Dose-to-duration encoding and signaling beyond saturation in intracellular signaling networks

Signal integration and integral feedback control with biochemical reaction networks

Biochemical reaction networks perform a variety of signal processing functions, one of which is computing the integrals of signal values. This is often used in integral feedback control, where it enables a system's output to respond to changing inputs, but to then return exactly back to some pre-determined setpoint value afterward. To gain a deeper understanding of how biochemical networks are able to both integrate signals and perform integral feedback control, we investigated these abilities for several simple reaction networks. We found imperfect overlap between these categories, with some networks able to perform both tasks, some able to perform integration but not integral feedback control, and some the other way around. Nevertheless, networks that could either integrate or perform integral feedback control shared key elements. In particular, they included a chemical species that was neutrally stable in the open loop system (no feedback), meaning that this species does not have a unique stable steady-state concentration. Neutral stability could arise from zeroth order decay reactions, binding to a partner that was produced at a constant rate (which occurs in antithetic control), or through a long chain of covalent cycles. Mathematically, it arose from rate equations for the reaction network that were underdetermined when evaluated at steady-state.

First-order ultrasensitivity in phosphorylation cycles

Cellular signal transduction takes place through a network of phosphorylation cycles. These pathways take the form of a multi-layered cascade of cycles. This work focuses on the sensitivity of single, double and n length cycles. Cycles that operate in the zero-order regime can become sensitive to changes in signal, resulting in zero-order ultrasensitivity (ZOU). Using frequency analysis, we confirm previous efforts that cascades can act as noise filters by computing the bandwidth. We show that n length cycles display what we term first-order ultrasensitivity which occurs even when the cycles are not operating in the zero-order regime. The magnitude of the sensitivity, however, has an upper bound equal to the number of cycles. It is known that ZOU can be significantly reduced in the presence of retroactivity. We show that the first-order ultrasensitivity is immune to retroactivity and that the ZOU and first-order ultrasensitivity can be blended to create systems with constant sensitivity over a wider range of signal. We show that the ZOU in a double cycle is only modestly higher compared with a single cycle. We therefore speculate that the double cycle has evolved to enable amplification even in the face of retroactivity.

Global quantitative understanding of non-equilibrium cell fate decision-making in response to pheromone

Cell-cycle arrest and polarized growth are commonly used to characterize the response of yeast to pheromone. However, the quantitative decision-making processes underlying time-dependent changes in cell fate remain unclear. In this study, we conducted single-cell level experiments to observe multidimensional responses, uncovering diverse fates of yeast cells. Multiple states are revealed, along with the kinetic switching rates and pathways among them, giving rise to a quantitative landscape of mating response. To quantify the experimentally observed cell fates, we developed a theoretical framework based on non-equilibrium landscape and flux theory. Additionally, we performed stochastic simulations of biochemical reactions to elucidate signal transduction and cell growth. Notably, our experimental findings have provided the first global quantitative evidence of the real-time synchronization between intracellular signaling, physiological growth, and morphological functions. These results validate the proposed underlying mechanism governing the emergence of multiple cell fate states. This study introduces an emerging mechanistic approach to understand non-equilibrium cell fate decision-making in response to pheromone.

Sensitivity and Frequency Response of Biochemical Cascades

Signal transduction from a cell's surface to cytoplasmic and nuclear targets takes place through a complex network of interconnected pathways. Phosphorylation cycles are common components of many pathways and may take the form of a multi-layered cascade of cycles or incorporate species with multiple phosphorylation sites that effectively create a sequence of cycles with increasing states of phosphorylation. This work focuses on the frequency response and sensitivity of such systems, two properties that have not been thoroughly examined. Starting with a singularly phosphorylated single-cycle system, we compare the sensitivity to perturbation at steady-state across a range of input signal strengths. This is followed by a frequency response analysis focusing on the gain and associated bandwidth. Next, we consider a two-layer cascade of single phosphorylation cycles and focus on how the two cycles interact to produce various effects on the bandwidth and damping properties. Then we consider the (ultra)sensitivity of a doubly phosphorylated system, where we describe in detail first-order ultrasensitivity, a unique property of these systems, which can be blended with zero-order ultrasensitivity to create systems with relatively constant gain over a range of signal input. Finally, we give an in-depth analysis of the sensitivity of an n-phosphorylated system.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance

Evolutionarily conserved insulin signaling is central to nutrient sensing, storage, and utilization across tissues. Dysfunctional insulin signaling is associated with metabolic disorders, cancer, and aging. Hence, the pathway components have emerged as key targets for pharmacological interventions in addition to insulin administration itself. Despite this, activation–inactivation dynamics of individual components, which exert regulatory control in a physiological context, is poorly understood. Now, with our systems-based approach, we reveal kinetic parameters, which define the flow of information through both metabolic and growth-factor arms and thus determine signaling architecture. We also provide a kinetic basis for 1) the advantage of pulsatile-fasted insulin signaling that enables fed-insulin response and 2) the detrimental impact of repeat fed-insulin inputs that causes resistance.

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

Molecular switch architecture determines response properties of signaling pathways

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states-on and off Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

Information transmission from NFkB signaling dynamics to gene expression

The dynamic signal encoding paradigm suggests that information flows from the extracellular environment into specific signaling patterns (encoding) that are then read by downstream effectors to control cellular behavior. Previous work empirically quantified the information content of dynamic signaling patterns. However, whether this information can be faithfully transmitted to the gene expression level is unclear. Here we used NFkB signaling as a model to understand the accuracy of information transmission from signaling dynamics into gene expression. Using a detailed mathematical model, we simulated realistic NFkB signaling patterns with different degrees of variability. The NFkB patterns were used as an input to a simple gene expression model. Analysis of information transmission between ligand and NFkB and ligand and gene expression allows us to determine information loss in transmission between receptors to dynamic signaling patterns and between signaling dynamics to gene expression. Information loss could occur due to biochemical noise or due to a lack of specificity. We found that noise-free gene expression has very little information loss suggesting that gene expression can preserve specificity in NFkB patterns. As expected, the addition of noise to the gene expression model results in information loss. Interestingly, this effect can be mitigated by a specific choice of parameters that can substantially reduce information loss due to biochemical noise during gene expression. Overall our results show that the cellular capacity for information transmission from dynamic signaling patterns to gene expression can be high enough to preserve ligand specificity and thereby the accuracy of cellular response to environmental cues.

Negative feedback-loop mechanisms regulating HOG- and pheromone-MAPK signaling in yeast

The pheromone response and the high osmolarity glycerol (HOG) pathways are considered the prototypical MAPK signaling systems. They are the best-understood pathways in eukaryotic cells, yet they continue to provide insights in how cells relate with the environment. These systems are subjected to tight regulatory circuits to prevent hyperactivation in length and intensity. Failure to do this may be a matter of life or death specially for unicellular organisms such as Saccharomyces cerevisiae. The signaling pathways are fine-tuned by positive and negative feedback loops exerted by pivotal control elements that allow precise responses to specific stimuli, despite the fact that some elements of the systems are common to different signaling pathways. Here we describe the experimentally proven negative feedback loops that modulate the pheromone response and the HOG pathways. As described in this review, MAP kinases are central mechanistic components of these feedback loops. They have the capacity to modulate basal signaling activity, a fast extranuclear response, and a longer-lasting transcriptional process.

Bistable switches as integrators and actuators during cell cycle progression

Progression through the cell cycle is driven by bistable switches-specialized molecular circuits that govern transitions from one cellular state to another. Although the mechanics of bistable switches are relatively well understood, it is less clear how cells integrate multiple sources of molecular information to engage these switches. Here, we describe how bistable switches act as hubs of information processing and examine how variability, competition, and inheritance of molecular signals determine the timing of the Rb-E2F bistable switch that controls cell cycle entry. Bistable switches confer both robustness and plasticity to cell cycle progression, ensuring that cell cycle events are performed completely and in the correct order, while still allowing flexibility to cope with ongoing stress and changing environmental conditions.

Quantitative analysis of the yeast pheromone pathway

The pheromone response pathway of the yeast Saccharomyces cerevisiae is a well-established model for the study of G proteins and mitogen-activated protein kinase (MAPK) cascades. Our longstanding ability to combine sophisticated genetic approaches with established functional assays has provided a thorough understanding of signalling mechanisms and regulation. In this report, we compare new and established methods used to quantify pheromone-dependent MAPK phosphorylation, transcriptional induction, mating morphogenesis, and gradient tracking. These include both single-cell and population-based assays of activity. We describe several technical advances, provide example data for benchmark mutants, highlight important differences between newer and established methodologies, and compare the advantages and disadvantages of each as applied to the yeast model. Quantitative measurements of pathway activity have been used to develop mathematical models and reveal new regulatory mechanisms in yeast. It is our expectation that experimental and computational approaches developed in yeast may eventually be adapted to human systems biology and pharmacology.

Autophagy facilitates the release of immunogenic signals following chemotherapy in 3D models of mesothelioma

We have previously shown that nearly half of mesothelioma patients have tumors with low autophagy and that these patients have a significantly worse outcome than those with high autophagy. We hypothesized that autophagy may be beneficial by facilitating immunogenic cell death (ICD) of tumor cells following chemotherapy. An important hallmark of ICD is that death of tumor cells is preceded or accompanied by the release of damage-associated molecular pattern molecules (DAMPs), which then can stimulate an antitumor immune response. Therefore, we measured how autophagy affected the release of three major DAMPs: high mobility group box 1 (HMGB1), ATP, and calreticulin following chemotherapy. We found that autophagy in three-dimensional (3D) models with low autophagy at baseline could be upregulated with the cell-permeant Tat-BECN1 peptide and confirmed that autophagy in 3D models with high autophagy at baseline could be inhibited with MRT 68921 or ATG7 RNAi, as we have previously shown. In in vitro 3D spheroids, we found that, when autophagy was high or upregulated, DAMPs were released following chemotherapy; however, when autophagy was low or inhibited, DAMPs release was significantly impaired. Similarly, in ex vivo tumors, when autophagy was high or upregulated, HMGB1 was released following chemotherapy but, when autophagy was low, HMGB1 release was not seen. We conclude that autophagy can be upregulated in at least some tumors with low autophagy and that upregulation of autophagy can restore the release of DAMPs following chemotherapy. Autophagy may be necessary for ICD in this tumor.

Communicate and Fuse: How Filamentous Fungi Establish and Maintain an Interconnected Mycelial Network

Cell-to-cell communication and cell fusion are fundamental biological processes across the tree of life. Survival is often dependent upon being able to identify nearby individuals and respond appropriately. Communication between genetically different individuals allows for the identification of potential mating partners, symbionts, prey, or predators. In contrast, communication between genetically similar (or identical) individuals is important for mediating the development of multicellular organisms or for coordinating density-dependent behaviors (i.e., quorum sensing). This review describes the molecular and genetic mechanisms that mediate cell-to-cell communication and cell fusion between cells of Ascomycete filamentous fungi, with a focus on Neurospora crassa. Filamentous fungi exist as a multicellular, multinuclear network of hyphae, and communication-mediated cell fusion is an important aspect of colony development at each stage of the life cycle. Asexual spore germination occurs in a density-dependent manner. Germinated spores (germlings) avoid cells that are genetically different at specific loci, while chemotropically engaging with cells that share identity at these recognition loci. Germlings with genetic identity at recognition loci undergo cell fusion when in close proximity, a fitness attribute that contributes to more rapid colony establishment. Communication and cell fusion also occur between hyphae in a colony, which are important for reinforcing colony architecture and supporting the development of complex structures such as aerial hyphae and sexual reproductive structures. Over 70 genes have been identified in filamentous fungi (primarily N. crassa) that are involved in kind recognition, chemotropic interactions, and cell fusion. While the hypothetical signal(s) and receptor(s) remain to be described, a dynamic molecular signaling network that regulates cell-cell interactions has been revealed, including two conserved MAP-Kinase cascades, a conserved STRIPAK complex, transcription factors, a NOX complex involved in the generation of reactive oxygen species, cell-integrity sensors, actin, components of the secretory pathway, and several other proteins. Together these pathways facilitate the integration of extracellular signals, direct polarized growth, and initiate a transcriptional program that reinforces signaling and prepares cells for downstream processes, such as membrane merger, cell fusion and adaptation to heterokaryon formation.

Experimental and engineering approaches to intracellular communication

Communication between and within cells is essential for multicellular life. While intracellular signal transduction pathways are often specified in molecular terms, the information content they transmit remains poorly defined. Here, we review research efforts to merge biological experimentation with concepts of communication that emerge from the engineering disciplines of signal processing and control theory. We discuss the challenges of performing experiments that quantitate information transfer at the molecular level, and we highlight recent studies that have advanced toward a clearer definition of the information content carried by signaling molecules. Across these studies, we emphasize a theme of increasingly well-matched experimental and theoretical approaches to decode the data streams directing cellular behavior.

In Vivo Decoding Mechanisms of the Temporal Patterns of Blood Insulin by the Insulin-AKT Pathway in the Liver

Cells respond to various extracellular stimuli through a limited number of signaling pathways. One strategy to process such stimuli is to code the information into the temporal patterns of molecules. Although we showed that insulin selectively regulated molecules depending on its temporal patterns using Fao cells, the in vivo mechanism remains unknown. Here, we show how the insulin-AKT pathway processes the information encoded into the temporal patterns of blood insulin. We performed hyperinsulinemic-euglycemic clamp experiments and found that, in the liver, all temporal patterns of insulin are encoded into the insulin receptor, and downstream molecules selectively decode them through AKT. S6K selectively decodes the additional secretion information. G6Pase interprets the basal secretion information through FoxO1, while GSK3β decodes all secretion pattern information. Mathematical modeling revealed the mechanism via differences in network structures and from sensitivity and time constants. Given that almost all hormones exhibit distinct temporal patterns, temporal coding may be a general principle of system homeostasis by hormones.

Analysis of the thresholds for transcriptional activation by the yeast MAP kinases Fus3 and Kss1

Signaling in the pheromone response pathway of budding yeast activates two distinct MAP kinases (MAPKs), Fus3 and Kss1. Either MAPK alone can mediate pheromone-induced transcription, but it has been unclear to what degree each one contributes to transcriptional output in wild-type cells. Here, we report that transcription reflects the ratio of active to inactive MAPK, and not simply the level of active MAPK. For Kss1 the majority of MAPK molecules must be converted to the active form, whereas for Fus3 only a small minority must be activated. These different activation thresholds reflect two opposing effects of each MAPK, in which the inactive forms inhibit transcription, whereas the active forms promote transcription. Moreover, negative feedback from Fus3 limits activation of Kss1 so that it does not meet its required threshold in wild-type cells but does so only when hyperactivated in cells lacking Fus3. The results suggest that the normal transcriptional response involves asymmetric contributions from the two MAPKs, in which pheromone signaling reduces the negative effect of Kss1 while increasing the positive effect of Fus3. These findings reveal new functional distinctions between these MAPKs, and help illuminate how inhibitory functions shape positive pathway outputs in both pheromone and filamentation pathways.

β-arrestin signalling and bias in hormone-responsive GPCRs

G protein-coupled receptors (GPCRs) play crucial roles in the ability of target organs to respond to hormonal cues. GPCRs' activation mechanisms have long been considered as a two-state process connecting the agonist-bound receptor to heterotrimeric G proteins. This view is now challenged as mounting evidence point to GPCRs being connected to large arrays of transduction mechanisms involving heterotrimeric G proteins as well as other players. Amongst the G protein-independent transduction mechanisms, those elicited by β-arrestins upon their recruitment to the active receptors are by far the best characterized and apply to most GPCRs. These concepts, in conjunction with remarkable advances made in the field of GPCR structural biology and biophysics, have supported the notion of ligand-selective signalling also known as pharmacological bias. Interestingly, recent reports have opened intriguing prospects to the way β-arrestins control GPCR-mediated signalling in space and time within the cells. In the present paper, we review the existing evidence linking endocrine-related GPCRs to β-arrestin recruitement, signalling, pathophysiological implications and selective activation by biased ligands and/or receptor modifications. Emerging concepts surrounding β-arrestin-mediated transduction are discussed in the light of the peculiarities of endocrine systems.

Sensory input attenuation allows predictive sexual response in yeast

Animals are known to adjust their sexual behaviour depending on mate competition. Here we report similar regulation for mating behaviour in a sexual unicellular eukaryote, the budding yeast Saccharomyces cerevisiae. We demonstrate that pheromone-based communication between the two mating types, coupled to input attenuation by recipient cells, enables yeast to robustly monitor relative mate abundance (sex ratio) within a mixed population and to adjust their commitment to sexual reproduction in proportion to their estimated chances of successful mating. The mechanism of sex-ratio sensing relies on the diffusible peptidase Bar1, which is known to degrade the pheromone signal produced by mating partners. We further show that such a response to sexual competition within a population can optimize the fitness trade-off between the costs and benefits of mating response induction. Our study thus provides an adaptive explanation for the known molecular mechanism of pheromone degradation in yeast.

Cells of the yeast Saccharomyces cerevisiae can mate with other cells of opposite mating type. Here, the authors show that the combination of a pheromone and a pheromone-degrading enzyme allows yeast cells to monitor relative mate abundance within a population and adjust their commitment to sexual reproduction.

What Scales the T Cell Response?

T cells are known to scale their clonal expansion and effector cytokine response according to the dose and strength of antigenic signal so as to balance their role of affecting protection with the intertwined and immunologically driven tissue damage. How T cells achieve this is now beginning to be understood. We underscore temporal integration of digital T cell receptor (TCR) signaling as the basis for achieving scaled response by means of accumulating crucial mediators over time. We also discuss the role of temporally integrated crosstalk between TCR and IL2 signaling in mediating a scaled, coherent, collective response by T cells. Finally, we highlight numerous known and putative regulatory interactions in the transcriptional program that are expected to quantitatively scale the T cell response, and also offer new mechanisms to hitherto unexplained observations.

Deactivation of a negative regulator: a distinct signal transduction mechanism, pronounced in Akt signaling

Kinase cascades, in which enzymes are sequentially activated by phosphorylation, are quintessential signaling pathways. Signal transduction is not always achieved by direct activation, however. Often, kinases activate pathways by deactivation of a negative regulator; this indirect mechanism, pervasive in Akt signaling, has yet to be systematically explored. Here, we show that the indirect mechanism has properties that are distinct from direct activation. With comparable parameters, the indirect mechanism yields a broader range of sensitivity to the input, beyond saturation of regulator phosphorylation, and kinetics that become progressively slower, not faster, with increasing input strength. These properties can be integrated in network motifs to produce desired responses, as in the case of feedforward loops.

Compartmentalization of a bistable switch enables memory to cross a feedback-driven transition

Cells make accurate decisions in the face of molecular noise and environmental fluctuations by relying not only on present pathway activity, but also on their memory of past signaling dynamics. Once a decision is made, cellular transitions are often rapid and switch-like due to positive feedback loops in the regulatory network. While positive feedback loops are good at promoting switch-like transitions, they are not expected to retain information to inform subsequent decisions. However, this expectation is based on our current understanding of network motifs that accounts for temporal, but not spatial, dynamics. Here, we show how spatial organization of the feedback-driven yeast G1/S switch enables the transmission of memory of past pheromone exposure across this transition. We expect this to be one of many examples where the exquisite spatial organization of the eukaryotic cell enables previously well-characterized network motifs to perform new and unexpected signal processing functions.

MAPK feedback encodes a switch and timer for tunable stress adaptation in yeast

Signaling pathways can behave as switches or rheostats, generating binary or graded responses to a given cell stimulus. We evaluated whether a single signaling pathway can simultaneously encode a switch and a rheostat. We found that the kinase Hog1 mediated a bifurcated cellular response: Activation and commitment to adaptation to osmotic stress are switchlike, whereas protein induction and the resolution of this commitment are graded. Through experimentation, bioinformatics analysis, and computational modeling, we determined that graded recovery is encoded through feedback phosphorylation and a gene induction program that is both temporally staggered and variable across the population. This switch-to-rheostat signaling mechanism represents a versatile stress adaptation system, wherein a broad range of inputs generate an "all-in" response that is later tuned to allow graded recovery of individual cells over time.

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.

Utilization of extracellular information before ligand-receptor binding reaches equilibrium expands and shifts the input dynamic range

Cell signaling systems sense and respond to ligands that bind cell surface receptors. These systems often respond to changes in the concentration of extracellular ligand more rapidly than the ligand equilibrates with its receptor. We demonstrate, by modeling and experiment, a general "systems level" mechanism cells use to take advantage of the information present in the early signal, before receptor binding reaches a new steady state. This mechanism, pre-equilibrium sensing and signaling (PRESS), operates in signaling systems in which the kinetics of ligand-receptor binding are slower than the downstream signaling steps, and it typically involves transient activation of a downstream step. In the systems where it operates, PRESS expands and shifts the input dynamic range, allowing cells to make different responses to ligand concentrations so high as to be otherwise indistinguishable. Specifically, we show that PRESS applies to the yeast directional polarization in response to pheromone gradients. Consideration of preexisting kinetic data for ligand-receptor interactions suggests that PRESS operates in many cell signaling systems throughout biology. The same mechanism may also operate at other levels in signaling systems in which a slow activation step couples to a faster downstream step.

Mathematical modelling of arsenic transport, distribution and detoxification processes in yeast

Arsenic has a dual role as causative and curative agent of human disease. Therefore, there is considerable interest in elucidating arsenic toxicity and detoxification mechanisms. By an ensemble modelling approach, we identified a best parsimonious mathematical model which recapitulates and predicts intracellular arsenic dynamics for different conditions and mutants, thereby providing novel insights into arsenic toxicity and detoxification mechanisms in yeast, which could partly be confirmed experimentally by dedicated experiments. Specifically, our analyses suggest that: (i) arsenic is mainly protein-bound during short-term (acute) exposure, whereas glutathione-conjugated arsenic dominates during long-term (chronic) exposure, (ii) arsenic is not stably retained, but can leave the vacuole via an export mechanism, and (iii) Fps1 is controlled by Hog1-dependent and Hog1-independent mechanisms during arsenite stress. Our results challenge glutathione depletion as a key mechanism for arsenic toxicity and instead suggest that (iv) increased glutathione biosynthesis protects the proteome against the damaging effects of arsenic and that (v) widespread protein inactivation contributes to the toxicity of this metalloid. Our work in yeast may prove useful to elucidate similar mechanisms in higher eukaryotes and have implications for the use of arsenic in medical therapy.

Multiplexing oscillatory biochemical signals

In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

Molecular editing of cellular responses by the high-affinity receptor for IgE

Cellular responses elicited by cell surface receptors differ according to stimulus strength. We investigated how the high-affinity receptor for immunoglobulin E (IgE) modulates the response of mast cells to a high- or low-affinity stimulus. Both high- and low-affinity stimuli elicited similar receptor phosphorylation; however, differences were observed in receptor cluster size, mobility, distribution, and the cells' effector responses. Low-affinity stimulation increased receptor association with the Src family kinase Fgr and shifted signals from the adapter LAT1 to the related adapter LAT2. LAT1-dependent calcium signals required for mast cell degranulation were dampened, but the role of LAT2 in chemokine production was enhanced, altering immune cell recruitment at the site of inflammation. These findings uncover how receptor discrimination of stimulus strength can be interpreted as distinct in vivo outcomes.

RECEPTOR-DEPENDENT SENSITIVITY OF NF-κB TO LOW PHYSIOLOGICAL LEVEL

In the NFκB signaling pathway, cells respond to different concentrations of the TNFα signal by means of NFκB transcription factors. Previous studies showed that most cells are activated under high-dose stimulations and NFκB activation results in oscillations in nuclear NFκB abundance. Here, by analyzing sensitivity gain for the response of the nuclear NFκB to the number of cell-surface receptors under low-dose stimulations, we show that changes in the receptor number can give rise to significant changes in the nonsaturation part of the dose–response curve, where the receptor activation rates are very sensitive to stimulations. In addition, the number of the activated receptors tends to increase in a large range of stimulation dose and can significantly influence the expression of the downstream genes. These results imply that the number of cell-surface receptors plays a role of information encoding like frequency or amplitude encoding described in previous studies.

Ciliates learn to diagnose and correct classical error syndromes in mating strategies

Preconjugal ciliates learn classical repetition error-correction codes to safeguard mating messages and replies from corruption by “rivals” and local ambient noise. Because individual cells behave as memory channels with Szilárd engine attributes, these coding schemes also might be used to limit, diagnose, and correct mating-signal errors due to noisy intracellular information processing. The present study, therefore, assessed whether heterotrich ciliates effect fault-tolerant signal planning and execution by modifying engine performance, and consequently entropy content of codes, during mock cell–cell communication. Socially meaningful serial vibrations emitted from an ambiguous artificial source initiated ciliate behavioral signaling performances known to advertise mating fitness with varying courtship strategies. Microbes, employing calcium-dependent Hebbian-like decision making, learned to diagnose then correct error syndromes by recursively matching Boltzmann entropies between signal planning and execution stages via “power” or “refrigeration” cycles. All eight serial contraction and reversal strategies incurred errors in entropy magnitude by the execution stage of processing. Absolute errors, however, subtended expected threshold values for single bit-flip errors in three-bit replies, indicating coding schemes protected information content throughout signal production. Ciliate preparedness for vibrations selectively and significantly affected the magnitude and valence of Szilárd engine performance during modal and non-modal strategy corrective cycles. But entropy fidelity for all replies mainly improved across learning trials as refinements in engine efficiency. Fidelity neared maximum levels for only modal signals coded in resilient three-bit repetition error-correction sequences. Together, these findings demonstrate microbes can elevate survival/reproductive success by learning to implement classical fault-tolerant information processing in social contexts.

P2 receptor networks regulate signaling duration over a wide dynamic range of ATP concentrations

The primordial intercellular signaling molecule ATP acts through two families of cell-surface P2 receptors - the P2Y family of G-protein-coupled receptors and the P2X family of ligand-gated cation channels. Multiple P2 receptors are expressed in a variety of cell types. However, the significance of these networks of receptors in any biological system remains unknown. Using osteoblasts as a model system, we found that a low concentration of ATP (10 µM, ATPlow) induced transient elevation of cytosolic Ca(2+), whereas a high concentration of ATP (1 mM, ATPhigh) elicited more sustained elevation. Moreover, graded increases in the Ca(2+) signal were achieved over a remarkable million-fold range of ATP concentrations (1 nM to 1 mM). Next, we demonstrated that ATPlow caused transient nuclear localization of the Ca(2+)-regulated transcription factor NFATc1; whereas, ATPhigh elicited more sustained localization. When stimulated with ATPhigh, osteoblasts from P2X7 loss-of-function mice showed only transient Ca(2+)-NFATc1 signaling; in contrast, sustained signaling was observed in wild-type cells. Additional experiments revealed a role for P2Y receptors in mediating transient signaling induced by low ATP concentrations. Thus, distinct P2 receptors with varying affinities for ATP account for this wide range of sensitivity to extracellular nucleotides. Finally, ATPhigh, but not ATPlow, was shown to elicit robust expression of the NFAT target gene Ptgs2 (encoding COX-2), consistent with a crucial role for the duration of Ca(2+)-NFAT signaling in regulating target gene expression. Taken together, ensembles of P2 receptors provide a mechanism by which cells sense ATP over a wide concentration range and transduce this input into distinct cellular signals.

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.

Combined computational and experimental analysis reveals mitogen-activated protein kinase-mediated feedback phosphorylation as a mechanism for signaling specificity

A series of mathematical models was used to quantitatively characterize pheromone-stimulated kinase activation and determine how mitogen-activated protein (MAP) kinase specificity is achieved. The findings reveal how feedback phosphorylation of a common pathway component can limit the activity of a competing MAP kinase through feedback phosphorylation of a common activator, and thereby promote signal fidelity.

Different environmental stimuli often use the same set of signaling proteins to achieve very different physiological outcomes. The mating and invasive growth pathways in yeast each employ a mitogen-activated protein (MAP) kinase cascade that includes Ste20, Ste11, and Ste7. Whereas proper mating requires Ste7 activation of the MAP kinase Fus3, invasive growth requires activation of the alternate MAP kinase Kss1. To determine how MAP kinase specificity is achieved, we used a series of mathematical models to quantitatively characterize pheromone-stimulated kinase activation. In accordance with the computational analysis, MAP kinase feedback phosphorylation of Ste7 results in diminished activation of Kss1, but not Fus3. These findings reveal how feedback phosphorylation of a common pathway component can limit the activity of a competing MAP kinase through feedback phosphorylation of a common activator, and thereby promote signal fidelity.

Short-term information processing, long-term responses: Insights by mathematical modeling of signal transduction. Early activation dynamics of key signaling mediators can be predictive for cell fate decisions

How do cells interpret information from their environment and translate it into specific cell fate decisions? We propose that cell fate is already encoded in early signaling events and thus can be predicted from defined signal properties. Specifically, we hypothesize that the time integral of activated key signaling molecules can be correlated to cellular behavior such as proliferation or differentiation. The identification of these decisive key signal mediators and their connection to cell fate is facilitated by mathematical modeling. A possible mechanistic linkage between signaling dynamics and cellular function is the directed control of gene regulatory networks by defined signals. Targeted experiments in combination with mathematical modeling can increase our understanding of how cells process information and realize distinct cell fates.

Sensitivity control through attenuation of signal transfer efficiency by negative regulation of cellular signalling

Sensitivity is one of the hallmarks of biological and pharmacological responses. However, the principle of controlling sensitivity remains unclear. Here we theoretically analyse a simple biochemical reaction and find that the signal transfer efficiency of the transient peak amplitude attenuates depending on the strength of negative regulation. We experimentally find that many signalling pathways in various cell lines, including the Akt and ERK pathways, can be approximated by simple biochemical reactions and that the same property of the attenuation of signal transfer efficiency was observed for such pathways. Because of this property, a downstream molecule should show higher sensitivity to an activator and lower sensitivity to an inhibitor than an upstream molecule. Indeed, we experimentally verify that S6, which lies downstream of Akt, shows lower sensitivity to an epidermal growth factor receptor inhibitor than Akt. Thus, cells can control downstream sensitivity through the attenuation of signal transfer efficiency by changing the expression level of negative regulators.

Receptor dynamics in signaling

Reliable inter- and intracellular communication is central to both the development and the integrity of multicellular organisms. Key mediators of these processes are cell surface receptors that perceive and convert extracellular cues to trigger intracellular signaling networks and ultimately a phenotypic response. Deregulation of signal transduction leads to a variety of diseases, and aberrations in receptor proteins are very common in various cancer types. Therefore, cell surface receptors have been established as major targets in drug discovery. However, in order to efficiently apply therapeutics, it is crucial to gain knowledge about design principles of receptor signaling. In this chapter, we will discuss signal transduction at the receptor level for examples from different receptor classes.

From Physics to Pharmacology?

Over the last fifty years there has been an explosion of biological data, leading to the realization that to fully explain biological mechanisms it is necessary to interpret them as complex dynamical systems. The first stage of this interpretation is to determine which components (proteins, genes or metabolites) of the system interact. This is usually represented by a graph, or network. The behavior of this network can then be investigated using mathematical modeling. In vivo these biological networks show several remarkable (and seemingly paradoxical) properties including robustness, plasticity and sensitivity. Erroneous behavior of these networks is often associated with disease. Hence understanding the system-level properties can have important implications for the treatment of disease. Systems biology is an organized approach to quantitatively describe and elucidate the behavior of these complex networks. This review focuses on the progress and future challenges of a systems approach to biology.

The effects of replacing Sst2 with the heterologous RGS4 on polarization and mating in yeast

RGS proteins stimulate the deactivation of heterotrimeric G-proteins. The yeast RGS protein Sst2 is regulated at both the transcriptional and posttranscriptional levels. We replaced the SST2 gene with the distantly related human RGS4 gene, which consists of the catalytic domain and an N-terminal membrane attachment peptide, and replaced the native promoter (P(SST2)) with the heterologous tetracycline-repressible promoter (P(TET)). We then measured the effect of the substitutions on pheromone sensitivity, mating, and polarization. Although the pheromone sensitivity was essentially normal, there were differences in mating and polarization. In particular, the RGS4-substituted strains did not form multiple mating projections at high levels of alpha-factor, but instead formed a single malformed projection, which frequently gave rise to a bud. We provide evidence that this phenotype arose because unlike Sst2, RGS4 did not localize to the projection. We use mathematical modeling to argue that localization of Sst2 to the projection prevents excess G-protein activation during the pheromone response. In addition, modeling and experiments demonstrate that the dose of Sst2 influences the frequency of mating projection formation.

Systematic quantification of negative feedback mechanisms in the extracellular signal-regulated kinase (ERK) signaling network

Cell responses are actuated by tightly controlled signal transduction pathways. Although the concept of an integrated signaling network replete with interpathway cross-talk and feedback regulation is broadly appreciated, kinetic data of the type needed to characterize such interactions in conjunction with mathematical models are lacking. In mammalian cells, the Ras/ERK pathway controls cell proliferation and other responses stimulated by growth factors, and several cross-talk and feedback mechanisms affecting its activation have been identified. In this work, we take a systematic approach to parse the magnitudes of multiple regulatory mechanisms that attenuate ERK activation through canonical (Ras-dependent) and non-canonical (PI3K-dependent) pathways. In addition to regulation of receptor and ligand levels, we consider three layers of ERK-dependent feedback: desensitization of Ras activation, negative regulation of MEK kinase (e.g. Raf) activities, and up-regulation of dual-specificity ERK phosphatases. Our results establish the second of these as the dominant mode of ERK self-regulation in mouse fibroblasts. We further demonstrate that kinetic models of signaling networks, trained on a sufficient diversity of quantitative data, can be reasonably comprehensive, accurate, and predictive in the dynamical sense.

Understanding the temporal codes of intra-cellular signals

The health of organisms and cells depends on appropriate responses to diverse internal and external cues, stimuli, or challenges, such as changes in hormone or cytokine levels, or exposure to a pathogen. Cellular responses must be tailored to the identity and intensity of the stimulus and therefore intra-cellular signals must carry information about both. However, signaling mediators often form intricate networks that react to multiple stimuli yet manage to produce stimulus-specific responses. The multi-functionality ('functional pleiotropism') of signaling nodes suggests that biological networks have evolved ways of passing physiologically relevant stimulus information through shared channels. Increasing evidence supports the notion that this is achieved in part through temporal regulation of signaling mediators' activities. The present challenge is to identify the features of temporal activity profile that represent information about a given stimulus and understand how cells read the temporal codes to control their responses.

Trade-offs and noise tolerance in signal detection by genetic circuits

Genetic circuits can implement elaborated tasks of amplitude or frequency signal detection. What type of constraints could circuits experience in the performance of these tasks, and how are they affected by molecular noise? Here, we consider a simple detection process–a signal acting on a two-component module–to analyze these issues. We show that the presence of a feedback interaction in the detection module imposes a trade-off on amplitude and frequency detection, whose intensity depends on feedback strength. A direct interaction between the signal and the output species, in a type of feed-forward loop architecture, greatly modifies these trade-offs. Indeed, we observe that coherent feed-forward loops can act simultaneously as good frequency and amplitude noise-tolerant detectors. Alternatively, incoherent feed-forward loop structures can work as high-pass filters improving high frequency detection, and reaching noise tolerance by means of noise filtering. Analysis of experimental data from several specific coherent and incoherent feed-forward loops shows that these properties can be realized in a natural context. Overall, our results emphasize the limits imposed by circuit structure on its characteristic stimulus response, the functional plasticity of coherent feed-forward loops, and the seemingly paradoxical advantage of improving signal detection with noisy circuit components.

BiP binding to the ER-stress sensor Ire1 tunes the homeostatic behavior of the unfolded protein response

Computational modeling and experimentation in the unfolded protein response reveals a role for the ER-resident chaperone protein BiP in fine-tuning the system's response dynamics.

The unfolded protein response (UPR) is an intracellular signaling pathway that counteracts variable stresses that impair protein folding in the endoplasmic reticulum (ER). As such, the UPR is thought to be a homeostat that finely tunes ER protein folding capacity and ER abundance according to need. The mechanism by which the ER stress sensor Ire1 is activated by unfolded proteins and the role that the ER chaperone protein BiP plays in Ire1 regulation have remained unclear. Here we show that the UPR matches its output to the magnitude of the stress by regulating the duration of Ire1 signaling. BiP binding to Ire1 serves to desensitize Ire1 to low levels of stress and promotes its deactivation when favorable folding conditions are restored to the ER. We propose that, mechanistically, BiP achieves these functions by sequestering inactive Ire1 molecules, thereby providing a barrier to oligomerization and activation, and a stabilizing interaction that facilitates de-oligomerization and deactivation. Thus BiP binding to or release from Ire1 is not instrumental for switching the UPR on and off as previously posed. By contrast, BiP provides a buffer for inactive Ire1 molecules that ensures an appropriate response to restore protein folding homeostasis to the ER by modulating the sensitivity and dynamics of Ire1 activity.

Secreted and membrane-spanning proteins constitute one of every three proteins produced by a eukaryotic cell. Many of these proteins initially fold and assemble in the endoplasmic reticulum (ER). A variety of physiological and environmental conditions can increase the demands on the ER, overwhelming the ER protein folding machinery. To restore homeostasis in response to ER stress, cells activate an intracellular signaling pathway called the unfolded protein response (UPR) that adjusts the folding capacity of the ER according to need. Its failure impairs cell viability and has been implicated in numerous disease states. In this study, we quantitatively interrogate the homeostatic capacity of the UPR. We arrive at a mechanistic model for how the ER stress sensor Ire1 cooperates with its binding partner BiP, a highly redundant ER chaperone, to fine-tune UPR activity. Moving between a predictive computational model and experiments, we show that BiP release from Ire1 is not the switch that activates Ire1; rather, BiP modulates Ire1 activation and deactivation dynamics. BiP binding to Ire1 and its dissociation in an ER stress-dependent manner buffers the system against mild stresses. Furthermore, BiP binding accelerates Ire1 deactivation when stress is removed. We conclude that BiP binding to Ire1 serves to fine-tune the dynamic behavior of the UPR by modulating its sensitivity and shutoff kinetics. This function of the interaction between Ire1 and BiP may be a general paradigm for other systems in which oligomer formation and disassembly must be finely regulated.

Regulation of smooth muscle contraction by small GTPases

Next to changes in cytosolic [Ca(2+)], members of the Rho subfamily of small GTPases, in particular Rho and its effector Rho kinase, also known as ROK or ROCK, emerged as key regulators of smooth muscle function in health and disease. In this review, we will focus on the regulation of the contractile machinery by Rho/ROK signaling and its interaction with PKC and cyclic nucleotide signaling. We will briefly discuss the emerging evidence that remodeling of cortical actin is necessary for contraction.

Cell signaling: what is the signal and what information does it carry?

This paper reviews key findings from quantitative study of the yeast pheromone response system. Most come from single cell experiments that quantify molecular events the system uses to operate. After induction, signal propagation is relatively slow; peak activity takes minutes to reach the nucleus. At each measurement point along the transmission chain, signal rises, overshoots, peaks, and declines toward steady state. At at least one measurement point, this decline depends on negative feedback. The system senses and relays percent receptor occupancy, and one effect of the feedback is to maximize precision of this transmitted information. Over time, the system constantly adjusts quantitative behaviors to convey extracellular ligand concentration faithfully. These behaviors and mechanisms that control them are likely to be general for metazoan signaling systems.

Information processing and signal integration in bacterial quorum sensing

Bacteria communicate using secreted chemical signaling molecules called autoinducers in a process known as quorum sensing. The quorum-sensing network of the marine bacterium Vibrio harveyi uses three autoinducers, each known to encode distinct ecological information. Yet how cells integrate and interpret the information contained within these three autoinducer signals remains a mystery. Here, we develop a new framework for analyzing signal integration on the basis of information theory and use it to analyze quorum sensing in V. harveyi. We quantify how much the cells can learn about individual autoinducers and explain the experimentally observed input–output relation of the V. harveyi quorum-sensing circuit. Our results suggest that the need to limit interference between input signals places strong constraints on the architecture of bacterial signal-integration networks, and that bacteria probably have evolved active strategies for minimizing this interference. Here, we analyze two such strategies: manipulation of autoinducer production and feedback on receptor number ratios.