Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

DYNAMICS OF GLI REGULATION AND A STRATEGY TO CONTROL CANCEROUS SITUATION: HEDGEHOG SIGNALING PATHWAY REVISITED

The hedgehog signaling cascade generates highly diverse, fine-tuned responses in response to the external stimulus by the sonic hedgehog (SHH) protein. This is required for the flawless functioning of the cell, its development, survival and proliferation; maintained through production of Glioma protein (GLI) and transcriptional activation of its target genes. Any change in the behavior of GLI response by ectopic expression of SHH or mutations in the core pathway components may cause serious consequences in the cell fate through rapid, uncontrolled and elevated production of GLI. Here, we present a simple but extensive computational model that considers the detailed reaction mechanisms involved in the hedgehog signal transduction and provides a detailed insight into regulation of GLI. For the first time, by explicit involvement of suppressor of fused (SUFU) and Hedgehog interacting protein (HHIP) reaction kinetics in the model, we try to demonstrate the vital importance of HHIP and SUFU in maintaining the graded response of GLI in response to SHH. By performing parameter variations, we capture the conversion of a graded response of GLI to an ultrasensitive switch under SUFU-deficient conditions that might predispose abnormal embryonic development and the irreversible switching response of GLI that corresponds to signal-independent pathway activation observed in cancers.

Rational Control of Folding Cooperativity in DNA Quadruplexes

Availability of basic tools for engineering molecular systems with precisely defined properties is crucial toward progress in development of new responsive materials. Among such materials are systems capable of generating an ultrasensitive response (i.e., large relative changes in output in response to small changes in input). Herein, we focus on a rational design of DNA quadruplex based structures as ultrasensitive response elements. In particular, we demonstrate how addition of allosteric guiding elements can be engineered into H(+)-responsive i-motif structure to yield maximized response sensitivity.

Logical-continuous modelling of post-translationally regulated bistability of curli fiber expression in Escherichia coli

BACKGROUND

Bacteria have developed a repertoire of signalling mechanisms that enable adaptive responses to fluctuating environmental conditions. The formation of biofilm, for example, allows persisting in times of external stresses, e.g. induced by antibiotics or a lack of nutrients. Adhesive curli fibers, the major extracellular matrix components in Escherichia coli biofilms, exhibit heterogeneous expression in isogenic cells exposed to identical external conditions. The dynamical mechanisms underlying this heterogeneity remain poorly understood. In this work, we elucidate the potential role of post-translational bistability as a source for this heterogeneity.

RESULTS

We introduce a structured modelling workflow combining logical network topology analysis with time-continuous deterministic and stochastic modelling. The aim is to evaluate the topological structure of the underlying signalling network and to identify and analyse model parameterisations that satisfy observations from a set of genetic knockout experiments. Our work supports the hypothesis that the phenotypic heterogeneity of curli expression in biofilm cells is induced by bistable regulation at the post-translational level. Stochastic modelling suggests diverse noise-induced switching behaviours between the stable states, depending on the expression levels of the c-di-GMP-producing (diguanylate cyclases, DGCs) and -degrading (phosphodiesterases, PDEs) enzymes and reveals the quantitative difference in stable c-di-GMP levels between distinct phenotypes. The most dominant type of behaviour is characterised by a fast switching from curli-off to curli-on with a slow switching in the reverse direction and the second most dominant type is a long-term differentiation into curli-on or curli-off cells. This behaviour may implicate an intrinsic feature of the system allowing for a fast adaptive response (curli-on) versus a slow transition to the curli-off state, in line with experimental observations.

CONCLUSION

The combination of logical and continuous modelling enables a thorough analysis of different determinants of bistable regulation, i.e. network topology and biochemical kinetics, and allows for an incorporation of experimental data from heterogeneous sources. Our approach yields a mechanistic explanation for the phenotypic heterogeneity of curli fiber expression. Furthermore, the presented work provides a detailed insight into the interactions between the multiple DGC- and PDE-type enzymes and the role of c-di-GMP in dynamical regulation of cellular decisions.

BioJazz: in silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx.

Microtiter plate tests for segregation of bioluminescent bacteria

It has been recently shown that bioluminescence imaging can be usefully applied to provide new insights into bacterial self-organization. In this work we employ bioluminescence imaging to record images of nutrient rich liquid cultures of the lux-gene reporter Escherichia coli in microtiter plate wells. The images show that patterns of inhomogenous bioluminescence form along the three-phase contact lines. The paper analyzes the dependencies of the average number of luminous aggregates (clouds) on various environmental factors. In particular, our results show that optimal (neutral) pH and high aeration rates determine the highest mean number of clouds, and that spatiotemporal patterns do not form in the pH buffered suspensions. In addition, a sigmoidal (switch-like) dependence of the number of aggregates on the rate of aeration was observed. The obtained bioluminescence imaging data was interpreted by employing the Keller-Segel-Fisher (KSF) model of chemotaxis and logistic growth, adapted to systems of metabolically flexible (two-state) bacteria. The modified KSF model successfully simulated the observed switch-like responses. The results of the microtiter plate tests and their simulations indicate that the segregation of bacteria with different activities proceeds in the three-phase contact line region.

Rapid engineering of versatile molecular logic gates using heterologous genetic transcriptional modules

Versatile modular molecular logic gates are engineered in Escherichia coli bacteria that can sense and integrate multiple chemical molecules in customised digital logic manner.

We designed and constructed versatile modular genetic logic gates in bacterial cells. These function as digital logic 1-input Buffer gate, 2-input and 3-input AND gates with one inverted input and integrate multiple chemical input signals in customised logic manners. Such rapidly engineered devices serve to achieve increased sensing signal selectivity.

The human toxome project

The Human Toxome Project, funded as an NIH Transformative Research grant 2011-2016, is focused on developing the concepts and the means for deducing, validating and sharing molecular pathways of toxicity (PoT). Using the test case of estrogenic endocrine disruption, the responses of MCF-7 human breast cancer cells are being phenotyped by transcriptomics and mass-spectroscopy-based metabolomics. The bioinformatics tools for PoT deduction represent a core deliverable. A number of challenges for quality and standardization of cell systems, omics technologies and bioinformatics are being addressed. In parallel, concepts for annotation, validation and sharing of PoT information, as well as their link to adverse outcomes, are being developed. A reasonably comprehensive public database of PoT, the Human Toxome Knowledge-base, could become a point of reference for toxicological research and regulatory test strategies.

Molecular signaling network motifs provide a mechanistic basis for cellular threshold responses

BACKGROUND

Increasingly, there is a move toward using in vitro toxicity testing to assess human health risk due to chemical exposure. As with in vivo toxicity testing, an important question for in vitro results is whether there are thresholds for adverse cellular responses. Empirical evaluations may show consistency with thresholds, but the main evidence has to come from mechanistic considerations.

OBJECTIVES

Cellular response behaviors depend on the molecular pathway and circuitry in the cell and the manner in which chemicals perturb these circuits. Understanding circuit structures that are inherently capable of resisting small perturbations and producing threshold responses is an important step towards mechanistically interpreting in vitro testing data.

METHODS

Here we have examined dose-response characteristics for several biochemical network motifs. These network motifs are basic building blocks of molecular circuits underpinning a variety of cellular functions, including adaptation, homeostasis, proliferation, differentiation, and apoptosis. For each motif, we present biological examples and models to illustrate how thresholds arise from specific network structures.

DISCUSSION AND CONCLUSION

Integral feedback, feedforward, and transcritical bifurcation motifs can generate thresholds. Other motifs (e.g., proportional feedback and ultrasensitivity)produce responses where the slope in the low-dose region is small and stays close to the baseline. Feedforward control may lead to nonmonotonic or hormetic responses. We conclude that network motifs provide a basis for understanding thresholds for cellular responses. Computational pathway modeling of these motifs and their combinations occurring in molecular signaling networks will be a key element in new risk assessment approaches based on in vitro cellular assays.

Three level signal transduction cascades lead to reliably timed switches

Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.

Quantification of pre-mRNA escape rate and synergy in splicing

Splicing reactions generally combine high speed with accuracy. However, some of the pre-mRNAs escape the nucleus with a retained intron. Intron retention can control gene expression and increase proteome diversity. We calculated the escape rate for the yeast PTC7 intron and pre-mRNA. This prediction was facilitated by the observation that splicing is a linear process and by deriving simple algebraic expressions from a model of co- and post-transcriptional splicing and RNA surveillance that determines the rate of the nonsense-mediated decay (NMD) of the pre-mRNAs with the retained intron. The escape rate was consistent with the observed threshold of splicing rate below which the mature mRNA level declined. When an mRNA contains multiple introns, the outcome of splicing becomes more difficult to predict since not only the escape rate of the pre-mRNA has to be considered, but also the possibility that the splicing of each intron is influenced by the others. We showed that the two adjacent introns in the SUS1 mRNA are spliced cooperatively, but this does not counteract the escape of the partially spliced mRNA. These findings will help to infer promoter activity and to predict the behavior of and to control splicing regulatory networks.

Impact of upstream and downstream constraints on a signaling module's ultrasensitivity

Much work has been done on the study of the biochemical mechanisms that result in ultrasensitive behavior of simple biochemical modules. However, in a living cell, such modules are embedded in a bigger network that constrains the range of inputs that the module will receive as well as the range of the module's outputs that network will be able to detect. Here, we studied how the effective ultrasensitivity of a modular system is affected by these restrictions. We use a simple setup to explore to what extent the dynamic range spanned by upstream and downstream components of an ultrasensitive module impact on the effective sensitivity of the system. Interestingly, we found for some ultrasensitive motifs that dynamic range limitations imposed by downstream components can produce effective sensitivities much larger than that of the original module when considered in isolation.

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.

Interplay of microRNA and epigenetic regulation in the human regulatory network

The expression of protein-coding genes is controlled by a complex network of regulatory interactions. It is becoming increasingly appreciated that post-transcriptional repression by microRNAs, a class of small non-coding RNAs, is a key layer of regulation in several biological processes. In this contribution, we discuss the interplay between microRNAs and epigenetic regulators. Among the mixed genetic circuits composed by these two different kinds of regulation, it seems that a central role is played by double-negative feedback loops in which a microRNA inhibits an epigenetic regulator and in turn is controlled at the epigenetic level by the same regulator. We discuss a few relevant properties of this class of network motifs and their potential role in cell differentiation. In particular, using mathematical modeling we show how this particular circuit can exhibit a switch-like behavior between two alternative steady states, while being robust to stochastic transitions between these two states, a feature presumably required for circuits involved in cell fate decision. Finally, we present a list of putative double-negative feedback loops from a literature survey combined with bioinformatic analysis, and discuss in detail a few examples.

Intrinsic disorder as a generalizable strategy for the rational design of highly responsive, allosterically cooperative receptors

Control over the sensitivity with which biomolecular receptors respond to small changes in the concentration of their target ligand is critical for the proper function of many cellular processes. Such control could likewise be of utility in artificial biotechnologies, such as biosensors, genetic logic gates, and "smart" materials, in which highly responsive behavior is of value. In nature, the control of molecular responsiveness is often achieved using "Hill-type" cooperativity, a mechanism in which sequential binding events on a multivalent receptor are coupled such that the first enhances the affinity of the next, producing a steep, higher-order dependence on target concentration. Here, we use an intrinsic-disorder-based mechanism that can be implemented without requiring detailed structural knowledge to rationally introduce this potentially useful property into several normally noncooperative biomolecules. To do so, we fabricate a tandem repeat of the receptor that is destabilized (unfolded) via the introduction of a long, unstructured loop. The first binding event requires the energetically unfavorable closing of this loop, reducing its affinity relative to that of the second binding event, which, in contrast occurs at a preformed site. Using this approach, we have rationally introduced cooperativity into three unrelated DNA aptamers, achieving in the best of these a Hill coefficient experimentally indistinguishable from the theoretically expected maximum. The extent of cooperativity and thus the steepness of the binding transition are, moreover, well modeled as simple functions of the energetic cost of binding-induced folding, speaking to the quantitative nature of this design strategy.

Stable heterogeneity for the production of diffusible factors in cell populations

The production of diffusible molecules that promote survival and growth is common in bacterial and eukaryotic cell populations, and can be considered a form of cooperation between cells. While evolutionary game theory shows that producers and non-producers can coexist in well-mixed populations, there is no consensus on the possibility of a stable polymorphism in spatially structured populations where the effect of the diffusible molecule extends beyond one-step neighbours. I study the dynamics of biological public goods using an evolutionary game on a lattice, taking into account two assumptions that have not been considered simultaneously in existing models: that the benefit of the diffusible molecule is a non-linear function of its concentration, and that the molecule diffuses according to a decreasing gradient. Stable coexistence of producers and non-producers is observed when the benefit of the molecule is a sigmoid function of its concentration, while strictly diminishing returns lead to coexistence only for very specific parameters and linear benefits never lead to coexistence. The shape of the diffusion gradient is largely irrelevant and can be approximated by a step function. Since the effect of a biological molecule is generally a sigmoid function of its concentration (as described by the Hill equation), linear benefits or strictly diminishing returns are not an appropriate approximations for the study of biological public goods. A stable polymorphism of producers and non-producers is in line with the predictions of evolutionary game theory and likely to be common in cell populations.

Using the population-shift mechanism to rationally introduce "Hill-type" cooperativity into a normally non-cooperative receptor

Allosteric cooperativity, which nature uses to improve the sensitivity with which biomolecular receptors respond to small changes in ligand concentration, could likewise be of use in improving the responsiveness of artificial biosystems. Thus motivated, we demonstrate here the rational design of cooperative molecular beacons, a widely employed DNA sensor, using a generalizable population-shift approach in which we engineer receptors that equilibrate between a low-affinity state and a high-affinity state exposing two binding sites. Doing so we achieve cooperativity within error of ideal behavior, greatly steepening the beacon's binding curve relative to that of the parent receptor. The ability to rationally engineer cooperativity should prove useful in applications such as biosensors, synthetic biology and "smart" biomaterials, in which improved responsiveness is of value.

Engineering modular and tunable genetic amplifiers for scaling transcriptional signals in cascaded gene networks

Synthetic biology aims to control and reprogram signal processing pathways within living cells so as to realize repurposed, beneficial applications. Here we report the design and construction of a set of modular and gain-tunable genetic amplifiers in Escherichia coli capable of amplifying a transcriptional signal with wide tunable-gain control in cascaded gene networks. The devices are engineered using orthogonal genetic components (hrpRS, hrpV and P_hrpL) from the hrp (hypersensitive response and pathogenicity) gene regulatory network in Pseudomonas syringae. The amplifiers can linearly scale up to 21-fold the transcriptional input with a large output dynamic range, yet not introducing significant time delay or significant noise during signal amplification. The set of genetic amplifiers achieves different gains and input dynamic ranges by varying the expression levels of the underlying ligand-free activator proteins in the device. As their electronic counterparts, these engineered transcriptional amplifiers can act as fundamental building blocks in the design of biological systems by predictably and dynamically modulating transcriptional signal flows to implement advanced intra- and extra-cellular control functions.

Principles and properties of eukaryotic mRNPs

The proper processing, export, localization, translation, and degradation of mRNAs are necessary for regulation of gene expression. These processes are controlled by mRNA-specific regulatory proteins, noncoding RNAs, and core machineries common to most mRNAs. These factors bind the mRNA in large complexes known as messenger ribonucleoprotein particles (mRNPs). Herein, we review the components of mRNPs, how they assemble and rearrange, and how mRNP composition differentially affects mRNA biogenesis, function, and degradation. We also describe how properties of the mRNP "interactome" lead to emergent principles affecting the control of gene expression.

Noise in multiple sclerosis: unwanted and necessary

As our knowledge about the etiology of multiple sclerosis (MS) increases, deterministic paradigms appear insufficient to describe the pathogenesis of the disease, and the impression is that stochastic phenomena (i.e. random events not necessarily resulting in disease in all individuals) may contribute to the development of MS. However, sources and mechanisms of stochastic behavior have not been investigated and there is no proposed framework to incorporate nondeterministic processes into disease biology. In this report, we will first describe analogies between physics of nonlinear systems and cell biology, showing how small-scale random perturbations can impact on large-scale phenomena, including cell function. We will then review growing and solid evidence showing that stochastic gene expression (or gene expression “noise”) can be a driver of phenotypic variation. Moreover, we will describe new methods that open unprecedented opportunities for the study of such phenomena in patients and the impact of this information on our understanding of MS course and therapy.

eEF1A is an S-RNase binding factor in self-incompatible Solanum chacoense

Self-incompatibility (SI) is a genetic mechanism that allows flowering plants to identify and block fertilization by self-pollen. In the Solanaceae, SI is controlled by a multiallelic S-locus encoding both S-RNases and F-box proteins as female and male determinants, respectively. S-RNase activity is essential for pollen rejection, and a minimum threshold value of S-RNases in the style is also required. Here we present biochemical evidence that eEF1A is a novel S-RNase-binding partner in vitro. We further show that the normal actin binding activity of eEF1A is enhanced by the presence of S-RNase. Lastly, we find that there is a co-localization of S-RNase and actin in the incompatible pollen tubes in structures reminiscent of the actin bundles formed by eEF1A. We propose that increased binding of eEF1A to actin in the presence of S-RNase could help explain the disruption of the actin cytoskeleton observed during SI reactions.

Digital and analog gene circuits for biotechnology

Biotechnology offers the promise of valuable chemical production via microbial processing of renewable and inexpensive substrates. Thus far, static metabolic engineering strategies have enabled this field to advance industrial applications. However, the industrial scaling of statically engineered microbes inevitably creates inefficiencies due to variable conditions present in large-scale microbial cultures. Synthetic gene circuits that dynamically sense and regulate different molecules can resolve this issue by enabling cells to continuously adapt to variable conditions. These circuits also have the potential to enable next-generation production programs capable of autonomous transitioning between steps in a bioprocess. Here, we review the design and application of two main classes of dynamic gene circuits, digital and analog, for biotechnology. Within the context of these classes, we also discuss the potential benefits of digital-analog interconversion, memory, and multi-signal integration. Though synthetic gene circuits have largely been applied for cellular computation to date, we envision that utilizing them in biotechnology will enhance the efficiency and scope of biochemical production with living cells.

Controlling long-term signaling: receptor dynamics determine attenuation and refractory behavior of the TGF-β pathway

Understanding the complex dynamics of growth factor signaling requires both mechanistic and kinetic information. Although signaling dynamics have been studied for pathways downstream of receptor tyrosine kinases and G protein (heterotrimeric guanine nucleotide-binding protein)-coupled receptors, they have not been investigated for the transforming growth factor-β (TGF-β) superfamily pathways. Using an integrative experimental and mathematical modeling approach, we dissected the dynamic behavior of the TGF-β to Smad pathway, which is mediated by type I and type II receptor serine/threonine kinases, in response to acute, chronic, and repeated ligand stimulations. TGF-β exposure produced a transient response that attenuated over time, resulting in desensitized cells that were refractory to further acute stimulation. This loss of signaling competence depended on ligand binding, but not on receptor activity, and was restored only after the ligand had been depleted. Furthermore, TGF-β binding triggered the rapid depletion of signaling-competent receptors from the cell surface, with the type I and type II receptors exhibiting different degradation and trafficking kinetics. A computational model of TGF-β signal transduction from the membrane to the nucleus that incorporates our experimental findings predicts that autocrine signaling, such as that associated with tumorigenesis, severely compromises the TGF-β response, which we confirmed experimentally. Thus, we have shown that the long-term signaling behavior of the TGF-β pathway is determined by receptor dynamics, does not require TGF-β-induced gene expression, and influences context-dependent responses in vivo.

Input-output relations in biological systems: measurement, information and the Hill equation

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system’s overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.

Reviewers

This article was reviewed by Eugene Koonin, Georg Luebeck and Sergei Maslov.

Determinants of cell-to-cell variability in protein kinase signaling

Cells reliably sense environmental changes despite internal and external fluctuations, but the mechanisms underlying robustness remain unclear. We analyzed how fluctuations in signaling protein concentrations give rise to cell-to-cell variability in protein kinase signaling using analytical theory and numerical simulations. We characterized the dose-response behavior of signaling cascades by calculating the stimulus level at which a pathway responds (‘pathway sensitivity’) and the maximal activation level upon strong stimulation. Minimal kinase cascades with gradual dose-response behavior show strong variability, because the pathway sensitivity and the maximal activation level cannot be simultaneously invariant. Negative feedback regulation resolves this trade-off and coordinately reduces fluctuations in the pathway sensitivity and maximal activation. Feedbacks acting at different levels in the cascade control different aspects of the dose-response curve, thereby synergistically reducing the variability. We also investigated more complex, ultrasensitive signaling cascades capable of switch-like decision making, and found that these can be inherently robust to protein concentration fluctuations. We describe how the cell-to-cell variability of ultrasensitive signaling systems can be actively regulated, e.g., by altering the expression of phosphatase(s) or by feedback/feedforward loops. Our calculations reveal that slow transcriptional negative feedback loops allow for variability suppression while maintaining switch-like decision making. Taken together, we describe design principles of signaling cascades that promote robustness. Our results may explain why certain signaling cascades like the yeast pheromone pathway show switch-like decision making with little cell-to-cell variability.

Cells sense their surroundings and respond to soluble factors in the extracellular space. Extracellular factors frequently induce heterogeneous responses, thereby restricting the biological outcome to a fraction of the cell population. However, the question arises how such cell-to-cell variability can be controlled, because some cellular systems show a very homogenous response at a defined level of an extracellular stimulus. We derived an analytical framework to systematically characterize the cell-to-cell variability of intracellular signaling pathways which transduce external signals. We analyzed how heterogeneity arises from fluctuations in the total concentrations of signaling proteins because this is the main source of variability in eukaryotic systems. We find that signaling pathways can be highly variable or inherently invariant, depending on the kinetic parameters and the structural features of the cascade. Our results indicate that the cell-to-cell variability can be reduced by negative feedback in the cascade or by signaling crosstalk between parallel pathways. We precisely define the role of negative feedback loops in variability suppression, and show that different aspects of the dose-response curve can be controlled, depending on the feedback kinetics and site of action in the cascade. This work constitutes a first step towards a systematic understanding of cell-to-cell variability in signal transduction.

Phosphorelays provide tunable signal processing capabilities for the cell

Achieving a complete understanding of cellular signal transduction requires deciphering the relation between structural and biochemical features of a signaling system and the shape of the signal-response relationship it embeds. Using explicit analytical expressions and numerical simulations, we present here this relation for four-layered phosphorelays, which are signaling systems that are ubiquitous in prokaryotes and also found in lower eukaryotes and plants. We derive an analytical expression that relates the shape of the signal-response relationship in a relay to the kinetic rates of forward, reverse phosphorylation and hydrolysis reactions. This reveals a set of mathematical conditions which, when satisfied, dictate the shape of the signal-response relationship. We find that a specific topology also observed in nature can satisfy these conditions in such a way to allow plasticity among hyperbolic and sigmoidal signal-response relationships. Particularly, the shape of the signal-response relationship of this relay topology can be tuned by altering kinetic rates and total protein levels at different parts of the relay. These findings provide an important step towards predicting response dynamics of phosphorelays, and the nature of subsequent physiological responses that they mediate, solely from topological features and few composite measurements; measuring the ratio of reverse and forward phosphorylation rate constants could be sufficient to determine the shape of the signal-response relationship the relay exhibits. Furthermore, they highlight the potential ways in which selective pressures on signal processing could have played a role in the evolution of the observed structural and biochemical characteristic in phosphorelays.

Two-component phosphorelays constitute the key signaling pathways in all prokaryotes, lower eukaryotes, and plants, where they underline diverse physiological responses such as virulence, cell-cycle progression and sporulation. Despite such prevalence, our understanding of the dynamics and function of these systems remains incomplete. In particular, it is not clear why all phosphorelays studied to date embed a four-layer architecture and how their dynamics could relate to phenotypic variability in the resulting responses. Here, we use analytical approaches and numerical simulations to analyze all possible phosphorelay topologies of length four and embedding reverse phosphorylation. We find that only two topologies can embed both hyperbolic and sigmoidal signal-response relationships, and that one of these can underlie high noise (i.e. phenotypic variability) in population responses. All of the remaining topologies are either non-functional or can embed only a hyperbolic signal-response relationship. Using analytical solutions of relay dynamics, we find that reverse phosphorylation from the third layer, a topological featured commonly observed in nature, is a necessary condition for sigmoidal signal-response relationship.