Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

Bimodality in Ras signaling originates from processivity of the Ras activator SOS without deterministic bistability

Ras is a small GTPase that is central to important functional decisions in diverse cell types. An important aspect of Ras signaling is its ability to exhibit bimodal or switch-like activity. We describe the total reconstitution of a receptor-mediated Ras activation-deactivation reaction catalyzed by SOS and p120-RasGAP on supported lipid membrane microarrays. The results reveal a bimodal Ras activation response, which is not a result of deterministic bistability but is rather driven by the distinct processivity of the Ras activator, SOS. Furthermore, the bimodal response is controlled by the condensation state of the scaffold protein, LAT, to which SOS is recruited. Processivity-driven bimodality leads to stochastic bursts of Ras activation even under strongly deactivating conditions. This behavior contrasts deterministic bistability and may be more resistant to pharmacological inhibition.

The mitogen-activated protein kinase network, wired to dynamically function at multiple scales

The mitogen-activated protein kinase (MAPK)/extracellular signal-regulated kinase (ERK) signaling network is a key transducer of signals from various receptors, including receptor tyrosine kinases (RTKs). It controls cell-cycle entry, survival, motility, differentiation, as well as other fates. After four decades of studying this pathway with biochemical methods, the use of fluorescent biosensors has revealed dynamic behaviors such as ERK pulsing, oscillations, and amplitude-modulated activity. Different RTKs equip the MAPK network with specific feedback mechanisms to encode these different ERK dynamics, which are then subsequently decoded into cytoskeletal events and transcriptional programs, actuating cellular fates. Recently, collective ERK wave behaviors have been observed in multiple systems to coordinate cytoskeletal dynamics with fate decisions within cell collectives. This emphasizes that a correct understanding of this pathway requires studying it at multiple scales.

Comprehensive molecular interaction map of TGFβ induced epithelial to mesenchymal transition in breast cancer

Breast cancer is one of the prevailing cancers globally, with a high mortality rate. Metastatic breast cancer (MBC) is an advanced stage of cancer, characterised by a highly nonlinear, heterogeneous process involving numerous singling pathways and regulatory interactions. Epithelial-mesenchymal transition (EMT) emerges as a key mechanism exploited by cancer cells. Transforming Growth Factor-β (TGFβ)-dependent signalling is attributed to promote EMT in advanced stages of breast cancer. A comprehensive regulatory map of TGFβ induced EMT was developed through an extensive literature survey. The network assembled comprises of 312 distinct species (proteins, genes, RNAs, complexes), and 426 reactions (state transitions, nuclear translocations, complex associations, and dissociations). The map was developed by following Systems Biology Graphical Notation (SBGN) using Cell Designer and made publicly available using MINERVA ( http://35.174.227.105:8080/minerva/?id=Metastatic_Breast_Cancer_1 ). While the complete molecular mechanism of MBC is still not known, the map captures the elaborate signalling interplay of TGFβ induced EMT-promoting MBC. Subsequently, the disease map assembled was translated into a Boolean model utilising CaSQ and analysed using Cell Collective. Simulations of these have captured the known experimental outcomes of TGFβ induced EMT in MBC. Hub regulators of the assembled map were identified, and their transcriptome-based analysis confirmed their role in cancer metastasis. Elaborate analysis of this map may help in gaining additional insights into the development and progression of metastatic breast cancer.

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.

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

Bimodality in Ras signaling originates from processivity of the Ras activator SOS without classic kinetic bistability

Ras is a small GTPase that is central to important functional decisions in diverse cell types. An important aspect of Ras signaling is its ability to exhibit bimodal, or switch-like activity. We describe the total reconstitution of a receptor-mediated Ras activation-deactivation reaction catalyzed by SOS and p120-RasGAP on supported lipid membrane microarrays. The results reveal a bimodal Ras activation response, which is not a result of classic kinetic bistability, but is rather driven by the distinct processivity of the Ras activator, SOS. Furthermore, the bimodal response is controlled by the condensation state of the scaffold protein, LAT, to which SOS is recruited. Processivity-driven bimodality leads to stochastic bursts of Ras activation even under strongly deactivating conditions. This behavior contrasts classic kinetic bistability and is distinctly more resistant to pharmacological inhibition.

Predictive power of non-identifiable models

Resolving practical non-identifiability of computational models typically requires either additional data or non-algorithmic model reduction, which frequently results in models containing parameters lacking direct interpretation. Here, instead of reducing models, we explore an alternative, Bayesian approach, and quantify the predictive power of non-identifiable models. We considered an example biochemical signalling cascade model as well as its mechanical analogue. For these models, we demonstrated that by measuring a single variable in response to a properly chosen stimulation protocol, the dimensionality of the parameter space is reduced, which allows for predicting the measured variable's trajectory in response to different stimulation protocols even if all model parameters remain unidentified. Moreover, one can predict how such a trajectory will transform in the case of a multiplicative change of an arbitrary model parameter. Successive measurements of remaining variables further reduce the dimensionality of the parameter space and enable new predictions. We analysed potential pitfalls of the proposed approach that can arise when the investigated model is oversimplified, incorrect, or when the training protocol is inadequate. The main advantage of the suggested iterative approach is that the predictive power of the model can be assessed and practically utilised at each step.

The MAPK/ERK channel capacity exceeds 6 bit/hour

Living cells utilize signaling pathways to sense, transduce, and process information. As the extracellular stimulation often has rich temporal characteristics which may govern dynamic cellular responses, it is important to quantify the rate of information flow through the signaling pathways. In this study, we used an epithelial cell line expressing a light-activatable FGF receptor and an ERK activity reporter to assess the ability of the MAPK/ERK pathway to transduce signal encoded in a sequence of pulses. By stimulating the cells with random light pulse trains, we demonstrated that the MAPK/ERK channel capacity is at least 6 bits per hour. The input reconstruction algorithm detects the light pulses with 1-min accuracy 5 min after their occurrence. The high information transmission rate may enable the pathway to coordinate multiple processes including cell movement and respond to rapidly varying stimuli such as chemoattracting gradients created by other cells.

MAPK Pathways in Ocular Pathophysiology: Potential Therapeutic Drugs and Challenges

Mitogen-activated protein kinase (MAPK) pathways represent ubiquitous cellular signal transduction pathways that regulate all aspects of life and are frequently altered in disease. Once activated through phosphorylation, these MAPKs in turn phosphorylate and activate transcription factors present either in the cytoplasm or in the nucleus, leading to the expression of target genes and, as a consequence, they elicit various biological responses. The aim of this work is to provide a comprehensive review focusing on the roles of MAPK signaling pathways in ocular pathophysiology and the potential to influence these for the treatment of eye diseases. We summarize the current knowledge of identified MAPK-targeting compounds in the context of ocular diseases such as macular degeneration, cataract, glaucoma and keratopathy, but also in rare ocular diseases where the cell differentiation, proliferation or migration are defective. Potential therapeutic interventions are also discussed. Additionally, we discuss challenges in overcoming the reported eye toxicity of some MAPK inhibitors.

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

Dynamic regulation of RAS and RAS signaling

RAS proteins regulate most aspects of cellular physiology. They are mutated in 30% of human cancers and 4% of developmental disorders termed Rasopathies. They cycle between active GTP-bound and inactive GDP-bound states. When active, they can interact with a wide range of effectors that control fundamental biochemical and biological processes. Emerging evidence suggests that RAS proteins are not simple on/off switches but sophisticated information processing devices that compute cell fate decisions by integrating external and internal cues. A critical component of this compute function is the dynamic regulation of RAS activation and downstream signaling that allows RAS to produce a rich and nuanced spectrum of biological outputs. We discuss recent findings how the dynamics of RAS and its downstream signaling is regulated. Starting from the structural and biochemical properties of wild-type and mutant RAS proteins and their activation cycle, we examine higher molecular assemblies, effector interactions and downstream signaling outputs, all under the aspect of dynamic regulation. We also consider how computational and mathematical modeling approaches contribute to analyze and understand the pleiotropic functions of RAS in health and disease.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise

The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.

Optogenetic actuator - ERK biosensor circuits identify MAPK network nodes that shape ERK dynamics

Combining single-cell measurements of ERK activity dynamics with perturbations provides insights into the MAPK network topology. We built circuits consisting of an optogenetic actuator to activate MAPK signaling and an ERK biosensor to measure single-cell ERK dynamics. This allowed us to conduct RNAi screens to investigate the role of 50 MAPK proteins in ERK dynamics. We found that the MAPK network is robust against most node perturbations. We observed that the ERK-RAF and the ERK-RSK2-SOS negative feedback operate simultaneously to regulate ERK dynamics. Bypassing the RSK2-mediated feedback, either by direct optogenetic activation of RAS, or by RSK2 perturbation, sensitized ERK dynamics to further perturbations. Similarly, targeting this feedback in a human ErbB2-dependent oncogenic signaling model increased the efficiency of a MEK inhibitor. The RSK2-mediated feedback is thus important for the ability of the MAPK network to produce consistent ERK outputs, and its perturbation can enhance the efficiency of MAPK inhibitors.

Network pharmacology explores the mechanisms of Eucommia ulmoides cortex against postmenopausal osteoporosis

Postmenopausal osteoporosis (PMOP) has become one of most frequent chronic disease worldwide with aging population. Eucommia ulmoides cortex (EU), a traditional Chinese medicine, has long since been used to treat PMOP. The aim of this study is to explore pharmacological mechanisms of EU against PMOP through using network pharmacology approach.The active ingredients of EU were obtained from Traditional Chinese Medicine System Pharmacology database, and target fishing was performed on these ingredients in UniProt database for identification of their relative targets. Then, we screened the targets of PMOP using GeneCards database and DisGeNET database. The overlapping genes between PMOP and EU were obtained to performed protein-protein interaction, Gene Ontology analysis, Kyoto encyclopedia of genes, and genomes analysis.Twenty-eight active ingredients were identified in EU, and corresponded to 207 targets. Also, 292 targets were closely associated with PMOP, and 50 of them matched with the targets of EU were considered as therapeutically relevant. Gene ontology enrichment analysis suggested that EU exerted anti-PMOP effects via modulating multiple biological processes including cell proliferation, angiogenesis, and inflammatory response. Kyoto encyclopedia of genes and genomes enrichment analysis revealed several pathways, such as PI3K-AKT pathway, mitogen-activated protein kinase pathway, hypoxia-inducible factors-1 pathway, tumor necrosis factor pathway, and interleukin-17 pathway that might be involved in regulating the above biological processes.Through the method of network pharmacology, we systematically investigated the mechanisms of EU against PMOP. The multi-targets and multi-pathways identified here could provide new insights for further determination of more exact mechanisms of EU.

Live imaging approach of dynamic multicellular responses in ERK signaling during vertebrate tissue development

The chemical and mechanical responses of cells via the exchange of information during growth and development result in the formation of biological tissues. Information processing within the cells through the signaling pathways and networks inherent to the constituent cells has been well-studied. However, the cell signaling mechanisms responsible for generating dynamic multicellular responses in developing tissues remain unclear. Here, I review the dynamic multicellular response systems during the development and growth of vertebrate tissues based on the extracellular signal-regulated kinase (ERK) pathway. First, an overview of the function of the ERK signaling network in cells is provided, followed by descriptions of biosensors essential for live imaging of the quantification of ERK activity in tissues. Then adducing four examples, I highlight the contribution of live imaging techniques for studying the involvement of spatio-temporal patterns of ERK activity change in tissue development and growth. In addition, theoretical implications of ERK signaling are also discussed from the viewpoint of dynamic systems. This review might help in understanding ERK-mediated dynamic multicellular responses and tissue morphogenesis.

Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning

Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.

Implications of glutathione-S transferase P1 in MAPK signaling as a CRAF chaperone: In memory of Dr. Irving Listowsky

Glutathione-S transferase P1 (GSTP1) is one of the glutathione-S transferase isozymes that belong to a family of phase II metabolic isozymes. The unique feature of GSTP1 compared with other GST isozymes is its relatively high expression in malignant tissues. Thus, clinically, GSTP1 serves as a tumor marker and as a refractory factor against certain types of anticancer drugs through its primary function as a detoxifying enzyme. Additionally, recent studies have identified a chaperone activity of GSTP1 involved in the regulation the function of various intracellular proteins, including factors of the growth signaling pathway. In this review, we will first describe the function of GSTP1 and then extend the details onto its role in the mitogen-activated protein kinase signal pathway, referring to the results of our recent study that proposed a novel autocrine signal loop formed by the CRAF/GSTP1 complex in mutated KRAS and BRAF cancers. Finally, the possibilities of new therapeutic approaches for these cancers by targeting this complex will be discussed.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

Design and implementation of a microfluidic device capable of temporal growth factor delivery reveal filtering capabilities of the EGFR/ERK pathway

Utilizing microfluidics to mimic the dynamic temporal changes of growth factor and cytokine concentrations in vivo has greatly increased our understanding of how signal transduction pathways are structured to encode extracellular stimuli. To date, these devices have focused on delivering pulses of varying frequency, and there are limited cell culture models for delivering slowly increasing concentrations of stimuli that cells may experience in vivo. To examine this setting, we developed and validated a microfluidic device that can deliver increasing concentrations of growth factor over periods ranging from 6 to 24 h. Using this device and a fluorescent biosensor of extracellular-regulated kinase (ERK) activity, we delivered a slowly increasing concentration of epidermal growth factor (EGF) to human mammary epithelial cells and surprisingly observed minimal ERK activation, even at concentrations that stimulate robust activity in bolus delivery. The cells remained unresponsive to subsequent challenges with EGF, and immunocytochemistry suggested that the loss of an epidermal growth factor receptor was responsible. Cells were then challenged with faster rates of change of EGF, revealing an increased ERK activity as a function of rate of change. Specifically, both the fraction of cells that responded and the length of ERK activation time increased with the rate of change. This microfluidic device fills a gap in the current repertoire of in vitro microfluidic devices and demonstrates that slower, more physiological changes in growth factor presentation can reveal new regulatory mechanisms for how signal transduction pathways encode changes in the extracellular growth factor milieu.

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.

Long-distance regressive signaling in neural development and disease

Nervous system development proceeds via well-orchestrated processes involving a balance between progressive and regressive events including stabilization or elimination of axons, synapses, and even entire neurons. These progressive and regressive events are driven by functionally antagonistic signaling pathways with the dominant pathway eventually determining whether a neural element is retained or removed. Many of these developmental sculpting events are triggered by final target innervation necessitating a long-distance mode of communication. While long-distance progressive signaling has been well characterized, particularly for neurotrophic factors, there remains relatively little known about how regressive events are triggered from a distance. Here we discuss the emergent phenomenon of long-distance regressive signaling pathways. In particular, we will cover (a) progressive and regressive cues known to be employed after target innervation, (b) the mechanisms of long-distance signaling from an endosomal platform, (c) recent evidence that long-distance regressive cues emanate from platforms like death receptors or repulsive axon guidance receptors, and (d) evidence that these pathways are exploited in pathological scenarios. This article is categorized under: Nervous System Development > Vertebrates: General Principles Signaling Pathways > Global Signaling Mechanisms Establishment of Spatial and Temporal Patterns > Cytoplasmic Localization.

A Quantitative Modular Modeling Approach Reveals the Effects of Different A20 Feedback Implementations for the NF-kB Signaling Dynamics

Signaling pathways involve complex molecular interactions and are controled by non-linear regulatory mechanisms. If details of regulatory mechanisms are not fully elucidated, they can be implemented by different, equally reasonable mathematical representations in computational models. The study presented here focusses on NF-κB signaling, which is regulated by negative feedbacks via IκBα and A20. A20 inhibits NF-κB activation indirectly through interference with proteins that transduce the signal from the TNF receptor complex to activate the IκB kinase (IKK) complex. A number of pathway models has been developed implementing the A20 effect in different ways. We here focus on the question how different A20 feedback implementations impact the dynamics of NF-κB. To this end, we develop a modular modeling approach that allows combining previously published A20 modules with a common pathway core module. The resulting models are fitted to a published comprehensive experimental data set and therefore show quantitatively comparable NF-κB dynamics. Based on defined measures for the initial and long-term behavior we analyze the effects of a wide range of changes in the A20 feedback strength, the IκBα feedback strength and the TNFα stimulation strength on NF-κB dynamics. This shows similarities between the models but also model-specific differences. In particular, the A20 feedback strength and the TNFα stimulation strength affect initial and long-term NF-κB concentrations differently in the analyzed models. We validated our model predictions experimentally by varying TNFα concentrations applied to HeLa cells. These time course data indicate that only one of the A20 feedback models appropriately describes the impact of A20 on the NF-κB dynamics in this cell type.

Strategic Combinations to Prevent and Overcome Resistance to Targeted Therapies in Oncology

Recent advances in the understanding of underlying molecular signaling mechanisms of cancer susceptibility and progression have led to an increase in the use of targeted therapies for cancer treatment. Despite improvements in survival with new treatment options in oncology, resistance to therapy is a major obstacle to the long-term effectiveness of targeted agents in metastatic cancer treatment, culminating in insensitivity to treatment and tumor outgrowth. Adaptive resistance can play an important role in primary and upfront resistance to therapy as well as in secondary or acquired resistance. By focusing on colorectal and breast tumors, we discuss how therapeutic combinations based on specific drivers of tumor biology can be used to overcome resistance. We present how monitoring tumor dynamics over time may allow early adaptation of treatment. Breast cancer is the most common malignancy in women worldwide, and the majority of these cancers are sensitive to endocrine therapy (ET) blocking the production of or response to estrogen. However, primary and acquired resistance limits efficacy. Recent combinations of agents targeted to pathways that drive tumor growth resistance with ET have resulted in remarkable improvements in disease response and control, improving survival in some settings. In this review, we summarize adaptive resistance mechanisms, approaches to combination strategies, and dynamic tumor monitoring to improve efficacy and overcome resistance. We provide examples of combination therapy to enhance the efficacy of targeted therapies in breast and colorectal tumors.

Revealing hidden information in osteoblast's mechanotransduction through analysis of time patterns of critical events

BACKGROUND

Mechanotransduction in bone cells plays a pivotal role in osteoblast differentiation and bone remodelling. Mechanotransduction provides the link between modulation of the extracellular matrix by mechanical load and intracellular activity. By controlling the balance between the intracellular and extracellular domains, mechanotransduction determines the optimum functionality of skeletal dynamics. Failure of this relationship was suggested to contribute to bone-related diseases such as osteoporosis.

RESULTS

A hybrid mechanical and agent-based model (Mech-ABM), simulating mechanotransduction in a single osteoblast under external mechanical perturbations, was utilised to simulate and examine modulation of the activation dynamics of molecules within mechanotransduction on the cellular response to mechanical stimulation. The number of molecules and their fluctuations have been analysed in terms of recurrences of critical events. A numerical approach has been developed to invert subordination processes and to extract the direction processes from the molecular signals in order to derive the distribution of recurring events. These predict that there are large fluctuations enclosing information hidden in the noise which is beyond the dynamic variations of molecular baselines. Moreover, studying the system under different mechanical load regimes and altered dynamics of feedback loops, illustrate that the waiting time distributions of each molecule are a signature of the system's state.

CONCLUSIONS

The behaviours of the molecular waiting times change with the changing of mechanical load regimes and altered dynamics of feedback loops, presenting the same variation of patterns for similar interacting molecules and identifying specific alterations for key molecules in mechanotransduction. This methodology could be used to provide a new tool to identify potent molecular candidates to modulate mechanotransduction, hence accelerate drug discovery towards therapeutic targets for bone mass upregulation.

Systems Biology of Cancer Metastasis

Cancer metastasis is no longer viewed as a linear cascade of events but rather as a series of concurrent, partially overlapping processes, as successfully metastasizing cells assume new phenotypes while jettisoning older behaviors. The lack of a systemic understanding of this complex phenomenon has limited progress in developing treatments for metastatic disease. Because metastasis has traditionally been investigated in distinct physiological compartments, the integration of these complex and interlinked aspects remains a challenge for both systems-level experimental and computational modeling of metastasis. Here, we present some of the current perspectives on the complexity of cancer metastasis, the multiscale nature of its progression, and a systems-level view of the processes underlying the invasive spread of cancer cells. We also highlight the gaps in our current understanding of cancer metastasis as well as insights emerging from interdisciplinary systems biology approaches to understand this complex phenomenon.

Interlinked GTPase cascades provide a motif for both robust switches and oscillators

GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, N_c, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.

Limits to the rate of information transmission through the MAPK pathway

Two important signalling pathways of NF-κB and ERK transmit merely 1 bit of information about the level of extracellular stimulation. It is thus unclear how such systems can coordinate complex cell responses to external cues. We analyse information transmission in the MAPK/ERK pathway that converts both constant and pulsatile EGF stimulation into pulses of ERK activity. Based on an experimentally verified computational model, we demonstrate that, when input consists of sequences of EGF pulses, transmitted information increases nearly linearly with time. Thus, pulse-interval transcoding allows more information to be relayed than the amplitude–amplitude transcoding considered previously for the ERK and NF-κB pathways. Moreover, the information channel capacity C, or simply bitrate, is not limited by the bandwidth B = 1/τ, where τ ≈ 1 h is the relaxation time. Specifically, when the input is provided in the form of sequences of short binary EGF pulses separated by intervals that are multiples of τ/n (but not shorter than τ), then for n = 2, C ≈ 1.39 bit h⁻¹; and for n = 4, C ≈ 1.86 bit h⁻¹. The capability to respond to random sequences of EGF pulses enables cells to propagate spontaneous ERK activity waves across tissue.

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.

Integrating chemical and mechanical signals through dynamic coupling between cellular protrusions and pulsed ERK activation

The Ras-ERK signaling pathway regulates diverse cellular processes in response to environmental stimuli and contains important therapeutic targets for cancer. Recent single cell studies revealed stochastic pulses of ERK activation, the frequency of which determines functional outcomes such as cell proliferation. Here we show that ERK pulses are initiated by localized protrusive activities. Chemically and optogenetically induced protrusions trigger ERK activation through various entry points into the feedback loop involving Ras, PI3K, the cytoskeleton, and cellular adhesion. The excitability of the protrusive signaling network drives stochastic ERK activation in unstimulated cells and oscillations upon growth factor stimulation. Importantly, protrusions allow cells to sense combined signals from substrate stiffness and the growth factor. Thus, by uncovering the basis of ERK pulse generation we demonstrate how signals involved in cell growth and differentiation are regulated by dynamic protrusions that integrate chemical and mechanical inputs from the environment.

Cellular ERK activation occurs as discrete pulses but their relationship to upstream Ras signaling is still under debate. Here, the authors show that Ras signaling associated with cellular protrusions triggers pulsed ERK activation, thereby enabling cells to integrate chemical and mechanical stimuli.

Initial state perturbations as a validation method for data-driven fuzzy models of cellular networks

Background

Data-driven methods that automatically learn relations between attributes from given data are a popular tool for building mathematical models in computational biology. Since measurements are prone to errors, approaches dealing with uncertain data are especially suitable for this task. Fuzzy models are one such approach, but they contain a large amount of parameters and are thus susceptible to over-fitting. Validation methods that help detect over-fitting are therefore needed to eliminate inaccurate models.

Results

We propose a method to enlarge the validation datasets on which a fuzzy dynamic model of a cellular network can be tested. We apply our method to two data-driven dynamic models of the MAPK signalling pathway and two models of the mammalian circadian clock. We show that random initial state perturbations can drastically increase the mean error of predictions of an inaccurate computational model, while keeping errors of predictions of accurate models small.

Conclusions

With the improvement of validation methods, fuzzy models are becoming more accurate and are thus likely to gain new applications. This field of research is promising not only because fuzzy models can cope with uncertainty, but also because their run time is short compared to conventional modelling methods that are nowadays used in systems biology.

Emergent memory in cell signaling: Persistent adaptive dynamics in cascades can arise from the diversity of relaxation time-scales

The mitogen-activated protein kinase (MAPK) signaling cascade, an evolutionarily conserved motif present in all eukaryotic cells, is involved in coordinating crucial cellular functions. While the asymptotic dynamical behavior of the pathway stimulated by a time-invariant signal is relatively well-understood, we show using a computational model that it exhibits a rich repertoire of transient adaptive responses to changes in stimuli. When the signal is switched on, the response is characterized by long-lived modulations in frequency as well as amplitude. On withdrawing the stimulus, the activity decays over long timescales, exhibiting reverberations characterized by repeated spiking in the activated MAPK concentration. The long-term persistence of such post-stimulus activity suggests that the cascade retains memory of the signal for a significant duration following its removal. The molecular mechanism underlying the reverberatory activity is related to the existence of distinct relaxation rates for the different cascade components. This results in the imbalance of fluxes between different layers of the cascade, with the reuse of activated kinases as enzymes when they are released from sequestration in complexes. The persistent adaptive response, indicative of a cellular “short-term” memory, suggests that this ubiquitous signaling pathway plays an even more central role in information processing by eukaryotic cells.

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.

Decoding Signal Processing at the Single-Cell Level

The feedforward circuitry regulating ERK-dependent early response genes acts as a signal integrator rather than a signal persistence detector.

Information processing in the NF-κB pathway

The NF-κB pathway is known to transmit merely 1 bit of information about stimulus level. We combined experimentation with mathematical modeling to elucidate how information about TNF concentration is turned into a binary decision. Using Kolmogorov-Smirnov distance, we quantified the cell’s ability to discern 8 TNF concentrations at each step of the NF-κB pathway, to find that input discernibility decreases as signal propagates along the pathway. Discernibility of low TNF concentrations is restricted by noise at the TNF receptor level, whereas discernibility of high TNF concentrations it is restricted by saturation/depletion of downstream signaling components. Consequently, signal discernibility is highest between 0.03 and 1 ng/ml TNF. Simultaneous exposure to TNF or LPS and a translation inhibitor, cycloheximide, leads to prolonged NF-κB activation and a marked increase of transcript levels of NF-κB inhibitors, IκBα and A20. The impact of cycloheximide becomes apparent after the first peak of nuclear NF-κB translocation, meaning that the NF-κB network not only relays 1 bit of information to coordinate the all-or-nothing expression of early genes, but also over a longer time course integrates information about other stimuli. The NF-κB system should be thus perceived as a feedback-controlled decision-making module rather than a simple information transmission channel.

Applications of Optobiology in Intact Cells and Multicellular Organisms

Temporal kinetics and spatial coordination of signal transduction in cells are vital for cell fate determination. Tools that allow for precise modulation of spatiotemporal regulation of intracellular signaling in intact cells and multicellular organisms remain limited. The emerging optobiological approaches use light to control protein-protein interaction in live cells and multicellular organisms. Optobiology empowers light-mediated control of diverse cellular and organismal functions such as neuronal activity, intracellular signaling, gene expression, cell proliferation, differentiation, migration, and apoptosis. In this review, we highlight recent developments in optobiology, focusing on new features of second-generation optobiological tools. We cover applications of optobiological approaches in the study of cellular and organismal functions, discuss current challenges, and present our outlook. Taking advantage of the high spatial and temporal resolution of light control, optobiology promises to provide new insights into the coordination of signaling circuits in intact cells and multicellular organisms.

RAF1/BRAF dimerization integrates the signal from RAS to ERK and ROKα

Downstream of growth factor receptors and of the guanine triphosphatase (GTPase) RAS, heterodimers of the serine/threonine kinases BRAF and RAF1 are critical upstream kinases and activators of the mitogen-activated protein kinase (MAPK) module containing the mitogen-activated and extracellular signal-regulated kinase kinase (MEK) and their targets, the extracellular signal-regulated kinase (ERK) family. Either direct or scaffold protein-mediated interactions among the components of the ERK module (the MAPKKKs BRAF and RAF1, MEK, and ERK) facilitate signal transmission. RAF1 also has essential functions in the control of tumorigenesis and migration that are mediated through its interaction with the kinase ROKα, an effector of the GTPase RHO and regulator of cytoskeletal rearrangements. We combined mutational and kinetic analysis with mathematical modeling to show that the interaction of RAF1 with ROKα is coordinated with the role of RAF1 in the ERK pathway. We found that the phosphorylated form of RAF1 that interacted with and inhibited ROKα was generated during the interaction of RAF1 with the ERK module. This mechanism adds plasticity to the ERK pathway, enabling signal diversification at the level of both ERK and RAF. Furthermore, by connecting ERK activation with the regulation of ROKα and cytoskeletal rearrangements by RAF1, this mechanism has the potential to precisely coordinate the proper timing of proliferation with changes in cell shape, adhesion, or motility.