Computational approaches for modeling regulatory cellular networks

Bayesian parameter estimation for dynamical models in systems biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

Optobiochemistry: Genetically Encoded Control of Protein Activity by Light

Optobiochemical control of protein activities allows the investigation of protein functions in living cells with high spatiotemporal resolution. Over the last two decades, numerous natural photosensory domains have been characterized and synthetic domains engineered and assembled into photoregulatory systems to control protein function with light. Here, we review the field of optobiochemistry, categorizing photosensory domains by chromophore, describing photoregulatory systems by mechanism of action, and discussing protein classes frequently investigated using optical methods. We also present examples of how spatial or temporal control of proteins in living cells has provided new insights not possible with traditional biochemical or cell biological techniques.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Conceptual Evolution of Cell Signaling

During the last 100 years, cell signaling has evolved into a common mechanism for most physiological processes across systems. Although the majority of cell signaling principles were initially derived from hormonal studies, its exponential growth has been supported by interdisciplinary inputs, e.g., from physics, chemistry, mathematics, statistics, and computational fields. As a result, cell signaling has grown out of scope for any general review. Here, we review how the messages are transferred from the first messenger (the ligand) to the receptor, and then decoded with the help of cascades of second messengers (kinases, phosphatases, GTPases, ions, and small molecules such as cAMP, cGMP, diacylglycerol, etc.). The message is thus relayed from the membrane to the nucleus where gene expression ns, subsequent translations, and protein targeting to the cell membrane and other organelles are triggered. Although there are limited numbers of intracellular messengers, the specificity of the response profiles to the ligands is generated by the involvement of a combination of selected intracellular signaling intermediates. Other crucial parameters in cell signaling are its directionality and distribution of signaling strengths in different pathways that may crosstalk to adjust the amplitude and quality of the final effector output. Finally, we have reflected upon its possible developments during the coming years.

Systems biology primer: the basic methods and approaches

Systems biology is an integrative discipline connecting the molecular components within a single biological scale and also among different scales (e.g. cells, tissues and organ systems) to physiological functions and organismal phenotypes through quantitative reasoning, computational models and high-throughput experimental technologies. Systems biology uses a wide range of quantitative experimental and computational methodologies to decode information flow from genes, proteins and other subcellular components of signaling, regulatory and functional pathways to control cell, tissue, organ and organismal level functions. The computational methods used in systems biology provide systems-level insights to understand interactions and dynamics at various scales, within cells, tissues, organs and organisms. In recent years, the systems biology framework has enabled research in quantitative and systems pharmacology and precision medicine for complex diseases. Here, we present a brief overview of current experimental and computational methods used in systems biology.

Structure, signaling and the drug discovery of the Ras oncogene protein

Mutations in Ras GTPase are among the most common genetic alterations in human cancers. Despite extensive research investigating Ras proteins, their functions still remain a challenge over a long period of time. The currently available data suggests that solving the outstanding issues regarding Ras could lead to development of effective drugs that could have a significant impact on cancer treatment. Developing a better understanding of their biochemical properties or modes of action, along with improvements in their pharmacologic profiles, clinical design and scheduling will enable the development of more effective therapies.

MAMMOTh: A new database for curated mathematical models of biomolecular systems

MOTIVATION

Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration.

RESULTS

The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources.

AVAILABILITY

http://mammoth.biomodelsgroup.ru.

The Biological Function of the Prion Protein: A Cell Surface Scaffold of Signaling Modules

The prion glycoprotein (PrP^C) is mostly located at the cell surface, tethered to the plasma membrane through a glycosyl-phosphatydil inositol (GPI) anchor. Misfolding of PrP^C is associated with the transmissible spongiform encephalopathies (TSEs), whereas its normal conformer serves as a receptor for oligomers of the β-amyloid peptide, which play a major role in the pathogenesis of Alzheimer’s Disease (AD). PrP^C is highly expressed in both the nervous and immune systems, as well as in other organs, but its functions are controversial. Extensive experimental work disclosed multiple physiological roles of PrP^C at the molecular, cellular and systemic levels, affecting the homeostasis of copper, neuroprotection, stem cell renewal and memory mechanisms, among others. Often each such process has been heralded as the bona fide function of PrP^C, despite restricted attention paid to a selected phenotypic trait, associated with either modulation of gene expression or to the engagement of PrP^C with a single ligand. In contrast, the GPI-anchored prion protein was shown to bind several extracellular and transmembrane ligands, which are required to endow that protein with the ability to play various roles in transmembrane signal transduction. In addition, differing sets of those ligands are available in cell type- and context-dependent scenarios. To account for such properties, we proposed that PrP^C serves as a dynamic platform for the assembly of signaling modules at the cell surface, with widespread consequences for both physiology and behavior. The current review advances the hypothesis that the biological function of the prion protein is that of a cell surface scaffold protein, based on the striking similarities of its functional properties with those of scaffold proteins involved in the organization of intracellular signal transduction pathways. Those properties are: the ability to recruit spatially restricted sets of binding molecules involved in specific signaling; mediation of the crosstalk of signaling pathways; reciprocal allosteric regulation with binding partners; compartmentalized responses; dependence of signaling properties upon posttranslational modification; and stoichiometric requirements and/or oligomerization-dependent impact on signaling. The scaffold concept may contribute to novel approaches to the development of effective treatments to hitherto incurable neurodegenerative diseases, through informed modulation of prion protein-ligand interactions.

Systems pharmacology and enhanced pharmacodynamic models for understanding antibody-based drug action and toxicity

Pharmacokinetic (PK) and pharmacodynamic (PD) models seek to describe the temporal pattern of drug exposures and their associated pharmacological effects produced at micro- and macro-scales of organization. Antibody-based drugs have been developed for a large variety of diseases, with effects exhibited through a comprehensive range of mechanisms of action. Mechanism-based PK/PD and systems pharmacology models can play a major role in elucidating and integrating complex antibody pharmacological properties, such as nonlinear disposition and dynamical intracellular signaling pathways triggered by ligation to their cognate targets. Such complexities can be addressed through the use of robust computational modeling techniques that have proven powerful tools for pragmatic characterization of experimental data and for theoretical exploration of antibody efficacy and adverse effects. The primary objectives of such multi-scale mathematical models are to generate and test competing hypotheses and to predict clinical outcomes. In this review, relevant systems pharmacology and enhanced PD (ePD) models that are used as predictive tools for antibody-based drug action are reported. Their common conceptual features are highlighted, along with approaches used for modeling preclinical and clinically available data. Key examples illustrate how systems pharmacology and ePD models codify the interplay among complex biology, drug concentrations, and pharmacological effects. New hybrid modeling concepts that bridge cutting-edge systems pharmacology models with established PK/ePD models will be needed to anticipate antibody effects on disease in subpopulations and individual patients.

On the importance of modelling the internal spatial dynamics of biological cells

Spatial effects such as cell shape have very often been considered negligible in models of cellular pathways, and many existing simulation infrastructures do not take such effects into consideration. Recent experimental results are reversing this judgement by showing that very small spatial variations can make a big difference in the fate of a cell. This is particularly the case when considering eukaryotic cells, which have a complex physical structure and many subtle control mechanisms, but bacteria are also interesting for the huge variation in shape both between species and in different phases of their lifecycle. In this work we perform simulations that measure the effect of three common bacterial shapes on the behaviour of model cellular pathways. To perform these experiments we develop ReDi-Cell, a highly scalable GPGPU cell simulation infrastructure for the modelling of cellular pathways in spatially detailed environments. ReDi-Cell is validated against known-good simulations, prior to its use in new work. We then use ReDi-Cell to conduct novel experiments that demonstrate the effect that three common bacterial shapes (Cocci, Bacilli and Spirilli) have on the behaviour of model cellular pathways. Pathway wavefront shape, pathway concentration gradients, and chemical species distribution are measured in the three different shapes. We also quantify the impact of internal cellular clutter on the same pathways. Through this work we show that variations in the shape or configuration of these common cell shapes alter model cell behaviour.

Network reconstruction based on proteomic data and prior knowledge of protein connectivity using graph theory

Modeling of signal transduction pathways is instrumental for understanding cells’ function. People have been tackling modeling of signaling pathways in order to accurately represent the signaling events inside cells’ biochemical microenvironment in a way meaningful for scientists in a biological field. In this article, we propose a method to interrogate such pathways in order to produce cell-specific signaling models. We integrate available prior knowledge of protein connectivity, in a form of a Prior Knowledge Network (PKN) with phosphoproteomic data to construct predictive models of the protein connectivity of the interrogated cell type. Several computational methodologies focusing on pathways’ logic modeling using optimization formulations or machine learning algorithms have been published on this front over the past few years. Here, we introduce a light and fast approach that uses a breadth-first traversal of the graph to identify the shortest pathways and score proteins in the PKN, fitting the dependencies extracted from the experimental design. The pathways are then combined through a heuristic formulation to produce a final topology handling inconsistencies between the PKN and the experimental scenarios. Our results show that the algorithm we developed is efficient and accurate for the construction of medium and large scale signaling networks. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGF/TNFA stimulation against made up experimental data. To avoid the possibility of erroneous predictions, we performed a cross-validation analysis. Finally, we validate that the introduced approach generates predictive topologies, comparable to the ILP formulation. Overall, an efficient approach based on graph theory is presented herein to interrogate protein–protein interaction networks and to provide meaningful biological insights.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Scaffolding proteins: not such innocent bystanders

Sequential transfer of information from one enzyme to the next within the confines of a protein kinase scaffold enhances signal transduction. Though frequently considered to be inert organizational elements, two recent reports implicate kinase-scaffolding proteins as active participants in signal relay.

CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation

The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis

In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Toxicity testing in the 21st century: a vision and a strategy

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Information flow during gene activation by signaling molecules: ethylene transduction in Arabidopsis cells as a study system

BACKGROUND

We study root cells from the model plant Arabidopsis thaliana and the communication channel conformed by the ethylene signal transduction pathway. A basic equation taken from our previous work relates the probability of expression of the gene ERF1 to the concentration of ethylene.

RESULTS

The above equation is used to compute the Shannon entropy (H) or degree of uncertainty that the genetic machinery has during the decoding of the message encoded by the ethylene specific receptors embedded in the endoplasmic reticulum membrane and transmitted into the nucleus by the ethylene signaling pathway. We show that the amount of information associated with the expression of the master gene ERF1 (Ethylene Response Factor 1) can be computed. Then we examine the system response to sinusoidal input signals with varying frequencies to determine if the cell can distinguish between different regimes of information flow from the environment. Our results demonstrate that the amount of information managed by the root cell can be correlated with the frequency of the input signal.

CONCLUSION

The ethylene signaling pathway cuts off very low and very high frequencies, allowing a window of frequency response in which the nucleus reads the incoming message as a sinusoidal input. Out of this window the nucleus reads the input message as an approximately non-varying one. From this frequency response analysis we estimate: a) the gain of the system during the synthesis of the protein ERF1 (approximately -5.6 dB); b) the rate of information transfer (0.003 bits) during the transport of each new ERF1 molecule into the nucleus and c) the time of synthesis of each new ERF1 molecule (approximately 21.3 s). Finally, we demonstrate that in the case of the system of a single master gene (ERF1) and a single slave gene (HLS1), the total Shannon entropy is completely determined by the uncertainty associated with the expression of the master gene. A second proposition shows that the Shannon entropy associated with the expression of the HLS1 gene determines the information content of the system that is related to the interaction of the antagonistic genes ARF1, 2 and HLS1.

Mathematical model of a network of interaction between p53 and Bcl-2 during genotoxic-induced apoptosis

Ionizing radiation like UV light, gamma and X rays, can produce genotoxic damage in fibroblast cells. This injury can be reverted by activation of specific nuclear molecules. However, intense genotoxic damage induces the activation of the p53 dependent apoptotic pathway. Activated nuclear p53 has the role of a transcription factor that switches on the transcription of the Puma protein, which once released into the cytoplasm leads to the activation of a network of chemical processes that produces cell death. This network is built up with the chemical interaction between pro-apoptotic p53, Puma and Bax proteins and the anti-apoptotic Bcl2 and Bcl-x(L) proteins. In this work we present a mathematical model of this modular network under different regimes of Puma release into the cytoplasm. In this model we use a set of coupled nonlinear differential equations, which is solved by numerical methods, to determine the nature of the equilibrium points of the dynamical system. With this information we construct the phase portrait associated with Puma induced apoptosis and we found that once the genotoxic injury is produced, Bax levels continuously increase. In this work we propose that a possible mechanism for the control of apoptosis is the Bax level in the cytoplasm, i.e., Bax is continuously released into the cytoplasm, even in absence of Puma, according to the kinetic properties of the set of chemical interactions in which the Bcl2/Bax complex takes part. If the damage is reverted before the Bax level reaches a threshold value the apoptotic process is stopped, otherwise the process goes on until cell death.

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.

Models of spatially restricted biochemical reaction systems

Many reactions within the cell occur only in specific intracellular regions. Such local reaction networks give rise to microdomains of activated signaling components. The dynamics of microdomains can be visualized by live cell imaging. Computational models using partial differential equations provide mechanistic insights into the interacting factors that control microdomain dynamics. The mathematical models show that, for membrane-initiated signaling, the ratio of the surface area of the plasma membrane to the volume of the cytoplasm, the topology of the signaling network, the negative regulators, and kinetic properties of key components together define microdomain dynamics. Thus, patterns of locally restricted signaling reaction systems can be considered an emergent property of the cell.

Rapidly exploring structural and dynamic properties of signaling networks using PathwayOracle

BACKGROUND

In systems biology the experimentalist is presented with a selection of software for analyzing dynamic properties of signaling networks. These tools either assume that the network is in steady-state or require highly parameterized models of the network of interest. For biologists interested in assessing how signal propagates through a network under specific conditions, the first class of methods does not provide sufficiently detailed results and the second class requires models which may not be easily and accurately constructed. A tool that is able to characterize the dynamics of a signaling network using an unparameterized model of the network would allow biologists to quickly obtain insights into a signaling network's behavior.

RESULTS

We introduce PathwayOracle, an integrated suite of software tools for computationally inferring and analyzing structural and dynamic properties of a signaling network. The feature which differentiates PathwayOracle from other tools is a method that can predict the response of a signaling network to various experimental conditions and stimuli using only the connectivity of the signaling network. Thus signaling models are relatively easy to build. The method allows for tracking signal flow in a network and comparison of signal flows under different experimental conditions. In addition, PathwayOracle includes tools for the enumeration and visualization of coherent and incoherent signaling paths between proteins, and for experimental analysis - loading and superimposing experimental data, such as microarray intensities, on the network model.

CONCLUSION

PathwayOracle provides an integrated environment in which both structural and dynamic analysis of a signaling network can be quickly conducted and visualized along side experimental results. By using the signaling network connectivity, analyses and predictions can be performed quickly using relatively easily constructed signaling network models. The application has been developed in Python and is designed to be easily extensible by groups interested in adding new or extending existing features. PathwayOracle is freely available for download and use.

Signaling networks during development: the case of asymmetric cell division in the Drosophila nervous system

Remarkable progress in genetics and molecular biology has made possible the sequencing of the genomes from numerous species. In the post-genomic era, technical developments in the fields of proteomics and bioinformatics are poised to further catapult our understanding of protein structure, function and organization into complex signaling networks. One of the greatest challenges in the field now is to unravel the functional signaling networks and their spatio-temporal regulation in living cells. Here, the need for such in vivo system-wide level approach is illustrated in relation to the mechanisms that underlie the biological process of asymmetric cell division. Genomic, post-genomic and live imaging techniques are reviewed in light of the huge impact they are having on this field for the discovering of new proteins and for the in vivo analysis of asymmetric cell division. The proteins, signals and the emerging networking of functional connections that is arising between them during this process in the Drosophila nervous system will be also discussed.

The signaling petri net-based simulator: a non-parametric strategy for characterizing the dynamics of cell-specific signaling networks

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.

Teaching resource. Quantitative models of mammalian cell signaling pathways

This teaching resource provides lecture notes and slides for a class on mathematical modeling of mammalian signaling pathways. This lecture was part of the course . Cell Signaling Systems: A Course for Graduate Students. and focused on quantitative modeling. The lecture describes how different types of mathematical representations are applied to different signaling systems to provide insight into how a signaling system controls cell behavior. The development of an ordinary differential equation.based model for a bistable switch and the predictions that can be obtained from the model are described. The lecture concludes with a description of how models can be tested experimentally and modified when the details of the models and the resultant predictive behavior are not confirmed by experimentation.

Computational models of tandem SRC homology 2 domain interactions and application to phosphoinositide 3-kinase

Intracellular signal transduction proteins typically utilize multiple interaction domains for proper targeting, and thus a broad diversity of distinct signaling complexes may be assembled. Considering the coordination of only two such domains, as in tandem Src homology 2 (SH2) domain constructs, gives rise to a kinetic scheme that is not adequately described by simple models used routinely to interpret in vitro binding measurements. To analyze the interactions between tandem SH2 domains and bisphosphorylated peptides, we formulated detailed kinetic models and applied them to the phosphoinositide 3-kinase p85 regulatory subunit/platelet-derived growth factor beta-receptor system. Data for this system from different in vitro assay platforms, including surface plasmon resonance, competition binding, and isothermal titration calorimetry, were reconciled to estimate the magnitude of the cooperativity characterizing the sequential binding of the high and low affinity SH2 domains (C-SH2 and N-SH2, respectively). Compared with values based on an effective volume approximation, the estimated cooperativity is 3 orders of magnitude lower, indicative of significant structural constraints. Homodimerization of full-length p85 was found to be an alternative mechanism for high avidity binding to phosphorylated platelet-derived growth factor receptors, which would render the N-SH2 domain dispensable for receptor binding.

Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathways

MOTIVATION

Cellular signaling networks are dynamic systems that propagate and process information, and, ultimately, cause phenotypical responses. Understanding the circuitry of the information flow in cells is one of the keys to understanding complex cellular processes. The development of computational quantitative models is a promising avenue for attaining this goal. Not only does the analysis of the simulation data based on the concentration variations of biological compounds yields information about systemic state changes, but it is also very helpful for obtaining information about the dynamics of signal propagation.

RESULTS

This article introduces a new method for analyzing the dynamics of signal propagation in signaling pathways using Petri net theory. The method is demonstrated with the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) regulation network. The results constitute temporal information about signal propagation in the network, a simplified graphical representation of the network and of the signal propagation dynamics and a characterization of some signaling routes as regulation motifs.

Genes2Networks: connecting lists of gene symbols using mammalian protein interactions databases

Background

In recent years, mammalian protein-protein interaction network databases have been developed. The interactions in these databases are either extracted manually from low-throughput experimental biomedical research literature, extracted automatically from literature using techniques such as natural language processing (NLP), generated experimentally using high-throughput methods such as yeast-2-hybrid screens, or interactions are predicted using an assortment of computational approaches. Genes or proteins identified as significantly changing in proteomic experiments, or identified as susceptibility disease genes in genomic studies, can be placed in the context of protein interaction networks in order to assign these genes and proteins to pathways and protein complexes.

Results

Genes2Networks is a software system that integrates the content of ten mammalian interaction network datasets. Filtering techniques to prune low-confidence interactions were implemented. Genes2Networks is delivered as a web-based service using AJAX. The system can be used to extract relevant subnetworks created from "seed" lists of human Entrez gene symbols. The output includes a dynamic linkable three color web-based network map, with a statistical analysis report that identifies significant intermediate nodes used to connect the seed list.

Conclusion

Genes2Networks is powerful web-based software that can help experimental biologists to interpret lists of genes and proteins such as those commonly produced through genomic and proteomic experiments, as well as lists of genes and proteins associated with disease processes. This system can be used to find relationships between genes and proteins from seed lists, and predict additional genes or proteins that may play key roles in common pathways or protein complexes.

Integrated modeling methodology for microtubule dynamics and Taxol kinetics with experimentally identifiable parameters

Microtubule dynamics play a critical role in cell function and stress response, modulating mitosis, morphology, signaling, and transport. Drugs such as paclitaxel (Taxol) can impact tubulin polymerization and affect microtubule dynamics. While theoretical methods have been previously proposed to simulate microtubule dynamics, we develop a methodology here that can be used to compare model predictions with experimental data. Our model is a hybrid of (1) a simple two-state stochastic formulation of tubulin polymerization kinetics and (2) an equilibrium approximation for the chemical kinetics of Taxol drug binding to microtubule ends. Model parameters are biologically realistic, with values taken directly from experimental measurements. Model validation is conducted against published experimental data comparing optical measurements of microtubule dynamics in cultured cells under normal and Taxol-treated conditions. To compare model predictions with experimental data requires applying a "windowing" strategy on the spatiotemporal resolution of the simulation. From a biological perspective, this is consistent with interpreting the microtubule "pause" phenomenon as at least partially an artifact of spatiotemporal resolution limits on experimental measurement.

Both ligand- and cell-specific parameters control ligand agonism in a kinetic model of g protein-coupled receptor signaling

G protein–coupled receptors (GPCRs) exist in multiple dynamic states (e.g., ligand-bound, inactive, G protein–coupled) that influence G protein activation and ultimately response generation. In quantitative models of GPCR signaling that incorporate these varied states, parameter values are often uncharacterized or varied over large ranges, making identification of important parameters and signaling outcomes difficult to intuit. Here we identify the ligand- and cell-specific parameters that are important determinants of cell-response behavior in a dynamic model of GPCR signaling using parameter variation and sensitivity analysis. The character of response (i.e., positive/neutral/inverse agonism) is, not surprisingly, significantly influenced by a ligand's ability to bias the receptor into an active conformation. We also find that several cell-specific parameters, including the ratio of active to inactive receptor species, the rate constant for G protein activation, and expression levels of receptors and G proteins also dramatically influence agonism. Expressing either receptor or G protein in numbers several fold above or below endogenous levels may result in system behavior inconsistent with that measured in endogenous systems. Finally, small variations in cell-specific parameters identified by sensitivity analysis as significant determinants of response behavior are found to change ligand-induced responses from positive to negative, a phenomenon termed protean agonism. Our findings offer an explanation for protean agonism reported in β₂--adrenergic and α_2A-adrenergic receptor systems.

G protein–coupled receptors (GPCRs) are transmembrane proteins involved in physiological functions ranging from vasodilation and immune response to memory. The binding of both endogenous ligands (e.g., hormones, neurotransmitters) and exogenous ligands (e.g., pharmaceuticals) to these receptors initiates intracellular events that ultimately lead to cell responses. We describe a dynamic model for G protein activation, an immediate outcome of GPCR signaling, and use it together with efficient parameter variation and sensitivity analysis techniques to identify the key cell- and ligand-specific parameters that influence G protein activation. Our results show that although ligand-specific parameters do strongly influence cell response (either causing increases or decreases in G protein activation), cellular parameters may also dictate the magnitude and direction of G protein activation. We apply our findings to describe how protean agonism, a phenomenon in which the same ligand may induce both positive and negative responses, may result from changes in cell-specific parameters. These findings may be used to understand the molecular basis of different responses of cell types and tissues to pharmacological treatment. In addition, these methods may be applied generally to models of cellular signaling and will help guide experimental resources toward further characterization of the key parameters in these networks.

Use of wavelet and fast Fourier transforms in pharmacodynamics

Progress has been made in the development and application of mechanism-based pharmacodynamic models for describing the drug-specific and physiological factors influencing the time course of responses to the diverse actions of drugs. However, the biological variability in biosignals and the complexity of pharmacological systems often complicate or preclude the direct application of traditional structural and nonstructural models. Mathematical transforms may be used to provide measures of drug effects, identify structural and temporal patterns, and visualize multidimensional data from analyses of biomedical signals and images. Fast Fourier transform (FFT) and wavelet analyses are two methodologies that have proven to be useful in this context. FFT converts a signal from the time domain to the frequency domain, whereas wavelet transforms colocalize in both domains and may be utilized effectively for nonstationary signals. Nonstationary drug effects are common but have not been well analyzed and characterized by other methods. In this review, we discuss specific applications of these transforms in pharmacodynamics and their potential role in ascertaining the dynamics of spatiotemporal properties of complex pharmacological systems.

Target validation in silico: does the virtual patient cure the pharma pipeline?

Genomics has multiplied the number of targets for new therapeutic interventions, but this has not yet lead to a marked increase of pharma pipeline outputs. The complexity of protein function in higher order biological systems is often underestimated. Translation from in vitro and in vivo results to the human setting frequently fails due to unforeseen toxicity and efficacy issues. Biosimulation addresses these issues by capturing the complex dynamics of interacting molecules and cells in mechanistic, predictive models. A central concept is that of the virtual patient, an encapsulation of a specific pathophysiological behaviour in a biosimulation model. The authors describe how virtual patients are being used in target identification, target validation and clinical development, and discuss challenges for the acceptance of biosimulation methods.

Rules for modeling signal-transduction systems

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system's behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

The application of systems biology to drug discovery

Recent advances in the 'omics' technologies, scientific computing and mathematical modeling of biological processes have started to fundamentally impact the way we approach drug discovery. Recent years have witnessed the development of genome-scale functional screens, large collections of reagents, protein microarrays, databases and algorithms for data and text mining. Taken together, they enable the unprecedented descriptions of complex biological systems, which are testable by mathematical modeling and simulation. While the methods and tools are advancing, it is their iterative and combinatorial application that defines the systems biology approach.

Current concepts in the biology of orthodontic tooth movement

Adaptive biochemical response to applied orthodontic force is a highly sophisticated process. Many layers of networked reactions occur in and around periodontal ligament and alveolar bone cells that change mechanical force into molecular events (signal transduction) and orthodontic tooth movement (OTM). Osteoblasts and osteoclasts are sensitive environment-to-genome-to-environment communicators, capable of restoring system homeostasis disturbed by orthodontic mechanics. Five micro-environments are altered by orthodontic force: extracellular matrix, cell membrane, cytoskeleton, nuclear protein matrix, and genome. Gene activation (or suppression) is the point at which input becomes output, and further changes occur in all 5 environments. Hundreds of genes and thousands of proteins participate in OTM. Gene-directed protein synthesis, modification, and integration form the essence of all life processes, including OTM. Bone adaptation to orthodontic force depends on normal osteoblast and osteoclast genes that correctly express needed proteins at the right times and places. Cell membrane receptor-ligand docking is an important initiator of signal transduction and a discovery target for new bone-enhancing drugs. Despite progress in identification of regulatory molecules, the genetic mechanism of "orchestrated synthesis" between different cells, tissues, and systems remains largely unknown. Interpatient variation in mechanobiological response is most likely due to differences in periodontal ligament and bone cell populations, genomes, and protein expression patterns. Discovery of mutations in OTM-associated genes of orthodontic patients, including those regulating osteoclast bone-matrix acidification, chloride channel function, and osteoblast-derived mineral and protein matrices, will permit gene therapy to restore normal matrix and protein synthesis and function. Achieving selectivity in targeting abnormal genes, cells, and tissues is a major obstacle to safe and effective clinical application of gene engineering and stem-cell mediated tissue growth. Orthodontic treatment is likely to evolve into a combination of mechanics and molecular-genetic-cellular interventions: a change from shotgun to tightly focused communication with OTM cells.

Integration of cell adhesion reactions—a balance of forces?

The rearrangement of receptors by oligomeric adhesion molecules constitutes a configurational mechanism able to sculpture membranes and dislocate receptors from cytoplasmic anchorage. This provides a conceptual framework for complex cellular processes in mechanical terms, as a dynamic balance between extracellular and intracellular driving forces.

Developmental control via GATA factor interplay at chromatin domains

Despite the extraordinary task of packaging mammalian DNA within the constraints of a cell nucleus, individual genes assemble into cell type-specific chromatin structures with high fidelity. This chromatin architecture is a crucial determinant of gene expression signatures that distinguish specific cell types. Whereas extensive progress has been made on defining biochemical and molecular mechanisms of chromatin modification and remodeling, many questions remain unanswered about how cell type-specific chromatin domains assemble and are regulated. This mini-review will discuss emerging studies on how interplay among members of the GATA family of transcription factors establishes and regulates chromatin domains. Dissecting mechanisms underlying the function of hematopoietic GATA factors has revealed fundamental insights into the control of blood cell development from hematopoietic stem cells and the etiology of pathological states in which hematopoiesis is perturbed.

Multiparameter Imaging for the Analysis of Intracellular Signaling

In biological experimentation and especially in drug discovery there is a trend towards more complex test systems. Cell-based assays are replacing conventional binding or enzyme assays more and more. This development is strongly driven by novel fluorescent probes that give insight into cellular processes. Target proteins are studied in their natural environment; this gives much more realistic test results, especially with respect to enzyme location and kinetics. However, in the complex environment of cells, many parameters contribute to the performance of the protein of interest. Therefore, it would be desirable to monitor simultaneously as many of the relevant cellular processes as possible. Here, we discuss the possibilities and limitations provided by multiparameter monitoring of cellular events with fluorescent probes. Some novel examples of the use of fluorescent probes and multiparameter imaging are shown.

Integration of biochemical signalling in spines

Short-term and long-term changes in the strength of synapses in neural networks underlie working memory and long-term memory storage in the brain. These changes are regulated by many biochemical signalling pathways in the postsynaptic spines of excitatory synapses. Recent findings about the roles and regulation of the small GTPases Ras, Rap and Rac in spines provide new insights into the coordination and cooperation of different pathways to effect synaptic plasticity. Here, we present an initial working representation of the interactions of five signalling cascades that are usually studied individually. We discuss their integrated function in the regulation of postsynaptic plasticity.