Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells

A guide to ERK dynamics, part 1: mechanisms and models

Extracellular signal-regulated kinase (ERK) has long been studied as a key driver of both essential cellular processes and disease. A persistent question has been how this single pathway is able to direct multiple cell behaviors, including growth, proliferation, and death. Modern biosensor studies have revealed that the temporal pattern of ERK activity is highly variable and heterogeneous, and critically, that these dynamic differences modulate cell fate. This two-part review discusses the current understanding of dynamic activity in the ERK pathway, how it regulates cellular decisions, and how these cell fates lead to tissue regulation and pathology. In part 1, we cover the optogenetic and live-cell imaging technologies that first revealed the dynamic nature of ERK, as well as current challenges in biosensor data analysis. We also discuss advances in mathematical models for the mechanisms of ERK dynamics, including receptor-level regulation, negative feedback, cooperativity, and paracrine signaling. While hurdles still remain, it is clear that higher temporal and spatial resolution provide mechanistic insights into pathway circuitry. Exciting new algorithms and advanced computational tools enable quantitative measurements of single-cell ERK activation, which in turn inform better models of pathway behavior. However, the fact that current models still cannot fully recapitulate the diversity of ERK responses calls for a deeper understanding of network structure and signal transduction in general.

Identification of DUSP4/6 overexpression as a potential rheostat to NRAS-induced hepatocarcinogenesis

BACKGROUND

Upregulation of the mitogen-activated protein kinase (MAPK) cascade is common in hepatocellular carcinoma (HCC). Neuroblastoma RAS viral oncogene homolog (NRAS) is mutated in a small percentage of HCC and is hitherto considered insufficient for hepatocarcinogenesis. We aimed to characterize the process of N-Ras-dependent carcinogenesis in the liver and to identify potential therapeutic vulnerabilities.

METHODS

NRAS V12 plasmid was delivered into the mouse liver via hydrodynamic tail vein injection (HTVI). The resulting tumours, preneoplastic lesions, and normal tissue were characterized by NanoString® gene expression analysis, Western Blot, and Immunohistochemistry (IHC). The results were further confirmed by in vitro analyses of HCC cell lines.

RESULTS

HTVI with NRAS V12 plasmid resulted in the gradual formation of preneoplastic and neoplastic lesions in the liver three months post-injection. These lesions mostly showed characteristics of HCC, with some exceptions of spindle cell/ cholangiocellular differentiation. Progressive upregulation of the RAS/RAF/MEK/ERK signalling was detectable in the lesions by Western Blot and IHC. NanoString® gene expression analysis of preneoplastic and tumorous tissue revealed a gradual overexpression of the cancer stem cell marker CD133 and Dual Specificity Phosphatases 4 and 6 (DUSP4/6). In vitro, transfection of HCC cell lines with NRAS V12 plasmid resulted in a coherent upregulation of DUSP4 and DUSP6. Paradoxically, this upregulation in PLC/PRF/5 cells was accompanied by a downregulation of phosphorylated extracellular-signal-regulated kinase (pERK), suggesting an overshooting compensation. Silencing of DUSP4 and DUSP6 increased proliferation in HCC cell lines.

CONCLUSIONS

Contrary to prior assumptions, the G12V NRAS mutant form is sufficient to elicit hepatocarcinogenesis in the mouse. Furthermore, the upregulation of the MAPK cascade was paralleled by the overexpression of DUSP4, DUSP6, and CD133 in vivo and in vitro. Therefore, DUSP4 and DUSP6 might fine-tune the excessive MAPK activation, a mechanism that can potentially be harnessed therapeutically.

Cooperativity and oscillations: Regulatory mechanisms of K-Ras nanoclusters

K-Ras nanoclusters (NCs) concentrate all required molecules belonging to the extracellular signal-regulated kinase (ERK) mitogen-activated protein kinase (MAPK) pathway in a small area where signaling events take place, increasing efficiency and specificity of signaling. Such nanostructures are characterized by controlled sizes and lifetimes distributions, but there is a poor understanding of the mechanisms involved in their dynamics of growth/decay. Here, a minimum computational model is presented to analyze the behavior of K-Ras NCs as cooperative dynamic structures that self-regulate their growth and decay according to their size. Indeed, the proposed model reveals that the growth and the local production of a K-Ras nanocluster depend positively on its actual size, whilst its lifetime is inversely proportional to the root of its size. The cooperative binding between the structural constituents of the NC (K-Ras proteins) induces oscillations in the size distributions of K-Ras NCs allowing them to range within controlled values, regulating the growth/decay dynamics of these NCs. Thereby, the size of a K-Ras NC is proposed as a key factor to regulate cell signaling, opening a range of possibilities to develop strategies for use in chronic diseases and cancer.

Proteins as fuzzy controllers: Auto tuning a biological fuzzy inference system to predict protein dynamics in complex biological networks

Biological systems such as mammalian cell cycle are complex systems consisting of a large number of molecular species interacting in ways that produce complex nonlinear systems dynamics. Discrete models such as Boolean models and continuous models such as Ordinary Differential Equations (ODEs) have been widely used to study these systems. Boolean models are simple and can capture qualitative systems behaviour, but they cannot capture the continuous trends of protein concentrations, while ODE models capture continuous trends but require kinetics parameters that are limited. Further, as systems get larger, complexity of these models becomes an issue for parameterization, analysis and interpretation. Also, molecular systems operate under the conditions of uncertainty and noise and our understanding of molecular processes in general is more at a qualitative level characterised by vagueness, imprecision and ambiguity. Hence, as more data are generated, there is a greater need for simpler data driven methods that can approximate continuous system behaviour while representing vagueness and ambiguity without requiring kinetic parameters. Fuzzy inferencing is one such promising method with the ability to work with qualitative vague/imprecise biological knowledge. In this study, we propose a fuzzy inference system for representing continuous behaviour of proteins and apply to some key proteins in the mammalian cell cycle system. The methods we introduced here is novel to protein interaction systems and cell cycle proteins. Our study proposes a three-stage approach to develop fuzzy protein controllers. In stage one, protein system is studied for interactions. We studied some significant core controllers of mammalian cell cycle and their producers and degraders as presented in a published ODE model. Based on the observations from a dataset generated from it, we developed Fuzzy inference systems (FIS) in the second stage, that involved deriving fuzzy IF-THEN rules and their processing, and manually tuned the FIS to predict the dynamics of individual proteins. In stage three, we employed Particle Swarm Optimisation (PSO) for optimising the FIS to further enhance prediction accuracy. Systems dynamics simulation results of the optimised FIS models were in close agreement with the benchmark ODE model results. The results show that the FIS models provide a close approximation to the comprehensive benchmark model in robustly representing continuous protein dynamics while representing the control of protein behavior in an intuitive and transparent format without requiring kinetic parameters. Therefore, FIS models can be an alternative to ODEs in network modelling. Further, FIS models can be assembled to develop large complex systems without losing information or accuracy.

A semantics, energy-based approach to automate biomodel composition

Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.

Signalling dynamics, cell decisions, and homeostatic control in health and disease

Cell signalling engenders cells with the capability to receive and process information from the intracellular and extracellular environments, trigger and execute biological responses, and communicate with each other. Ultimately, cell signalling is responsible for maintaining homeostasis at the cellular, tissue and systemic level. For this reason, cell signalling is a topic of intense research efforts aimed to elucidate how cells coordinate transitions between states in developing and adult organisms in physiological and pathological conditions. Here, we review current knowledge of how cell signalling operates at multiple spatial and temporal scales, focusing on how single-cell analytical techniques reveal mechanisms underpinning cell-to-cell variability, signalling plasticity, and collective cellular responses.

The partition representation of enzymatic reaction networks and its application for searching bi-stable reaction systems

The signal transduction system, which is known as a regulatory mechanism for biochemical reaction systems in the cell, has been the subject of intensive research in recent years, and its design methods have become necessary from the viewpoint of synthetic biology. We proposed the partition representation of enzymatic reaction networks consisting of post-translational modification reactions such as phosphorylation, which is an important basic component of signal transduction systems, and attempted to find enzymatic reaction networks with bistability to demonstrate the effectiveness of the proposed representation method. The partition modifiers can be naturally introduced into the partition representation of enzymatic reaction networks when applied to search. By randomly applying the partition modifiers as appropriate, we searched for bistable and resettable enzymatic reaction networks consisting of four post-translational modification reactions. The proposed search algorithm worked well and we were able to find various bistable enzymatic reaction networks, including a typical bistable enzymatic reaction network with positive auto-feedbacks and mutually negative regulations. Since the search algorithm is divided into an evaluation function specific to the characteristics of the enzymatic reaction network to be searched and an independent algorithm part, it may be applied to search for dynamic properties such as biochemical adaptation, the ability to reset the biochemical state after responding to a stimulus, by replacing the evaluation function with one for other characteristics.

BDE-47 induced PC-12 cell differentiation via TrkA downstream pathways and caused the loss of hippocampal neurons in BALB/c mice

As the most abundant congener of polybrominated diphenyl ethers (PBDEs) detected in environment and human biotic samples, 2, 2', 4, 4'-tetrabromodiphenyl ether (BDE-47) has been found to accumulate in brain and induce neurotoxicity, however, the detailed mechanism has not been clearly elucidated. To investigate the neurotoxicity of BDE-47, undifferentiated PC-12 cells were exposed to different doses of BDE-47, and BDE-47 dissolved in corn oil was orally administered to mice for 8 consecutive weeks. Our data showed that BDE-47 obviously changed cell morphology, altered cell viability, promoted cell apoptosis, and induced reactive oxygen species (ROS) production. BDE-47 promoted the differentiation of PC-12 cells by enhancing the expression of TrkA receptor and the phosphorylation levels of ERK and Akt. Moreover, BDE-47-induced differentiation of PC-12 cells was suppressed by inhibitors of corresponding pathways (MAPK/ERK and PI3K/Akt). H&E staining of brain showed neurons in DG and CA1 areas of hippocampus decreased after BDE-47 exposure. Transcriptome sequencing of brain tissue suggested that multiple signaling pathways related to neuron death and nerve function were significantly regulated. In conclusion, these results provided new evidence for revealing the neurotoxicity of BDE-47, and offered important experimental basis for environmental controlling and post-exposure health risk assessment of BDE-47.

Quantifying ERK activity in response to inhibition of the BRAFV600E-MEK-ERK cascade using mathematical modelling

BACKGROUND

Simultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanism of how vertical inhibition synergistically suppresses intracellular ERK activity, and consequently cell proliferation, are yet to be fully elucidated.

METHODS

We develop a mechanistic mathematical model that describes how the mutant BRAF inhibitor, dabrafenib, and the MEK inhibitor, trametinib, affect BRAFV600E-MEK-ERK signalling. The model is based on a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations that are parameterised by in vitro data and solved numerically to obtain the temporal evolution of cascade component concentrations.

RESULTS

The model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E-mutant melanoma cells. The model elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated BRAF concentrations generate drug resistance to dabrafenib and trametinib. The computational simulations further suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib.

CONCLUSIONS

The model can be used to systematically motivate which dabrafenib-trametinib dose combinations, for treating BRAFV600E-mutated melanoma, warrant experimental investigation.

Regulation of the Small GTPase Ras and Its Relevance to Human Disease

Ras research has experienced a considerable boost in recent years, not least prompted by the Ras initiative launched by the NCI in 2013 ( https://www.cancer.gov/research/key-initiatives/ras ), accompanied and conditioned by a strongly reinvigorated determination within the Ras community to develop therapeutics attacking directly the Ras oncoproteins. As a member of the small G-protein superfamily, function and transforming activity of Ras all revolve about its GDP/GTP loading status. For one thing, the extent of GTP loading will determine the proportion of active Ras in the cell, with implications for intensity and quality of downstream signaling. But also the rate of nucleotide exchange, i.e., the Ras-GDP/GTP cycling rate, can have a major impact on Ras function, as illustrated perhaps most impressively by newly discovered fast-cycling oncogenic mutants of the Ras-related GTPase Rac1. Thus, while the last years have witnessed memorable new findings and technical developments in the Ras field, leading to an improved insight into many aspects of Ras biology, they have not jolted at the basics, but rather deepened our view of the fundamental regulatory principles of Ras activity control. In this brief review, we revisit the role and mechanisms of Ras nucleotide loading and its implications for cancer in the light of recent findings.

Stochastic modulation evidences a transitory EGF-Ras-ERK MAPK activity induced by PRMT5

The extracellular signal-regulated kinase (ERK) mitogen-activated protein kinase (MAPK) pathway involves a three-step cascade of kinases that transduce signals and promote processes such as cell growth, development, and apoptosis. An aberrant response of this pathway is related to the proliferation of cell diseases and tumors. By using simulation modeling, we document that the protein arginine methyltransferase 5 (PRMT5) modulates the MAPK pathway and thus avoids an aberrant behavior. PRMT5 methylates the Raf kinase, reducing its catalytic activity and thereby, reducing the activation of ERK in time and amplitude. Two minimal computational models of the epidermal growth factor (EGF)-Ras-ERK MAPK pathway influenced by PRMT5 were proposed: a first model in which PRMT5 is activated by EGF and a second one in which PRMT5 is stimulated by the cascade response. The reported results show that PRMT5 reduces the time duration and the expression of the activated ERK in both cases, but only in the first model PRMT5 limits the EGF range that generates an ERK activation. Based on our data, we propose the protein PRMT5 as a regulatory factor to develop strategies to fight against an excessive activity of the MAPK pathway, which could be of use in chronic diseases and cancer.

PEGylated CuInS2/ZnS quantum dots inhibit neurite outgrowth by downregulating the NGF/p75NTR/MAPK pathway

The widespread application of cadmium-free CuInS₂/ZnS QDs has raised great concern regarding their potential toxicity to humans. To date, toxicological data related to CuInS₂/ZnS QDs are scarce. Neurons play extraordinary roles in regulating the activities of organs and systems, and serious consequences occur when neurons are damaged. Currently, the potential toxicity of CuInS₂/ZnS QDs on neurons has not been fully elucidated. Here, we investigate the neurotoxicity of PEGylated CuInS₂/ZnS (CuInS₂/ZnS-PEG) QDs on neuron-like PC12 cells. We found that CuInS₂/ZnS-PEG QDs were taken up by PC12 cells, but at a concentration range from 0 to 100 μg/mL, they did not affect the survival rate of the PC12 cells. In addition, we found that CuInS₂/ZnS-PEG QDs significantly inhibited neurite outgrowth from and the differentiation of PC12 cells in the presence of NGF, while COOH-modified CuInS₂/ZnS QDs or free PEG did not have a similar effect. Further studies showed that CuInS₂/ZnS-PEG QDs obviously downregulated the expression of low-affinity NGF receptor (p75^NTR) and subsequently negatively regulated the downstream MAPK cascade by dephosphorylating ERK1/2 and AKT. Taken together, these results suggest that CuInS₂/ZnS-PEG QDs disturb NGF signal transduction from external stimuli to relevant internal signals, thus affecting normal biological processes such as neurite outgrowth and cell differentiation.

Mechanistic Model of Signaling Dynamics Across an Epithelial Mesenchymal Transition

Intracellular signaling pathways are at the core of cellular information processing. The states of these pathways and their inputs determine signaling dynamics and drive cell function. Within a cancerous tumor, many combinations of cell states and microenvironments can lead to dramatic variations in responses to treatment. Network rewiring has been thought to underlie these context-dependent differences in signaling; however, from a biochemical standpoint, rewiring of signaling networks should not be a prerequisite for heterogeneity in responses to stimuli. Here we address this conundrum by analyzing an in vitro model of the epithelial mesenchymal transition (EMT), a biological program implicated in increased tumor invasiveness, heterogeneity, and drug resistance. We used mass cytometry to measure EGF signaling dynamics in the ERK and AKT signaling pathways before and after induction of EMT in Py2T murine breast cancer cells. Analysis of the data with standard network inference methods suggested EMT-dependent network rewiring. In contrast, use of a modeling approach that adequately accounts for single-cell variation demonstrated that a single reaction-based pathway model with constant structure and near-constant parameters is sufficient to represent differences in EGF signaling across EMT. This result indicates that rewiring of the signaling network is not necessary for heterogeneous responses to a signal and that unifying reaction-based models should be employed for characterization of signaling in heterogeneous environments, such as cancer.

Kinetics of receptor tyrosine kinase activation define ERK signaling dynamics

In responses to activation of receptor tyrosine kinases (RTKs), crucial cell fate decisions depend on the duration and dynamics of ERK signaling. In PC12 cells, epidermal growth factor (EGF) induces transient ERK activation that leads to cell proliferation, whereas nerve growth factor (NGF) promotes sustained ERK activation and cell differentiation. These differences have typically been assumed to reflect distinct feedback mechanisms in the Raf-MEK-ERK signaling network, with the receptors themselves acting as simple upstream inputs. We failed to confirm the expected differences in feedback type when investigating transient versus sustained signaling downstream of the EGF receptor (EGFR) and NGF receptor (TrkA). Instead, we found that ERK signaling faithfully followed RTK dynamics when receptor signaling was modulated in different ways. EGFR activation kinetics, and consequently ERK signaling dynamics, were switched from transient to sustained when receptor internalization was inhibited with drugs or mutations, or when cells expressed a chimeric receptor likely to have impaired dimerization. In addition, EGFR and ERK signaling both became more sustained when substoichiometric levels of erlotinib were added to reduce duration of EGFR kinase activation. Our results argue that RTK activation kinetics play a crucial role in determining MAP kinase cascade signaling dynamics and cell fate decisions, and that signaling outcome can be modified by activating a given RTK in different ways.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

The road to ERK activation: Do neurons take alternate routes?

The ERK cascade is a central signaling pathway that regulates a wide variety of cellular processes including proliferation, differentiation, learning and memory, development, and synaptic plasticity. A wide range of inputs travel from the membrane through different signaling pathway routes to reach activation of one set of output kinases, ERK1&2. The classical ERK activation pathway beings with growth factor activation of receptor tyrosine kinases. Numerous G-protein coupled receptors and ionotropic receptors also lead to ERK through increases in the second messengers calcium and cAMP. Though both types of pathways are present in diverse cell types, a key difference is that most stimuli to neurons, e.g. synaptic inputs, are transient, on the order of milliseconds to seconds, whereas many stimuli acting on non-neural tissue, e.g. growth factors, are longer duration. The ability to consolidate these inputs to regulate the activation of ERK in response to diverse signals raises the question of which factors influence the difference in ERK activation pathways. This review presents both experimental studies and computational models aimed at understanding the control of ERK activation and whether there are fundamental differences between neurons and other cells. Our main conclusion is that differences between cell types are quite subtle, often related to differences in expression pattern and quantity of some molecules such as Raf isoforms. In addition, the spatial location of ERK is critical, with regulation by scaffolding proteins producing differences due to colocalization of upstream molecules that may differ between neurons and other cells.

Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

Laminin-modified gellan gum hydrogels loaded with the nerve growth factor to enhance the proliferation and differentiation of neuronal stem cells

The reconstruction of peripheral nerves has lately received great attention as many patients suffer from peripheral nerve injury every year around the world. However, the damage to human nerve cells has different degrees of irreversibility due to a slow growth speed and low adhesion with the surrounding tissues. In an effort to overcome this challenge, we applied novel laminin (LN)-modified thiolated gellan gum (TGG) and loaded the nerve growth factor (NGF) as a tissue engineering scaffold for facilitating neuronal stem cell proliferation via a synergy effect for the ERK–MAPK pathway. TGG was characterized by ¹H NMR spectroscopy and scanning electron microscopy, and its rheological behavior was also studied. The NGF release curve fitted the Korsmeyer–Peppas model and belonged to a Fickian diffusion-controlled release mechanism. The neuronal stem cells from newborn SD rats could adhere tightly and proliferate at a relatively rapid speed, showing excellent biocompatibility and the ability to promote growth in the modified TGG. LN and NGF could decrease the apoptosis effects of neuronal stem cells, as shown via the flow cytometry results. In a three-dimensional culture environment, LN and NGF could facilitate neuronal stem cells to differentiate into neurons, as proved by immunofluorescence, q-PCR, and western blot analyses. Therefore, the rational design of the TGG gel loaded with NGF has promising applications in the reconstruction of peripheral nerves.

Laminin-modified thiolated gellan gum and loaded with the nerve growth factor in facilitateding neuronal stem cell proliferation and differentiation.

Quantification of the Dynamic Phosphorylation Process of ERK Using Stable Isotope Dilution Selective Reaction Monitoring Mass Spectrometry

Mitogen-activated protein (MAP) kinase signaling is critical for various cellular responses, including cell proliferation, differentiation, and cell death. The MAP kinase cascade is conserved in the eukaryotic kingdom as a three-tiered kinase module-MAP kinase kinase kinase, MAP kinase kinase, and MAP kinase-that transduces signals via sequential phosphorylation upon stimulation. Dual phosphorylation of MAP kinase on the conserved threonine-glutamic acid-tyrosine (TEY) motif is essential for its catalytic activity and signal activation; however, the molecular mechanism by which the two residues are phosphorylated remains elusive. In the present study, the pattern of dual phosphorylation of extracellular signal-regulated kinase (ERK) is profiled on the TEY motif using stable isotope dilution (SID)-selective reaction monitoring (SRM) mass spectrometry (MS) to elucidate the order and magnitude of endogenous ERK phosphorylation in cellular model systems. The SID-SRM-MS analysis of phosphopeptides demonstrates that tyrosine phosphorylation in the TEY motif is dynamic, while threonine phosphorylation is static. Analyses of the mono-phosphorylatable mutants ERK^T202A and ERK^Y204F indicate that phosphorylation of tyrosine is not affected by the phosphorylation state of threonine, while threonine phosphorylation depends on tyrosine phosphorylation. The data suggest that dual phosphorylation of ERK is a highly ordered and restricted mechanism determined by tyrosine phosphorylation.

New insights into RAS biology reinvigorate interest in mathematical modeling of RAS signaling

RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.

Up-regulation of DUSP5 and DUSP6 by gonadotropin-releasing hormone in cultured hypothalamic neurons, GT1-7 cells

Gonadotropin-releasing hormone (GnRH) is secreted from hypothalamic neurons (GnRH neurons) and stimulates anterior pituitary gonadotrophs to synthesize and secrete gonadotropins. In addition to gonadotrophs, GnRH neurons also express GnRH receptors, and the autocrine action of GnRH is reportedly involved in the regulation of functions of GnRH neurons. There is accumulating evidence that extracellular signal-regulated kinase (ERK), one of mitogen-activated protein kinases (MAPKs), is activated by GnRH and involved in various effects of GnRH in GnRH neurons. In the present study, we performed microarray analysis to examine the types of genes whose expression was regulated by GnRH in immortalized mouse GnRH neurons (GT1-7 cells). We found that 257 genes among 55,681 genes examined were up-regulated after 30-min treatment of GT1-7 cells with GnRH. These up-regulated genes included four dual-specificity MAPK phosphatases (DUSPs), DUSP1, DUSP2, DUSP5, and DUSP6. Reverse transcription-polymerase chain reaction analysis confirmed that the mRNA levels of DUSP5 and DUSP6 were robustly increased within 30 min. U0126, an inhibitor of ERK activation, completely inhibited the increases in the mRNA levels of DUSP5 and DUSP6. Immunoblotting analysis revealed that ERK activation peaked at 5 min and declined steeply at 60 min, whereas DUSP5 and DUSP6 proteins were increased from 60 min. It was notable that down-regulation of DUSP6 augmented GnRH-induced ERK activation approximately 1.7-fold at 60 min. These results suggested that the up-regulation of DUSP6 regulates the duration of ERK activation at least in part.

Stochasticity and robustness analysis of microRNA-mediated ERK signaling network

MicroRNAs (miRNAs) play a critical role in regulating the signaling network such as the extracellular signal regulated kinase (ERK) pathway. However, the mechanisms of miRNA-mediated posttranscriptional regulations with regard to their impacts on signaling require further investigation from a systematic level. Therefore, we develop a mathematical model by analyzing the precise dynamic mechanisms with a bevy of miRNAs involved in the Ras/Raf/MEK/ERK pathway. A systems-based analysis approach is introduced into this model and the dynamics have been implemented deterministically and stochastically. Our analysis reveals that miRNAs are key participants regulating the gene expression of ERK network, and the cooperative actions of miRNAs are important in keeping the normal biological characteristics and amplification effects of the system. Meanwhile, the appearance of system disorder in the absence of miRNAs suggests that miRNAs may play a role in the pathological processes, such as tumor and inflammation. The sensitivity analysis and the kinetic parameter perturbation show that the binding of receptor (EGFR) and adaptor protein (Shc, Grb2 and Sos) under normal physiological conditions is crucial for the robustness of the whole pathway. In addition, the stochastic dynamic patterns are in a good agreement with the deterministic results, further demonstrating that the variability of the system due to the presence of some stochastic noise is low. All these will be helpful for a deeper understanding of the dynamic mechanism of miRNA-mediated ERK signal network, which might present a rich area of future research with the relevant regulatory roles of miRNAs in cell signaling pathway.

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.

System identification of signaling dependent gene expression with different time-scale data

Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input-output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales.

Regulatory role of NGFs in neurocognitive functions

Nerve growth factors (NGFs), especially the prototype NGF and brain-derived neurotrophic factor (BDNF), have a diverse array of functions in the central nervous system through their peculiar set of receptors and intricate signaling. They are implicated not only in the development of the nervous system but also in regulation of neurocognitive functions like learning, memory, synaptic transmission, and plasticity. Evidence even suggests their role in continued neurogenesis and experience-dependent neural network remodeling in adult brain. They have also been associated extensively with brain disorders characterized by neurocognitive dysfunction. In the present article, we aimed to make an exhaustive review of literature to get a comprehensive view on the role of NGFs in neurocognitive functions in health and disease. Starting with historical perspective, distribution in adult brain, implied molecular mechanisms, and developmental basis, this article further provides a detailed account of NGFs’ role in specified neurocognitive functions. Furthermore, it discusses plausible NGF-based homeostatic and adaptation mechanisms operating in the pathogenesis of neurocognitive disorders and has presents a survey of such disorders. Finally, it elaborates on current evidence and future possibilities in therapeutic applications of NGFs with an emphasis on recent research updates in drug delivery mechanisms. Conclusive remarks of the article make a strong case for plausible role of NGFs in comprehensive regulation of the neurocognitive functions and pathogenesis of related disorders and advocate that future research should be directed to explore use of NGF-based mechanisms in the prevention of implicated diseases as well as to target these molecules pharmacologically.

Modelling of the cancer cell cycle as a tool for rational drug development: A systems pharmacology approach to cyclotherapy

The dynamic of cancer is intimately linked to a dysregulation of the cell cycle and signalling pathways. It has been argued that selectivity of treatments could exploit loss of checkpoint function in cancer cells, a concept termed "cyclotherapy". Quantitative approaches that describe these dysregulations can provide guidance in the design of novel or existing cancer therapies. We describe and illustrate this strategy via a mathematical model of the cell cycle that includes descriptions of the G1-S checkpoint and the spindle assembly checkpoint (SAC), the EGF signalling pathway and apoptosis. We incorporated sites of action of four drugs (palbociclib, gemcitabine, paclitaxel and actinomycin D) to illustrate potential applications of this approach. We show how drug effects on multiple cell populations can be simulated, facilitating simultaneous prediction of effects on normal and transformed cells. The consequences of aberrant signalling pathways or of altered expression of pro- or anti-apoptotic proteins can thus be compared. We suggest that this approach, particularly if used in conjunction with pharmacokinetic modelling, could be used to predict effects of specific oncogene expression patterns on drug response. The strategy could be used to search for synthetic lethality and optimise combination protocol designs.

Sampling-based Bayesian approaches reveal the importance of quasi-bistable behavior in cellular decision processes on the example of the MAPK signaling pathway in PC-12 cell lines

BACKGROUND

Positive and negative feedback loops are ubiquitous motifs in biochemical signaling pathways. The mitogen-activated protein kinase (MAPK) pathway module is part of many distinct signaling networks and comprises several of these motifs, whose functioning depends on the cell line at hand and on the particular context. The maintainance of specificity of the response of the MAPK module to distinct stimuli has become a key paradigm especially in PC-12 cells, where the same module leads to different cell fates, depending on the stimulating growth factor. This cell fate is regulated by differences in the ERK (MAPK) activation profile, which shows a transient response upon stimulation with EGF, while the response is sustained in case of NGF. This behavior was explained by different effective network topologies. It is widely believed that this sustained response requires a bistable system.

RESULTS

In this study we present a sampling-based Bayesian model analysis on a dataset, in which PC-12 cells have been stimulated with different growth factors. This is combined with novel analysis methods to investigate the role of feedback interconnections to shape ERK response. Results strongly suggest that, besides bistability, an additional effect called quasi-bistability can contribute to explain the observed responses of the system to different stimuli. Quasi-bistability is the ability of a monostable system to maintain two distinct states over a long time period upon a transient signal, which is also related to positive feedback, but cannot be detected by standard steady state analysis methods.

CONCLUSIONS

Although applied on a specific example, our framework is generic enough to be also relevant for other regulatory network modeling studies that comprise positive feedback to explain cellular decision making processes. Overall, this study advices to focus not only on steady states, but also to take transient behavior into account in the analysis.

Dissecting Cell-Fate Determination Through Integrated Mathematical Modeling of the ERK/MAPK Signaling Pathway

The past three decades have witnessed an enormous progress in the elucidation of the ERK/MAPK signaling pathway and its involvement in various cellular processes. Because of its importance and complex wiring, the ERK pathway has been an intensive subject for mathematical modeling, which facilitates the unraveling of key dynamic properties and behaviors of the pathway. Recently, however, it became evident that the pathway does not act in isolation but closely interacts with many other pathways to coordinate various cellular outcomes under different pathophysiological contexts. This has led to an increasing number of integrated, large-scale models that link the ERK pathway to other functionally important pathways. In this chapter, we first discuss the essential steps in model development and notable models of the ERK pathway. We then use three examples of integrated, multipathway models to investigate how crosstalk of ERK signaling with other pathways regulates cell-fate decision-making in various physiological and disease contexts. Specifically, we focus on ERK interactions with the phosphoinositide-3 kinase (PI3K), c-Jun N-terminal kinase (JNK), and β-adrenergic receptor (β-AR) signaling pathways. We conclude that integrated modeling in combination with wet-lab experimentation have been and will be instrumental in gaining an in-depth understanding of ERK signaling in multiple biological contexts.

Negative feedback regulation of the ERK1/2 MAPK pathway

The extracellular signal-regulated kinase 1/2 (ERK1/2) mitogen-activated protein kinase (MAPK) signalling pathway regulates many cellular functions, including proliferation, differentiation, and transformation. To reliably convert external stimuli into specific cellular responses and to adapt to environmental circumstances, the pathway must be integrated into the overall signalling activity of the cell. Multiple mechanisms have evolved to perform this role. In this review, we will focus on negative feedback mechanisms and examine how they shape ERK1/2 MAPK signalling. We will first discuss the extensive number of negative feedback loops targeting the different components of the ERK1/2 MAPK cascade, specifically the direct posttranslational modification of pathway components by downstream protein kinases and the induction of de novo gene synthesis of specific pathway inhibitors. We will then evaluate how negative feedback modulates the spatiotemporal signalling dynamics of the ERK1/2 pathway regarding signalling amplitude and duration as well as subcellular localisation. Aberrant ERK1/2 activation results in deregulated proliferation and malignant transformation in model systems and is commonly observed in human tumours. Inhibition of the ERK1/2 pathway thus represents an attractive target for the treatment of malignant tumours with increased ERK1/2 activity. We will, therefore, discuss the effect of ERK1/2 MAPK feedback regulation on cancer treatment and how it contributes to reduced clinical efficacy of therapeutic agents and the development of drug resistance.

Modular bond-graph modelling and analysis of biomolecular systems

Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control-theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter-module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen-activated protein kinase cascade (Raf-MEK-ERK pathway) is used as an illustrative example.

Dynamic Modeling and Analysis of the Cross-Talk between Insulin/AKT and MAPK/ERK Signaling Pathways

Feedback loops play a key role in the regulation of the complex interactions in signal transduction networks. By studying the network of interactions among the biomolecules present in signaling pathways at the systems level, it is possible to understand how the biological functions are regulated and how the diseases emerge from their deregulations. This paper identifies the key feedback loops involved in the cross-talk among the insulin-AKT and MAPK/ERK signaling pathways. We developed a mathematical model that can be used to study the steady-state and dynamic behavior of the interactions among these two important signaling pathways. Modeling analysis and simulation case studies identify the key interaction parameters and the feedback loops that determine the normal and disease phenotypes.

Spatio-temporal dynamics of a cell signal pathway with negative feedbacks: the MAPK/ERK pathway

We studied the spatio-temporal dynamics of a cell signal cascade with negative feedback that quantitatively emulates the regulative process that occurs in the Mitogen Activated Protein Kinase/Extracellular Regulated Kinase (MAPK/ERK) pathway. The model consists of a set of six coupled reaction-diffusion equations that describes the dynamics of the six-module pathway. In the basic module the active form of the protein transmits the signal to the next pathway’s module. As suggested by experiments, the model considers that the fifth module's kinase down-regulates the first and third modules. The feedback parameter is defined as, μ(r)( j)= k(kin)5/k(kin)(j), (j = 1, 3). We analysed the pathway's dynamics for μ(r)( j) = 0.10, 1.0, and 10 in the kinetic regimes: i) saturation of both kinases and phosphatases, ii) saturation of the phosphatases and iii) saturation of the kinases. For a regulated pathway the Total Activated Protein Profiles (TAPPs) as a function of time develop a maximum during the transient stage in the three kinetic regimes. These maxima become higher and their positions shift to longer times downstream. This scenario also applies to the TAPP's regulatory kinase that sums up its inhibitory action to that of the phosphatases leading to a maximum. Nevertheless, when μ(r)(j)= 1.0 , the TAPPs develop two maxima, with the second maximum being almost imperceptible. These results are in qualitative agreement with experimental data obtained from NIH 3T3 mouse fibroblasts. In addition, analyses of the stationary states as a function of position indicate that in the kinetic regime i) which is of physiological interest, signal transduction occurs with a relatively large propagation length for the three values of the regulative parameter. However, for μ(r)(j)= 0.10 , the sixth module concentration profile is transmitted with approximately 45% of its full value. The results obtained for μ(r)(j) = 10 , indicate that the first five concentration profiles are small with a short propagation length; nonetheless, the last concentration profile, c6, attains more than 90% of its full value with a relatively large propagation length as an indication of signal transduction. Signal transduction also occurred favourably in the kinetic regimes ii) and iii), but the signal was longer-ranged in the regime ii).

Feedback activation of neurofibromin terminates growth factor-induced Ras activation

Background

Growth factors induce a characteristically short-lived Ras activation in cells emerging from quiescence. Extensive work has shown that transient as opposed to sustained Ras activation is critical for the induction of mitogenic programs. Mitogen-induced accumulation of active Ras-GTP results from increased nucleotide exchange driven by the nucleotide exchange factor Sos. In contrast, the mechanism accounting for signal termination and prompt restoration of basal Ras-GTP levels is unclear, but has been inferred to involve feedback inhibition of Sos. Remarkably, how GTP-hydrolase activating proteins (GAPs) participate in controlling the rise and fall of Ras-GTP levels is unknown.

Results

Monitoring nucleotide exchange of Ras in permeabilized cells we find, unexpectedly, that the decline of growth factor-induced Ras-GTP levels proceeds in the presence of unabated high nucleotide exchange, pointing to GAP activation as a major mechanism of signal termination. Experiments with non-hydrolysable GTP analogues and mathematical modeling confirmed and rationalized the presence of high GAP activity as Ras-GTP levels decline in a background of high nucleotide exchange. Using pharmacological and genetic approaches we document a raised activity of the neurofibromatosis type I tumor suppressor Ras-GAP neurofibromin and an involvement of Rsk1 and Rsk2 in the down-regulation of Ras-GTP levels.

Conclusions

Our findings show that, in addition to feedback inhibition of Sos, feedback stimulation of the RasGAP neurofibromin enforces termination of the Ras signal in the context of growth-factor signaling. These findings ascribe a precise role to neurofibromin in growth factor-dependent control of Ras activity and illustrate how, by engaging Ras-GAP activity, mitogen-challenged cells play safe to ensure a timely termination of the Ras signal irrespectively of the reigning rate of nucleotide exchange.

Electronic supplementary material

The online version of this article (doi:10.1186/s12964-016-0128-z) contains supplementary material, which is available to authorized users.

Context-specific flow through the MEK/ERK module produces cell- and ligand-specific patterns of ERK single and double phosphorylation

The same pathway, such as the mitogen-activated protein kinase (MAPK) pathway, can produce different cellular responses, depending on stimulus or cell type. We examined the phosphorylation dynamics of the MAPK kinase MEK and its targets extracellular signal-regulated kinase 1 and 2 (ERK1/2) in primary hepatocytes and the transformed keratinocyte cell line HaCaT A5 exposed to either hepatocyte growth factor or interleukin-6. By combining quantitative mass spectrometry with dynamic modeling, we elucidated network structures for the reversible threonine and tyrosine phosphorylation of ERK in both cell types. In addition to differences in the phosphorylation and dephosphorylation reactions, the HaCaT network model required two feedback mechanisms, which, as the experimental data suggested, involved the induction of the dual-specificity phosphatase DUSP6 and the scaffold paxillin. We assayed and modeled the accumulation of the double-phosphorylated and active form of ERK1/2, as well as the dynamics of the changes in the monophosphorylated forms of ERK1/2. Modeling the differences in the dynamics of the changes in the distributions of the phosphorylated forms of ERK1/2 suggested that different amounts of MEK activity triggered context-specific responses, with primary hepatocytes favoring the formation of double-phosphorylated ERK1/2 and HaCaT A5 cells that produce both the threonine-phosphorylated and the double-phosphorylated form. These differences in phosphorylation distributions explained the threshold, sensitivity, and saturation of the ERK response. We extended the findings of differential ERK phosphorylation profiles to five additional cultured cell systems and matched liver tumor and normal tissue, which revealed context-specific patterns of the various forms of phosphorylated ERK.

Novel Reporter for Faithful Monitoring of ERK2 Dynamics in Living Cells and Model Organisms

Uncoupling of ERK1/2 phosphorylation from subcellular localization is essential towards the understanding of molecular mechanisms that control ERK1/2-mediated cell-fate decision. ERK1/2 non-catalytic functions and discoveries of new specific anchors responsible of the subcellular compartmentalization of ERK1/2 signaling pathway have been proposed as regulation mechanisms for which dynamic monitoring of ERK1/2 localization is necessary. However, studying the spatiotemporal features of ERK2, for instance, in different cellular processes in living cells and tissues requires a tool that can faithfully report on its subcellular distribution. We developed a novel molecular tool, ERK2-LOC, based on the T2A-mediated coexpression of strictly equimolar levels of eGFP-ERK2 and MEK1, to faithfully visualize ERK2 localization patterns. MEK1 and eGFP-ERK2 were expressed reliably and functionally both in vitro and in single living cells. We then assessed the subcellular distribution and mobility of ERK2-LOC using fluorescence microscopy in non-stimulated conditions and after activation/inhibition of the MAPK/ERK1/2 signaling pathway. Finally, we used our coexpression system in Xenopus laevis embryos during the early stages of development. This is the first report on MEK1/ERK2 T2A-mediated coexpression in living embryos, and we show that there is a strong correlation between the spatiotemporal subcellular distribution of ERK2-LOC and the phosphorylation patterns of ERK1/2. Our approach can be used to study the spatiotemporal localization of ERK2 and its dynamics in a variety of processes in living cells and embryonic tissues.

State machine modeling of MAPK signaling pathways

Mitogen activated protein kinase (MAPK) signaling pathways are frequently deregulated in human cancers with potential involvement in most if not all cellular processes leading to tumorigenesis. Mathematical/computational models of MAPK signaling are indispensable to the study of pathway deregulation dynamics and their nonlinear effects on cell fate and carcinogenesis. A finite state machine model of MAPK cellular signaling is explored as an alternative to differential equations-based models of kinetics. The proposed approach is applied to the Ras-Extracellular signal-regulated kinase (Ras-ERK) pathway which includes the frequently mutated Ras and RAF proteins in many types of carcinomas.

ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics

Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.

In this manuscript, we introduce ODE constrained mixture models for the analysis of population snapshot data of kinetics and dose responses. Population snapshot data can for instance be derived from flow cytometry or single-cell microscopy and provide information about the population structure and the dynamics of subpopulations. Currently available methods enable, however, only the extraction of this information if the subpopulations are very different. By combining pathway-specific ODE and mixture models, a more sensitive method is obtained, which can simultaneously analyse a variety of experimental conditions. ODE constrained mixture models facilitate the reconstruction of subpopulation sizes and dynamics, even in situations where the subpopulations are hardly distinguishable. This is shown for a simulation example as well as for the process of NGF-induced Erk1/2 phosphorylation in primary sensory neurones. We find that the proposed method allows for a simple but pervasive analysis of heterogeneous cell systems and more profound, mechanistic insights.

Convergence in parameters and predictions using computational experimental design

Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design techniques can select sets of experiments whose members probe complementary aspects of a biochemical network that together can account for its full behaviour. Here, we implemented an experimental design approach for selecting sets of experiments that constrain parameter uncertainty. We demonstrated with a model of the epidermal growth factor–nerve growth factor pathway that, after synthetically performing a handful of optimal experiments, the uncertainty in all 48 parameters converged below 10 per cent. Furthermore, the fitted parameters converged to their true values with a small error consistent with the residual uncertainty. When untested experimental conditions were simulated with the fitted models, the predicted species concentrations converged to their true values with errors that were consistent with the residual uncertainty. This paper suggests that accurate parameter estimation is achievable with complementary experiments specifically designed for the task, and that the resulting parametrized models are capable of accurate predictions.

Negative feedback self-regulation contributes to robust and high-fidelity transmembrane signal transduction

We present a minimal motif model for transmembrane cell signalling. The model assumes signalling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects can be modulated to provide a robust and high-fidelity response behaviour without invoking sophisticated modelling of the signalling process as a sequence of cascade reactions and fine-tuned parameters. Our results show that the fact that the distributed signalling events take place in nanoclusters with a finite lifetime regulated by local production is sufficient to obtain a robust and high-fidelity response.

Integrative modelling of the influence of MAPK network on cancer cell fate decision

The Mitogen-Activated Protein Kinase (MAPK) network consists of tightly interconnected signalling pathways involved in diverse cellular processes, such as cell cycle, survival, apoptosis and differentiation. Although several studies reported the involvement of these signalling cascades in cancer deregulations, the precise mechanisms underlying their influence on the balance between cell proliferation and cell death (cell fate decision) in pathological circumstances remain elusive. Based on an extensive analysis of published data, we have built a comprehensive and generic reaction map for the MAPK signalling network, using CellDesigner software. In order to explore the MAPK responses to different stimuli and better understand their contributions to cell fate decision, we have considered the most crucial components and interactions and encoded them into a logical model, using the software GINsim. Our logical model analysis particularly focuses on urinary bladder cancer, where MAPK network deregulations have often been associated with specific phenotypes. To cope with the combinatorial explosion of the number of states, we have applied novel algorithms for model reduction and for the compression of state transition graphs, both implemented into the software GINsim. The results of systematic simulations for different signal combinations and network perturbations were found globally coherent with published data. In silico experiments further enabled us to delineate the roles of specific components, cross-talks and regulatory feedbacks in cell fate decision. Finally, tentative proliferative or anti-proliferative mechanisms can be connected with established bladder cancer deregulations, namely Epidermal Growth Factor Receptor (EGFR) over-expression and Fibroblast Growth Factor Receptor 3 (FGFR3) activating mutations.

Depending on environmental conditions, strongly intertwined cellular signalling pathways are activated, involving activation/inactivation of proteins and genes in response to external and/or internal stimuli. Alterations of some components of these pathways can lead to wrong cell behaviours. For instance, cancer-related deregulations lead to high proliferation of malignant cells enabling sustained tumour growth. Understanding the precise mechanisms underlying these pathways is necessary to delineate efficient therapeutical approaches for each specific tumour type. We particularly focused on the Mitogen-Activated Protein Kinase (MAPK) signalling network, whose involvement in cancer is well established, although the precise conditions leading to its positive or negative influence on cell proliferation are still poorly understood. We tackled this problem by first collecting sparse published biological information into a comprehensive map describing the MAPK network in terms of stylised chemical reactions. This information source was then used to build a dynamical Boolean model recapitulating network responses to characteristic stimuli observed in selected bladder cancers. Systematic model simulations further allowed us to link specific network components and interactions with proliferative/anti-proliferative cell responses.

Intracellular regulation of cell signaling cascades: how location makes a difference

Organelles such as endosomes and the Golgi apparatus play a critical role in regulating signal transmission to the nucleus. Recent experiments have shown that appropriate positioning of these organelles within the intracellular space is critical for effective signal regulation. To understand the mechanism behind this observation, we consider a reaction-diffusion model of an intracellular signaling cascade and investigate the effect on the signaling of intracellular regulation in the form of a small release of phosphorylated signaling protein, kinase, and/or phosphatase. Variational analysis is applied to characterize the most effective regions for the localization of this intracellular regulation. The results demonstrate that signals reaching the nucleus are most effectively regulated by localizing the release of phosphorylated substrate protein and kinase near the nucleus. Phosphatase release, on the other hand, is nearly equally effective throughout the intracellular space. The effectiveness of the intracellular regulation is affected strongly by the characteristics of signal propagation through the cascade. For signals that are amplified as they propagate through the cascade, reactions in the upstream levels of the cascade exhibit much larger sensitivities to regulation by release of phosphorylated substrate protein and kinase than downstream reactions. On the other hand, for signals that decay through the cascade, downstream reactions exhibit larger sensitivity than upstream reactions. For regulation by phosphatase release, all reactions within the cascade show large sensitivity for amplified signals but lose this sensitivity for decaying signals. We use the analysis to develop a simple model of endosome-mediated regulation of cell signaling. The results demonstrate that signal regulation by the modeled endosome is most effective when the endosome is positioned in the vicinity of the nucleus. The present findings may explain at least in part why endosomes in many cell types localize near the nucleus.