Recurrent design patterns in the feedback regulation of the mammalian signalling network

Mechanisms underlying divergent relationships between Ca2+ and YAP/TAZ signalling

Yes-associated protein (YAP) and its homologue TAZ are transducers of several biochemical and biomechanical signals, integrating multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation and migration. Emerging evidence suggests that Ca2+ is a key second messenger that connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: in some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others, an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+ -mediated YAP/TAZ signalling to investigate how temporal dynamics and crosstalk of signalling pathways interacting with Ca2+ can alter the YAP/TAZ response, as observed in experiments. By including six signalling modules (e.g. GPCR, IP3-Ca2+ , kinases, RhoA, F-actin and Hippo-YAP/TAZ) that interact with Ca2+ , we investigated both transient and steady-state cell response to angiotensin II and thapsigargin stimuli. The model predicts that stimuli, Ca2+ transients and frequency-dependent relationships between Ca2+ and YAP/TAZ are primarily mediated by cPKC, DAG, CaMKII and F-actin. Simulation results illustrate the role of Ca2+ dynamics and CaMKII bistable response in switching the direction of changes in Ca2+ -induced YAP/TAZ activity. A frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. This study provides new insights into underlying mechanisms responsible for the controversial Ca2+ -YAP/TAZ relationship observed in experiments. KEY POINTS: YAP/TAZ integrates biochemical and biomechanical inputs to regulate cellular functions, and Ca2+ acts as a key second messenger linking cellular inputs to YAP/TAZ. Studies have reported contradictory Ca2+ -YAP/TAZ relationships for different cell types and stimuli. A network model of Ca2+ -mediated YAP/TAZ signalling was developed to investigate the underlying mechanisms of divergent Ca2+ -YAP/TAZ relationships. The model predicts context-dependent Ca2+ transient, CaMKII bistable response and frequency-dependent activation of LATS1/2 upstream regulators as mechanisms governing the Ca2+ -YAP/TAZ relationship. This study provides new insights into the underlying mechanisms of the controversial Ca2+ -YAP/TAZ relationship to better understand the dynamics of cellular functions controlled by YAP/TAZ activity.

Stochastic Modelling of HIV-1 Replication in a CD4 T Cell with an IFN Response

A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of viral replication. The model includes viral replication inhibition by interferon-induced antiviral factors and their inactivation by the viral proteins Vpu and Vif. Both deterministic and stochastic model formulations are presented. The stochastic model was used to predict efficiency of IFN-I-induced suppression of viral replication in different initial conditions for autocrine and paracrine effects. The probability of virion excretion for various MOIs and various amounts of IFN-I was evaluated and the statistical properties of the heterogeneity of HIV-1 and IFN-I production characterised.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling

Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-β/SMAD signaling encodes various cell fates, controls tissue homeostasis and is deregulated in diseases such as cancer. The pathway shows strong heterogeneity at the single-cell level, but quantitative insights into mechanisms underlying fluctuations at various time scales are still missing, partly due to inefficiency in the calibration of stochastic models that mechanistically describe signaling processes. In this work we analyze single-cell TGF-β/SMAD signaling and show that it exhibits temporal stochastic bursts which are dose-dependent and whose number and magnitude correlate with cell migration. We propose a stochastic modeling approach to mechanistically describe these pathway fluctuations with high computational efficiency. Employing high-order numerical integration and fitting to burst statistics we enable efficient quantitative parameter estimation and discriminate models that assume noise in different reactions at the receptor level. This modeling approach suggests that stochasticity in the internalization of TGF-β receptors into endosomes plays a key role in the observed temporal bursting. Further, the model predicts the single-cell dynamics of TGF-β/SMAD signaling in untested conditions, e.g., successfully reflects memory effects of signaling noise and cellular sensitivity towards repeated stimulation. Taken together, our computational framework based on burst analysis, noise modeling and path computation scheme is a suitable tool for the data-based modeling of complex signaling pathways, capable of identifying the source of temporal noise.

Fluctuations in molecular networks give rise to heterogeneity in cellular behavior and therefore promote the diversification of tissues. For a better understanding of cellular decision making, it is important to identify sources of molecular fluctuations and to quantitatively describe them by predictive mathematical models. In this work, we focused on temporal fluctuations of the TGF-β signaling pathway that is important for controlling cell division and migration.

We characterized a single-cell dataset comprising hundreds of cells using time series analysis and a large-scale stochastic model. By fitting several model variants to the data, we identified the stochastic internalization of cell surface receptors into endosomes as a main source of temporal fluctuations (’bursts’) in the signaling pathway. The corresponding model accurately predicted novel experimental data, and provided insights into the long-term memory of signaling fluctuations. In summary, we propose a modeling approach to quantitatively describe heterogeneous behavior in large-scale single-cell datasets and to identify the underlying biological mechanisms.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

Molecular noise filtering in the β-adrenergic signaling network by phospholamban pentamers

Phospholamban (PLN) is an important regulator of cardiac calcium handling due to its ability to inhibit the calcium ATPase SERCA. β-Adrenergic stimulation reverses SERCA inhibition via PLN phosphorylation and facilitates fast calcium reuptake. PLN also forms pentamers whose physiological significance has remained elusive. Using mathematical modeling combined with biochemical and cell biological experiments, we show that pentamers regulate both the dynamics and steady-state levels of monomer phosphorylation. Substrate competition by pentamers and a feed-forward loop involving inhibitor-1 can delay monomer phosphorylation by protein kinase A (PKA), whereas cooperative pentamer dephosphorylation enables bistable PLN steady-state phosphorylation. Simulations show that phosphorylation delay and bistability act as complementary filters that reduce the effect of random fluctuations in PKA activity, thereby ensuring consistent monomer phosphorylation and SERCA activity despite noisy upstream signals. Preliminary analyses suggest that the PLN mutation R14del could impair noise filtering, offering a new perspective on how this mutation causes cardiac arrhythmias.

Cauliflower fractal forms arise from perturbations of floral gene networks

Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the "memory" of their transient passage in a floral state. Additional mutations affecting meristem growth can induce the production of conical structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics.

Integrated in silico and 3D in vitro model of macrophage migration in response to physical and chemical factors in the tumor microenvironment

Macrophages are abundant in the tumor microenvironment (TME), serving as accomplices to cancer cells for their invasion. Studies have explored the biochemical mechanisms that drive pro-tumor macrophage functions; however the role of TME interstitial flow (IF) is often disregarded. Therefore, we developed a three-dimensional microfluidic-based model with tumor cells and macrophages to study how IF affects macrophage migration and its potential contribution to cancer invasion. The presence of either tumor cells or IF individually increased macrophage migration directedness and speed. Interestingly, there was no additive effect on macrophage migration directedness and speed under the simultaneous presence of tumor cells and IF. Further, we present an in silico model that couples chemokine-mediated signaling with mechanosensing networks to explain our in vitro observations. In our model design, we propose IL-8, CCL2, and β-integrin as key pathways that commonly regulate various Rho GTPases. In agreement, in vitro macrophage migration remained elevated when exposed to a saturating concentration of recombinant IL-8 or CCL2 or to the co-addition of a sub-saturating concentration of both cytokines. Moreover, antibody blockade against IL-8 and/or CCL2 inhibited migration that could be restored by IF, indicating cytokine-independent mechanisms of migration induction. Importantly, we demonstrate the utility of an integrated in silico and 3D in vitro approach to aid the design of tumor-associated macrophage-based immunotherapeutic strategies.

Signaling pathways have an inherent need for noise to acquire information

BACKGROUND

All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways. Such pathways rely on reversible binding interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell's interior. These interactions are inherently stochastic and thus noisy. On the one hand, noise can cause a signaling pathway to produce the same response for different stimuli, which reduces the amount of information a pathway acquires. On the other hand, in processes such as stochastic resonance, noise can improve the detection of weak stimuli and thus the acquisition of information. It is not clear whether the kinetic parameters that determine a pathway's operation cause noise to reduce or increase the acquisition of information.

RESULTS

We analyze how the kinetic properties of the reversible binding interactions used by signaling pathways affect the relationship between noise, the response to a signal, and information acquisition. Our results show that, under a wide range of biologically sensible parameter values, a noisy dynamic of reversible binding interactions is necessary to produce distinct responses to different stimuli. As a consequence, noise is indispensable for the acquisition of information in signaling pathways.

CONCLUSIONS

Our observations go beyond previous work by showing that noise plays a positive role in signaling pathways, demonstrating that noise is essential when such pathways acquire information.

Computational modeling reveals MAP3K8 as mediator of resistance to vemurafenib in thyroid cancer stem cells

MOTIVATION

Val600Glu (V600E) mutation is the most common BRAF mutation detected in thyroid cancer. Hence, recent research efforts have been performed trying to explore several inhibitors of the V600E mutation-containing BRAF kinase as potential therapeutic options in thyroid cancer refractory to standard interventions. Among them, vemurafenib is a selective BRAF inhibitor approved by Food and Drug Administration for clinical practice. Unfortunately, vemurafenib often displays limited efficacy in poorly differentiated and anaplastic thyroid carcinomas probably because of intrinsic and/or acquired resistance mechanisms. In this view, cancer stem cells (CSCs) may represent a possible mechanism of resistance to vemurafenib, due to their self-renewal and chemo resistance properties.

RESULTS

We present a computational framework to suggest new potential targets to overcome drug resistance. It has been validated with an in vitro model based upon a spheroid-forming method able to isolate thyroid CSCs that may mimic resistance to vemurafenib. Indeed, vemurafenib did not inhibit cell proliferation of BRAF V600E thyroid CSCs, but rather stimulated cell proliferation along with a paradoxical over-activation of ERK and AKT pathways. The computational model identified a fundamental role of mitogen-activated protein kinase 8 (MAP3K8), a serine/threonine kinase expressed in thyroid CSCs, in mediating this drug resistance. To confirm model prediction, we set a suitable in vitro experiment revealing that the treatment with MAP3K8 inhibitor restored the effect of vemurafenib in terms of both DNA fragmentation and poly (ADP-ribose) polymerase cleavage (apoptosis) in thyroid CSCs. Moreover, MAP3K8 expression levels may be a useful marker to predict the response to vemurafenib.

AVAILABILITY AND IMPLEMENTATION

The model is available in GitHub repository visiting the following URL: https://github.com/francescopappalardo/MAP3K8-Thyroid-Spheres-V-3.0.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Neural Differentiation Dynamics Controlled by Multiple Feedback Loops in a Comprehensive Molecular Interaction Network

Mathematical model simulation is a useful method for understanding the complex behavior of a living system. The construction of mathematical models using comprehensive information is one of the techniques of model construction. Such a comprehensive knowledge-based network tends to become a large-scale network. As a result, the variation of analyses is limited to a particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we propose a contractive method that preserves the dynamic behavior of a large network. The method consists of the following two steps: comprehensive network building and network reduction. The reduction phase can extract network loop structures from a large-scale regulatory network, and the subnetworks were combined to preserve the dynamics of the original large-scale network. We confirmed that the extracted loop combination reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of the overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop, which has not been focused on. The model extracted by our method has the potential to reveal the critical mechanisms of neural differentiation. The method is applicable to other biological events.

ProTargetMiner as a proteome signature library of anticancer molecules for functional discovery

Deconvolution of targets and action mechanisms of anticancer compounds is fundamental in drug development. Here, we report on ProTargetMiner as a publicly available expandable proteome signature library of anticancer molecules in cancer cell lines. Based on 287 A549 adenocarcinoma proteomes affected by 56 compounds, the main dataset contains 7,328 proteins and 1,307,859 refined protein-drug pairs. These proteomic signatures cluster by compound targets and action mechanisms. The targets and mechanistic proteins are deconvoluted by partial least square modeling, provided through the website http://protargetminer.genexplain.com. For 9 molecules representing the most diverse mechanisms and the common cancer cell lines MCF-7, RKO and A549, deep proteome datasets are obtained. Combining data from the three cell lines highlights common drug targets and cell-specific differences. The database can be easily extended and merged with new compound signatures. ProTargetMiner serves as a chemical proteomics resource for the cancer research community, and can become a valuable tool in drug discovery.

Anticancer drugs often have widespread effects on the cellular proteome. Here, the authors generate a proteome signature library of drug-treated cancer cell lines and develop a software tool to deconvolute drug targets and gain insights into their mechanisms of action.

Of Gene Expression and Cell Division Time: A Mathematical Framework for Advanced Differential Gene Expression and Data Analysis

Estimating fold changes of average mRNA and protein molecule counts per cell is the most common way to perform differential expression analysis. However, these gene expression data may be affected by cell division, an often-neglected phenomenon. Here, we develop a quantitative framework that links population-based mRNA and protein measurements to rates of gene expression in single cells undergoing cell division. The equations we derive are easy-to-use and widely robust against biological variability. They integrate multiple "omics" data into a coherent, quantitative description of single-cell gene expression and improve analysis when comparing systems or states with different cell division times. We explore these ideas in the context of resting versus activated B cells. Analyzing differences in protein synthesis rates enables to account for differences in cell division times. We demonstrate that this improves the resolution and hit rate of differential gene expression analysis when compared to analyzing population protein abundances alone.

Mathematical model identifies effective P53 accumulation with target gene binding affinity in DNA damage response for cell fate decision

Functional p53 signaling is essential for appropriate responses to diverse stimuli. P53 dynamics employs the information from the stimulus leading to selective gene expression and cell fate decision. However, the decoding mechanism of p53 dynamics under DNA damage challenge remains poorly understood. Here we mathematically modeled the recently dual-phase p53 dynamics under doxorubicin treatment. We found that p53 could perform sequential pulses followed by a high-amplitude terminal pulse at relatively low doxorubicin treatment, whereas p53 became steadily accumulated when damage level was high. The effective p53 integral above a threshold but not the absolute accumulation of p53 precisely discriminated survival and death. Silencing negative regulators in p53 network might promote the occurrence of terminal pulse. Furthermore, lower binding affinity and degradation rate of p53 target genes could favorably discriminate high and low dose doxorubicin treatment. Grouping by temporal profiles suggested that the p53 dynamics rather than the doxorubicin doses could better discriminate cellular outcomes and confer less variation for effective p53 integral reemphasizing the importance of p53 level regulation. Our model has established a theoretical framework that p53 dynamics can work cooperatively with its binding affinity to target genes leading to cell fate choice, providing new clues of optimized clinical design by manipulating p53 dynamics.

A System-wide Approach to Monitor Responses to Synergistic BRAF and EGFR Inhibition in Colorectal Cancer Cells

Intrinsic and/or acquired resistance represents one of the great challenges in targeted cancer therapy. A deeper understanding of the molecular biology of cancer has resulted in more efficient strategies, where one or multiple drugs are adopted in novel therapies to tackle resistance. This beneficial effect of using combination treatments has also been observed in colorectal cancer patients harboring the BRAF(V600E) mutation, whereby dual inhibition of BRAF(V600E) and EGFR increases antitumor activity. Notwithstanding this success, it is not clear whether this combination treatment is the only or most effective treatment to block intrinsic resistance to BRAF inhibitors. Here, we investigate molecular responses upon single and multi-target treatments, over time, using BRAF(V600E) mutant colorectal cancer cells as a model system. Through integration of transcriptomic, proteomic and phosphoproteomics data we obtain a comprehensive overview, revealing both known and novel responses. We primarily observe widespread up-regulation of receptor tyrosine kinases and metabolic pathways upon BRAF inhibition. These findings point to mechanisms by which the drug-treated cells switch energy sources and enter a quiescent-like state as a defensive response, while additionally compensating for the MAPK pathway inhibition.

Continuous Petri Nets and microRNA Analysis in Melanoma

Personalized target therapies represent one of the possible treatment strategies to fight the ongoing battle against cancer. New treatment interventions are still needed for an effective and successful cancer therapy. In this scenario, we simulated and analyzed the dynamics of BRAF V600E melanoma patients treated with BRAF inhibitors in order to find potentially interesting targets that may make standard treatments more effective in particularly aggressive tumors that may not respond to selective inhibitor drugs. To this aim, we developed a continuous Petri Net model that simulates fundamental signalling cascades involved in melanoma development, such as MAPK and PI3K/AKT, in order to deeply analyze these complex kinase cascades and predict new crucial nodes involved in melanomagenesis. The model pointed out that some microRNAs, like hsa-mir-132, downregulates expression levels of p120RasGAP: under high concentrations of p120RasGAP, MAPK pathway activation is significantly decreased and consequently also PI3K/PDK1/AKT activation. Furthermore, our analysis carried out through the Genomic Data Commons (GDC) Data Portal shows the evidence that hsa-mir-132 is significantly associated with clinical outcome in melanoma cancer genomic data sets of BRAF-mutated patients. In conclusion, targeting miRNAs through antisense oligonucleotides technology may suggest the way to enhance the action of BRAF-inhibitors.

Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction

The spatial architecture of signaling pathways and the interaction with cell size and morphology are complex, but little understood. With the advances of single cell imaging and single cell biology, it becomes crucial to understand intracellular processes in time and space. Activation of cell surface receptors often triggers a signaling cascade including the activation of membrane-attached and cytosolic signaling components, which eventually transmit the signal to the cell nucleus. Signaling proteins can form steep gradients in the cytosol, which cause strong cell size dependence. We show that the kinetics at the membrane-cytosolic interface and the ratio of cell membrane area to the enclosed cytosolic volume change the behavior of signaling cascades significantly. We suggest an estimate of average concentration for arbitrary cell shapes depending on the cell volume and cell surface area. The normalized variance, known from image analysis, is suggested as an alternative measure to quantify the deviation from the average concentration. A mathematical analysis of signal transduction in time and space is presented, providing analytical solutions for different spatial arrangements of linear signaling cascades. Quantification of signaling time scales reveals that signal propagation is faster at the membrane than at the nucleus, while this time difference decreases with the number of signaling components in the cytosol. Our investigations are complemented by numerical simulations of non-linear cascades with feedback and asymmetric cell shapes. We conclude that intracellular signal propagation is highly dependent on cell geometry and, thereby, conveys information on cell size and shape to the nucleus.

Cell-specific responses to the cytokine TGFβ are determined by variability in protein levels

The cytokine TGFβ provides important information during embryonic development, adult tissue homeostasis, and regeneration. Alterations in the cellular response to TGFβ are involved in severe human diseases. To understand how cells encode the extracellular input and transmit its information to elicit appropriate responses, we acquired quantitative time-resolved measurements of pathway activation at the single-cell level. We established dynamic time warping to quantitatively compare signaling dynamics of thousands of individual cells and described heterogeneous single-cell responses by mathematical modeling. Our combined experimental and theoretical study revealed that the response to a given dose of TGFβ is determined cell specifically by the levels of defined signaling proteins. This heterogeneity in signaling protein expression leads to decomposition of cells into classes with qualitatively distinct signaling dynamics and phenotypic outcome. Negative feedback regulators promote heterogeneous signaling, as a SMAD7 knock-out specifically affected the signal duration in a subpopulation of cells. Taken together, we propose a quantitative framework that allows predicting and testing sources of cellular signaling heterogeneity.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Signaling Architectures that Transmit Unidirectional Information Despite Retroactivity

A signaling pathway transmits information from an upstream system to downstream systems, ideally in a unidirectional fashion. A key obstacle to unidirectional transmission is retroactivity, the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the fundamental question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general procedure based on mathematical analysis that provides an answer to this question. Using this procedure, we analyze the ability of a variety of signaling architectures to transmit one-way (from upstream to downstream) signals, as key biological parameters are tuned. We find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show a stringent design tradeoff that hampers their ability to overcome retroactivity. Interestingly, cascades of these architectures, which are highly represented in nature, can overcome this tradeoff and thus enable unidirectional transmission. By contrast, phosphotransfer systems, and single and double phosphorylation cycles that transmit signals from a substrate, are unable to mitigate retroactivity effects, even when cascaded, and hence are not well suited for unidirectional information transmission. These results are largely independent of the specific reaction-rate constant values, and depend on the topology of the architectures. Our results therefore identify signaling architectures that, allowing unidirectional transmission of signals, embody modular processes that conserve their input/output behavior across multiple contexts. These findings can be used to decompose natural signal transduction networks into modules, and at the same time, they establish a library of devices that can be used in synthetic biology to facilitate modular circuit design.

Operating regimes of covalent modification cycles at high enzyme concentrations

The Goldbeter-Koshland model has been a paradigm for ultrasensitivity in biological networks for more than 30 years. Despite its simplicity the validity of this model is restricted to conditions when the substrate is in excess over the converter enzymes - a condition that is easy to satisfy in vitro, but which is rarely satisfied in vivo. Here, we analyze the Goldbeter-Koshland model by means of the total quasi-steady state approximation which yields a comprehensive classification of the steady state operating regimes under conditions when the enzyme concentrations are comparable to or larger than that of the substrate. Where possible we derive simple expressions characterizing the input-output behavior of the system. Our analysis suggests that enhanced sensitivity occurs if the concentration of at least one of the converter enzymes is smaller (but not necessarily much smaller) than that of the substrate and if that enzyme is saturated. Conversely, if both enzymes are saturated and at least one of the enzyme concentrations exceeds that of the substrate the system exhibits concentration robustness with respect to changes in that enzyme concentration. Also, depending on the enzyme's saturation degrees and the ratio between their maximal reaction rates the total fraction of phosphorylated substrate may increase, decrease or change nonmonotonically as a function of the total substrate concentration. The latter finding may aid the interpretation of experiments involving genetic perturbations of enzyme and substrate abundances.

An immediate-late gene expression module decodes ERK signal duration

The RAF‐MEK‐ERK signalling pathway controls fundamental, often opposing cellular processes such as proliferation and apoptosis. Signal duration has been identified to play a decisive role in these cell fate decisions. However, it remains unclear how the different early and late responding gene expression modules can discriminate short and long signals. We obtained both protein phosphorylation and gene expression time course data from HEK293 cells carrying an inducible construct of the proto‐oncogene RAF. By mathematical modelling, we identified a new gene expression module of immediate–late genes (ILGs) distinct in gene expression dynamics and function. We find that mRNA longevity enables these ILGs to respond late and thus translate ERK signal duration into response amplitude. Despite their late response, their GC‐rich promoter structure suggested and metabolic labelling with 4SU confirmed that transcription of ILGs is induced immediately. A comparative analysis shows that the principle of duration decoding is conserved in PC12 cells and MCF7 cells, two paradigm cell systems for ERK signal duration. Altogether, our findings suggest that ILGs function as a gene expression module to decode ERK signal duration.

Vertebrate Cryptochromes are Vestigial Flavoproteins

All cryptochromes are currently classified as flavoproteins. In animals their best-described role is as components of the circadian clock. This circadian function is variable, and can be either light-dependent or -independent; the molecular origin of this difference is unknown. Type I animal cryptochromes are photoreceptors that entrain an organism's clock to its environment, whereas Type II (including mammals) regulate circadian timing in a light-independent manner. Here, we reveal that, in contrast to Type I, Type II animal cryptochromes lack the structural features to securely bind the photoactive flavin cofactor. We provide a molecular basis for the distinct circadian roles of different animal cryptochromes, which also has significant implications for the putative role of Type II cryptochromes in animal photomagnetoreception.

A new efficient approach to fit stochastic models on the basis of high-throughput experimental data using a model of IRF7 gene expression as case study

Background

Mathematical models are used to gain an integrative understanding of biochemical processes and networks. Commonly the models are based on deterministic ordinary differential equations. When molecular counts are low, stochastic formalisms like Monte Carlo simulations are more appropriate and well established. However, compared to the wealth of computational methods used to fit and analyze deterministic models, there is only little available to quantify the exactness of the fit of stochastic models compared to experimental data or to analyze different aspects of the modeling results.

Results

Here, we developed a method to fit stochastic simulations to experimental high-throughput data, meaning data that exhibits distributions. The method uses a comparison of the probability density functions that are computed based on Monte Carlo simulations and the experimental data. Multiple parameter values are iteratively evaluated using optimization routines. The method improves its performance by selecting parameters values after comparing the similitude between the deterministic stability of the system and the modes in the experimental data distribution. As a case study we fitted a model of the IRF7 gene expression circuit to time-course experimental data obtained by flow cytometry. IRF7 shows bimodal dynamics upon IFN stimulation. This dynamics occurs due to the switching between active and basal states of the IRF7 promoter. However, the exact molecular mechanisms responsible for the bimodality of IRF7 is not fully understood.

Conclusions

Our results allow us to conclude that the activation of the IRF7 promoter by the combination of IRF7 and ISGF3 is sufficient to explain the observed bimodal dynamics.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0406-4) contains supplementary material, which is available to authorized users.

Exosomal miRs in Lung Cancer: A Mathematical Model

Lung cancer, primarily non-small-cell lung cancer (NSCLC), is the leading cause of cancer deaths in the United States and worldwide. While early detection significantly improves five-year survival, there are no reliable diagnostic tools for early detection. Several exosomal microRNAs (miRs) are overexpressed in NSCLC, and have been suggested as potential biomarkers for early detection. The present paper develops a mathematical model for early stage of NSCLC with emphasis on the role of the three highest overexpressed miRs, namely miR-21, miR-205 and miR-155. Simulations of the model provide quantitative relationships between the tumor volume and the total mass of each of the above miRs in the tumor. Because of the positive correlation between these miRs in the tumor tissue and in the blood, the results of the paper may be viewed as a first step toward establishing a combination of miRs 21, 205, 155 and possibly other miRs as serum biomarkers for early detection of NSCLC.

Regulation of HBEGF by Micro-RNA for Survival of Developing Human Trophoblast Cells

Introduction

The growth factor HBEGF is upregulated post-transcriptionally in the low O₂ environment of the human placenta during the first 10 weeks of pregnancy. We have examined the possible roles of HBEGF turnover and micro-RNA (miRNA) in its regulation by O₂ in human first trimester trophoblast.

Methods

HTR-8/SVneo trophoblast cells were cultured at 2% or 20% O₂. The cells were transfected with a dual luciferase reporter construct (psiCHECK-2) containing no insert (control), the HBEGF 3’ untranslated region (3’UTR), or sub-regions of the 3’UTR, as well as with siRNA for DGCR8. RNA was extracted from trophoblast cells cultured at 2% O₂ for 0–4 h for next-generation sequencing. HBEGF was quantified by ELISA. HBEGF, DGCR8, and β–actin were examined by western blotting.

Results

Protein turnover studies, using 10 μg/ml cyclohexamide, 1 μg/ml lactocystin, or 100 μg/ml MG132, demonstrated faster HBEGF degradation at 20% O₂ than 2% O₂, mediated by the proteasome. However, proteasome inhibition failed to initiate HBEGF accumulation at 20% O₂. Reporter assays, comparing to empty vector, demonstrated that the intact HBEGF 3’ UTR inhibited expression (0.26), while fragments containing only its flanking regions increased reporter activity (3.15; 3.43). No differential expression of miRNAs was found in trophoblast cells cultured at 2% and 20% O₂. Nevertheless, HBEGF upregulation at 2% O₂ was blocked when the miRNA-processing protein DGCR8 was silenced, suggesting a role for miRNA.

Conclusion

Our findings suggest involvement of flanking regions of the 3’UTR in activating HBEGF protein synthesis in response to 2% O₂, possibly through a miRNA-mediated mechanism.

How time delay and network design shape response patterns in biochemical negative feedback systems

BACKGROUND

Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks.

RESULTS

We investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not.

CONCLUSIONS

Our theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.

Conservation of protein abundance patterns reveals the regulatory architecture of the EGFR-MAPK pathway

Various genetic mutations associated with cancer are known to alter cell signaling, but it is not clear whether they dysregulate signaling pathways by altering the abundance of pathway proteins. Using a combination of RNA sequencing and ultrasensitive targeted proteomics, we defined the primary components-16 core proteins and 10 feedback regulators-of the epidermal growth factor receptor (EGFR)-mitogen-activated protein kinase (MAPK) pathway in normal human mammary epithelial cells and then quantified their absolute abundance across a panel of normal and breast cancer cell lines as well as fibroblasts. We found that core pathway proteins were present at very similar concentrations across all cell types, with a variance similar to that of proteins previously shown to display conserved abundances across species. In contrast, EGFR and transcriptionally controlled feedback regulators were present at highly variable concentrations. The absolute abundance of most core proteins was between 50,000 and 70,000 copies per cell, but the adaptors SOS1, SOS2, and GAB1 were found at far lower amounts (2000 to 5000 copies per cell). MAPK signaling showed saturation in all cells between 3000 and 10,000 occupied EGFRs, consistent with the idea that adaptors limit signaling. Our results suggest that the relative stoichiometry of core MAPK pathway proteins is very similar across different cell types, with cell-specific differences mostly restricted to variable amounts of feedback regulators and receptors. The low abundance of adaptors relative to EGFR could be responsible for previous observations that only a fraction of total cell surface EGFR is capable of rapid endocytosis, high-affinity binding, and mitogenic signaling.

The role of time delay in adaptive cellular negative feedback systems

Adaptation in cellular systems is often mediated by negative feedbacks, which usually come with certain time delays causing several characteristic response patterns including an overdamped response, damped or sustained oscillations. Here, we analyse generic two-dimensional delay differential equations with delayed negative feedback describing the dynamics of biochemical adaptive signal-response networks. We derive explicit thresholds and boundaries showing how time delay determines characteristic response patterns of these networks. Applying our theoretical analyses to concrete data we show that adaptation to osmotic stress in yeast is optimal in the sense of minimizing adaptation time without causing oscillatory behaviour, i.e., a critically damped response. In addition, our framework demonstrates that a slight increase of time delay in the NF-κB system might induce a switch from damped to sustained oscillatory behaviour. Thus, we demonstrate how delay differential equations can be used to explicitly study the delay in biochemical negative feedback systems. Our analysis also provides insight into how time delay may tune biological signal-response patterns and control the systems behaviour.

The whole-genome expression analysis of peripheral blood mononuclear cells from aspirin sensitive asthmatics versus aspirin tolerant patients and healthy donors after in vitro aspirin challenge

Background

Up to 30 % of adults with severe asthma are hypersensitive to aspirin and no unambiguous theory exists which provides a satisfactory explanation for the occurrence of aspirin-induced asthma (AIA) in some asthmatic patients. Therefore, the aim of this study was to compare the AIA expression profile against aspirin tolerant asthma (ATA) and healthy volunteers (HV) profile in peripheral blood mononuclear cells (PBMCs) after in vitro aspirin challenge in Caucasian population.

Methods

PBMCs were separated from blood of three groups of subjects - 11 AIA, 7 ATA and 15 HV and then stimulated by either 2 μM lysine aspirin or 20 μM lysine as a control. Subsequently, RNA was isolated, transcribed into cDNA and subjected to microarray and qPCR studies. Simultaneously, protein was extracted from PBMCs and used in further immunoblotting analysis.

Results

The validation of results at mRNA level has shown only three genes, whose expression was significantly altered between comprising groups. mRNA expression of CNPY3 in PBMCs in AIA was significantly lower (-0.41 ± 2.67) than in HV (1.04 ± 2.69), (p = 0.02); mRNA expression of FOSL1 in PBMCs in AIA was also significantly decreased (-0.66 ± 2.97) as opposed to HV (0.31 ± 4.83), (p = 0.02). While mRNA expression of ERAS in PBMCs was increased (1.15 ± 0.23) in AIA in comparison to HV (-1.32 ± 0.41), (p = 0.03). At protein level the changed expression of one protein was confirmed. Protein expression of FOSL1 in PBMCs in AIA was both significantly lower (-0.86 ± 0.08) than in ATA (0.39 ± 0.42), (p = 0.046) and in HV (0.9 ± 0.27), (p = 0.007).

Conclusions

This pilot study implies a positive association between CNPY3, ERAS, FOSL1 and aspirin-intolerant asthma, suggesting that these findings would be useful for further investigations of NSAIDs mechanism.

Electronic supplementary material

The online version of this article (doi:10.1186/s12931-015-0305-4) contains supplementary material, which is available to authorized users.

Systems toxicology identifies mechanistic impacts of 2-amino-4,6-dinitrotoluene (2A-DNT) exposure in Northern Bobwhite

Background

A systems toxicology investigation comparing and integrating transcriptomic and proteomic results was conducted to develop holistic effects characterizations for the wildlife bird model, Northern bobwhite (Colinus virginianus) dosed with the explosives degradation product 2-amino-4,6-dinitrotoluene (2A-DNT). A subchronic 60d toxicology bioassay was leveraged where both sexes were dosed via daily gavage with 0, 3, 14, or 30 mg/kg-d 2A-DNT. Effects on global transcript expression were investigated in liver and kidney tissue using custom microarrays for C. virginianus in both sexes at all doses, while effects on proteome expression were investigated in liver for both sexes and kidney in males, at 30 mg/kg-d.

Results

As expected, transcript expression was not directly indicative of protein expression in response to 2A-DNT. However, a high degree of correspondence was observed among gene and protein expression when investigating higher-order functional responses including statistically enriched gene networks and canonical pathways, especially when connected to toxicological outcomes of 2A-DNT exposure. Analysis of networks statistically enriched for both transcripts and proteins demonstrated common responses including inhibition of programmed cell death and arrest of cell cycle in liver tissues at 2A-DNT doses that caused liver necrosis and death in females. Additionally, both transcript and protein expression in liver tissue was indicative of induced phase I and II xenobiotic metabolism potentially as a mechanism to detoxify and excrete 2A-DNT. Nuclear signaling assays, transcript expression and protein expression each implicated peroxisome proliferator-activated receptor (PPAR) nuclear signaling as a primary molecular target in the 2A-DNT exposure with significant downstream enrichment of PPAR-regulated pathways including lipid metabolic pathways and gluconeogenesis suggesting impaired bioenergetic potential.

Conclusion

Although the differential expression of transcripts and proteins was largely unique, the consensus of functional pathways and gene networks enriched among transcriptomic and proteomic datasets provided the identification of many critical metabolic functions underlying 2A-DNT toxicity as well as impaired PPAR signaling, a key molecular initiating event known to be affected in di- and trinitrotoluene exposures.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1798-4) contains supplementary material, which is available to authorized users.

Systems biology of IL-6, IL-12 family cytokines

Interleukin-6-type cytokines play important roles in the communication between cells of multicellular organisms. They are involved in the regulation of complex cellular processes such as proliferation and differentiation and act as key player during inflammation and immune response. A major challenge is to understand how these complex non-linear processes are connected and regulated. Systems biology approaches are used to tackle this challenge in an iterative process of quantitative experimental and mathematical analyses. Here we review quantitative experimental studies and systems biology approaches dealing with the function of Interleukin-6-type cytokines in physiological and pathophysiological conditions. These approaches cover the analyses of signal transduction on a cellular level up to pharmacokinetic and pharmacodynamic studies on a whole organism level.

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

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.

Intrinsically disordered segments affect protein half-life in the cell and during evolution

Precise control of protein turnover is essential for cellular homeostasis. The ubiquitin-proteasome system is well established as a major regulator of protein degradation, but an understanding of how inherent structural features influence the lifetimes of proteins is lacking. We report that yeast, mouse, and human proteins with terminal or internal intrinsically disordered segments have significantly shorter half-lives than proteins without these features. The lengths of the disordered segments that affect protein half-life are compatible with the structure of the proteasome. Divergence in terminal and internal disordered segments in yeast proteins originating from gene duplication leads to significantly altered half-life. Many paralogs that are affected by such changes participate in signaling, where altered protein half-life will directly impact cellular processes and function. Thus, natural variation in the length and position of disordered segments may affect protein half-life and could serve as an underappreciated source of genetic variation with important phenotypic consequences.

Protein synthesis rate is the predominant regulator of protein expression during differentiation

The contribution of transcription, protein synthesis and degradation rates to the control of protein expression during differentiation was analyzed using quantitative proteomics and transcriptomics data. Protein synthesis rate was identified as the main determinant of protein expression.

The lack of correlation usually observed between transcript and protein levels can be fully explained when correcting for the synthesis and degradation rates of the individual proteins.

Synthesis rates for individual proteins are extensively regulated, in contrast to degradation rates that mostly remain constant in response to differentiation.

The modularity of macromolecular complexes is maintained during synthesis and degradation of the complexes.

External perturbations, by forcing cells to adapt to a new environment, often elicit large-scale changes in gene expression resulting in an altered proteome that improves the cell's fitness in the new conditions. Steady-state levels of a proteome depend on transcription, the levels of transcripts, translation and protein degradation but system-level contribution that each of these processes make to the final protein expression change has yet to be explored. We therefore applied a systems biology approach to characterize the regulation of protein expression during cellular differentiation using quantitative proteomics. As a general rule, it seems that protein expression during cellular differentiation is largely controlled by changes in the relative synthesis rate, whereas the relative degradation rate of the majority of proteins stays constant. In these data, we also observe that the proteins in defined sub-structures of larger protein complexes tend to have highly correlated synthesis and degradation rates but that this does not necessarily extend to the holo-complex. Finally, we provide strong evidence that the generally poor correlation observed between transcript and protein levels can fully be explained once the protein synthesis and degradation rates are taken into account.

Altered dynamics of a lipid raft associated protein in a kidney model of Fabry disease

Accumulation of globotriaosylceramide (Gb3) and other neutral glycosphingolipids with galactosyl residues is the hallmark of Fabry disease, a lysosomal storage disorder caused by deficiency of the enzyme alpha-galactosidase A (α-gal A). These lipids are incorporated into the plasma membrane and intracellular membranes, with a preference for lipid rafts. Disruption of raft mediated cell processes is implicated in the pathogenesis of several human diseases, but little is known about the effects of the accumulation of glycosphingolipids on raft dynamics in the context of Fabry disease. Using siRNA technology, we have generated a polarized renal epithelial cell model of Fabry disease in Madin-Darby canine kidney cells. These cells present increased levels of Gb3 and enlarged lysosomes, and progressively accumulate zebra bodies. The polarized delivery of both raft-associated and raft-independent proteins was unaffected by α-gal A knockdown, suggesting that accumulation of Gb3 does not disrupt biosynthetic trafficking pathways. To assess the effect of α-gal A silencing on lipid raft dynamics, we employed number and brightness (N&B) analysis to measure the oligomeric status and mobility of the model glycosylphosphatidylinositol (GPI)-anchored protein GFP-GPI. We observed a significant increase in the oligomeric size of antibody-induced clusters of GFP-GPI at the plasma membrane of α-gal A silenced cells compared with control cells. Our results suggest that the interaction of GFP-GPI with lipid rafts may be altered in the presence of accumulated Gb3. The implications of our results with respect to the pathogenesis of Fabry disease are discussed.

Towards a comprehensive picture of the genetic landscape of complex traits

The formation of phenotypic traits, such as biomass production, tumor volume and viral abundance, undergoes a complex process in which interactions between genes and developmental stimuli take place at each level of biological organization from cells to organisms. Traditional studies emphasize the impact of genes by directly linking DNA-based markers with static phenotypic values. Functional mapping, derived to detect genes that control developmental processes using growth equations, has proven powerful for addressing questions about the roles of genes in development. By treating phenotypic formation as a cohesive system using differential equations, a different approach-systems mapping-dissects the system into interconnected elements and then map genes that determine a web of interactions among these elements, facilitating our understanding of the genetic machineries for phenotypic development. Here, we argue that genetic mapping can play a more important role in studying the genotype-phenotype relationship by filling the gaps in the biochemical and regulatory process from DNA to end-point phenotype. We describe a new framework, named network mapping, to study the genetic architecture of complex traits by integrating the regulatory networks that cause a high-order phenotype. Network mapping makes use of a system of differential equations to quantify the rule by which transcriptional, proteomic and metabolomic components interact with each other to organize into a functional whole. The synthesis of functional mapping, systems mapping and network mapping provides a novel avenue to decipher a comprehensive picture of the genetic landscape of complex phenotypes that underlie economically and biomedically important traits.

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.

Nested autoinhibitory feedbacks alter the resistance of homeostatic adaptive biochemical networks

Negative feedback control is a ubiquitous feature of biochemical systems, as is time delay between a signal and its response. Negative feedback in conjunction with time delay can lead to oscillations. In a cellular context, it might be beneficial to mitigate oscillatory behaviour to avoid recurring stress situations. This can be achieved by increasing the distance between the parameters of the system and certain thresholds, beyond which oscillations occur. This distance has been termed resistance. Here, we prove that in a generic three-dimensional negative feedback system the resistance of the system is modified by nested autoinhibitory feedbacks. Our system features negative feedbacks through both input-inhibition as well as output-activation, a signalling component with mass conservation and perfect adaptation. We show that these features render the system applicable to biological data, exemplified by the high osmolarity glycerol system in yeast and the mammalian p53 system. Output-activation is better supported by data than input-inhibition and also shows distinguished properties with respect to the system's stimulus. Our general approach might be useful in designing synthetic systems in which oscillations can be tuned by synthetic autoinhibitory feedbacks.

Network quantification of EGFR signaling unveils potential for targeted combination therapy

The epidermal growth factor receptor (EGFR) signaling network is activated in most solid tumors, and small-molecule drugs targeting this network are increasingly available. However, often only specific combinations of inhibitors are effective. Therefore, the prediction of potent combinatorial treatments is a major challenge in targeted cancer therapy. In this study, we demonstrate how a model-based evaluation of signaling data can assist in finding the most suitable treatment combination. We generated a perturbation data set by monitoring the response of RAS/PI3K signaling to combined stimulations and inhibitions in a panel of colorectal cancer cell lines, which we analyzed using mathematical models. We detected that a negative feedback involving EGFR mediates strong cross talk from ERK to AKT. Consequently, when inhibiting MAPK, AKT activity is increased in an EGFR-dependent manner. Using the model, we predict that in contrast to single inhibition, combined inactivation of MEK and EGFR could inactivate both endpoints of RAS, ERK and AKT. We further could demonstrate that this combination blocked cell growth in BRAF- as well as KRAS-mutated tumor cells, which we confirmed using a xenograft model.

Pseudophosphatase STYX modulates cell-fate decisions and cell migration by spatiotemporal regulation of ERK1/2

Serine/threonine/tyrosine-interacting protein (STYX) is a catalytically inactive member of the dual-specificity phosphatases (DUSPs) family. Whereas the role of DUSPs in cellular signaling is well explored, the function of STYX is still unknown. Here, we identify STYX as a spatial regulator of ERK signaling. We used predictive-model simulation to test several hypotheses for possible modes of STYX action. We show that STYX localizes to the nucleus, competes with nuclear DUSP4 for binding to ERK, and acts as a nuclear anchor that regulates ERK nuclear export. Depletion of STYX increases ERK activity in both cytosol and nucleus. Importantly, depletion of STYX causes an ERK-dependent fragmentation of the Golgi apparatus and inhibits Golgi polarization and directional cell migration. Finally, we show that overexpression of STYX reduces ERK1/2 activation, thereby blocking PC12 cell differentiation. Overall, our results identify STYX as an important regulator of ERK1/2 signaling critical for cell migration and PC12 cell differentiation.