Margaritis Voliotis

Information transfer by leaky, heterogeneous, protein kinase signaling systems.

Significance Extracellular concentrations convey information to cells about their environment. To sense these signals, cells use biomolecular networks that exhibit inevitable cell-to-cell variability and basal activity. Basal activity is widespread under physiological conditions (with phenotypic consequences), is often raised in disease, and can eradicate the transfer of information. In an experimental study of ERK signaling by single cells exhibiting heterogeneous ERK expression and basal activity, we verify our central theoretical prediction: Negative feedback substantially increases information transfer to the nucleus by preventing a near-flat average response curve and reducing sensitivity to variation in the ERK expression level. Our results reveal an important role for negative feedback mechanisms in protecting information transfer by saturable cell signaling systems from basal activity. Cells must sense extracellular signals and transfer the information contained about their environment reliably to make appropriate decisions. To perform these tasks, cells use signal transduction networks that are subject to various sources of noise. Here, we study the effects on information transfer of two particular types of noise: basal (leaky) network activity and cell-to-cell variability in the componentry of the network. Basal activity is the propensity for activation of the network output in the absence of the signal of interest. We show, using theoretical models of protein kinase signaling, that the combined effect of the two types of noise makes information transfer by such networks highly vulnerable to the loss of negative feedback. In an experimental study of ERK signaling by single cells with heterogeneous ERK expression levels, we verify our theoretical prediction: In the presence of basal network activity, negative feedback substantially increases information transfer to the nucleus by both preventing a near-flat average response curve and reducing sensitivity to variation in substrate expression levels. The interplay between basal network activity, heterogeneity in network componentry, and feedback is thus critical for the effectiveness of protein kinase signaling. Basal activity is widespread in signaling systems under physiological conditions, has phenotypic consequences, and is often raised in disease. Our results reveal an important role for negative feedback mechanisms in protecting the information transfer function of saturable, heterogeneous cell signaling systems from basal activity.

The fidelity of dynamic signaling by noisy biomolecular networks.

Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the systems fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.

The magnitude and colour of noise in genetic negative feedback systems

The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or ‘noise’ in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier—for transcriptional autorepression, it is frequently negligible.

Stochastic Simulation of Biomolecular Networks in Dynamic Environments

Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.

Information Transfer in Gonadotropin-releasing Hormone (GnRH) Signaling: EXTRACELLULAR SIGNAL-REGULATED KINASE (ERK)-MEDIATED FEEDBACK LOOPS CONTROL HORMONE SENSING.

Cell signaling pathways are noisy communication channels, and statistical measures derived from information theory can be used to quantify the information they transfer. Here we use single cell signaling measures to calculate mutual information as a measure of information transfer via gonadotropin-releasing hormone (GnRH) receptors (GnRHR) to extracellular signal-regulated kinase (ERK) or nuclear factor of activated T-cells (NFAT). This revealed mutual information values <1 bit, implying that individual GnRH-responsive cells cannot unambiguously differentiate even two equally probable input concentrations. Addressing possible mechanisms for mitigation of information loss, we focused on the ERK pathway and developed a stochastic activation model incorporating negative feedback and constitutive activity. Model simulations revealed interplay between fast (min) and slow (min-h) negative feedback loops with maximal information transfer at intermediate feedback levels. Consistent with this, experiments revealed that reducing negative feedback (by expressing catalytically inactive ERK2) and increasing negative feedback (by Egr1-driven expression of dual-specificity phosphatase 5 (DUSP5)) both reduced information transfer from GnRHR to ERK. It was also reduced by blocking protein synthesis (to prevent GnRH from increasing DUSP expression) but did not differ for different GnRHRs that do or do not undergo rapid homologous desensitization. Thus, the first statistical measures of information transfer via these receptors reveals that individual cells are unreliable sensors of GnRH concentration and that this reliability is maximal at intermediate levels of ERK-mediated negative feedback but is not influenced by receptor desensitization.

Mathematical modeling of gonadotropin-releasing hormone signaling

Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are Gq-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field.

Pulsatile Hormonal Signaling to Extracellular Signal-regulated Kinase EXPLORING SYSTEM SENSITIVITY TO GONADOTROPIN-RELEASING HORMONE PULSE FREQUENCY AND WIDTH

Background: Cellular decoding of stimulus dynamics is poorly understood. Results: GnRH pulses activate ERK, and response kinetics determine sensitivity to different pulse features. Conclusion: The system is sensitive to pulse frequency but robust to width; this distinction develops through the cascade and is dictated by response kinetics. Significance: We describe mathematical and biochemical “design features” for pulsatile hormonal signaling. Gonadotropin-releasing hormone (GnRH) is secreted in brief pulses that stimulate synthesis and secretion of pituitary gonadotropin hormones and thereby mediate control of reproduction. It acts via G-protein-coupled receptors to stimulate effectors, including ERK. Information could be encoded in GnRH pulse frequency, width, amplitude, or other features of pulse shape, but the relative importance of these features is unknown. Here we examine this using automated fluorescence microscopy and mathematical modeling, focusing on ERK signaling. The simplest scenario is one in which the system is linear, and response dynamics are relatively fast (compared with the signal dynamics). In this case integrated system output (ERK activation or ERK-driven transcription) will be roughly proportional to integrated input, but we find that this is not the case. Notably, we find that relatively slow response kinetics lead to ERK activity beyond the GnRH pulse, and this reduces sensitivity to pulse width. More generally, we show that the slowing of response kinetics through the signaling cascade creates a system that is robust to pulse width. We, therefore, show how various levels of response kinetics synergize to dictate system sensitivity to different features of pulsatile hormone input. We reveal the mathematical and biochemical basis of a dynamic GnRH signaling system that is robust to changes in pulse amplitude and width but is sensitive to changes in receptor occupancy and frequency, precisely the features that are tightly regulated and exploited to exert physiological control in vivo.

Distributing tasks via multiple input pathways increases cellular survival in stress

Improving in one aspect of a task can undermine performance in another, but how such opposing demands play out in single cells and impact on fitness is mostly unknown. Here we study budding yeast in dynamic environments of hyperosmotic stress and show how the corresponding signalling network increases cellular survival both by assigning the requirements of high response speed and high response accuracy to two separate input pathways and by having these pathways interact to converge on Hog1, a p38 MAP kinase. Cells with only the less accurate, reflex-like pathway are fitter in sudden stress, whereas cells with only the slow, more accurate pathway are fitter in increasing but fluctuating stress. Our results demonstrate that cellular signalling is vulnerable to trade-offs in performance, but that these trade-offs can be mitigated by assigning the opposing tasks to different signalling subnetworks. Such division of labour could function broadly within cellular signal transduction. DOI: http://dx.doi.org/10.7554/eLife.21415.001

Proofreading of misincorporated nucleotides in DNA transcription

The accuracy of DNA transcription is crucial for the proper functioning of the cell. Although RNA polymerases demonstrate selectivity for correct nucleotides, additional active mechanisms of transcriptional error correction are required to achieve observed levels of fidelity. Recent experimental findings have shed light on a particular mechanism of transcriptional error correction involving: (i) diffusive translocation of the RNA polymerase along the DNA (backtracking) and (ii) irreversible RNA cleavage. This mechanism achieves preferential cleavage of misincorporated nucleotides by biasing the local rates of translocation. Here, we study how misincorporated nucleotides affect backtracking dynamics and how this effect determines the level of transcriptional fidelity. We consider backtracking as a diffusive process in a periodic, one-dimensional energy landscape, which at a coarse-grained level gives rise to a hopping process between neighboring local minima. We propose a model for how misincorporated nucleotides deform this energy landscape and hence affect the hopping rates. In particular, we show that this model can be used to derive both the theoretical limit on the fidelity (i.e. the minimum fraction of misincorporated nucleotides) and the actual fidelity relative to this optimum, achieved for specific combinations of the cleavage and polymerization rates. Finally, we study how external factors influencing backtracking dynamics affect transcriptional fidelity. We show that biologically relevant loads, similar to those exerted by nucleosomes or other transcriptional barriers, increase error correction.

Information Transfer via Gonadotropin-Releasing Hormone Receptors to ERK and NFAT: Sensing GnRH and Sensing Dynamics

Information theoretic approaches can be used to quantify information transfer via cell signaling networks. In this study, we do so for gonadotropin-releasing hormone (GnRH) activation of extracellular signal-regulated kinase (ERK) and nuclear factor of activated T cells (NFAT) in large numbers of individual fixed LβT2 and HeLa cells. Information transfer, measured by mutual information between GnRH and ERK or NFAT, was <1 bit (despite 3-bit system inputs). It was increased by sensing both ERK and NFAT, but the increase was <50%. In live cells, information transfer via GnRH receptors to NFAT was also <1 bit and was increased by consideration of response trajectory, but the increase was <10%. GnRH secretion is pulsatile, so we explored information gained by sensing a second pulse, developing a model of GnRH signaling to NFAT with variability introduced by allowing effectors to fluctuate. Simulations revealed that when cell–cell variability reflects rapidly fluctuating effector levels, additional information is gained by sensing two GnRH pulses, but where it is due to slowly fluctuating effectors, responses in one pulse are predictive of those in another, so little information is gained from sensing both. Wet laboratory experiments revealed that the latter scenario holds true for GnRH signaling; within the timescale of our experiments (1 to 2 hours), cell–cell variability in the NFAT pathway remains relatively constant, so trajectories are reproducible from pulse to pulse. Accordingly, joint sensing, sensing of response trajectories, and sensing of repeated pulses can all increase information transfer via GnRH receptors, but in each case the increase is small.