Inferring signaling pathway topologies from multiple perturbation measurements of specific biochemical species

Reverse engineering validation using a benchmark synthetic gene circuit in human cells

Multicomponent biological networks are often understood incompletely, in large part due to the lack of reliable and robust methodologies for network reverse engineering and characterization. As a consequence, developing automated and rigorously validated methodologies for unraveling the complexity of biomolecular networks in human cells remains a central challenge to life scientists and engineers. Today, when it comes to experimental and analytical requirements, there exists a great deal of diversity in reverse engineering methods, which renders the independent validation and comparison of their predictive capabilities difficult. In this work we introduce an experimental platform customized for the development and verification of reverse engineering and pathway characterization algorithms in mammalian cells. Specifically, we stably integrate a synthetic gene network in human kidney cells and use it as a benchmark for validating reverse engineering methodologies. The network, which is orthogonal to endogenous cellular signaling, contains a small set of regulatory interactions that can be used to quantify the reconstruction performance. By performing successive perturbations to each modular component of the network and comparing protein and RNA measurements, we study the conditions under which we can reliably reconstruct the causal relationships of the integrated synthetic network.

Finding novel pharmaceuticals in the systems biology era using multiple effective drug targets, phenotypic screening and knowledge of transporters: where drug discovery went wrong and how to fix it

Despite the sequencing of the human genome, the rate of innovative and successful drug discovery in the pharmaceutical industry has continued to decrease. Leaving aside regulatory matters, the fundamental and interlinked intellectual issues proposed to be largely responsible for this are: (a) the move from 'function-first' to 'target-first' methods of screening and drug discovery; (b) the belief that successful drugs should and do interact solely with single, individual targets, despite natural evolution's selection for biochemical networks that are robust to individual parameter changes; (c) an over-reliance on the rule-of-5 to constrain biophysical and chemical properties of drug libraries; (d) the general abandoning of natural products that do not obey the rule-of-5; (e) an incorrect belief that drugs diffuse passively into (and presumably out of) cells across the bilayers portions of membranes, according to their lipophilicity; (f) a widespread failure to recognize the overwhelmingly important role of proteinaceous transporters, as well as their expression profiles, in determining drug distribution in and between different tissues and individual patients; and (g) the general failure to use engineering principles to model biology in parallel with performing 'wet' experiments, such that 'what if?' experiments can be performed in silico to assess the likely success of any strategy. These facts/ideas are illustrated with a reasonably extensive literature review. Success in turning round drug discovery consequently requires: (a) decent systems biology models of human biochemical networks; (b) the use of these (iteratively with experiments) to model how drugs need to interact with multiple targets to have substantive effects on the phenotype; (c) the adoption of polypharmacology and/or cocktails of drugs as a desirable goal in itself; (d) the incorporation of drug transporters into systems biology models, en route to full and multiscale systems biology models that incorporate drug absorption, distribution, metabolism and excretion; (e) a return to 'function-first' or phenotypic screening; and (f) novel methods for inferring modes of action by measuring the properties on system variables at all levels of the 'omes. Such a strategy offers the opportunity of achieving a state where we can hope to predict biological processes and the effect of pharmaceutical agents upon them. Consequently, this should both lower attrition rates and raise the rates of discovery of effective drugs substantially.

Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

P38 and JNK have opposing effects on persistence of in vivo leukocyte migration in zebrafish

The recruitment and migration of macrophages and neutrophils is an important process during the early stages of the innate immune system in response to acute injury. Transgenic pu.1:EGFP zebrafish permit the acquisition of leukocyte migration trajectories during inflammation. Currently, these high-quality live-imaging data are mainly analysed using general statistics, for example, cell velocity. Here, we present a spatio-temporal analysis of the cell dynamics using transition matrices, which provide information of the type of cell migration. We find evidence that leukocytes exhibit types of migratory behaviour, which differ from previously described random walk processes. Dimethyl sulfoxide treatment decreased the level of persistence at early time points after wounding and ablated temporal dependencies observed in untreated embryos. We then use pharmacological inhibition of p38 and c-Jun N-terminal kinase mitogen-activated protein kinases to determine their effects on in vivo leukocyte migration patterns and discuss how they modify the characteristics of the cell migration process. In particular, we find that their respective inhibition leads to decreased and increased levels of persistent motion in leukocytes following wounding. This example shows the high level of information content, which can be gained from live-imaging data if appropriate statistical tools are used.

Properties of cell death models calibrated and compared using Bayesian approaches

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass-action models of receptor-mediated cell death. The width of the individual parameter distributions is largely determined by non-identifiability but covariation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model-based predictions whereas ignoring it (e.g., by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (∼20-fold) for competing 'direct' and 'indirect' apoptosis models having different numbers of parameters. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single-cell data represent a generally useful and rigorous approach to discriminate between competing hypotheses in the face of parametric and topological uncertainty.

Bayesian inference of signaling network topology in a cancer cell line

MOTIVATION

Protein signaling networks play a key role in cellular function, and their dysregulation is central to many diseases, including cancer. To shed light on signaling network topology in specific contexts, such as cancer, requires interrogation of multiple proteins through time and statistical approaches to make inferences regarding network structure.

RESULTS

In this study, we use dynamic Bayesian networks to make inferences regarding network structure and thereby generate testable hypotheses. We incorporate existing biology using informative network priors, weighted objectively by an empirical Bayes approach, and exploit a connection between variable selection and network inference to enable exact calculation of posterior probabilities of interest. The approach is computationally efficient and essentially free of user-set tuning parameters. Results on data where the true, underlying network is known place the approach favorably relative to existing approaches. We apply these methods to reverse-phase protein array time-course data from a breast cancer cell line (MDA-MB-468) to predict signaling links that we independently validate using targeted inhibition. The methods proposed offer a general approach by which to elucidate molecular networks specific to biological context, including, but not limited to, human cancers.

AVAILABILITY

http://mukherjeelab.nki.nl/DBN (code and data).

The response of cancers to BRAF inhibition underscores the importance of cancer systems biology

The BRAF inhibitor vemurafenib has become an important treatment option for melanoma patients, the majority of whom have a BRAF(V600E) mutation driving their malignancy. However, this same agent does not generally benefit colon cancer patients who have the BRAF(V600E) mutation. Recent work suggests that BRAF(V600E) inhibition by vemurafenib results in decreased negative feedback to the epidermal growth factor receptor (EGFR) pathway and that the different clinical responses are due to differences in the amount of EGFR present in these two cancers. The experimental work that identified the feedback signaling was an elegant mix of functional genomic approaches and focused, hypothesis-driven cellular and molecular biology. The results of these studies suggest that combined treatment of BRAF(V600E)-driven colon cancers with both vemurafenib and EGFR inhibitors is worth clinical evaluation.

Network inference using steady-state data and Goldbeter-Koshland kinetics. [corrected]

MOTIVATION

Network inference approaches are widely used to shed light on regulatory interplay between molecular players such as genes and proteins. Biochemical processes underlying networks of interest (e.g. gene regulatory or protein signalling networks) are generally nonlinear. In many settings, knowledge is available concerning relevant chemical kinetics. However, existing network inference methods for continuous, steady-state data are typically rooted in statistical formulations, which do not exploit chemical kinetics to guide inference.

RESULTS

Herein, we present an approach to network inference for steady-state data that is rooted in non-linear descriptions of biochemical mechanism. We use equilibrium analysis of chemical kinetics to obtain functional forms that are in turn used to infer networks using steady-state data. The approach we propose is directly applicable to conventional steady-state gene expression or proteomic data and does not require knowledge of either network topology or any kinetic parameters. We illustrate the approach in the context of protein phosphorylation networks, using data simulated from a recent mechanistic model and proteomic data from cancer cell lines. In the former, the true network is known and used for assessment, whereas in the latter, results are compared against known biochemistry. We find that the proposed methodology is more effective at estimating network topology than methods based on linear models.

AVAILABILITY

mukherjeelab.nki.nl/CODE/GK_Kinetics.zip

CONTACT

c.j.oates@warwick.ac.uk; s.mukherjee@nki.nl

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Network Inference and Biological Dynamics

Network inference approaches are now widely used in biological applications to probe regulatory relationships between molecular components such as genes or proteins. Many methods have been proposed for this setting, but the connections and differences between their statistical formulations have received less attention. In this paper, we show how a broad class of statistical network inference methods, including a number of existing approaches, can be described in terms of variable selection for the linear model. This reveals some subtle but important differences between the methods, including the treatment of time intervals in discretely observed data. In developing a general formulation, we also explore the relationship between single-cell stochastic dynamics and network inference on averages over cells. This clarifies the link between biochemical networks as they operate at the cellular level and network inference as carried out on data that are averages over populations of cells. We present empirical results, comparing thirty-two network inference methods that are instances of the general formulation we describe, using two published dynamical models. Our investigation sheds light on the applicability and limitations of network inference and provides guidance for practitioners and suggestions for experimental design.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Bayesian model selection validates a biokinetic model for zirconium processing in humans

BACKGROUND

In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection.

RESULTS

We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler.

CONCLUSIONS

In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology.

Optimal experiment selection for parameter estimation in biological differential equation models

BACKGROUND

Parameter estimation in biological models is a common yet challenging problem. In this work we explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.

RESULTS

A minimization formulation is used to find the parameter values that best fit the experiment data. When the data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show that selecting a new experiment based on the local Fisher Information of one local minimum generates additional data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices are roughly independent of which local minima is used to calculate the local Fisher Information.

CONCLUSIONS

We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment selection can also allow one to restrict model predictions without constraining the parameters using many fewer experiments. We suggest that predicting model behaviors and inferring parameters represent two different approaches to model calibration with different requirements on data and experimental cost.

Elucidating the in vivo phosphorylation dynamics of the ERK MAP kinase using quantitative proteomics data and Bayesian model selection

Ever since reversible protein phosphorylation was discovered, it has been clear that it plays a key role in the regulation of cellular processes. Proteins often undergo double phosphorylation, which can occur through two possible mechanisms: distributive or processive. Which phosphorylation mechanism is chosen for a particular cellular regulation bears biological significance, and it is therefore in our interest to understand these mechanisms. In this paper we study dynamics of the MEK/ERK phosphorylation. We employ a model selection algorithm based on approximate Bayesian computation to elucidate phosphorylation dynamics from quantitative time course data obtained from PC12 cells in vivo. The algorithm infers the posterior distribution over four proposed models for phosphorylation and dephosphorylation dynamics, and this distribution indicates the amount of support given to each model. We evaluate the robustness of our inferential framework by systematically exploring different ways of parameterizing the models and for different prior specifications. The models with the highest inferred posterior probability are the two models employing distributive dephosphorylation, whereas we are unable to choose decisively between the processive and distributive phosphorylation mechanisms.

Identification of aberrant pathways and network activities from high-throughput data

Many complex diseases such as cancer are associated with changes in biological pathways and molecular networks rather than being caused by single gene alterations. A major challenge in the diagnosis and treatment of such diseases is to identify characteristic aberrancies in the biological pathways and molecular network activities and elucidate their relationship to the disease. This review presents recent progress in using high-throughput biological assays to decipher aberrant pathways and network activities. In particular, this review provides specific examples in which high-throughput data have been applied to identify relationships between diseases and aberrant pathways and network activities. The achievements in this field have been remarkable, but many challenges have yet to be addressed.

Competing G protein-coupled receptor kinases balance G protein and β-arrestin signaling

The molecular mechanisms and hidden dynamics governing ERK activation by the angiotensin II type 1A receptor are studied and deciphered, revealing a signal balancing mechanism that is found to be relevant to a range of other seven transmembrane receptors.

An ODE-based dynamical model of ERK activation by the prototypical angiotensin II type-1A seven transmembrane receptor has been built and validated.

In order to deal with a limited number of experimental read-outs, unknown parameters have been inferred by simultaneously fitting control and perturbed conditions.

In addition to its well-established function in G-protein uncoupling, G protein-coupled receptor kinase 2 has been shown to exert a strong negative effect on β-arrestin-dependent signaling and by doing so, to balance G-protein and β-arrestin signaling.

This novel function of G protein-coupled receptor kinase 2 has also been evidenced in primary vascular smooth muscle cells naturally expressing the AT_1AR and in HEK293 cells expressing other 7TMRs.

Seven-transmembrane receptors (7TMRs) are involved in nearly all aspects of chemical communications and represent major drug targets. 7TMRs transmit their signals not only via heterotrimeric G proteins but also through β-arrestins, whose recruitment to the activated receptor is regulated by G protein-coupled receptor kinases (GRKs). In this paper, we combined experimental approaches with computational modeling to decipher the molecular mechanisms as well as the hidden dynamics governing extracellular signal-regulated kinase (ERK) activation by the angiotensin II type 1A receptor (AT_1AR) in human embryonic kidney (HEK)293 cells. We built an abstracted ordinary differential equations (ODE)-based model that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, in addition to its well-established function in the desensitization of G-protein activation, GRK2 exerts a strong negative effect on β-arrestin-dependent signaling through its competition with GRK5 and 6 for receptor phosphorylation. Importantly, we experimentally confirmed the validity of this novel GRK2-dependent mechanism in both primary vascular smooth muscle cells naturally expressing the AT_1AR, and HEK293 cells expressing other 7TMRs.

Computational approaches for analyzing information flow in biological networks

The advancements in "omics" (proteomics, genomics, lipidomics, and metabolomics) technologies have yielded large inventories of genes, transcripts, proteins, and metabolites. The challenge is to find out how these entities work together to regulate the processes by which cells respond to external and internal signals. Mathematical and computational modeling of signaling networks has a key role in this task, and network analysis provides insights into biological systems and has applications for medicine. Here, we review experimental and theoretical progress and future challenges toward this goal. We focus on how networks are reconstructed from data, how these networks are structured to control the flow of biological information, and how the design features of the networks specify biological decisions.

Cross-regulation between FOXA1 and ErbB2 signaling in estrogen receptor-negative breast cancer

Molecular apocrine is a subtype of estrogen receptor-negative (ER.) breast cancer, which is characterized by a steroid-response gene signature that includes androgen receptor, FOXA1, and a high frequency of ErbB2 overexpression. In this study, we demonstrate that there is a strong association between the overexpression of FOXA1 and ErbB2 in ER- breast tumors. This has led us to identify a cross-regulation network between FOXA1 and ErbB2 signaling in ER- breast cancer. We present two mechanisms to explain the association between FOXA1 and ErbB2 overexpression in molecular apocrine cells. In one process, ErbB2 signaling genes CREB1 and c-Fos regulate FOXA1 transcription, and in another process, AP2α regulates the expression of both FOXA1 and ErbB2. Moreover, we demonstrate that FOXA1, in turn, regulates the transcription of ErbB2 signaling genes. This includes a core gene signature that is shared across two molecular apocrine cell lines. Importantly, the most upregulated (RELB) and downregulated (PAK1) genes in this signature are direct FOXA1 targets. Our data suggest that FOXA1 acts as a dual-function transcription factor and the repressive function of FOXA1 on RELB can be explained by the recruitment of its binding partner corepressor TLE3. It is notable that a group of FOXA1-regulated genes vary across molecular apocrine cell lines leading to the differences in the functional effects of FOXA1 on extracellular signal-regulated kinase phosphorylation and cell viability between these lines. This study demonstrates that there is a cross-regulation network between FOXA1 and ErbB2 signaling that connects FOXA1 to some of the key signaling pathways in ER-breast cancer.

A dynamic network model of mTOR signaling reveals TSC-independent mTORC2 regulation

The kinase mammalian target of rapamycin (mTOR) exists in two multiprotein complexes (mTORC1 and mTORC2) and is a central regulator of growth and metabolism. Insulin activation of mTORC1, mediated by phosphoinositide 3-kinase (PI3K), Akt, and the inhibitory tuberous sclerosis complex 1/2 (TSC1-TSC2), initiates a negative feedback loop that ultimately inhibits PI3K. We present a data-driven dynamic insulin-mTOR network model that integrates the entire core network and used this model to investigate the less well understood mechanisms by which insulin regulates mTORC2. By analyzing the effects of perturbations targeting several levels within the network in silico and experimentally, we found that, in contrast to current hypotheses, the TSC1-TSC2 complex was not a direct or indirect (acting through the negative feedback loop) regulator of mTORC2. Although mTORC2 activation required active PI3K, this was not affected by the negative feedback loop. Therefore, we propose an mTORC2 activation pathway through a PI3K variant that is insensitive to the negative feedback loop that regulates mTORC1. This putative pathway predicts that mTORC2 would be refractory to Akt, which inhibits TSC1-TSC2, and, indeed, we found that mTORC2 was insensitive to constitutive Akt activation in several cell types. Our results suggest that a previously unknown network structure connects mTORC2 to its upstream cues and clarifies which molecular connectors contribute to mTORC2 activation.

Optimal structural inference of signaling pathways from unordered and overlapping gene sets

MOTIVATION

A plethora of bioinformatics analysis has led to the discovery of numerous gene sets, which can be interpreted as discrete measurements emitted from latent signaling pathways. Their potential to infer signaling pathway structures, however, has not been sufficiently exploited. Existing methods accommodating discrete data do not explicitly consider signal cascading mechanisms that characterize a signaling pathway. Novel computational methods are thus needed to fully utilize gene sets and broaden the scope from focusing only on pairwise interactions to the more general cascading events in the inference of signaling pathway structures.

RESULTS

We propose a gene set based simulated annealing (SA) algorithm for the reconstruction of signaling pathway structures. A signaling pathway structure is a directed graph containing up to a few hundred nodes and many overlapping signal cascades, where each cascade represents a chain of molecular interactions from the cell surface to the nucleus. Gene sets in our context refer to discrete sets of genes participating in signal cascades, the basic building blocks of a signaling pathway, with no prior information about gene orderings in the cascades. From a compendium of gene sets related to a pathway, SA aims to search for signal cascades that characterize the optimal signaling pathway structure. In the search process, the extent of overlap among signal cascades is used to measure the optimality of a structure. Throughout, we treat gene sets as random samples from a first-order Markov chain model. We evaluated the performance of SA in three case studies. In the first study conducted on 83 KEGG pathways, SA demonstrated a significantly better performance than Bayesian network methods. Since both SA and Bayesian network methods accommodate discrete data, use a 'search and score' network learning strategy and output a directed network, they can be compared in terms of performance and computational time. In the second study, we compared SA and Bayesian network methods using four benchmark datasets from DREAM. In our final study, we showcased two context-specific signaling pathways activated in breast cancer.

AVAILABILITY

Source codes are available from http://dl.dropbox.com/u/16000775/sa_sc.zip.

Dynamic modelling under uncertainty: the case of Trypanosoma brucei energy metabolism

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies.

Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods

Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions.

GSGS: a computational approach to reconstruct signaling pathway structures from gene sets

Reconstruction of signaling pathway structures is essential to decipher complex regulatory relationships in living cells. Existing approaches often rely on unrealistic biological assumptions and do not explicitly consider signal transduction mechanisms. Signal transduction events refer to linear cascades of reactions from cell surface to nucleus and characterize a signaling pathway. We propose a novel approach, Gene Set Gibbs Sampling, to reverse engineer signaling pathway structures from gene sets related to pathways. We hypothesize that signaling pathways are structurally an ensemble of overlapping linear signal transduction events which we encode as Information Flows (IFs). We infer signaling pathway structures from gene sets, referred to as Information Flow Gene Sets (IFGSs), corresponding to these events. Thus, an IFGS only reflects which genes appear in the underlying IF but not their ordering. GSGS offers a Gibbs sampling procedure to reconstruct the underlying signaling pathway structure by sequentially inferring IFs from the overlapping IFGSs related to the pathway. In the proof-of-concept studies, our approach is shown to outperform existing network inference approaches using data generated from benchmark networks in DREAM. We perform a sensitivity analysis to assess the robustness of our approach. Finally, we implement GSGS to reconstruct signaling mechanisms in breast cancer cells.

Spatiotemporally regulated protein kinase A activity is a critical regulator of growth factor-stimulated extracellular signal-regulated kinase signaling in PC12 cells

PC12 cells exhibit precise temporal control of growth factor signaling in which stimulation with epidermal growth factor (EGF) leads to transient extracellular signal-regulated kinase (ERK) activity and cell proliferation, whereas nerve growth factor (NGF) stimulation leads to sustained ERK activity and differentiation. While cyclic AMP (cAMP)-mediated signaling has been shown to be important in conferring the sustained ERK activity achieved by NGF, little is known about the regulation of cAMP and cAMP-dependent protein kinase (PKA) in these cells. Using fluorescence resonance energy transfer (FRET)-based biosensors localized to discrete subcellular locations, we showed that both NGF and EGF potently activate PKA at the plasma membrane, although they generate temporally distinct activity patterns. We further show that both stimuli fail to induce cytosolic PKA activity and identify phosphodiesterase 3 (PDE3) as a critical regulator in maintaining this spatial compartmentalization. Importantly, inhibition of PDE3, and thus perturbation of the spatiotemporal regulation of PKA activity, dramatically increases the duration of EGF-stimulated nuclear ERK activity in a PKA-dependent manner. Together, these findings identify EGF and NGF as potent activators of PKA activity specifically at the plasma membrane and reveal a novel regulatory mechanism contributing to the growth factor signaling specificity achieved by NGF and EGF in PC12 cells.

Dynamic modeling and analysis of cancer cellular network motifs

With the advent of high-throughput biology, we now routinely scan cells and organisms at practically all levels, from genome to protein, metabolism, signaling and other cellular functions. This methodology allowed biological studies to move from a reductionist approach, such as isolation of specific pathways and mechanisms, to a more integrative approach, where biological systems are seen as a network of interconnected components that provide specific outputs and functions in response to stimuli. Recent literature on biological networks demonstrates two important concepts that we will consider in this review: (i) cellular pathways are highly interconnected and should not be studied separately, but as a network; (ii) simple, recurrent feedback motifs within the network can produce very specific functions that favor their modular use. The first theme differs from the traditional approach in biology because it provides a framework (i.e., the network view) in which large datasets are analyzed with an unbiased view. The second theme (feedback motifs) shows the importance of locally analyzing the dynamic properties of biological networks in order to better understand their functionality. We will review these themes with examples from cell signaling networks, gene regulatory networks and metabolic pathways. The deregulation of cellular networks (metabolism, signaling etc.) is involved in cancer, but the size of the networks and resulting non-linear behavior do not allow for intuitive reasoning. In that context, we argue that the qualitative classification of the 'building blocs' of biological networks (i.e. the motifs) in terms of dynamics and functionality will be critical to improve our understanding of cancer biology and rationalize the wealth of information from high-throughput experiments. From the examples highlighted in this review, it is clear that dynamic feedback motifs can be used to provide a unified view of various cellular processes involved in cancer and this will be critical for future research on personalized and predictive cancer therapies.

Structure-based systems biology for analyzing off-target binding

Here off-target binding implies the binding of a small molecule of therapeutic interest to a protein target other than the primary target for which it was intended. Increasingly such off-targeting appears to be the norm rather than the exception, rational drug design notwithstanding, and can lead to detrimental side-effects, or opportunities to reposition a therapeutic agent to treat a different condition. Not surprisingly, there is significant interest in determining a priori what off-targets exist on a proteome-wide scale. Beyond determining putative off-targets is the need to understand the impact of such binding on the complete biological system, with the ultimate goal of being able to predict the phenotypic outcome. While a very ambitious goal, some progress is being made.

Raf family kinases: old dogs have learned new tricks

First identified in the early 1980s as retroviral oncogenes, the Raf proteins have been the objects of intense research. The discoveries 10 years later that the Raf family members (Raf-1, B-Raf, and A-Raf) are bona fide Ras effectors and upstream activators of the ubiquitous ERK pathway increased the interest in these proteins primarily because of the central role that this cascade plays in cancer development. The important role of Raf in cancer was corroborated in 2002 with the discovery of B-Raf genetic mutations in a large number of tumors. This led to intensified drug development efforts to target Raf signaling in cancer. This work yielded not only recent clinical successes but also surprising insights into the regulation of Raf proteins by homodimerization and heterodimerization. Surprising insights also came from the hunt for new Raf targets. Although MEK remains the only widely accepted Raf substrate, new kinase-independent roles for Raf proteins have emerged. These include the regulation of apoptosis by suppressing the activity of the proapoptotic kinases, ASK1 and MST2, and the regulation of cell motility and differentiation by controlling the activity of Rok-α. In this review, we discuss the regulation of Raf proteins and their role in cancer, with special focus on the interacting proteins that modulate Raf signaling. We also describe the new pathways controlled by Raf proteins and summarize the successes and failures in the development of efficient anticancer therapies targeting Raf. Finally, we also argue for the necessity of more systemic approaches to obtain a better understanding of how the Ras-Raf signaling network generates biological specificity.

Regulation by Ca2+-signaling pathways of adenylyl cyclases

Interplay between the signaling pathways of the intracellular second messengers, cAMP and Ca(2+), has vital consequences for numerous essential physiological processes. Although cAMP can impact on Ca(2+)-homeostasis at many levels, Ca(2+) either directly, or indirectly (via calmodulin [CaM], CaM-binding proteins, protein kinase C [PKC] or Gβγ subunits) may also regulate cAMP synthesis. Here, we have evaluated the evidence for regulation of adenylyl cyclases (ACs) by Ca(2+)-signaling pathways, with an emphasis on verification of this regulation in a physiological context. The effects of compartmentalization and protein signaling complexes on the regulation of AC activity by Ca(2+)-signaling pathways are also addressed. Major gaps are apparent in the interactions that have been assumed, revealing a need to comprehensively clarify the effects of Ca(2+) signaling on individual ACs, so that the important ramifications of this critical interplay between Ca(2+) and cAMP are fully appreciated.