Dynamics and Variability of ERK2 Response to EGF in Individual Living Cells

Intracellular Information Processing through Encoding and Decoding of Dynamic Signaling Features

Cell signaling dynamics and transcriptional regulatory activities are variable within specific cell types responding to an identical stimulus. In addition to studying the network interactions, there is much interest in utilizing single cell scale data to elucidate the non-random aspects of the variability involved in cellular decision making. Previous studies have considered the information transfer between the signaling and transcriptional domains based on an instantaneous relationship between the molecular activities. These studies predict a limited binary on/off encoding mechanism which underestimates the complexity of biological information processing, and hence the utility of single cell resolution data. Here we pursue a novel strategy that reformulates the information transfer problem as involving dynamic features of signaling rather than molecular abundances. We pursue a computational approach to test if and how the transcriptional regulatory activity patterns can be informative of the temporal history of signaling. Our analysis reveals (1) the dynamic features of signaling that significantly alter transcriptional regulatory patterns (encoding), and (2) the temporal history of signaling that can be inferred from single cell scale snapshots of transcriptional activity (decoding). Immediate early gene expression patterns were informative of signaling peak retention kinetics, whereas transcription factor activity patterns were informative of activation and deactivation kinetics of signaling. Moreover, the information processing aspects varied across the network, with each component encoding a selective subset of the dynamic signaling features. We developed novel sensitivity and information transfer maps to unravel the dynamic multiplexing of signaling features at each of these network components. Unsupervised clustering of the maps revealed two groups that aligned with network motifs distinguished by transcriptional feedforward vs feedback interactions. Our new computational methodology impacts the single cell scale experiments by identifying downstream snapshot measures required for inferring specific dynamical features of upstream signals involved in the regulation of cellular responses.

Single cell studies have shown that differential patterns in the dynamics of signaling proteins, transcription factor activity, gene expression, etc. produce distinct downstream outcomes. The opposite also holds true where particular cellular outcomes have been found to be associated with the dynamical pattern of one or more signaling molecules. Signaling pathways, therefore, serve as signal processing units to inform specific downstream regulation. However, the functional capabilities of the dynamic aspects of signaling are not well understood. To address this issue, we developed a new approach that evaluates information processing between dynamic features in signaling patterns and transcriptional regulatory activity. Our work demonstrates that the information transfer occur through decoding of temporal history of signals rather than only through instantaneous correlations. Moreover, our results identify regulatory network motifs as the critical components in the information processing and filtering of variability in signaling dynamics to produce distinct patterns of downstream transcriptional responses. Our methodology can be broadly applied to single cell scale data on experimentally accessible downstream measures to infer dynamic aspects of upstream signaling.

Combinatorial gene regulation by modulation of relative pulse timing

Studies of individual living cells have revealed that many transcription factors activate in dynamic, and often stochastic, pulses within the same cell. However, it has remained unclear whether cells might modulate the relative timing of these pulses to control gene expression. Here, using quantitative single-cell time-lapse imaging of Saccharomyces cerevisiae, we show that the pulsatile transcription factors Msn2 and Mig1 combinatorially regulate their target genes through modulation of their relative pulse timing. The activator Msn2 and repressor Mig1 pulsed in either a temporally overlapping or non-overlapping manner during their transient response to different inputs, with only the non-overlapping dynamics efficiently activating target gene expression. Similarly, under constant environmental conditions, where Msn2 and Mig1 exhibit sporadic pulsing, glucose concentration modulated the temporal overlap between pulses of the two factors. Together, these results reveal a time-based mode of combinatorial gene regulation. Regulation through relative signal timing is common in engineering and neurobiology, and these results suggest that it could also function broadly within the signaling and regulatory systems of the cell.

Receptor Level Mechanisms Are Required for Epidermal Growth Factor (EGF)-stimulated Extracellular Signal-regulated Kinase (ERK) Activity Pulses

In both physiological and cell culture systems, EGF-stimulated ERK activity occurs in discrete pulses within individual cells. Many feedback loops are present in the EGF receptor (EGFR)-ERK network, but the mechanisms driving pulsatile ERK kinetics are unknown. Here, we find that in cells that respond to EGF with frequency-modulated pulsatile ERK activity, stimulation through a heterologous TrkA receptor system results in non-pulsatile, amplitude-modulated activation of ERK. We further dissect the kinetics of pulse activity using a combination of FRET- and translocation-based reporters and find that EGFR activity is required to maintain ERK activity throughout the 10-20-minute lifetime of pulses. Together, these data indicate that feedbacks operating within the core Ras-Raf-MEK-ERK cascade are insufficient to drive discrete pulses of ERK activity and instead implicate mechanisms acting at the level of EGFR.

Extracellular signal-regulated kinases 1/2 as regulators of cardiac hypertrophy

Cardiac hypertrophy results from increased mechanical load on the heart and through the actions of local and systemic neuro-humoral factors, cytokines and growth factors. These mechanical and neuroendocrine effectors act through stretch, G protein–coupled receptors and tyrosine kinases to induce the activation of a myriad of intracellular signaling pathways including the extracellular signal-regulated kinases 1/2 (ERK1/2). Since most stimuli that provoke myocardial hypertrophy also elicit an acute phosphorylation of the threonine-glutamate-tyrosine (TEY) motif within the activation loops of ERK1 and ERK2 kinases, resulting in their activation, ERKs have long been considered promotors of cardiac hypertrophy. Several mouse models were generated in order to directly understand the causal role of ERK1/2 activation in the heart. These models include direct manipulation of ERK1/2 such as overexpression, mutagenesis or knockout models, manipulations of upstream kinases such as MEK1 and manipulations of the phosphatases that dephosphorylate ERK1/2 such as DUSP6. The emerging understanding from these studies, as will be discussed here, is more complex than originally considered. While there is little doubt that ERK1/2 activation or the lack of it modulates the hypertrophic process or the type of hypertrophy that develops, it appears that not all ERK1/2 activation events are the same. While much has been learned, some questions remain regarding the exact role of ERK1/2 in the heart, the upstream events that result in ERK1/2 activation and the downstream effector in hypertrophy.

Extracellular matrix stiffness modulates VEGF calcium signaling in endothelial cells: individual cell and population analysis

Vascular disease and its associated complications are the number one cause of death in the Western world. Both extracellular matrix stiffening and dysfunctional endothelial cells contribute to vascular disease. We examined endothelial cell calcium signaling in response to VEGF as a function of extracellular matrix stiffness. We developed a new analytical tool to analyze both population based and individual cell responses. Endothelial cells on soft substrates, 4 kPa, were the most responsive to VEGF, whereas cells on the 125 kPa substrates exhibited an attenuated response. Magnitude of activation, not the quantity of cells responding or the number of local maximums each cell experienced distinguished the responses. Individual cell analysis, across all treatments, identified two unique cell clusters. One cluster, containing most of the cells, exhibited minimal or slow calcium release. The remaining cell cluster had a rapid, high magnitude VEGF activation that ultimately defined the population based average calcium response. Interestingly, at low doses of VEGF, the high responding cell cluster contained smaller cells on average, suggesting that cell shape and size may be indicative of VEGF-sensitive endothelial cells. This study provides a new analytical tool to quantitatively analyze individual cell signaling response kinetics, that we have used to help uncover outcomes that are hidden within the average. The ability to selectively identify highly VEGF responsive cells within a population may lead to a better understanding of the specific phenotypic characteristics that define cell responsiveness, which could provide new insight for the development of targeted anti- and pro-angiogenic therapies.

G Protein-Coupled Receptor Signaling Networks from a Systems Perspective

The signal-transduction network of a mammalian cell integrates internal and external cues to initiate adaptive responses. Among the cell-surface receptors are the G protein-coupled receptors (GPCRs), which have remarkable signal-integrating capabilities. Binding of extracellular signals stabilizes intracellular-domain conformations that selectively activate intracellular proteins. Hereby, multiple signaling routes are activated simultaneously to degrees that are signal-combination dependent. Systems-biology studies indicate that signaling networks have emergent processing capabilities that go far beyond those of single proteins. Such networks are spatiotemporally organized and capable of gradual, oscillatory, all-or-none, and subpopulation-generating responses. Protein-protein interactions, generating feedback and feedforward circuitry, are generally required for these spatiotemporal phenomena. Understanding of information processing by signaling networks therefore requires network theories in addition to biochemical and biophysical concepts. Here we review some of the key signaling systems behaviors that have been discovered recurrently across signaling networks. We emphasize the role of GPCRs, so far underappreciated receptors in systems-biology research.

Consequences of feedback in signal transduction for targeted therapies

Over the last two decades, many small-molecule inhibitors that target kinase signalling have been developed. More than 20 of these inhibitors are FDA (U.S. Food and Drug Administration)-approved and are now being used in the clinics to treat tumours; even more have entered clinical trials. However, resistance to these inhibitors, either intrinsic to the tumour or acquired during treatment, remains a major problem in targeted therapeutics. One of the mechanisms by which tumours become resistant is the rewiring of the signalling networks via feedback, by which the tumour cells re-activate signalling or activate alternative signalling pathways. In the present article, we review insights from recent quantitative signalling studies combining mathematical modelling and experiments that revealed how feedback rewires MAPK (mitogen-activated protein kinase)/PI3K (phosphoinositide 3-kinase) signalling upon treatment and how that affects drug sensitivity.

Three-Dimensional Gradients of Cytokine Signaling between T Cells

Immune responses are regulated by diffusible mediators, the cytokines, which act at sub-nanomolar concentrations. The spatial range of cytokine communication is a crucial, yet poorly understood, functional property. Both containment of cytokine action in narrow junctions between immune cells (immunological synapses) and global signaling throughout entire lymph nodes have been proposed, but the conditions under which they might occur are not clear. Here we analyze spatially three-dimensional reaction-diffusion models for the dynamics of cytokine signaling at two successive scales: in immunological synapses and in dense multicellular environments. For realistic parameter values, we observe local spatial gradients, with the cytokine concentration around secreting cells decaying sharply across only a few cell diameters. Focusing on the well-characterized T-cell cytokine interleukin-2, we show how cytokine secretion and competitive uptake determine this signaling range. Uptake is shaped locally by the geometry of the immunological synapse. However, even for narrow synapses, which favor intrasynaptic cytokine consumption, escape fluxes into the extrasynaptic space are expected to be substantial (≥20% of secretion). Hence paracrine signaling will generally extend beyond the synapse but can be limited to cellular microenvironments through uptake by target cells or strong competitors, such as regulatory T cells. By contrast, long-range cytokine signaling requires a high density of cytokine producers or weak consumption (e.g., by sparsely distributed target cells). Thus in a physiological setting, cytokine gradients between cells, and not bulk-phase concentrations, are crucial for cell-to-cell communication, emphasizing the need for spatially resolved data on cytokine signaling.

The adaptive immune system fights pathogens through the activation of immune cell clones that specifically recognize a particular pathogen. Tight contacts, so-called immunological synapses, of immune cells with cells that present ‘digested’ pathogen molecules are pivotal for ensuring specificity. The discovery that immune responses are regulated by small diffusible proteins – the cytokines – has been surprising because cytokine diffusion to ‘bystander’ cells might compromise specificity. It has therefore been argued that cytokines are trapped in immunological synapses, whereas other authors have found that cytokines act on a larger scale through entire lymph nodes. Measurements of cytokine concentrations with fine spatial resolution have not been achieved. Here, we study the spatio-temporal dynamics of cytokines through mathematical analysis and three-dimensional numerical simulation and identify key parameters that control signaling range. We predict that even tight immunological synapses leak a substantial portion of the secreted cytokines. Nevertheless, rapid cellular uptake will render cytokine signals short-range and thus incidental activation of bystander cells can be limited. Long-range signals will only occur with multiple secreting cells or/and slow consumption by sparse target cells. Thus our study identifies key determinants of the spatial range of cytokine communication in realistic multicellular geometries.

A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and characterization of variability within a population of genetically identical cells. Nonlinear mixed effects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be exploited. Here we take advantage of this novel application of NLME modeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particular, we investigate a recently discovered phenomenon where Mig1 during a short and transient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equations describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLME methodology the parameters of this model are in turn modeled by a multivariate probability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate this parameter distribution according to the approach of maximizing the population likelihood. Based on the estimated distribution, parameter values for individual cells are furthermore characterized and the resulting Mig1 dynamics are compared to the single cell times-series data. The proposed NLME framework is also compared to the intuitive but limited standard two-stage (STS) approach. We demonstrate that the latter may overestimate variabilities by up to almost five fold. Finally, Monte Carlo simulations of the inferred population model are used to predict the distribution of key characteristics of the Mig1 transient response. We find that with decreasing levels of post-shift glucose, the transient response of Mig1 tend to be faster, more extended, and displays an increased cell-to-cell variability.

Dynamic tuning of lymphocytes: physiological basis, mechanisms, and function

Dynamic tuning of cellular responsiveness as a result of repeated stimuli improves the ability of cells to distinguish physiologically meaningful signals from each other and from noise. In particular, lymphocyte activation thresholds are subject to tuning, which contributes to maintaining tolerance to self-antigens and persisting foreign antigens, averting autoimmunity and immune pathogenesis, but allowing responses to strong, structured perturbations that are typically associated with acute infection. Such tuning is also implicated in conferring flexibility to positive selection in the thymus, in controlling the magnitude of the immune response, and in generating memory cells. Additional functional properties are dynamically and differentially tuned in parallel via subthreshold contact interactions between developing or mature lymphocytes and self-antigen-presenting cells. These interactions facilitate and regulate lymphocyte viability, maintain their functional integrity, and influence their responses to foreign antigens and accessory signals, qualitatively and quantitatively. Bidirectional tuning of T cells and antigen-presenting cells leads to the definition of homeostatic set points, thus maximizing clonal diversity.

Sources of dynamic variability in NF-κB signal transduction: a mechanistic model

The transcription factor NF-κB (p65/p50) plays a central role in the coordination of cellular responses by activating the transcription of numerous target genes. The precise role of the dynamics of NF-κB signalling in regulating gene expression is still an open question. Here, we show that besides external stimulation intracellular parameters can influence the dynamics of NF-κB. By applying mathematical modelling and bifurcation analyses, we show that NF-κB is capable of exhibiting different types of dynamics in response to the same stimulus. We identified the total NF-κB concentration and the IκBα transcription rate constant as two critical parameters that modulate the dynamics and the fold change of NF-κB. Both parameters might vary as a result of cell-to-cell variability. The regulation of the IκBα transcription rate constant, e.g. by co-factors, provides the possibility of regulating the NF-κB dynamics by crosstalk.

Systems biology. Accurate information transmission through dynamic biochemical signaling networks

Stochasticity inherent to biochemical reactions (intrinsic noise) and variability in cellular states (extrinsic noise) degrade information transmitted through signaling networks. We analyzed the ability of temporal signal modulation--that is, dynamics--to reduce noise-induced information loss. In the extracellular signal-regulated kinase (ERK), calcium (Ca(2+)), and nuclear factor kappa-B (NF-κB) pathways, response dynamics resulted in significantly greater information transmission capacities compared to nondynamic responses. Theoretical analysis demonstrated that signaling dynamics has a key role in overcoming extrinsic noise. Experimental measurements of information transmission in the ERK network under varying signal-to-noise levels confirmed our predictions and showed that signaling dynamics mitigate, and can potentially eliminate, extrinsic noise-induced information loss. By curbing the information-degrading effects of cell-to-cell variability, dynamic responses substantially increase the accuracy of biochemical signaling networks.

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.

Computational analysis of signaling patterns in single cells

Signaling proteins are flexible in both form and function. They can bind to multiple molecular partners and integrate diverse types of cellular information. When imaged by time-lapse microscopy, many signaling proteins show complex patterns of activity or localization that vary from cell to cell. This heterogeneity is so prevalent that it has spurred the development of new computational strategies to analyze single-cell signaling patterns. A collective observation from these analyses is that cells appear less heterogeneous when their responses are normalized to, or synchronized with, other single-cell measurements. In many cases, these transformed signaling patterns show distinct dynamical trends that correspond with predictable phenotypic outcomes. When signaling mechanisms are unclear, computational models can suggest putative molecular interactions that are experimentally testable. Thus, computational analysis of single-cell signaling has not only provided new ways to quantify the responses of individual cells, but has helped resolve longstanding questions surrounding many well-studied human signaling proteins including NF-κB, p53, ERK1/2, and CDK2. A number of specific challenges lie ahead for single-cell analysis such as quantifying the contribution of non-cell autonomous signaling as well as the characterization of protein signaling dynamics in vivo.

Cellular sensory mechanisms for detecting specific fold-changes in extracellular cues

Cellular sensory systems often respond not to the absolute levels of inputs but to the fold-changes in inputs. Such a property is called fold-change detection (FCD) and is important for accurately sensing dynamic changes in environmental signals in the presence of fluctuations in their absolute levels. Previous studies defined FCD as input-scale invariance and proposed several biochemical models that achieve such a condition. Here, we prove that the previous FCD models can be approximated by a log-differentiator. Although the log-differentiator satisfies the input-scale invariance requirement, its response amplitude and response duration strongly depend on the input timescale. This creates limitations in the specificity and repeatability of detecting fold-changes in inputs. Nevertheless, FCD with specificity and repeatability by cells has been reported in the context of Drosophila wing development. Motivated by this fact and by extending previous FCD models, we here propose two possible mechanisms to achieve FCD with specificity and repeatability. One is the integrate-and-fire type: a system integrates the rate of temporal change in input and makes a response when the integrated value reaches a constant threshold, and this is followed by the reset of the integrated value. The other is the dynamic threshold type: a system response occurs when the input level reaches a threshold, whose value is multiplied by a certain constant after each response. These two mechanisms can be implemented biochemically by appropriately combining feed-forward and feedback loops. The main difference between the two models is their memory of input history; we discuss possible ways to distinguish between the two models experimentally.

Logarithmic and power law input-output relations in sensory systems with fold-change detection

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.

One of the first measurements an experimentalist makes to understand a sensory system is to explore the relation between input signal and the systems response amplitude. Here, we show using mathematical models that this measurement can give important clues about the possible mechanism of sensing. We use models that incorporate the nearly-universal features of sensory systems, including hearing and vision, and the sensing pathways of individual cells. These nearly-universal features include exact adaptation-the ability to ignore prolonged input stimuli and return to basal activity, and fold-change detection- response to relative changes in input, not absolute changes. Together with information on the input-output relationship-e.g. is it a logarithmic or a power law relationship-we show that these conditions provide enough constraints to allow the researcher to reject certain circuit designs; it also predicts, if one assumes a given design, one of its key parameters. This study can thus help unify our understanding of sensory systems, and help pinpoint the possible biological circuits based on physiological measurements.

Decipher the dynamic coordination between enzymatic activity and structural modulation at focal adhesions in living cells

Focal adhesions (FAs) are dynamic subcellular structures crucial for cell adhesion, migration and differentiation. It remains an enigma how enzymatic activities in these local complexes regulate their structural remodeling in live cells. Utilizing biosensors based on fluorescence resonance energy transfer (FRET), we developed a correlative FRET imaging microscopy (CFIM) approach to quantitatively analyze the subcellular coordination between the enzymatic Src activation and the structural FA disassembly. CFIM reveals that the Src kinase activity only within the microdomain of lipid rafts at the plasma membrane is coupled with FA dynamics. FA disassembly at cell periphery was linearly dependent on this raft-localized Src activity, although cells displayed heterogeneous levels of response to stimulation. Within lipid rafts, the time delay between Src activation and FA disassembly was 1.2 min in cells seeded on low fibronectin concentration ([FN]) and 4.3 min in cells on high [FN]. CFIM further showed that the level of Src-FA coupling, as well as the time delay, was regulated by cell-matrix interactions, as a tight enzyme-structure coupling occurred in FA populations mediated by integrin αvβ₃, but not in those by integrin α₅β₁. Therefore, different FA subpopulations have distinctive regulation mechanisms between their local kinase activity and structural FA dynamics.

Dynamic signal encoding--from cells to organisms

Encoding information at the level of signal dynamics is characterized by distinct features, such as robustness to noise and high information content. Currently, a growing number of studies are unravelling the functional importance of signalling dynamics at the single cell level. In addition, first insights are emerging into how the principles of dynamic signal encoding apply to a multicellular context, such as development. In this review, we will first discuss general concepts of information transmission via signalling dynamics and recent experimental examples focusing on underlying principles, including the role of intracellular network topologies. How multicellular organisms use temporal modulation of specific signalling pathways, such as signalling gradients or oscillations, to faithfully control cell fate decisions and pattern formation will also be addressed. Finally, we will consider how technical advancements in the detection and perturbation of signalling dynamics contribute to reshaping our understanding of dynamic signalling in developing organisms.

Reliable encoding of stimulus intensities within random sequences of intracellular Ca2+ spikes

Ca(2+) is a ubiquitous intracellular messenger that regulates diverse cellular activities. Extracellular stimuli often evoke sequences of intracellular Ca(2+) spikes, and spike frequency may encode stimulus intensity. However, the timing of spikes within a cell is random because each interspike interval has a large stochastic component. In human embryonic kidney (HEK) 293 cells and rat primary hepatocytes, we found that the average interspike interval also varied between individual cells. To evaluate how individual cells reliably encoded stimuli when Ca(2+) spikes exhibited such unpredictability, we combined Ca(2+) imaging of single cells with mathematical analyses of the Ca(2+) spikes evoked by receptors that stimulate formation of inositol 1,4,5-trisphosphate (IP3). This analysis revealed that signal-to-noise ratios were improved by slow recovery from feedback inhibition of Ca(2+) spiking operating at the whole-cell level and that they were robust against perturbations of the signaling pathway. Despite variability in the frequency of Ca(2+) spikes between cells, steps in stimulus intensity caused the stochastic period of the interspike interval to change by the same factor in all cells. These fold changes reliably encoded changes in stimulus intensity, and they resulted in an exponential dependence of average interspike interval on stimulation strength. We conclude that Ca(2+) spikes enable reliable signaling in a cell population despite randomness and cell-to-cell variability, because global feedback reduces noise, and changes in stimulus intensity are represented by fold changes in the stochastic period of the interspike interval.

Altered serine/threonine kinase activity in schizophrenia

Converging evidence implicates alterations in multiple signaling pathways in the etiology of schizophrenia. Previously, these studies were limited to the analysis of one or a few phosphoproteins at a time. Here, we use a novel kinase array platform to simultaneously investigate the convergence of multiple signaling cascades implicated in schizophrenia. This technology uses consensus peptide substrates to assess activity levels of a large number (>100) of serine/threonine protein kinases. 19 peptide substrates were differentially phosphorylated (>15% change) in the frontal cortex in schizophrenia. These peptide substrates were examined using Ingenuity Pathway Analysis to group them according to the functions and to identify processes most likely affected in schizophrenia. Pathway analysis placed 14 of the 19 peptides into cellular homeostatic pathways, 10 into pathways governing cytoskeletal organization, and 8 into pathways governing ion homeostasis. These data are the first to simultaneously investigate comprehensive changes in signaling cascades in a severe psychiatric disorder. The examination of kinase activity in signaling pathways may facilitate the identification of novel substrates for drug discovery and the development of safer and more effective pharmacological treatment for schizophrenia.

Synthetic circuit for exact adaptation and fold-change detection

Biological organisms use their sensory systems to detect changes in their environment. The ability of sensory systems to adapt to static inputs allows wide dynamic range as well as sensitivity to input changes including fold-change detection, a response that depends only on fold changes in input, and not on absolute changes. This input scale invariance underlies an important strategy for search that depends solely on the spatial profile of the input. Synthetic efforts to reproduce the architecture and response of cellular circuits provide an important step to foster understanding at the molecular level. We report the bottom-up assembly of biochemical systems that show exact adaptation and fold-change detection. Using a malachite green aptamer as the output, a synthetic transcriptional circuit with the connectivity of an incoherent feed-forward loop motif exhibits pulse generation and exact adaptation. A simple mathematical model was used to assess the amplitude and duration of pulse response as well as the parameter regimes required for fold-change detection. Upon parameter tuning, this synthetic circuit exhibits fold-change detection for four successive rounds of two-fold input changes. The experimental realization of fold-change detection circuit highlights the programmability of transcriptional switches and the ability to obtain predictive dynamical systems in a cell-free environment for technological applications.

Intra- and interdimeric caspase-8 self-cleavage controls strength and timing of CD95-induced apoptosis

Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8 and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis.

Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module

The complex, interconnected architecture of cell-signaling networks makes it challenging to disentangle how cells process extracellular information to make decisions. We have developed an optogenetic approach to selectively activate isolated intracellular signaling nodes with light and use this method to follow the flow of information from the signaling protein Ras. By measuring dose and frequency responses in single cells, we characterize the precision, timing, and efficiency with which signals are transmitted from Ras to Erk. Moreover, we elucidate how a single pathway can specify distinct physiological outcomes: by combining distinct temporal patterns of stimulation with proteomic profiling, we identify signaling programs that differentially respond to Ras dynamics, including a paracrine circuit that activates STAT3 only after persistent (>1 hr) Ras activation. Optogenetic stimulation provides a powerful tool for analyzing the intrinsic transmission properties of pathway modules and identifying how they dynamically encode distinct outcomes.

Fold change of nuclear NF-κB determines TNF-induced transcription in single cells

In response to tumor necrosis factor (TNF), NF-κB enters the nucleus and promotes inflammatory and stress-responsive gene transcription. Because NF-κB deregulation is associated with disease, one might expect strict control of NF-κB localization. However, nuclear NF-κB levels exhibit considerable cell-to-cell variability, even in unstimulated cells. To resolve this paradox and determine how transcription-inducing signals are encoded, we quantified single-cell NF-κB translocation dynamics and transcription in the same cells. We show that TNF-induced transcription correlates best with fold change in nuclear NF-κB, not absolute nuclear NF-κB abundance. Using computational modeling, we find that an incoherent feedforward loop, from competition for binding to κB motifs, could provide memory of the preligand state necessary for fold-change detection. Experimentally, we observed three gene-specific transcriptional patterns that our model recapitulates by modulating competition strength alone. Fold-change detection buffers against stochastic variation in signaling molecules and explains how cells tolerate variability in NF-κB abundance and localization.

Data-driven modeling reconciles kinetics of ERK phosphorylation, localization, and activity states

The extracellular signal‐regulated kinase (ERK) signaling pathway controls cell proliferation and differentiation in metazoans. Two hallmarks of its dynamics are adaptation of ERK phosphorylation, which has been linked to negative feedback, and nucleocytoplasmic shuttling, which allows active ERK to phosphorylate protein substrates in the nucleus and cytosol. To integrate these complex features, we acquired quantitative biochemical and live‐cell microscopy data to reconcile phosphorylation, localization, and activity states of ERK. While maximal growth factor stimulation elicits transient ERK phosphorylation and nuclear translocation responses, ERK activities available to phosphorylate substrates in the cytosol and nuclei show relatively little or no adaptation. Free ERK activity in the nucleus temporally lags the peak in nuclear translocation, indicating a slow process. Additional experiments, guided by kinetic modeling, show that this process is consistent with ERK's modification of and release from nuclear substrate anchors. Thus, adaptation of whole‐cell ERK phosphorylation is a by‐product of transient protection from phosphatases. Consistent with this interpretation, predictions concerning the dose‐dependence of the pathway response and its interruption by inhibition of MEK were experimentally confirmed.

Functional roles of pulsing in genetic circuits

A fundamental problem in biology is to understand how genetic circuits implement core cellular functions. Time-lapse microscopy techniques are beginning to provide a direct view of circuit dynamics in individual living cells. Unexpectedly, we are discovering that key transcription and regulatory factors pulse on and off repeatedly, and often stochastically, even when cells are maintained in constant conditions. This type of spontaneous dynamic behavior is pervasive, appearing in diverse cell types from microbes to mammalian cells. Here, we review recent work showing how pulsing is generated and controlled by underlying regulatory circuits and how it provides critical capabilities to cells in stress response, signaling, and development. A major theme is the ability of pulsing to enable time-based regulation analogous to strategies used in engineered systems. Thus, pulsatile dynamics is emerging as a central, and still largely unexplored, layer of temporal organization in the cell.

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.

Models of signalling networks - what cell biologists can gain from them and give to them

Computational models of cell signalling are perceived by many biologists to be prohibitively complicated. Why do math when you can simply do another experiment? Here, we explain how conceptual models, which have been formulated mathematically, have provided insights that directly advance experimental cell biology. In the past several years, models have influenced the way we talk about signalling networks, how we monitor them, and what we conclude when we perturb them. These insights required wet-lab experiments but would not have arisen without explicit computational modelling and quantitative analysis. Today, the best modellers are cross-trained investigators in experimental biology who work closely with collaborators but also undertake experimental work in their own laboratories. Biologists would benefit by becoming conversant in core principles of modelling in order to identify when a computational model could be a useful complement to their experiments. Although the mathematical foundations of a model are useful to appreciate its strengths and weaknesses, they are not required to test or generate a worthwhile biological hypothesis computationally.

In silico modeling of Itk activation kinetics in thymocytes suggests competing positive and negative IP4 mediated feedbacks increase robustness

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP₄) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP₄ can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP₃). PIP₃ recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP₄ binding to the Itk PH domain surprisingly promoted and high-dose IP₄ inhibited PIP₃ binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP₄ and PIP₃ remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP₄ action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP₄ and PIP₃, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP₄ controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP₄ involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP₃ signaling.

A versatile toolkit to produce sensitive FRET biosensors to visualize signaling in time and space

Genetically encoded, ratiometric biosensors based on fluorescence resonance energy transfer (FRET) are powerful tools to study the spatiotemporal dynamics of cell signaling. However, many biosensors lack sensitivity. We present a biosensor library that contains circularly permutated mutants for both the donor and acceptor fluorophores, which alter the orientation of the dipoles and thus better accommodate structural constraints imposed by different signaling molecules while maintaining FRET efficiency. Our strategy improved the brightness and dynamic range of preexisting RhoA and extracellular signal-regulated protein kinase (ERK) biosensors. Using the improved RhoA biosensor, we found micrometer-sized zones of RhoA activity at the tip of F-actin bundles in growth cone filopodia during neurite extension, whereas RhoA was globally activated throughout collapsing growth cones. RhoA was also activated in filopodia and protruding membranes at the leading edge of motile fibroblasts. Using the improved ERK biosensor, we simultaneously measured ERK activation dynamics in multiple cells using low-magnification microscopy and performed in vivo FRET imaging in zebrafish. Thus, we provide a construction toolkit consisting of a vector set, which enables facile generation of sensitive biosensors.

Analysing the impact of nucleo-cytoplasmic shuttling of β-catenin and its antagonists APC, Axin and GSK3 on Wnt/β-catenin signalling

The canonical Wnt signalling pathway plays a critical role in development and disease. The key player of the pathway is β-catenin. Its activity is mainly regulated by the destruction complex consisting of APC, Axin and GSK3. In the nucleus, the complex formation of β-catenin and TCF initiates target gene expression. Our study provides a comprehensive analysis of the role of nucleo-cytoplasmic shuttling of APC, Axin, and GSK3 and the inactivation of β-catenin by the destruction complex in Wnt/β-catenin signalling. We address the following questions: Can nucleo-cytoplasmic shuttling of APC, Axin and GSK3 increase the [β-catenin/TCF] concentration? And, how is the [β-catenin/TCF] concentration influenced by phosphorylation and subsequent degradation of nuclear β-catenin? Based on experimental findings, we develop a compartmental model and conduct several simulation experiments. Our analysis reveals the following key findings: 1) nucleo-cytoplasmic shuttling of β-catenin and its antagonists can yield a spatial separation between the said proteins, which results in a breakdown of β-catenin degradation, followed by an accumulation of β-catenin and hence leads to an increase of the [β-catenin/TCF] concentration. Our results strongly suggest that Wnt signalling can benefit from nucleo-cytoplasmic shuttling of APC, Axin and GSK3, although they are in general β-catenin antagonising proteins. 2) The total robustness of the [β-catenin/TCF] output is closely linked to its absolute concentration levels. We demonstrate that the compartmental separation of β-catenin and the destruction complex does not only lead to a maximization, but additionally to an increased robustness of [β-catenin/TCF] signalling against perturbations in the cellular environment. 3) A nuclear accumulation of the destruction complex renders the pathway robust against fluctuations in Wnt signalling and against changes in the compartmental distribution of β-catenin. 4) Elucidating the impact of destruction complex inhibition, we show that the [β-catenin/TCF] concentration is more effectively enhanced by inhibition of the kinase GSK3 rather than the binding of β-catenin to the destruction complex.

Robustness of signal transduction pathways

Signal transduction pathways transduce information about the outside of the cell to the nucleus, regulating gene expression and cell fate. To reliably inform the cell about its surroundings, information transfer has to be robust against typical perturbation that a cell experiences. Robustness of several mammalian signaling pathways has been studied recently by quantitative experimentation and using mathematical modeling. Here, we review these studies, and describe the emerging concepts of robustness and the underlying mechanisms.

Diversity training for signal transduction: leveraging cell-to-cell variability to dissect cellular signaling, differentiation and death

Populations of 'identical' cells are rarely truly identical. Even when in the same state of differentiation, isogenic cells may vary in expression of key signaling regulators, activate signal transduction at different thresholds, and consequently respond heterogeneously to a given stimulus. Here, we review how new experimental and analytical techniques are suited to connect these different levels of variability, quantitatively mapping the effects of cell-to-cell variability on cellular decision-making. In particular, we summarize how this helps classify signaling regulators according to the impact of their variability on biological functions. We further discuss how variability can also be leveraged to shed light on the molecular mechanisms regulating cellular signaling, from the individual cell to the population of cells as a whole.

A checklist for successful quantitative live cell imaging in systems biology

Mathematical modeling of signaling and gene regulatory networks has provided unique insights about systems behaviors for many cell biological problems of medical importance. Quantitative single cell monitoring has a crucial role in advancing systems modeling of molecular networks. However, due to the multidisciplinary techniques that are necessary for adaptation of such systems biology approaches, dissemination to a wide research community has been relatively slow. In this essay, I focus on some technical aspects that are often under-appreciated, yet critical in harnessing live cell imaging methods to achieve single-cell-level understanding and quantitative modeling of molecular networks. The importance of these technical considerations will be elaborated with examples of successes and shortcomings. Future efforts will benefit by avoiding some pitfalls and by utilizing the lessons collectively learned from recent applications of imaging in systems biology.

Encoding and decoding cellular information through signaling dynamics

A growing number of studies are revealing that cells can send and receive information by controlling the temporal behavior (dynamics) of their signaling molecules. In this Review, we discuss what is known about the dynamics of various signaling networks and their role in controlling cellular responses. We identify general principles that are emerging in the field, focusing specifically on how the identity and quantity of a stimulus is encoded in temporal patterns, how signaling dynamics influence cellular outcomes, and how specific dynamical patterns are both shaped and interpreted by the structure of molecular networks. We conclude by discussing potential functional roles for transmitting cellular information through the dynamics of signaling molecules and possible applications for the treatment of disease.

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.

The utility of paradoxical components in biological circuits

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

Formation of subnuclear foci is a unique spatial behavior of mating MAPKs during hyperosmotic stress

The assembly of signaling components and transcription factors in ordered subcellular structures is increasingly implicated as an important regulatory strategy for modulating the activity of cellular pathways. Here, we document the inducible formation of subnuclear foci formed by two mitogen-activated protein kinases (MAPKs) in Saccharomyces cerevisiae upon hyperosmotic stress. Specifically, we demonstrate that activation of the hyperosmotic stress response pathway induces the mating pathway MAPK Fus3 and the filamentation pathway MAPK Kss1 to form foci in the nucleus that are organized by their shared downstream transcription factor Ste12. Foci formation of colocalized Ste12, Fus3, and Kss1 requires the kinase activity of the hyperosmotic response MAPK Hog1 and correlates with attenuated signaling in the mating pathway. Conversely, activation of the mating pathway prevents foci formation upon subsequent hyperosmotic stress. These results suggest that Hog1-mediated spatial localization of Fus3 and Ste12 into subnuclear foci could contribute to uncoupling the pheromone and osmolarity pathways, which share signaling components, under high-osmolarity conditions.

Rate of environmental change determines stress response specificity

Cells use general stress response pathways to activate diverse target genes in response to a variety of stresses. However, general stress responses coexist with more specific pathways that are activated by individual stresses, provoking the fundamental question of whether and how cells control the generality or specificity of their response to a particular stress. Here we address this issue using quantitative time-lapse microscopy of the Bacillus subtilis environmental stress response, mediated by σ(B). We analyzed σ(B) activation in response to stresses such as salt and ethanol imposed at varying rates of increase. Dynamically, σ(B) responded to these stresses with a single adaptive activity pulse, whose amplitude depended on the rate at which the stress increased. This rate-responsive behavior can be understood from mathematical modeling of a key negative feedback loop in the underlying regulatory circuit. Using RNAseq we analyzed the effects of both rapid and gradual increases of ethanol and salt stress across the genome. Because of the rate responsiveness of σ(B) activation, salt and ethanol regulons overlap under rapid, but not gradual, increases in stress. Thus, the cell responds specifically to individual stresses that appear gradually, while using σ(B) to broaden the cellular response under more rapidly deteriorating conditions. Such dynamic control of specificity could be a critical function of other general stress response pathways.

Frequency-modulated pulses of ERK activity transmit quantitative proliferation signals

The EGF-stimulated ERK/MAPK pathway is a key conduit for cellular proliferation signals and a therapeutic target in many cancers. Here, we characterize two central quantitative aspects of this pathway: the mechanism by which signal strength is encoded and the response curve relating signal output to proliferation. Under steady-state conditions, we find that ERK is activated in discrete, asynchronous pulses with frequency and duration determined by extracellular concentrations of EGF spanning the physiological range. In genetically identical sister cells, cell-to-cell variability in pulse dynamics influences the decision to enter S phase. While targeted inhibition of EGFR reduces the frequency of ERK activity pulses, inhibition of MEK reduces their amplitude. Continuous response curves measured in multiple cell lines reveal that proliferation is effectively silenced only when ERK pathway output falls below a threshold of ~10%, indicating that high-dose targeting of the pathway is necessary to achieve therapeutic efficacy.

A characterization of scale invariant responses in enzymatic networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of three-node enzymatic networks (and sufficient for any number of nodes). Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.

Sensory systems often adapt, meaning that certain measured variables return to their basal levels after a transient response to a stimulus. An additional property that many adapting systems enjoy is that of scale invariance: the transient response remains the same when a stimulus is scaled. This work presents a mathematical study of biochemical enzymatic networks that exhibit scale-invariant behavior.

Systems biology. How information theory handles cell signaling and uncertainty

Information theory allows analyses of cell signaling capabilities without necessarily requiring detailed knowledge of the signaling networks.

Gene autoregulation via intronic microRNAs and its functions

Background

MicroRNAs, post-transcriptional repressors of gene expression, play a pivotal role in gene regulatory networks. They are involved in core cellular processes and their dysregulation is associated to a broad range of human diseases. This paper focus on a minimal microRNA-mediated regulatory circuit, in which a protein-coding gene (host gene) is targeted by a microRNA located inside one of its introns.

Results

Autoregulation via intronic microRNAs is widespread in the human regulatory network, as confirmed by our bioinformatic analysis, and can perform several regulatory tasks despite its simple topology. Our analysis, based on analytical calculations and simulations, indicates that this circuitry alters the dynamics of the host gene expression, can induce complex responses implementing adaptation and Weber’s law, and efficiently filters fluctuations propagating from the upstream network to the host gene. A fine-tuning of the circuit parameters can optimize each of these functions. Interestingly, they are all related to gene expression homeostasis, in agreement with the increasing evidence suggesting a role of microRNA regulation in conferring robustness to biological processes. In addition to model analysis, we present a list of bioinformatically predicted candidate circuits in human for future experimental tests.

Conclusions

The results presented here suggest a potentially relevant functional role for negative self-regulation via intronic microRNAs, in particular as a homeostatic control mechanism of gene expression. Moreover, the map of circuit functions in terms of experimentally measurable parameters, resulting from our analysis, can be a useful guideline for possible applications in synthetic biology.

Crosstalk between Fgf and Wnt signaling in the zebrafish tailbud

Fibroblast growth factor (Fgf) and Wnt signaling are necessary for the intertwined processes of tail elongation, mesodermal development and somitogenesis. Here, we use pharmacological modifiers and time-resolved quantitative analysis of both nascent transcription and protein phosphorylation in the tailbud, to distinguish early effects of signal perturbation from later consequences related to cell fate changes. We demonstrate that Fgf activity elevates Wnt signaling by inhibiting transcription of the Wnt antagonists dkk1 and notum1a. PI3 kinase signaling also increases Wnt signaling via phosphorylation of Gsk3β. Conversely, Wnt can increase signaling within the Mapk branch of the Fgf pathway as Gsk3β phosphorylation elevates phosphorylation levels of Erk. Despite the reciprocal positive regulation between Fgf and Wnt, the two pathways generally have opposing effects on the transcription of co-regulated genes. This opposing regulation of target genes may represent a rudimentary relationship that manifests as out-of-phase oscillation of Fgf and Wnt target genes in the mouse and chick tailbud. In summary, these data suggest that Fgf and Wnt signaling are tightly integrated to maintain proportional levels of activity in the zebrafish tailbud, and this balance is important for axis elongation, cell fate specification and somitogenesis.

Optimality principles in the regulation of metabolic networks

One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular "task" of the network-its function-should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.

Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

BACKGROUND

Cell-to-cell variability in protein expression can be large, and its propagation through signaling networks affects biological outcomes. Here, we apply deterministic and probabilistic models and biochemical measurements to study how network topologies and cell-to-cell protein abundance variations interact to shape signaling responses.

RESULTS

We observe bimodal distributions of extracellular signal-regulated kinase (ERK) responses to epidermal growth factor (EGF) stimulation, which are generally thought to indicate bistable or ultrasensitive signaling behavior in single cells. Surprisingly, we find that a simple MAPK/ERK-cascade model with negative feedback that displays graded, analog ERK responses at a single cell level can explain the experimentally observed bimodality at the cell population level. Model analysis suggests that a conversion of graded input-output responses in single cells to digital responses at the population level is caused by a broad distribution of ERK pathway activation thresholds brought about by cell-to-cell variability in protein expression.

CONCLUSIONS

Our results show that bimodal signaling response distributions do not necessarily imply digital (ultrasensitive or bistable) single cell signaling, and the interplay between protein expression noise and network topologies can bring about digital population responses from analog single cell dose responses. Thus, cells can retain the benefits of robustness arising from negative feedback, while simultaneously generating population-level on/off responses that are thought to be critical for regulating cell fate decisions.

Modeling the latent dimensions of multivariate signaling datasets

Cellular signal transduction is coordinated by modifications of many proteins within cells. Protein modifications are not independent, because some are connected through shared signaling cascades and others jointly converge upon common cellular functions. This coupling creates a hidden structure within a signaling network that can point to higher level organizing principles of interest to systems biology. One can identify important covariations within large-scale datasets by using mathematical models that extract latent dimensions-the key structural elements of a measurement set. In this paper, we introduce two principal component-based methods for identifying and interpreting latent dimensions. Principal component analysis provides a starting point for unbiased inspection of the major sources of variation within a dataset. Partial least-squares regression reorients these dimensions toward a specific hypothesis of interest. Both approaches have been used widely in studies of cell signaling, and they should be standard analytical tools once highly multivariate datasets become straightforward to accumulate.

ERK1/2 regulate exocytosis through direct phosphorylation of the exocyst component Exo70

The exocyst is a multiprotein complex essential for exocytosis and plasma membrane remodeling. The assembly of the exocyst complex mediates the tethering of post-Golgi secretory vesicles to the plasma membrane prior to fusion. Elucidating the mechanisms regulating exocyst assembly is important for the understanding of exocytosis. Here we show that the exocyst component Exo70 is a direct substrate of the extracellular signal-regulated kinases 1/2 (ERK1/2). ERK1/2 phosphorylation enhances the binding of Exo70 to other exocyst components and promotes the assembly of the exocyst complex in response to epidermal growth factor (EGF) signaling. We further demonstrate that ERK1/2 regulates exocytosis, because blocking ERK1/2 signaling by a chemical inhibitor or the expression of an Exo70 mutant defective in ERK1/2 phosphorylation inhibited exocytosis. In tumor cells, blocking Exo70 phosphorylation inhibits matrix metalloproteinase secretion and invadopodia formation. ERK1/2 phosphorylation of Exo70 may thus coordinate exocytosis with other cellular events in response to growth factor signaling.