlate positively at each constant condition, although the proteins correlate negatively when all conditions are combined. We demonstrate that the phenomenon arises from competition for translational resources, with the correlation modulated by heterogeneity of both mRNA and ribosomes. We further show that heterogeneity coordinates multiple functional modules, conferring an evolutionary advantage on the population. Our work discloses that heterogeneity in the form of Simpson’s paradox is an important phenomenon in coordinating multi-gene expression.

Competing endogenous RNA crosstalk at system level

microRNAs (miRNAs) regulate gene expression at post-transcriptional level by repressing target RNA molecules. Competition to bind miRNAs tends in turn to correlate their targets, establishing effective RNA-RNA interactions that can influence expression levels, buffer fluctuations and promote signal propagation. Such a potential has been characterized mathematically for small motifs both at steady state and away from stationarity. Experimental evidence, on the other hand, suggests that competing endogenous RNA (ceRNA) crosstalk is rather weak. Extended miRNA-RNA networks could however favour the integration of many crosstalk interactions, leading to significant large-scale effects in spite of the weakness of individual links. To clarify the extent to which crosstalk is sustained by the miRNA interactome, we have studied its emergent systemic features in silico in large-scale miRNA-RNA network reconstructions. We show that, although generically weak, system-level crosstalk patterns (i) are enhanced by transcriptional heterogeneities, (ii) can achieve high-intensity even for RNAs that are not co-regulated, (iii) are robust to variability in transcription rates, and (iv) are significantly non-local, i.e. correlate weakly with miRNA-RNA interaction parameters. Furthermore, RNA levels are generically more stable when crosstalk is strongest. As some of these features appear to be encoded in the network's topology, crosstalk may functionally be favoured by natural selection. These results suggest that, besides their repressive role, miRNAs mediate a weak but resilient and context-independent network of cross-regulatory interactions that interconnect the transcriptome, stabilize expression levels and support system-level responses.

On signalling and estimation limits for molecular birth-processes

Understanding and uncovering the mechanisms or motifs that molecular networks employ to regulate noise is a key problem in cell biology. As it is often difficult to obtain direct and detailed insight into these mechanisms, many studies instead focus on assessing the best precision attainable on the signalling pathways that compose these networks. Molecules signal one another over such pathways to solve noise regulating estimation and control problems. Quantifying the maximum precision of these solutions delimits what is achievable and allows hypotheses about underlying motifs to be tested without requiring detailed biological knowledge. The pathway capacity, which defines the maximum rate of transmitting information along it, is a widely used proxy for precision. Here it is shown, for estimation problems involving elementary yet biologically relevant birth-process networks, that capacity can be surprisingly misleading. A time-optimal signalling motif, called birth-following, is derived and proven to better the precision expected from the capacity, provided the maximum signalling rate constraint is large and the mean one above a certain threshold. When the maximum constraint is relaxed, perfect estimation is predicted by the capacity. However, the true achievable precision is found highly variable and sensitive to the mean constraint. Since the same capacity can map to different combinations of rate constraints, it can only equivocally measure precision. Deciphering the rate constraints on a signalling pathway may therefore be more important than computing its capacity.

Growth Defects and Loss-of-Function in Synthetic Gene Circuits

Synthetic gene circuits perturb the physiology of their cellular host. The extra load on endogenous processes shifts the equilibrium of resource allocation in the host, leading to slow growth and reduced biosynthesis. Here we built integrated host-circuit models to quantify growth defects caused by synthetic gene circuits. Simulations reveal a complex relation between circuit output and cellular capacity for gene expression. For weak induction of heterologous genes, protein output can be increased at the expense of growth defects. Yet for stronger induction, cellular capacity reaches a tipping point, beyond which both gene expression and growth rate drop sharply. Extensive simulations across various growth conditions and large regions of the design space suggest that the critical capacity is a result of ribosomal scarcity. We studied the impact of growth defects on various gene circuits and transcriptional logic gates, which highlights the extent to which cellular burden can limit, shape, and even break down circuit function. Our approach offers a comprehensive framework to assess the impact of host-circuit interactions in silico, with wide-ranging implications for the design and optimization of bacterial gene circuits.

Networks of ribosome flow models for modeling and analyzing intracellular traffic

The ribosome flow model with input and output (RFMIO) is a deterministic dynamical system that has been used to study the flow of ribosomes during mRNA translation. The input of the RFMIO controls its initiation rate and the output represents the ribosome exit rate (and thus the protein production rate) at the 3′ end of the mRNA molecule. The RFMIO and its variants encapsulate important properties that are relevant to modeling ribosome flow such as the possible evolution of “traffic jams” and non-homogeneous elongation rates along the mRNA molecule, and can also be used for studying additional intracellular processes such as transcription, transport, and more. Here we consider networks of interconnected RFMIOs as a fundamental tool for modeling, analyzing and re-engineering the complex mechanisms of protein production. In these networks, the output of each RFMIO may be divided, using connection weights, between several inputs of other RFMIOs. We show that under quite general feedback connections the network has two important properties: (1) it admits a unique steady-state and every trajectory converges to this steady-state; and (2) the problem of how to determine the connection weights so that the network steady-state output is maximized is a convex optimization problem. These mathematical properties make these networks highly suitable as models of various phenomena: property (1) means that the behavior is predictable and ordered, and property (2) means that determining the optimal weights is numerically tractable even for large-scale networks. For the specific case of a feed-forward network of RFMIOs we prove an additional useful property, namely, that there exists a spectral representation for the network steady-state, and thus it can be determined without any numerical simulations of the dynamics. We describe the implications of these results to several fundamental biological phenomena and biotechnological objectives.

Towards an Aspect-Oriented Design and Modelling Framework for Synthetic Biology

Work on synthetic biology has largely used a component-based metaphor for system construction. While this paradigm has been successful for the construction of numerous systems, the incorporation of contextual design issues-either compositional, host or environmental-will be key to realising more complex applications. Here, we present a design framework that radically steps away from a purely parts-based paradigm by using aspect-oriented software engineering concepts. We believe that the notion of concerns is a powerful and biologically credible way of thinking about system synthesis. By adopting this approach, we can separate core concerns, which represent modular aims of the design, from cross-cutting concerns, which represent system-wide attributes. The explicit handling of cross-cutting concerns allows for contextual information to enter the design process in a modular way. As a proof-of-principle, we implemented the aspect-oriented approach in the Python tool, SynBioWeaver, which enables the combination, or weaving, of core and cross-cutting concerns. The power and flexibility of this framework is demonstrated through a number of examples covering the inclusion of part context, combining circuit designs in a context dependent manner, and the generation of rule, logic and reaction models from synthetic circuit designs.

Macromolecular Crowding Induces Spatial Correlations That Control Gene Expression Bursting Patterns

Recent superresolution microscopy studies in E. coli demonstrate that the cytoplasm has highly variable local concentrations where macromolecular crowding plays a central role in establishing membrane-less compartmentalization. This spatial inhomogeneity significantly influences molecular transport and association processes central to gene expression. Yet, little is known about how macromolecular crowding influences gene expression bursting-the episodic process where mRNA and proteins are produced in bursts. Here, we simultaneously measured mRNA and protein reporters in cell-free systems, showing that macromolecular crowding decoupled the well-known relationship between fluctuations in the protein population (noise) and mRNA population statistics. Crowded environments led to a 10-fold increase in protein noise even though there were only modest changes in the mRNA population and fluctuations. Instead, cell-like macromolecular crowding created an inhomogeneous spatial distribution of mRNA ("spatial noise") that led to large variability in the protein production burst size. As a result, the mRNA spatial noise created large temporal fluctuations in the protein population. These results highlight the interplay between macromolecular crowding, spatial inhomogeneities, and the resulting dynamics of gene expression, and provide insights into using these organizational principles in both cell-based and cell-free synthetic biology.

Computational analysis of the oscillatory behavior at the translation level induced by mRNA levels oscillations due to finite intracellular resources

Recent studies have demonstrated how the competition for the finite pool of available gene expression factors has important effect on fundamental gene expression aspects. In this study, based on a whole-cell model simulation of translation in S. cerevisiae, we evaluate for the first time the expected effect of mRNA levels fluctuations on translation due to the finite pool of ribosomes. We show that fluctuations of a single gene or a group of genes mRNA levels induce periodic behavior in all S. cerevisiae translation factors and aspects: the ribosomal densities and the translation rates of all S. cerevisiae mRNAs oscillate. We numerically measure the oscillation amplitudes demonstrating that fluctuations of endogenous and heterologous genes can cause a significant fluctuation of up to 50% in the steady-state translation rates of the rest of the genes. Furthermore, we demonstrate by synonymous mutations that oscillating the levels of mRNAs that experience high ribosomal occupancy (e.g. ribosomal “traffic jam”) induces the largest impact on the translation of the S. cerevisiae genome.

The results reported here should provide novel insights and principles related to the design of synthetic gene expression circuits and related to the evolutionary constraints shaping gene expression of endogenous genes.

Each cell contains a limited number of macromolecules and factors that participate in the gene expression process. These expression resources are shared between the different molecules that encode the genetic code, resulting in non-trivial couplings and competitions between the different gene expression stages. Such competitions should be considered when analyzing the cellular economy of the cell, the genome evolution, and the design of synthetic expression circuits. Here we study the effect of couplings and competitions for ribosomes by performing a whole-cell simulation of translation of S. cerevisiae, with parameters estimated from experimental data. We demonstrate that by periodically changing the mRNA levels of a single gene (endogenous or heterologous) or a set of genes, the translation of all S. cerevisiae genes are affected in a periodic manner. We numerically estimate the exact impact of the mRNA levels periodicity on the translation process dynamics, as well as on the dynamics of the free ribosomal pool and the way it is affected by parameters such as the codon composition of the oscillating gene, its initiation rate and mRNA levels. Furthermore, we show that the codon compositions of synthetically highly expressed heterologous genes that are expected to oscillate must be carefully considered. For example, synonymous mutations resulting in “traffic jams” of ribosomes along the fluctuated mRNAs may cause significant fluctuations of up to 50% in the steady-state translation rates of all genes.

Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

Metabolic division of labor in microbial systems

Metabolic pathways are often engineered in single microbial populations. However, the introduction of heterologous circuits into the host can create a substantial metabolic burden that limits the overall productivity of the system. This limitation could be overcome by metabolic division of labor (DOL), whereby distinct populations perform different steps in a metabolic pathway, reducing the burden each population will experience. While conceptually appealing, the conditions when DOL is advantageous have not been rigorously established. Here, we have analyzed 24 common architectures of metabolic pathways in which DOL can be implemented. Our analysis reveals general criteria defining the conditions that favor DOL, accounting for the burden or benefit of the pathway activity on the host populations as well as the transport and turnover of enzymes and intermediate metabolites. These criteria can help guide engineering of metabolic pathways and have implications for understanding evolution of natural microbial communities.

Leveraging genome-wide datasets to quantify the functional role of the anti-Shine-Dalgarno sequence in regulating translation efficiency

Studies dating back to the 1970s established that sequence complementarity between the anti-Shine–Dalgarno (aSD) sequence on prokaryotic ribosomes and the 5′ untranslated region of mRNAs helps to facilitate translation initiation. The optimal location of aSD sequence binding relative to the start codon, the full extents of the aSD sequence and the functional form of the relationship between aSD sequence complementarity and translation efficiency have not been fully resolved. Here, we investigate these relationships by leveraging the sequence diversity of endogenous genes and recently available genome-wide estimates of translation efficiency. We show that—after accounting for predicted mRNA structure—aSD sequence complementarity increases the translation of endogenous mRNAs by roughly 50%. Further, we observe that this relationship is nonlinear, with translation efficiency maximized for mRNAs with intermediate levels of aSD sequence complementarity. The mechanistic insights that we observe are highly robust: we find nearly identical results in multiple datasets spanning three distantly related bacteria. Further, we verify our main conclusions by re-analysing a controlled experimental dataset.

Resource Competition Shapes the Response of Genetic Circuits

A common approach to design genetic circuits is to compose gene expression cassettes together. While appealing, this modular approach is challenged by the fact that expression of each gene depends on the availability of transcriptional/translational resources, which is in turn determined by the presence of other genes in the circuit. This raises the question of how competition for resources by different genes affects a circuit's behavior. Here, we create a library of genetic activation cascades in E. coli bacteria, where we explicitly tune the resource demand by each gene. We develop a general Hill-function-based model that incorporates resource competition effects through resource demand coefficients. These coefficients lead to nonregulatory interactions among genes that reshape the circuit's behavior. For the activation cascade, such interactions result in surprising biphasic or monotonically decreasing responses. Finally, we use resource demand coefficients to guide the choice of ribosome binding site and DNA copy number to restore the cascade's intended monotonically increasing response. Our results demonstrate how unintended circuit's behavior arises from resource competition and provide a model-guided methodology to minimize the resulting effects.

Criticality and Adaptivity in Enzymatic Networks

The contrast between the stochasticity of biochemical networks and the regularity of cellular behavior suggests that biological networks generate robust behavior from noisy constituents. Identifying the mechanisms that confer this ability on biological networks is essential to understanding cells. Here we show that queueing for a limited shared resource in broad classes of enzymatic networks in certain conditions leads to a critical state characterized by strong and long-ranged correlations between molecular species. An enzymatic network reaches this critical state when the input flux of its substrate is balanced by the maximum processing capacity of the network. We then consider enzymatic networks with adaptation, when the limiting resource (enzyme or cofactor) is produced in proportion to the demand for it. We show that the critical state becomes an attractor for these networks, which points toward the onset of self-organized criticality. We suggest that the adaptive queueing motif that leads to significant correlations between multiple species may be widespread in biological systems.

mTOR referees memory and disease through mRNA repression and competition

Mammalian target of rapamycin (mTOR) activity is required for memory and is dysregulated in disease. Activation of mTOR promotes protein synthesis; however, new studies are demonstrating that mTOR activity also represses the translation of mRNAs. Almost three decades ago, Kandel and colleagues hypothesised that memory was due to the induction of positive regulators and removal of negative constraints. Are these negative constraints repressed mRNAs that code for proteins that block memory formation? Herein, we will discuss the mRNAs coded by putative memory suppressors, how activation/inactivation of mTOR repress protein expression at the synapse, how mTOR activity regulates RNA binding proteins, mRNA stability, and translation, and what the possible implications of mRNA repression are to memory and neurodegenerative disorders.

Resource Sharing Controls Gene Expression Bursting

Episodic gene expression, with periods of high expression separated by periods of no expression, is a pervasive biological phenomenon. This bursty pattern of expression draws from a finite reservoir of expression machinery in a highly time variant way, i.e., requiring no resources most of the time but drawing heavily on them during short intense bursts, that intimately links expression bursting and resource sharing. Yet, most recent investigations have focused on specific molecular mechanisms intrinsic to the bursty behavior of individual genes, while little is known about the interplay between resource sharing and global expression bursting behavior. Here, we confine Escherichia coli cell extract in both cell-sized microfluidic chambers and lipid-based vesicles to explore how resource sharing influences expression bursting. Interestingly, expression burst size, but not burst frequency, is highly sensitive to the size of the shared transcription and translation resource pools. The intriguing implication of these results is that expression bursts are more readily amplified than initiated, suggesting that burst formation occurs through positive feedback or cooperativity. When extrapolated to prokaryotic cells, these results suggest that large translational bursts may be correlated with large transcriptional bursts. This correlation is supported by recently reported transcription and translation bursting studies in E. coli. The results reported here demonstrate a strong intimate link between global expression burst patterns and resource sharing, and they suggest that bursting plays an important role in optimizing the use of limited, shared expression resources.

A model for competition for ribosomes in the cell

A single mammalian cell includes an order of 10(4)-10(5) mRNA molecules and as many as 10(5)-10(6) ribosomes. Large-scale simultaneous mRNA translation induces correlations between the mRNA molecules, as they all compete for the finite pool of available ribosomes. This has important implications for the cell's functioning and evolution. Developing a better understanding of the intricate correlations between these simultaneous processes, rather than focusing on the translation of a single isolated transcript, should help in gaining a better understanding of mRNA translation regulation and the way elongation rates affect organismal fitness. A model of simultaneous translation is specifically important when dealing with highly expressed genes, as these consume more resources. In addition, such a model can lead to more accurate predictions that are needed in the interconnection of translational modules in synthetic biology. We develop and analyse a general dynamical model for large-scale simultaneous mRNA translation and competition for ribosomes. This is based on combining several ribosome flow models (RFMs) interconnected via a pool of free ribosomes. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady state. We show that the compound system always converges to a steady state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We then study the effect of changing the transition rates in one mRNA molecule on the steady-state translation rates of the other mRNAs that results from the competition for ribosomes. We show that increasing any of the codon translation rates in a specific mRNA molecule yields a local effect, an increase in the translation rate of this mRNA, and also a global effect, the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production is more complicated than previously thought. In addition, we show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs.

On the Dependency of Cellular Protein Levels on mRNA Abundance

The question of how genomic information is expressed to determine phenotypes is of central importance for basic and translational life science research and has been studied by transcriptomic and proteomic profiling. Here, we review the relationship between protein and mRNA levels under various scenarios, such as steady state, long-term state changes, and short-term adaptation, demonstrating the complexity of gene expression regulation, especially during dynamic transitions. The spatial and temporal variations of mRNAs, as well as the local availability of resources for protein biosynthesis, strongly influence the relationship between protein levels and their coding transcripts. We further discuss the buffering of mRNA fluctuations at the level of protein concentrations. We conclude that transcript levels by themselves are not sufficient to predict protein levels in many scenarios and to thus explain genotype-phenotype relationships and that high-quality data quantifying different levels of gene expression are indispensable for the complete understanding of biological processes.

Predictive biophysical modeling and understanding of the dynamics of mRNA translation and its evolution

mRNA translation is the fundamental process of decoding the information encoded in mRNA molecules by the ribosome for the synthesis of proteins. The centrality of this process in various biomedical disciplines such as cell biology, evolution and biotechnology, encouraged the development of dozens of mathematical and computational models of translation in recent years. These models aimed at capturing various biophysical aspects of the process. The objective of this review is to survey these models, focusing on those based and/or validated on real large-scale genomic data. We consider aspects such as the complexity of the models, the biophysical aspects they regard and the predictions they may provide. Furthermore, we survey the central systems biology discoveries reported on their basis. This review demonstrates the fundamental advantages of employing computational biophysical translation models in general, and discusses the relative advantages of the different approaches and the challenges in the field.

A Minimal Model of Ribosome Allocation Dynamics Captures Trade-offs in Expression between Endogenous and Synthetic Genes

Cells contain a finite set of resources that must be distributed across many processes to ensure survival. Among them, the largest proportion of cellular resources is dedicated to protein translation. Synthetic biology often exploits these resources in executing orthogonal genetic circuits, yet the burden this places on the cell is rarely considered. Here, we develop a minimal model of ribosome allocation dynamics capturing the demands on translation when expressing a synthetic construct together with endogenous genes required for the maintenance of cell physiology. Critically, it contains three key variables related to design parameters of the synthetic construct covering transcript abundance, translation initiation rate, and elongation time. We show that model-predicted changes in ribosome allocation closely match experimental shifts in synthetic protein expression rate and cellular growth. Intriguingly, the model is also able to accurately infer transcript levels and translation times after further exposure to additional ambient stress. Our results demonstrate that a simple model of resource allocation faithfully captures the redistribution of protein synthesis resources when faced with the burden of synthetic gene expression and environmental stress. The tractable nature of the model makes it a versatile tool for exploring the guiding principles of efficient heterologous expression and the indirect interactions that can arise between synthetic circuits and their host chassis because of competition for shared translational resources.

Synthetic strategies for plant signalling studies: molecular toolbox and orthogonal platforms

Plants deploy a wide array of signalling networks integrating environmental cues with growth, defence and developmental responses. The high level of complexity, redundancy and connection between several pathways hampers a comprehensive understanding of involved functional and regulatory mechanisms. The implementation of synthetic biology approaches is revolutionizing experimental biology in prokaryotes, yeasts and animal systems and can likewise contribute to a new era in plant biology. This review gives an overview on synthetic biology approaches for the development and implementation of synthetic molecular tools and techniques to interrogate, understand and control signalling events in plants, ranging from strategies for the targeted manipulation of plant genomes up to the spatiotemporally resolved control of gene expression using optogenetic approaches. We also describe strategies based on the partial reconstruction of signalling pathways in orthogonal platforms, like yeast, animal and in vitro systems. This allows a targeted analysis of individual signalling hubs devoid of interconnectivity with endogenous interacting components. Implementation of the interdisciplinary synthetic biology tools and strategies is not exempt of challenges and hardships but simultaneously most rewarding in terms of the advances in basic and applied research. As witnessed in other areas, these original theoretical-experimental avenues will lead to a breakthrough in the ability to study and comprehend plant signalling networks.

Isocost Lines Describe the Cellular Economy of Genetic Circuits

Genetic circuits in living cells share transcriptional and translational resources that are available in limited amounts. This leads to unexpected couplings among seemingly unconnected modules, which result in poorly predictable circuit behavior. In this study, we determine these interdependencies between products of different genes by characterizing the economy of how transcriptional and translational resources are allocated to the production of proteins in genetic circuits. We discover that, when expressed from the same plasmid, the combinations of attainable protein concentrations are constrained by a linear relationship, which can be interpreted as an isocost line, a concept used in microeconomics. We created a library of circuits with two reporter genes, one constitutive and the other inducible in the same plasmid, without a regulatory path between them. In agreement with the model predictions, experiments reveal that the isocost line rotates when changing the ribosome binding site strength of the inducible gene and shifts when modifying the plasmid copy number. These results demonstrate that isocost lines can be employed to predict how genetic circuits become coupled when sharing resources and provide design guidelines for minimizing the effects of such couplings.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Mechanistic links between cellular trade-offs, gene expression, and growth

Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod's law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host-circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.

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

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

A model for sigma factor competition in bacterial cells

Sigma factors control global switches of the genetic expression program in bacteria. Different sigma factors compete for binding to a limited pool of RNA polymerase (RNAP) core enzymes, providing a mechanism for cross-talk between genes or gene classes via the sharing of expression machinery. To analyze the contribution of sigma factor competition to global changes in gene expression, we develop a theoretical model that describes binding between sigma factors and core RNAP, transcription, non-specific binding to DNA and the modulation of the availability of the molecular components. The model is validated by comparison with in vitro competition experiments, with which excellent agreement is found. Transcription is affected via the modulation of the concentrations of the different types of holoenzymes, so saturated promoters are only weakly affected by sigma factor competition. However, in case of overlapping promoters or promoters recognized by two types of sigma factors, we find that even saturated promoters are strongly affected. Active transcription effectively lowers the affinity between the sigma factor driving it and the core RNAP, resulting in complex cross-talk effects. Sigma factor competition is not strongly affected by non-specific binding of core RNAPs, sigma factors and holoenzymes to DNA. Finally, we analyze the role of increased core RNAP availability upon the shut-down of ribosomal RNA transcription during the stringent response. We find that passive up-regulation of alternative sigma-dependent transcription is not only possible, but also displays hypersensitivity based on the sigma factor competition. Our theoretical analysis thus provides support for a significant role of passive control during that global switch of the gene expression program.

Bacteria respond to changing environmental conditions by switching the global pattern of expressed genes. A key mechanism for global switches of the transcriptional program depends on alternative sigma factors that bind the RNA polymerase core enzyme and direct it towards the appropriate stress response genes. Competition of different sigma factors for a limited amount of RNA polymerase is believed to play a central role in this global switch. Here, a theoretical approach is used towards a quantitative understanding of sigma factor competition and its effects on gene expression. The model is used to quantitatively describe in vitro competition assays and to address the question of indirect or passive control in the stringent response upon amino acids starvation. We show that sigma factor competition provides a mechanism for a passive up-regulation of the stress specific sigma-driven genes due to the increased availability of RNA polymerase in the stringent response. Moreover, we find that active separation of sigma factor from the RNA polymerase during early transcript elongation weakens the sigma factor-RNA polymerase equilibrium constant, raising the question of how their in vitro measure is relevant in the cell.

Gene circuit performance characterization and resource usage in a cell-free "breadboard"

The many successes of synthetic biology have come in a manner largely different from those in other engineering disciplines; in particular, without well-characterized and simplified prototyping environments to play a role analogous to wind-tunnels in aerodynamics and breadboards in electrical engineering. However, as the complexity of synthetic circuits increases, the benefits--in cost savings and design cycle time--of a more traditional engineering approach can be significant. We have recently developed an in vitro "breadboard" prototyping platform based on E. coli cell extract that allows biocircuits to operate in an environment considerably simpler than, but functionally similar to, in vivo. The simplicity of this system makes it a promising tool for rapid biocircuit design and testing, as well as for probing fundamental aspects of gene circuit operation normally masked by cellular complexity. In this work, we characterize the cell-free breadboard using real-time and simultaneous measurements of transcriptional and translational activities of a small set of reporter genes and a transcriptional activation cascade. We determine the effects of promoter strength, gene concentration, and nucleoside triphosphate concentration on biocircuit properties, and we isolate the specific contributions of essential biomolecular resources-core RNA polymerase and ribosomes-to overall performance. Importantly, we show how limits on resources, particularly those involved in translation, are manifested as reduced expression in the presence of orthogonal genes that serve as additional loads on the system.

Principles of genetic circuit design

Cells navigate environments, communicate and build complex patterns by initiating gene expression in response to specific signals. Engineers seek to harness this capability to program cells to perform tasks or create chemicals and materials that match the complexity seen in nature. This Review describes new tools that aid the construction of genetic circuits. Circuit dynamics can be influenced by the choice of regulators and changed with expression 'tuning knobs'. We collate the failure modes encountered when assembling circuits, quantify their impact on performance and review mitigation efforts. Finally, we discuss the constraints that arise from circuits having to operate within a living cell. Collectively, better tools, well-characterized parts and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the atomic manufacturing of functional materials.

Noise in biology

Noise permeates biology on all levels, from the most basic molecular, sub-cellular processes to the dynamics of tissues, organs, organisms and populations. The functional roles of noise in biological processes can vary greatly. Along with standard, entropy-increasing effects of producing random mutations, diversifying phenotypes in isogenic populations, limiting information capacity of signaling relays, it occasionally plays more surprising constructive roles by accelerating the pace of evolution, providing selective advantage in dynamic environments, enhancing intracellular transport of biomolecules and increasing information capacity of signaling pathways. This short review covers the recent progress in understanding mechanisms and effects of fluctuations in biological systems of different scales and the basic approaches to their mathematical modeling.