A computational study of feedback effects on signal dynamics in a mitogen-activated protein kinase (MAPK) pathway model

PI3K signaling through a biochemical systems lens

Following 3 decades of extensive research into PI3K signaling, it is now evidently clear that the underlying network does not equate to a simple ON/OFF switch. This is best illustrated by the multifaceted nature of the many diseases associated with aberrant PI3K signaling, including common cancers, metabolic disease, and rare developmental disorders. However, we are still far from a complete understanding of the fundamental control principles that govern the numerous phenotypic outputs that are elicited by activation of this well-characterized biochemical signaling network, downstream of an equally diverse set of extrinsic inputs. At its core, this is a question on the role of PI3K signaling in cellular information processing and decision making. Here, we review the determinants of accurate encoding and decoding of growth factor signals and discuss outstanding questions in the PI3K signal relay network. We emphasize the importance of quantitative biochemistry, in close integration with advances in single-cell time-resolved signaling measurements and mathematical modeling.

Phosphatidylserine-Specific Phospholipase A1 Alleviates Lipopolysaccharide-Induced Macrophage Inflammation by Inhibiting MAPKs Activation

Macrophages are key in innate immune responses and play vital roles in homeostasis and inflammatory diseases. Phosphatidylserine-specific phospholipase A1 (PS-PLA1) is a specific phospholipase which hydrolyzes fatty acid from the sn-1 position of phosphatidylserine (PS) to produce lysophosphatidylserine (lysoPS). Both PS and lysoPS are associated with activation of immune cells including macrophages. However, the effect of PS-PLA1 on macrophage inflammation remains unclear. The purpose of this study is to evaluate the role of PS-PLA1 in lipopolysaccharide (LPS)-induced macrophage inflammation. Alterations of PS-PLA1 expression in LPS-stimulated RAW264.7 macrophages were investigated via Western blot. PS-PLA1 stable knockdown and overexpression RAW264.7 cell lines were generated by infecting cells with appropriate lentiviral vectors, respectively. PS-PLA1 expression was found to be dramatically upregulated in RAW264.7 macrophages after LPS stimulation. PS-PLA1 knockdown promotes while PS-PLA1 overexpression ameliorates the release of TNF-α, IL-1β and nitric oxide from RAW264.7 cells and M1 macrophage polarization. Additionally, PS-PLA1 knockdown facilitates phosphorylation of p38, ERK and JNK, while PS-PLA1 overexpression attenuates their phosphorylation. Moreover, mitogen-activated protein kinase (MAPK) inhibitors blocks the release of TNF-α and IL-1β in PS-PLA1 knockdown RAW264.7 cells after LPS stimulation. These findings suggest PS-PLA1 ameliorates LPS-induced macrophage inflammation by inhibiting MAPKs activation, and PS-PLA1 might be considered as a target for modulating macrophage inflammation.

Robust and tunable signal processing in mammalian cells via engineered covalent modification cycles

Engineered signaling networks can impart cells with new functionalities useful for directing differentiation and actuating cellular therapies. For such applications, the engineered networks must be tunable, precisely regulate target gene expression, and be robust to perturbations within the complex context of mammalian cells. Here, we use bacterial two-component signaling proteins to develop synthetic phosphoregulation devices that exhibit these properties in mammalian cells. First, we engineer a synthetic covalent modification cycle based on kinase and phosphatase proteins derived from the bifunctional histidine kinase EnvZ, enabling analog tuning of gene expression via its response regulator OmpR. By regulating phosphatase expression with endogenous miRNAs, we demonstrate cell-type specific signaling responses and a new strategy for accurate cell type classification. Finally, we implement a tunable negative feedback controller via a small molecule-stabilized phosphatase, reducing output expression variance and mitigating the context-dependent effects of off-target regulation and resource competition. Our work lays the foundation for establishing tunable, precise, and robust control over cell behavior with synthetic signaling networks.

All-Trans Retinoic Acid Ameliorates the Early Experimental Cerebral Ischemia-Reperfusion Injury in Rats by Inhibiting the Loss of the Blood-Brain Barrier via the JNK/P38MAPK Signaling Pathway

All-trans retinoic acid (ATRA) influences the outcomes of cerebral ischemic reperfusion (CIR) injury, but the mechanism remains unclear. The present study aimed to investigate the effects of ATRA on loss of the blood brain barrier (BBB) following CIR and to explore the possible mechanisms. Transient middle cerebral artery occlusion was performed on male SD rats to construct an in vivo CIR model. Neurological deficits, BBB permeability, brain edema, MRI and JNK/P38 MAPK proteins were detected at 24 h following CIR. We demonstrated that ATRA pretreatment could alleviate CIR-induced neurological deficits, increase of BBB permeability, infarct volume, degradation of tight junction proteins, inhibit MMP-9 protein expression and activity. ATRA treatment also reduced the p-P38 and p-JNK protein level. However the protective effect of ATRA on CIR could be reversed by administration of retinoic acid alpha receptor antagonist Ro41-5253. SP600125 and SB203580, which is the JNK/P38 pathway inhibitors has the same protective effect as ATRA. These results indicated that ATRA may inhibit the JNK/P38 MAPK pathway to alleviate BBB disruption and improve CIR outcomes.

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

In biological systems, pathways define complex interaction networks where multiple molecular elements are involved in a series of controlled reactions producing responses to specific biomolecular signals. These biosystems are dynamic and there is a need for mathematical and computational methods able to analyze the symbolic elements and the interactions between them and produce adequate readouts of such systems. In this work, we use rewriting logic to analyze the cellular signaling of epidermal growth factor (EGF) and its cell surface receptor (EGFR) in order to induce cellular proliferation. Signaling is initiated by binding the ligand protein EGF to the membrane-bound receptor EGFR so as to trigger a reactions path which have several linked elements through the cell from the membrane till the nucleus. We present two different types of search for analyzing the EGF/proliferation system with the help of Pathway Logic tool, which provides a knowledge-based development environment to carry out the modeling of the signaling. The first one is a standard (forward) search. The second one is a novel approach based on narrowing, which allows us to trace backwards the causes of a given final state. The analysis allows the identification of critical elements that have to be activated to provoke proliferation.

A comparative review of computational methods for pathway perturbation analysis: dynamical and topological perspectives

Stem cells offer great promise within the field of regenerative medicine but despite encouraging results, the large scale use of stem cells for therapeutic applications still faces challenges when it comes to controlling signaling pathway responses with respect to environmental perturbations.

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.

Quantitative measures for redox signaling

Redox signaling is now recognized as an important regulatory mechanism for a number of cellular processes including the antioxidant response, phosphokinase signal transduction and redox metabolism. While there has been considerable progress in identifying the cellular machinery involved in redox signaling, quantitative measures of redox signals have been lacking, limiting efforts aimed at understanding and comparing redox signaling under normoxic and pathogenic conditions. Here we have outlined some of the accepted principles for redox signaling, including the description of hydrogen peroxide as a signaling molecule and the role of kinetics in conferring specificity to these signaling events. Based on these principles, we then develop a working definition for redox signaling and review a number of quantitative methods that have been employed to describe signaling in other systems. Using computational modeling and published data, we show how time- and concentration- dependent analyses, in particular, could be used to quantitatively describe redox signaling and therefore provide important insights into the functional organization of redox networks. Finally, we consider some of the key challenges with implementing these methods.

Modelling and analysis of an ensemble of eukaryotic translation initiation models

Programmed protein synthesis plays an important role in the cell cycle. Deregulated translation has been observed in several cancers. In this study, the authors constructed an ensemble of mathematical models describing the integration of growth factor signals with translation initiation. Using these models, the authors estimated critical structural features of the translation architecture. Sensitivity and robustness analysis with and without growth factors suggested that a balance between competing regulatory programmes governed translation initiation. Proteins such as Akt and mTor promoted initiation by integrating growth factor signals with the assembly of the 80S initiation complex. However, negative regulators such as PTEN and 4EBP1 restrained initiation in the absence of stimulation. Other proteins such as eIF4E were also found to be structurally critical as deletion of amplification of these components resulted in a network incapable of nominal operation. These findings could help understand the molecular basis of translation deregulation observed in cancer and perhaps lead to new anti-cancer therapeutic strategies. [Includes supplementary material].

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).

In silico investigation of new binding pocket for mitogen activated kinase kinase (MEK): Development of new promising inhibitors

It has been previously shown that the inhibition of mitogen activated protein kinase kinase (MEK) contributes to apoptosis and suppression of different cancer cells. Correspondingly, a number of MEK1/2 inhibitors have been designed and evaluated since 2001. However, they did not satisfy essential pharmacokinetic (PK) and pharmacodynamic (PD) properties thus, almost most of them were terminated in pre-clinical or clinical studies. This study aims to design new specific MEK1/2 inhibitors with improved PK/PD profiles to be used as alternative cancer medications. In first part of this study, a comprehensive screening, for the first time, was done on well-known MEK1/2 inhibitors using a number of computational programs such as AutoDock Tools 4.2 (ADT) and AutoDock Vina. Therefore a valuable training dataset as well as a reliable pharmacophore model were provided which were then used to design new inhibitors. According to the results of training dataset, Trametinib was determined as the best inhibitor provided, so far. So, Trametinib was used as the lead structure to design new inhibitors in this study. In second part of this investigation, a set of new allosteric MEK1/2 inhibitors were designed significantly improving the binding energy as well as the ADMET properties, suggesting more specific and stable ligand-receptor complexes. Consequently, the structures 14 and 15 of our inhibitors, as the most potent structures, are great substituents for Trametinib to be used and evaluated in clinical trials as alternative cancer drugs.

Paradoxical results in perturbation-based signaling network reconstruction

Mathematical models are extensively employed to understand physicochemical processes in biological systems. In the absence of detailed mechanistic knowledge, models are often based on network inference methods, which in turn rely upon perturbations to nodes by biochemical means. We have discovered a potential pitfall of the approach underpinning such methods when applied to signaling networks. We first show experimentally, and then explain mathematically, how even in the simplest signaling systems, perturbation methods may lead to paradoxical conclusions: for any given pair of two components X and Y, and depending upon the specific intervention on Y, either an activation or a repression of X could be inferred. This effect is of a different nature from incomplete network identification due to underdetermined data and is a phenomenon intrinsic to perturbations. Our experiments are performed in an in vitro minimal system, thus isolating the effect and showing that it cannot be explained by feedbacks due to unknown intermediates. Moreover, our in vitro system utilizes proteins from a pathway in mammalian (and other eukaryotic) cells that play a central role in proliferation, gene expression, differentiation, mitosis, cell survival, and apoptosis. This pathway is the perturbation target of contemporary therapies for various types of cancers. The results presented here show that the simplistic view of intracellular signaling networks being made up of activation and repression links is seriously misleading, and call for a fundamental rethinking of signaling network analysis and inference methods.

MAPK's networks and their capacity for multistationarity due to toric steady states

Mitogen-activated protein kinase (MAPK) signaling pathways play an essential role in the transduction of environmental stimuli to the nucleus, thereby regulating a variety of cellular processes, including cell proliferation, differentiation and programmed cell death. The components of the MAPK extracellular activated protein kinase (ERK) cascade represent attractive targets for cancer therapy as their aberrant activation is a frequent event among highly prevalent human cancers. MAPK networks are a model for computational simulation, mostly using ordinary and partial differential equations. Key results showed that these networks can have switch-like behavior, bistability and oscillations. In this work, we consider three representative ERK networks, one with a negative feedback loop, which present a binomial steady state ideal under mass-action kinetics. We therefore apply the theoretical result present in to find a set of rate constants that allow two significantly different stable steady states in the same stoichiometric compatibility class for each network. Our approach makes it possible to study certain aspects of the system, such as multistationarity, without relying on simulation, since we do not assume a priori any constant but the topology of the network. As the performed analysis is general it could be applied to many other important biochemical networks.

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.

Autocrine FGF feedback can establish distinct states of Nanog expression in pluripotent stem cells: a computational analysis

Background

The maintenance of stem cell pluripotency is controlled by a core cluster of transcription factors, NANOG, OCT4 and SOX2 – genes that jointly regulate each other’s expression. The expression of some of these genes, especially of Nanog, is heterogeneous in a population of undifferentiated stem cells in culture. Transient changes in expression levels, as well as heterogeneity of the population is not restricted to this core regulator, but involve a large number of other genes that include growth factors, transcription factors or signal transduction proteins.

Results

As the molecular mechanisms behind NANOG expression heterogeneity is not yet understood, we explore by computational modeling the core transcriptional regulatory circuit and its input from autocrine FGF signals that act through the MAP kinase cascade. We argue that instead of negative feedbacks within the core NANOG-OCT4-SOX2 transcriptional regulatory circuit, autocrine signaling loops such as the Esrrb - FGF - ERK feedback considered here are likely to generate distinct sub-states within the “ON” state of the core Nanog switch. Thus, the experimentally observed fluctuations in Nanog transcription levels are best explained as noise-induced transitions between negative feedback-generated sub-states. We also demonstrate that ERK phosphorilation is altered and being anti-correlated with fluctuating Nanog expression – in accord with model simulations. Our modeling approach assigns an empirically testable function to the transcriptional regulators Klf4 and Esrrb, and predict differential regulation of FGF family members.

Conclusions

We argue that slow fluctuations in Nanog expression likely reflect individual cell-specific changes in parameters of an autocrine feedback loop, such as changes in ligand capture efficiency, receptor numbers or the presence of crosstalks within the MAPK signal transduction pathway. We proposed a model that operates with binding affinities of multiple transcriptional regulators of pluripotency, and the activity of an autocrine signaling pathway. The resulting model produces varied expression levels of several components of pluripotency regulation, largely consistent with empirical observations reported previously and in this present work.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0112-4) contains supplementary material, which is available to authorized users.

F-box only protein 31 (FBXO31) negatively regulates p38 mitogen-activated protein kinase (MAPK) signaling by mediating lysine 48-linked ubiquitination and degradation of mitogen-activated protein kinase kinase 6 (MKK6)

The p38 MAPK signal transduction pathway plays an important role in inflammatory and stress responses. MAPKK6 (MKK6), a dual specificity protein kinase, is a p38 activator. Activation of the MKK6-p38 pathway is kept in check by multiple layers of regulations, including autoinhibition, dimerization, scaffold proteins, and Lys-63-linked polyubiquitination. However, the mechanisms underlying deactivation of MKK6-p38, which is crucial for maintaining the magnitude and duration of signal transduction, are not well understood. Lys-48-linked ubiquitination, which marks substrates for proteasomal degradation, is an important negative posttranslational regulatory machinery for signal pathway transduction. Here we report that the accumulation of F-box only protein 31 (FBXO31), a component of Skp1 · Cul1 · F-box protein E3 ligase, negatively regulated p38 activation in cancer cells upon genotoxic stresses. Our results show that FBXO31 binds to MKK6 and mediates its Lys-48-linked polyubiquitination and degradation, thereby functioning as a negative regulator of MKK6-p38 signaling and protecting cells from stress-induced cell apoptosis. Taken together, our findings uncover a new mechanism of deactivation of MKK6-p38 and substantiate a novel regulatory role of FBXO31 in stress response.

Decoding information in cell shape

Shape is an indicator of cell health. But how is the information in shape decoded? We hypothesize that decoding occurs by modulation of signaling through changes in plasma membrane curvature. Using analytical approaches and numerical simulations, we studied how elongation of cell shape affects plasma membrane signaling. Mathematical analyses reveal transient accumulation of activated receptors at regions of higher curvature with increasing cell eccentricity. This distribution of activated receptors is periodic, following the Mathieu function, and it arises from local imbalance between reaction and diffusion of soluble ligands and receptors in the plane of the membrane. Numerical simulations show that transient microdomains of activated receptors amplify signals to downstream protein kinases. For growth factor receptor pathways, increasing cell eccentricity elevates the levels of activated cytoplasmic Src and nuclear MAPK1,2. These predictions were experimentally validated by changing cellular eccentricity, showing that shape is a locus of retrievable information storage in cells.

A new mathematical approach for qualitative modeling of the insulin-TOR-MAPK network

In this paper we develop a novel mathematical model of the insulin-TOR-MAPK signaling network that controls growth. Most data on the properties of the insulin and MAPK signaling networks are static and the responses to experimental interventions, such as knockouts, overexpression, and hormonal input are typically reported as scaled quantities. The modeling paradigm we develop here uses scaled variables and is ideally suited to simulate systems in which much of the available data are scaled. Our mathematical representation of signaling networks provides a way to reconcile theory and experiments, thus leading to a better understanding of the properties and function of these signaling networks. We test the performance of the model against a broad diversity of experimental data. The model correctly reproduces experimental insulin dose-response relationships. We study the interaction between insulin and MAPK signaling in the control of protein synthesis, and the interactions between amino acids, insulin and TOR signaling. We study the effects of variation in FOXO expression on protein synthesis and glucose transport capacity, and show that a FOXO knockout can partially rescue protein synthesis capacity of an insulin receptor (INR) knockout. We conclude that the modeling paradigm we develop provides a simple tool to investigate the qualitative properties of signaling networks.

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.

Monte carlo study elucidates the type 1/type 2 choice in apoptotic death signaling in healthy and cancer cells

Apoptotic cell death is coordinated through two distinct (type 1 and type 2) intracellular signaling pathways. How the type 1/type 2 choice is made remains a central problem in the biology of apoptosis and has implications for apoptosis related diseases and therapy. We study the problem of type 1/type 2 choice in silico utilizing a kinetic Monte Carlo model of cell death signaling. Our results show that the type 1/type 2 choice is linked to deterministic versus stochastic cell death activation, elucidating a unique regulatory control of the apoptotic pathways. Consistent with previous findings, our results indicate that caspase 8 activation level is a key regulator of the choice between deterministic type 1 and stochastic type 2 pathways, irrespective of cell types. Expression levels of signaling molecules downstream also regulate the type 1/type 2 choice. A simplified model of DISC clustering elucidates the mechanism of increased active caspase 8 generation and type 1 activation in cancer cells having increased sensitivity to death receptor activation. We demonstrate that rapid deterministic activation of the type 1 pathway can selectively target such cancer cells, especially if XIAP is also inhibited; while inherent cell-to-cell variability would allow normal cells stay protected.

The energy costs of insulators in biochemical networks

Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of modules--semiindependent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic futile cycles that consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a possible new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular plug-and-play interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.

A characterization of scale invariant responses in enzymatic networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of three-node enzymatic networks (and sufficient for any number of nodes). Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.

Sensory systems often adapt, meaning that certain measured variables return to their basal levels after a transient response to a stimulus. An additional property that many adapting systems enjoy is that of scale invariance: the transient response remains the same when a stimulus is scaled. This work presents a mathematical study of biochemical enzymatic networks that exhibit scale-invariant behavior.

Structural properties of the MAPK pathway topologies in PC12 cells

In this paper we propose and analyze parameter-free models for the mitogen-activated protein kinase (MAPK) pathway in PC12 rat neural cells. Experiments show that the dynamic behavior of this pathway depends on the input growth factor. The response to epidermal growth factor (EGF) is a short peak followed by a relaxation, while the response to nerve growth factor (NGF) is sustained. In the latter case, the system can be driven to a new state, which persists after the stimulus has vanished. Ultimately, these dynamic behaviors correspond to different cell fates: EFG stimulation induces proliferation, while NGF stimulation induces differentiation. The biochemical mechanisms responsible for the different input-dependent dynamic response are still unclear. One hypothesis is that each input generates a specific interaction topology among the kinases. Starting from experimental results that support this hypothesis, we derive and analyze qualitative models for the two network topologies. Our approach is based on invariant set theory and non-smooth Lyapunov functions. We demonstrate analytically that the network behaviors and stability properties are structurally dependent on the topology, and do not depend on specific parameter values of the underlying biochemical interactions.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Exploration of trade-offs between steady-state and dynamic properties in signaling cycles

In the intracellular signaling networks that regulate important cell processes, the base pattern comprises the cycle of reversible phosphorylation of a protein, catalyzed by kinases and opposing phosphatases. Mathematical modeling and analysis have been used for gaining a better understanding of their functions and to capture the rules governing system behavior. Since biochemical parameters in signaling pathways are not easily accessible experimentally, it is necessary to explore possibilities for both steady-state and dynamic responses in these systems. While a number of studies have focused on analyzing these properties separately, it is necessary to take into account both of these responses simultaneously in order to be able to interpret a broader range of phenotypes. This paper investigates the trade-offs between optimal characteristics of both steady-state and dynamic responses. Following an inverse sensitivity analysis approach, we use systematic optimization methods to find the biochemical and biophysical parameters that simultaneously achieve optimal steady-state and dynamic performance. Remarkably, we find that even a single covalent modification cycle can simultaneously and robustly achieve high ultrasensitivity, high amplification and rapid signal transduction. We also find that the response rise and decay times can be modulated independently by varying the activating- and deactivating-enzyme-to-interconvertible-protein ratios.

Signalling by protein phosphatases and drug development: a systems-centred view

Protein modification cycles catalysed by opposing enzymes, such as kinases and phosphatases, form the backbone of signalling networks. Although, historically, kinases have been at the research forefront, a systems-centred approach reveals predominant roles for phosphatases in controlling the network response times and spatio-temporal profiles of signalling activities. Emerging evidence suggests that phosphatase kinetics are critical for network function and cell-fate decisions. Protein phosphatases operate as both immediate and delayed regulators of signal transduction, capable of attenuating or amplifying signalling. This versatility of phosphatase action emphasizes the need for systems biology approaches to understand cellular signalling networks and predict the cellular outcomes of combinatorial drug interventions.

Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans

Cortisol, secreted in the adrenal cortex in response to stress, is an informative biomarker that distinguishes anxiety disorders such as major depression and post-traumatic stress disorder (PTSD) from normal subjects. Yehuda et al. proposed a hypothesis that, in humans, the hypersensitive hypothalamus-pituitary-adrenal (HPA) axis is responsible for the occurrence of differing levels of cortisol in anxiety disorders. Specifically, PTSD subjects have lower cortisol levels during the late subjective night in comparison to normal subjects, and this was assumed to occur due to strong negative feedback loops in the HPA axis. In the present work, to address this hypothesis, we modeled the cortisol dynamics using nonlinear ordinary differential equations and estimated the kinetic parameters of the model to fit the experimental data of three categories, namely, normal, depressed, and PTSD human subjects. We concatenated the subjects (n = 3) in each category and created a model subject (n = 1) without considering the patient-to-patient variability in each case. The parameters of the model for the three categories were simultaneously obtained through global optimization. Bifurcation analysis carried out with the optimized parameters exhibited two supercritical Hopf points and, for the choice of parameters, the oscillations were found to be circadian in nature. The fitted kinetic parameters indicate that PTSD subjects have a strong negative feedback loop and, as a result, the predicted oscillating cortisol levels are extremely low at the nadir in contrast to normal subjects, albeit within the endocrinologic range. We also simulated the phenotypes for each of the categories and, as observed in the clinical data of PTSD patients, the simulated cortisol levels are consistently low at the nadir, and correspondingly the negative feedback was found to be extremely strong. These results from the model support the hypothesis that high stress intensity and strong negative feedback loop may cause hypersensitive neuro-endocrine axis that results in hypocortisolemia in PTSD.

PTSD is an anxiety disorder that occurs among persons exposed to a traumatic event involving life threat and injury. This is a co-morbid psychiatric disorder that occurs along with depression. Cortisol is an informative endocrine biomarker that can distinguish PTSD from other co-morbid disorders. In comparison to normal subjects, hypocortisolemia was observed during the night in PTSD, while hypercortisolemia was observed in depressed subjects. From analyzing the clinical data, Yehuda et al. hypothesized that hypocortisolemia in PTSD was due to the strong negative feedback loop operating in the neuroendocrine axis under severe stress. We complemented this hypothesis by constructing a mathematical model for cortisol dynamics in HPA axis and estimated the kinetic parameters that fitted the cortisol time series obtained from the clinical data of normal, depressed and PTSD patients. The parameters obtained from the simulated phenotypes also strongly support the hypothesis that, due to disruptive negative feedback loops, cortisol levels are different in normal, PTSD and depressed subjects during the night. Importantly, the model predicted the transitions from normal to various diseased states, and these transitions were shown to occur due to changes in the strength of the negative feedback loop and the stress intensity in the neuro-endocrine axis.

Modeling and analysis of retinoic acid induced differentiation of uncommitted precursor cells

Manipulation of differentiation programs has therapeutic potential in a spectrum of human cancers and neurodegenerative disorders. In this study, we integrated computational and experimental methods to unravel the response of a lineage uncommitted precursor cell-line, HL-60, to Retinoic Acid (RA). HL-60 is a human myeloblastic leukemia cell-line used extensively to study human differentiation programs. Initially, we focused on the role of the BLR1 receptor in RA-induced differentiation and G1/0-arrest in HL-60. BLR1, a putative G protein-coupled receptor expressed following RA exposure, is required for RA-induced cell-cycle arrest and differentiation and causes persistent MAPK signaling. A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell-lines with and without RA. The current model described the dynamics of 729 proteins and protein complexes interconnected by 1356 interactions. An ensemble strategy was used to compensate for uncertain model parameters. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. The ensemble of models also correctly predicted Rb and p47phox regulation and the correlation between p21-CDK4-cyclin D formation and G1/0-arrest following exposure to RA. Finally, we investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. Taken together, the model presented here was a first step toward a systematic framework for analysis of programmed differentiation. These studies also demonstrated that mechanistic network modeling can help prioritize experimental directions by generating falsifiable hypotheses despite uncertainty.

In silico models of cancer

Cancer is a complex disease that involves multiple types of biological interactions across diverse physical, temporal, and biological scales. This complexity presents substantial challenges for the characterization of cancer biology, and motivates the study of cancer in the context of molecular, cellular, and physiological systems. Computational models of cancer are being developed to aid both biological discovery and clinical medicine. The development of these in silico models is facilitated by rapidly advancing experimental and analytical tools that generate information-rich, high-throughput biological data. Statistical models of cancer at the genomic, transcriptomic, and pathway levels have proven effective in developing diagnostic and prognostic molecular signatures, as well as in identifying perturbed pathways. Statistically inferred network models can prove useful in settings where data overfitting can be avoided, and provide an important means for biological discovery. Mechanistically based signaling and metabolic models that apply a priori knowledge of biochemical processes derived from experiments can also be reconstructed where data are available, and can provide insight and predictive ability regarding the behavior of these systems. At longer length scales, continuum and agent-based models of the tumor microenvironment and other tissue-level interactions enable modeling of cancer cell populations and tumor progression. Even though cancer has been among the most-studied human diseases using systems approaches, significant challenges remain before the enormous potential of in silico cancer biology can be fully realized.

2,3,7,8-tetrachlorodibenzo-p-dioxin-mediated suppression of toll-like receptor stimulated B-lymphocyte activation and initiation of plasmacytic differentiation

2,3,7,8-Tetrachlordibenzo-p-dioxin (TCDD) is a potent suppressor of humoral immunity, disrupting antibody production in response to both T cell-dependent and T cell-independent antigens. Among the cell types required for humoral responses, the B cell is highly, and directly, sensitive to TCDD. B cells become antibody-secreting cells via plasmacytic differentiation, a process regulated by several transcription factors, including activator protein-1, B-cell CLL/lymphoma 6 (BCL-6), and B lymphocyte-induced maturation protein 1 (Blimp-1). The overarching conceptual framework guiding experimentation is that TCDD disrupts plasmacytic differentiation by altering the expression or activity for upstream regulators of Blimp-1. Multiparametric flow cytometry was used to investigate TCDD-induced alterations in both activation marker and transcription factor expression following lipopolysaccharide (LPS) activation of purified B cells. TCDD significantly impaired LPS-activated expression of major histocompatibility complex class II, cluster of differentiation (CD)69, CD80, and CD86. Immunosuppressive concentrations of TCDD also suppressed LPS-activated Blimp-1 and phosphorylated c-Jun expression, whereas elevating BCL-6 expression. Because BCL-6 and c-Jun are directly and indirectly regulated by the kinases AKT, extracellular signal-regulated kinase (ERK), and Jun N-terminal kinase (JNK), it was hypothesized that TCDD alters toll-like receptor-activated kinase phosphorylation. TCDD at 0.03 and 0.3 nM significantly impaired phosphorylation of AKT, ERK, and JNK in CH12.LX B cells activated with LPS, CpG oligonucleotides, or resiquimod (R848). In primary B cells, R848-activated phosphorylation of AKT, ERK, and JNK was also impaired by TCDD at 30 nM. These results suggest that impairment of plasmacytic differentiation by TCDD involves altered transcription factor expression, in part, by suppressed kinase phosphorylation.

Lose and gain: impacts of ERK5 and JNK cascades on each other

Kinase cascades in ERK5 (Extracellular signal-regulated kinases) and JNK (c-Jun N-terminal kinases) signaling pathways mediate the sensing and processing of stimuli. Cross-talks between signaling cascades is a likely phenomenon that can cause apparently different biological responses from a single pathway, on its activation. Feedback loops have the potential to greatly alter the properties of a pathway and its response to stimuli. Based on enzyme kinetic reactions, mathematical models have been developed to predict and analyze the impacts of cross-talks and feedback loops in ERK5 and JNK cascades. It has been observed that, there is no significant impact on neither ERK5 activation nor JNKs' activation due to cross-talks between them. But it is due to cross-talks and feedback loops in ERK5 and JNK cascade, ERK5 gets activated in a transient manner in the absence of input signals. Planning to obtain the parameter values from the experimentalist and the result should be validated by experimental verification.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-010-9061-4) contains supplementary material, which is available to authorized users.

Analysis of the molecular networks in androgen dependent and independent prostate cancer revealed fragile and robust subsystems

Androgen ablation therapy is currently the primary treatment for metastatic prostate cancer. Unfortunately, in nearly all cases, androgen ablation fails to permanently arrest cancer progression. As androgens like testosterone are withdrawn, prostate cancer cells lose their androgen sensitivity and begin to proliferate without hormone growth factors. In this study, we constructed and analyzed a mathematical model of the integration between hormone growth factor signaling, androgen receptor activation, and the expression of cyclin D and Prostate-Specific Antigen in human LNCaP prostate adenocarcinoma cells. The objective of the study was to investigate which signaling systems were important in the loss of androgen dependence. The model was formulated as a set of ordinary differential equations which described 212 species and 384 interactions, including both the mRNA and protein levels for key species. An ensemble approach was chosen to constrain model parameters and to estimate the impact of parametric uncertainty on model predictions. Model parameters were identified using 14 steady-state and dynamic LNCaP data sets taken from literature sources. Alterations in the rate of Prostatic Acid Phosphatase expression was sufficient to capture varying levels of androgen dependence. Analysis of the model provided insight into the importance of network components as a function of androgen dependence. The importance of androgen receptor availability and the MAPK/Akt signaling axes was independent of androgen status. Interestingly, androgen receptor availability was important even in androgen-independent LNCaP cells. Translation became progressively more important in androgen-independent LNCaP cells. Further analysis suggested a positive synergy between the MAPK and Akt signaling axes and the translation of key proliferative markers like cyclin D in androgen-independent cells. Taken together, the results support the targeting of both the Akt and MAPK pathways. Moreover, the analysis suggested that direct targeting of the translational machinery, specifically eIF4E, could be efficacious in androgen-independent prostate cancers.

In silico models of cancer

Cancer is a complex disease that involves multiple types of biological interactions across diverse physical, temporal, and biological scales. This complexity presents substantial challenges for the characterization of cancer biology, and motivates the study of cancer in the context of molecular, cellular, and physiological systems. Computational models of cancer are being developed to aid both biological discovery and clinical medicine. The development of these in silico models is facilitated by rapidly advancing experimental and analytical tools that generate information-rich, high-throughput biological data. Statistical models of cancer at the genomic, transcriptomic, and pathway levels have proven effective in developing diagnostic and prognostic molecular signatures, as well as in identifying perturbed pathways. Statistically inferred network models can prove useful in settings where data overfitting can be avoided, and provide an important means for biological discovery. Mechanistically based signaling and metabolic models that apply a priori knowledge of biochemical processes derived from experiments can also be reconstructed where data are available, and can provide insight and predictive ability regarding the behavior of these systems. At longer length scales, continuum and agent-based models of the tumor microenvironment and other tissue-level interactions enable modeling of cancer cell populations and tumor progression. Even though cancer has been among the most-studied human diseases using systems approaches, significant challenges remain before the enormous potential of in silico cancer biology can be fully realized.

Growing heterogeneous tumors in silico

An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. Building such a tool requires the development and successful integration of a number of biophysical and mathematical models. In this paper, we work toward this long-term goal by formulating a cellular automaton model of tumor growth that accounts for several different inter-tumor processes and host-tumor interactions. In particular, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass and considers the impact that organ-imposed physical confinement and environmental heterogeneity have on tumor size and shape. Furthermore, the algorithm is able to account for cell-level heterogeneity, allowing us to explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. This computational tool we have built has a number of applications in its current form in both predicting tumor growth and predicting response to treatment. Moreover, the latent power of our algorithm is that it also suggests other tumor-related processes that need to be accounted for and calls for the conduction of new experiments to validate the model's predictions.

Mechanistic systems biology of inflammatory gene expression in airway smooth muscle as tool for asthma drug development

There is compelling evidence that airway smooth muscle cells may function as inflammatory cells in the airway system by producing multiple inflammatory cytokines in response to a large array of external stimuli such as acetylcholine, bradykinin, inflammatory cytokines, and toll-like receptor activators. However, how multiple extracellular stimuli interact in the regulation of inflammatory gene expression in an airway smooth muscle cell remains poorly understood. This review addresses the mechanistic systems biology of inflammatory gene expression in airway smooth muscle by discussing: a) redundancy underlying multiple stimulus-product relations in receptor-mediated inflammatory gene expression, and their regulation by convergent activation of Erk1/2 mitogen-activated protein kinase (MAPK), b) Erk1/2 MAPK-dependent induction of phosphatase expression as a negative feedback mechanism in the robust maintenance of inflammatory gene expression, and c) cyclooxygenase 2-dependent regulation of the differential temporal dynamics of early and late inflammatory gene expression. It is becoming recognized that a single-target approach is unlikely to be effective for the treatment of inflammatory airway diseases because airway inflammation is a result of complex interactions among multiple inflammatory mediators and cells types in the airway system. Understanding the mechanistic systems biology of inflammatory gene expression in airway smooth muscle and other cell types in the airway system may lead to the development of multi-target drug regimens for the treatment of inflammatory airway diseases such as asthma.

Positional information generated by spatially distributed signaling cascades

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus.

Investigating differential dynamics of the MAPK signaling cascade using a multi-parametric global sensitivity analysis

Cell growth critically depends on signalling pathways whose regulation is the focus of intense research. Without utilizing a priori knowledge of the relative importance of pathway components, we have applied in silico computational methods to the EGF-induced MAPK cascade. Specifically, we systematically perturbed the entire parameter space, including initial conditions, using a Monte Carlo approach, and investigate which protein components or kinetic reaction steps contribute to the differentiation of ERK responses. The model, based on previous work by Brightman and Fell (2000), is composed of 28 reactions, 27 protein molecules, and 48 parameters from both mass action and Michaelis-Menten kinetics. Our multi-parametric systems analysis confirms that Raf inactivation is one of the key steps regulating ERK responses to be either transient or sustained. Furthermore, the results of amplitude-differential ERK phosphorylations within the transient case are mainly attributed to the balance between activation and inactivation of Ras while duration-differential ERK responses for the sustained case are, in addition to Ras, markedly affected by dephospho-/phosphorylation of both MEK and ERK. Our sub-module perturbations showed that MEK and ERK's contribution to this differential ERK activation originates from fluctuations in intermediate pathway module components such as Ras and Raf, implicating a cooperative regulatory mode among the key components. The initial protein concentrations of corresponding reactions such as Ras, GAP, and Raf also influence the distinct signalling outputs of ERK activation. We then compare these results with those obtained from a single-parametric perturbation approach using an overall state sensitivity (OSS) analysis. The OSS findings indicate a more pronounced role of ERK's inhibitory feedback effect on catalysing the dissociation of the SOS complex. Both approaches reveal the presence of multiple specific reactions involved in the distinct dynamics of ERK responses and the cell fate decisions they trigger. This work adds a mechanistic insight of the contribution of key pathway components, thus may support the identification of biomarkers for pharmaceutical drug discovery processes.

A systems biological approach suggests that transcriptional feedback regulation by dual-specificity phosphatase 6 shapes extracellular signal-related kinase activity in RAS-transformed fibroblasts

Mitogen-activated protein kinase (MAPK) signaling determines crucial cell fate decisions in most cell types, and mediates cellular transformation in many types of cancer. The activity of MAPK is controlled by reversible phosphorylation, and the quantitative characteristics of MAPK activation determine the cellular response. Many systems biological studies have analyzed the activation kinetics and the dose-response behavior of the MAPK signaling pathway. Here we investigate how the pathway activity is controlled by transcriptional feedback loops. Initially, we predict that MAPK signaling regulates phosphatases, by integrating promoter sequence data and ontology-based classification of gene function. From this, we deduce that MAPK signaling might be controlled by transcriptional negative feedback regulation via dual-specificity phosphatases (DUSPs), and implement a mathematical model to further test this hypothesis. Using time-resolved measurements of pathway activity and gene expression, we employ a model selection approach, and select DUSP6 as a highly likely candidate for shaping the activity of the MAPK pathway during cellular transformation caused by oncogenic RAS. Two predictions from the model were confirmed: first, feedback regulation requires that DUSP6 mRNA and protein are unstable; and second, the activation kinetics of MAPK are ultrasensitive. Taken together, an integrated systems biological approach reveals that transcriptional negative feedback controls the kinetics and the extent of MAPK activation under both physiological and pathological conditions.

Modelling cellular signalling systems

Cell signalling pathways and networks are complex and often non-linear. Signalling pathways can be represented as systems of biochemical reactions that can be modelled using differential equations. Computational modelling of cell signalling pathways is emerging as a tool that facilitates mechanistic understanding of complex biological systems. Mathematical models are also used to generate predictions that may be tested experimentally. In the present chapter, the various steps involved in building models of cell signalling pathways are discussed. Depending on the nature of the process being modelled and the scale of the model, different mathematical formulations, ranging from stochastic representations to ordinary and partial differential equations are discussed. This is followed by a brief summary of some recent modelling successes and the state of future models.

Signal duration and the time scale dependence of signal integration in biochemical pathways

Background

Signal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.

Results

Here we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.

Conclusion

We show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.

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

The cellular response elicited by an environmental cue typically varies with the strength of the stimulus. For example, in the yeast Saccharomyces cerevisiae, the concentration of mating pheromone determines whether cells undergo vegetative growth, chemotropic growth, or mating. This implies that the signaling pathways responsible for detecting the stimulus and initiating a response must transmit quantitative information about the intensity of the signal. Our previous experimental results suggest that yeast encode pheromone concentration as the duration of the transmitted signal. Here we use mathematical modeling to analyze possible biochemical mechanisms for performing this “dose-to-duration” conversion. We demonstrate that modulation of signal duration increases the range of stimulus concentrations for which dose-dependent responses are possible; this increased dynamic range produces the counterintuitive result of “signaling beyond saturation” in which dose-dependent responses are still possible after apparent saturation of the receptors. We propose a mechanism for dose-to-duration encoding in the yeast pheromone pathway that is consistent with current experimental observations. Most previous investigations of information processing by signaling pathways have focused on amplitude encoding without considering temporal aspects of signal transduction. Here we demonstrate that dose-to-duration encoding provides cells with an alternative mechanism for processing and transmitting quantitative information about their surrounding environment. The ability of signaling pathways to convert stimulus strength into signal duration results directly from the nonlinear nature of these systems and emphasizes the importance of considering the dynamic properties of signaling pathways when characterizing their behavior. Understanding how signaling pathways encode and transmit quantitative information about the external environment will not only deepen our understanding of these systems but also provide insight into how to reestablish proper function of pathways that have become dysregulated by disease.

Cells must be able to detect and respond to changes in their surroundings. Often environmental cues, such as hormones or growth factors, are received by membrane receptors that in turn activate intracellular signaling pathways. These pathways then transmit information about the stimulus to the cellular components required to elicit an appropriate response. In many cases, the nature of the response depends on the dose of the stimulus. Thus, in addition to relaying qualitative information (e.g., the presence or absence of a stimulus), signaling pathways must also transmit quantitative information about the intensity of the stimulus. Here we introduce “dose-to-duration” encoding as an effective strategy for relaying such information. We demonstrate that by providing a mechanism for overcoming saturation effects, modulation of signal duration increases the range of stimulus concentrations for which dose-dependent responses are possible. This increased dynamic range produces the counterintuitive result of “signaling beyond saturation” in which dose-dependent responses are still possible after apparent saturation of the receptors. Finally, we demonstrate that dose-to-duration encoding is used in the yeast mating response pathway and presents a simple mechanism that can account for current experimental observations.