Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

细胞信号网络功能鲁棒的简并性拓扑特征

细胞信号网络对于外界环境的干扰表现出优良的鲁棒性,但是其维持功能鲁棒的内在机制尚未明确,本文研究了细胞信号网络功能鲁棒性的拓扑特征。选择布尔网络模型模拟细胞网络的动态行为,利用网络节点状态的扰动模拟外界环境干扰。基于演化策略探寻不同网络拓扑的功能并分析其在干扰环境下的鲁棒性,采用埃德尔曼提出的基于信息论的计算方法评估网络拓扑的简并度、冗余度和复杂度等拓扑属性,对比分析它们与功能鲁棒度的相关性及作用机理。结果显示,在网络模型的演化过程中,其拓扑简并度与功能鲁棒度显著正相关,相关性水平高于拓扑冗余度与鲁棒度的相关性。并且,随着鲁棒度的提升,网络的节点数和复杂度也随之升高,同样简并度与网络的节点数和复杂度的相关性高于拓扑冗余度与网络的节点数和复杂度的相关性。这说明增加的网络节点以简并的方式同时提高了网络拓扑的鲁棒度和复杂度。因此,细胞网络功能鲁棒性的拓扑特征是简并而不是冗余,简并为解决生物系统的复杂问题提供了有效手段,为人工系统的可靠性设计提供有益的借鉴。     

Short-term information processing, long-term responses: Insights by mathematical modeling of signal transduction. Early activation dynamics of key signaling mediators can be predictive for cell fate decisions

How do cells interpret information from their environment and translate it into specific cell fate decisions? We propose that cell fate is already encoded in early signaling events and thus can be predicted from defined signal properties. Specifically, we hypothesize that the time integral of activated key signaling molecules can be correlated to cellular behavior such as proliferation or differentiation. The identification of these decisive key signal mediators and their connection to cell fate is facilitated by mathematical modeling. A possible mechanistic linkage between signaling dynamics and cellular function is the directed control of gene regulatory networks by defined signals. Targeted experiments in combination with mathematical modeling can increase our understanding of how cells process information and realize distinct cell fates.     

On the robustness of update schedules in Boolean networks

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems.     

Calcium and signal transduction in plants

Environmental and hormonal signals control diverse physiological processes in plants. The mechanisms by which plant cells perceive and transduce these signals are poorly understood. Understanding biochemical and molecular events involved in signal transduction pathways has become one of the most active areas of plant research. Research during the last 15 years has established that Ca2+ acts as a messenger in transducing external signals. The evidence in support of Ca2+ as a messenger is unequivocal and fulfills all the requirements of a messenger. The role of Ca2+ becomes even more important because it is the only messenger known so far in plants. Since our last review on the Ca2+ messenger system in 1987, there has been tremendous progress in elucidating various aspects of Ca(2+) -signaling pathways in plants. These include demonstration of signal-induced changes in cytosolic Ca2+, calmodulin and calmodulin-like proteins, identification of different Ca2+ channels, characterization of Ca(2+) -dependent protein kinases (CDPKs) both at the biochemical and molecular levels, evidence for the presence of calmodulin-dependent protein kinases, and increased evidence in support of the role of inositol phospholipids in the Ca(2+) -signaling system. Despite the progress in Ca2+ research in plants, it is still in its infancy and much more needs to be done to understand the precise mechanisms by which Ca2+ regulates a wide variety of physiological processes. The purpose of this review is to summarize some of these recent developments in Ca2+ research as it relates to signal transduction in plants.     

Chemosensory signal transduction in Caenorhabditis elegans

Chemosensory neurons translate perception of external chemical cues, including odorants, tastants, and pheromones, into information that drives attraction or avoidance motor programs. In the laboratory, robust behavioral assays, coupled with powerful genetic, molecular and optical tools, have made Caenorhabditis elegans an ideal experimental system in which to dissect the contributions of individual genes and neurons to ethologically relevant chemosensory behaviors. Here, we review current knowledge of the neurons, signal transduction molecules and regulatory mechanisms that underlie the response of C. elegans to chemicals, including pheromones. The majority of identified molecules and pathways share remarkable homology with sensory mechanisms in other organisms. With the development of new tools and technologies, we anticipate that continued study of chemosensory signal transduction and processing in C. elegans will yield additional new insights into the mechanisms by which this animal is able to detect and discriminate among thousands of chemical cues with a limited sensory neuron repertoire.     

Bile acids and signal transduction: role in glucose homeostasis

Bile acids are mainly recognized for their role in dietary lipid absorption and cholesterol homeostasis. However, recent progress in bile acid research suggests that bile acids are important signaling molecules that play a role in glucose homeostasis. Among the various supporting evidence, several reports have demonstrated an improvement of the glycemic index of type 2 diabetic patients treated with diverse bile acid binding resins. Herein, we review the diverse interactions of bile acids with various signaling/response pathways, including calcium mobilization and protein kinase activation, membrane receptor-mediated responses, and nuclear receptor responses. Some of the effects of the bile acids are direct through the activation of specific receptors, i.e., TGR5, CAR, VDR, and FXR, while others imply modulation of the hormonal, growth factor and/or neuromediator responses, i.e., glucagon, EGF, and acetylcholine. We also discuss recent evidence implicating the interaction of bile acids with glucose homeostasis mechanisms, with the integration of our understanding of how the signaling mechanisms modulated by bile acid could regulate glucose metabolism.     

Hysteretic and graded responses in bacterial two-component signal transduction

Bacterial two-component systems (TCS) are key signal transduction networks regulating global responses to environmental change. Environmental signals may modulate the phosphorylation state of sensor kinases (SK). The phosphorylated SK transfers the phosphate to its cognate response regulator (RR), which causes physiological response to the signal. Frequently, the SK is bifunctional and, when unphosphorylated, it is also capable of dephosphorylating the RR. The phosphatase activity may also be modulated by environmental signals. Using the EnvZ/OmpR system as an example, we constructed mathematical models to examine the steady-state and kinetic properties of the network. Mathematical modelling reveals that the TCS can show bistable behaviour for a given range of parameter values if unphosphorylated SK and RR form a dead-end complex that prevents SK autophosphorylation. Additionally, for bistability to exist the major dephosphorylation flux of the RR must not depend on the unphosphorylated SK. Structural modelling and published affinity studies suggest that the unphosphorylated SK EnvZ and the RR OmpR form a dead-end complex. However, bistability is not possible because the dephosphorylation of OmpR approximately P is mainly done by unphosphorylated EnvZ. The implications of this potential bistability in the design of the EnvZ/OmpR network and other TCS are discussed.     

Localization of receptors in lipid rafts can inhibit signal transduction

Processes of cell survival, division, differentiation, and death are guided by the binding of signal molecules to receptors, which activates intracellular signaling networks and ultimately elicits genetic, biochemical, or biomechanical responses within the cell. While intracellular mechanisms for these processes have been well studied, little attention has been given to the role extracellular ligand transport and binding may play in signal initiation. Recent studies have found that the localization of receptors in lipid rafts is critical for the functions of many signaling pathways. By concentrating membrane components, rafts may promote essential interactions for signaling. Lipid rafts can also have negative effects on signaling, but mechanisms remain elusive. We propose that raft-mediated receptor clustering can reduce signaling by prolonging the diffusion of ligands to their receptors. We quantify this effect using a simple diffusion-limited binding model that accounts for the spatial distribution of lipid rafts and receptors on the cell surface. We find that receptor clustering can reduce the apparent rate of receptor binding by up to 80%, consistent with observed increases in epidermal growth factor (EGF) binding by up to 100% following disruption of lipid rafts (Pike and Casey 2002 Biochemistry 41:10315-10322; Roepstorff et al. 2002 J Biol Chem 277:18954-18960). Failure to account for the effects of receptor clustering on rates of ligand binding can skew the interpretation of current methods of cancer diagnosis and treatment. Finally, we discuss how the activation of particular signaling pathways can change over time, depending, in part, on the overall level and spatial distribution of the receptors.     

Membrane receptors for steroid hormones: signal transduction and physiological significance

Membrane receptors for steroid hormones affect signaling pathways that modulate nuclear function, influence neuronal activity, ion flow, and the circulatory system. Indeed, 'new' steroid hormones have been identified by their interaction with membrane-initiated signaling systems. A brief summary of the FASEB Summer Research Conference devoted to these topics is presented in this mini-review. In addition, attendees of the meeting propose introduction of the following terminology: membrane-initiated steroid signaling (MISS) and nuclear-initiated steroid signaling (NISS) to replace more inaccurate terms in current use.     

Dynamic stability of signal transduction networks depending on downstream and upstream specificity of protein kinases

Mathematical methods are used for explaining the structural design of signal transduction networks, e.g. MAP kinase cascades, which control cell proliferation, differentation or apoptosis. Taking into account protein kinases and phosphatases the interrelation between the topology of signaling networks and the stability of their ground state are analysed. It is shown that the stability is closely related to the system's dimension and to the number of cycles within the network. Systems with a higher number of kinases and/or cycles tend to be more unstable. In contrast to that increasing phosphatase activity stabilises the ground state.     

The role of hexokinase in plant sugar signal transduction and growth and development

Previous studies have revealed a central role of Arabidopsis thaliana hexokinases (AtHXK1 and AtHXK2) in the glucose repression of photosynthetic genes and early seedling development. However, it remains unclear whether HXK can modulate the expression of diverse sugar-regulated genes. On the basis of the results of analyses of gene expression in HXK transgenic plants, we suggest that three distinct glucose signal transduction pathways exist in plants. The first is an AtHXK1-dependent pathway in which gene expression is correlated with the AtHXK1-mediated signaling function. The second is a glycolysis-dependent pathway that is influenced by the catalytic activity of both AtHXK1 and the heterologous yeast Hxk2. The last is an AtHXK1-independent pathway in which gene expression is independent of AtHXK1. Further investigation of HXK transgenic Arabidopsis discloses a role of HXK in glucose-dependent growth and senescence. In the absence of exogenous glucose, plant growth is limited to the seedling stage with restricted true leaf development even after a 3-week culture on MS medium. In the presence of glucose, however, over-expressing Arabidopsis or yeast HXK in plants results in the repression of growth and true leaf development, and early senescence, while under-expressing AtHXK1 delays the senescence process. These studies reveal multiple glucose signal transduction pathways that control diverse genes and processes that are intimately linked to developmental stages and environmental conditions.     

MAPK信号转导通路对炎症反应的调控

丝裂原活化蛋白激酶 (mitogen -activatedproteinkinase ,MAPK)是生物体内重要的信号转导系统之一 ,参与介导生长、发育、分裂、分化、死亡以及细胞间的功能同步等多种细胞过程。在哺乳动物细胞中已发现和克隆了ERKJNK/SAPK、p38/RK、ERK5/BMK1四个MAPK亚族。这些MAPK能被多种炎性刺激所激活 ,并对炎症的发生、发展起重要调控作用。研究感染和炎症反应过程中这些MAPK被激活的机制及其生物学效应 ,探讨MAPK特异性抑制剂的药理学作用及分子基础 ,对于感染的防治及炎症反应的控制有着广泛的应用前景。     

Anti-apoptotic action of stem cell factor on oocytes in primordial follicles and its signal transduction

Stem cell factor (SCF) is essential for the development of primordial follicles. One of its functions is to prevent oocytes from apoptosis. However, the underlying mechanism remains largely unknown. By using cultured ovaries that are rich in primordial follicles, the anti-apoptotic action of SCF and the potential signal transduction pathways were investigated. The apoptosis was evaluated by means of in situ 3'-end labeling. The expressions of proteins were analyzed with immunohistochemistry and Western blot. The data showed that SCF significantly prevented oocytes from apoptosis in the cultured organs. Addition of a specific pharmacological inhibitor of PI3K abolished the anti-apoptotic action of SCF while that of a MEK inhibitor did not. The phosphorylation of two mitogen activated protein kinases (MAPKs) (p42 and p44) and AKT, the respective substrates of MEK and PI3K, were enhanced by SCF treatment. Not surprisingly, the MAPK activation occurred only in theca cells. The expressions of apoptosis-related gene products, the Bcl-2 family proteins, in response to SCF treatment were also investigated. While SCF up-regulated the expression of the anti-apoptotic proteins Bcl-2 and Bcl-xL, it did the opposite to the pro-apoptotic factor Bax. The PI3K inhibitor reversed the regulation of SCF on Bcl-xL and Bax but not on Bcl-2. Therefore, it seemed that SCF initiated an anti-apoptotic signal starting from its membrane receptor c-kit to Bcl-2 family members through PI3K/AKT and other signaling cascades in the oocytes of primordial follicles.     

Aging of signal transduction pathways, and pathology

The major cell signaling pathways, and their specific mechanisms of transduction, have been a subject of investigation for many years. As our understanding of these pathways advances, we find that they are evolutionarily well-conserved not only individually, but also at the level of their crosstalk and signal integration. Productive interactions within the key signal transduction networks determine success in embryonic organogenesis, and postnatal tissue repair throughout adulthood. However, aside from clues revealed through examining age-related degenerative diseases, much remains uncertain about imbalances within these pathways during normal aging. Further, little is known about the molecular mechanisms by which alterations in the major cell signal transduction networks cause age-related pathologies. The aim of this review is to describe the complex interplay between the Notch, TGFβ, WNT, RTK-Ras and Hh signaling pathways, with a specific focus on the changes introduced within these networks by the aging process, and those typical of age-associated human pathologies.     

Quantitative phosphoproteomics strategies for understanding protein kinase-mediated signal transduction pathways

Protein phosphorylation is a central regulatory mechanism of cell signaling pathways. This highly controlled biochemical process is involved in most cellular functions, and defects in protein kinases and phosphatases have been implicated in many diseases, highlighting the importance of understanding phosphorylation-mediated signaling networks. However, phosphorylation is a transient modification, and phosphorylated proteins are often less abundant. Therefore, the large-scale identification and quantification of phosphoproteins and their phosphorylation sites under different conditions are one of the most interesting and challenging tasks in the field of proteomics. Both 2D gel electrophoresis and liquid chromatography-tandem mass spectrometry serve as key phosphoproteomic technologies in combination with prefractionation, such as enrichment of phosphorylated proteins/peptides. Recently, new possibilities for quantitative phosphoproteomic analysis have been offered by technical advances in sample preparation, enrichment, separation, instrumentation, quantification and informatics. In this article, we present an overview of several strategies for quantitative phosphoproteomics and discuss how phosphoproteomic analysis can help to elucidate signaling pathways that regulate various cellular processes.     

Boolean modeling techniques for protein co-expression networks in systems medicine

Introduction: Application of systems biology/systems medicine approaches is promising for proteomics/biomedical research, but requires selection of an adequate modeling type.

Areas covered: This article reviews the existing Boolean network modeling approaches, which provide in comparison with alternative modeling techniques several advantages for the processing of proteomics data. Application of methods for inference, reduction and validation of protein co-expression networks that are derived from quantitative high-throughput proteomics measurements is presented. It’s also shown how Boolean models can be used to derive system-theoretic characteristics that describe both the dynamical behavior of such networks as a whole and the properties of different cell states (e.g. healthy or diseased cell states). Furthermore, application of methods derived from control theory is proposed in order to simulate the effects of therapeutic interventions on such networks, which is a promising approach for the computer-assisted discovery of biomarkers and drug targets. Finally, the clinical application of Boolean modeling analyses is discussed.

Expert commentary: Boolean modeling of proteomics data is still in its infancy. Progress in this field strongly depends on provision of a repository with public access to relevant reference models. Also required are community supported standards that facilitate input of both proteomics and patient related data (e.g. age, gender, laboratory results, etc.).