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.     

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.     

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.     

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.     

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.).     

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.     

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.     

Boolean network analysis of a neurotransmitter signaling pathway

BACKGROUND: A Boolean network is a simple computational model that may provide insight into the overall behavior of genetic networks and is represented by variables with two possible states (on/off), of the individual nodes/genes of the network. In this study, a Boolean network model has been used to simulate a molecular pathway between two neurotransmitter receptor, dopamine and glutamate receptor, systems in order to understand the consequence of using logic gate rules between nodes, which have two possible states (active and inactive). RESULTS: The dynamical properties of this Boolean network model of the biochemical pathway shows that, the pathway is stable and that, deletion/knockout of certain biologically important nodes cause significant perturbation to this network. The analysis clearly shows that in addition to the expected components dopamine and dopamine receptor 2 (DRD2), Ca(2+) ions play a critical role in maintaining stability of the pathway. CONCLUSION: So this method may be useful for the identification of potential genetic targets, whose loss of function in biochemical pathways may be responsible for disease onset. The molecular pathway considered in this study has been implicated with a complex disorder like schizophrenia, which has a complex multifactorial etiology.     

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。     

Shuffling the cards in signal transduction: Calcium, arachidonic acid and mechanosensitivity

Cell signaling is a very complex network of biochemical reactions triggered by a huge number of stimuli coming from the external medium. The function of any single signaling component depends not only on its own structure but also on its connections with other biomolecules. During prokaryotic-eukaryotic transition, the rearrangement of cell organization in terms of diffusional compartmentalization exerts a deep change in cell signaling functional potentiality. In this review I briefly introduce an intriguing ancient relationship between pathways involved in cell responses to chemical agonists (growth factors, nutrients, hormones) as well as to mechanical forces (stretch, osmotic changes). Some biomolecules (ion channels and enzymes) act as "hubs", thanks to their ability to be directly or indirectly chemically/mechanically co-regulated. In particular calcium signaling machinery and arachidonic acid metabolism are very ancient networks, already present before eukaryotic appearance. A number of molecular "hubs", including phospholipase A2 and some calcium channels, appear tightly interconnected in a cross regulation leading to the cellular response to chemical and mechanical stimulations.     

心脏发育过程中的信号调控机制研究

我国是出生缺陷高发国家,其中先天性心脏病在各类出生缺陷中居于首位,严重地影响我国的人口素质.同样,后天性心脏血管疾病（心血管疾病）也是影响国民健康和社会发展的主要疾病.近年来研究表明,所谓＂后天性＂心脏血管疾病虽然大多不在胚胎期表现出功能异常,但遗传因素在发病过程中也起关键作用,因此,＂后天性＂心血管疾病也有其发育生物学基础.在一些心血管疾病中,胚胎发育基因如ANF和β-MHC的表达说明胚胎发育的某些机制参与了发病过程.由于出生缺陷和心血管疾病的防治是我国公共卫生和社会发展中亟待解决的重大健康问题,了解心血管系统正常发生发育规律和机制及发病机理并在此基础上建立新的防治策略和防治措施是生命科学需要解决的重大基础科学问题.本文主要综述了目前模式动物,特别是小鼠心脏发育过程中的信号传导调控机制的研究现状及进展.     

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

Background

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

Results

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

Conclusions

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-256) contains supplementary material, which is available to authorized users.     

Potential role for triglycerides in signal transduction

We previously reported that endothelin-1 or platelet-derived growth factor promoted in aortic smooth muscle cells a rapid hydrolysis of 1-O-alkyl-2-acyl-sn-glycero-3-phosphoethanolamine (alkyl-PE) which was immediately converted into 1-O-alkyl-2,3-diacyl-sn-glycerol (alkyl-TG) within 5 s or 60 s respectively [C. Comminges et al. (1996) Biochem. Biophys. Res. Commun. 220, 1008-1013 and C. Comminges et al. (1997) Biochim. Biophys. Acta 1355, 69-80]. In this study, we show that this alkyl-PE hydrolysis is triggered by a transient activation of a specific phospholipase C (PLC) regulated by pertussis toxin-sensitive heterotrimeric G-proteins. Moreover, this PLC can be triggered through a Ca2+ influx depending on L-type Ca2+ channel activation, as suggested by the use of a specific 'activator' S(-)-BayK 8644 and of selective inhibitors such as nimodipine. Interestingly, low concentrations (10(-8)-10(-7)M) of alkyl-TG block the opening of L-type Ca2+ channels, whereas identical concentrations of DG do not alter L-type Ca2+ channels. This study thus unravels a hitherto unrecognized signaling pathway generating alkyl-TG as a novel lipid second messenger, potentially acting as a negative feedback regulator of L-type Ca2+ channels.