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Cite this:Mol. BioSyst., 2014,

10, 537

In silico identification of potential therapeutictargets in the TGF-b signal transduction pathway†

Daniel Nicklas and Leonor Saiz*

The transforming growth factor-b (TGF-b) superfamily of cytokines controls fundamental cellular

processes, such as proliferation, motility, differentiation, and apoptosis. This fundamental role is

emphasized by the widespread presence of mutations of the core components of the TGF-b signal

transduction pathway in a number of human diseases. Therefore, there is an increasing interest in the

development of therapies to specifically target this pathway. Here we develop a computational approach

to identify potential intervention points that are capable of restoring the normal signaling dynamics to

the mutated system while maintaining the behavior of normal cells substantially unperturbed. We apply

this approach explicitly to the TGF-b pathway to study the signaling dynamics of mutated and normal

cells treated with inhibitory drugs and identify the processes in the pathway that are most susceptible to

therapeutic intervention.

Introduction

The transforming growth factor-b (TGF-b) signal transductionpathway controls multiple cellular processes, including prolif-eration, motility, differentiation, and apoptosis, that are essen-tial for regulating embryonic development, tissue homeostasis,and wound healing.1 Dysregulation of the pathway throughmutations of its core components is associated with a numberof human diseases, such as cancer, fibrotic conditions ofkidneys, liver, and lungs, and vascular and autoimmunedisorders.2–4 Because of its involvement in many aspects ofhuman health, a significant effort of clinical research focuseson developing therapies targeting the activity of the TGF-bsignaling pathway.5,6

TGF-b-superfamily ligands signal through a network ofinteracting molecular components with complex patterns ofcoupled signaling and feedback regulation. At the plasmamembrane, the ligands initiate signaling by binding to twotypes of serine–threonine kinases, known as type I and type IIreceptors. The active ligand–receptor complex propagates thesignal through the intracellular mediator Smad proteins uponinternalization into the endosome, where it may recruit andphosphorylate a receptor-regulated Smad (R-Smad). Phosphory-lated R-Smads bind to Smad4 and translocate into the nucleus,where the resulting macromolecular complex regulates the

expression of several hundred genes, including Smad7. Smad7,an inhibitory Smad, negatively regulates signaling by binding toactive ligand–receptor complexes at the plasma membrane andinducing their degradation. TGF-b-superfamily ligands use twoparallel R-Smad channels, grouped as Smad1/5/8 and Smad2/3,to transmit the signal. Bone morphogenetic proteins (BMPs)and nodal/activin ligands induce phosphorylation of theSmad1/5/8 and Smad2/3 groups, respectively, while TGF-binduces phosphorylation of both R-Smad groups.7

A number of mutations affecting the TGF-b pathway signal-ing components have been identified in a variety of humancancers.2,6 While TGF-b is typically a growth suppressor, itsdysregulated activation may promote invasion and growth oftumors in cancer cells.8 Therefore, a number of strategies havebeen developed to abrogate this effect by inhibiting TGF-bactivity, such as the use of antisense oligonucleotides andmonoclonal antibodies targeting TGF-b mRNA and protein,respectively, and small molecule kinase inhibitors that targetthe receptors, blocking R-Smad phosphorylation.6,9

Quantitative and predictive models have been successfullyused to study key modules in the TGF-b signal transductionpathway, including receptor trafficking,10–12 Smad nucleocyto-plasmic shuttling,13,14 and transcriptional feedback loops.15–20

Several models have combined these components into compre-hensive mathematical representations of the signaling path-way.19,21–23 In addition to providing insight into the underlyingmechanisms, computational models of signaling pathways havebeen used to study the effects of mutations in disease.22,24–26 In theTGF-b signaling pathway, for instance, Chung et al. investigated theeffects of cancerous mutations on Smad-dependent signaling.Specifically, they used their model to predict how different

Modeling of Biological Networks Laboratory, Department of Biomedical Engineering,

University of California, 451 East Health Sciences Drive, Davis, CA 95616, USA.

E-mail: lsaiz@ucdavis.edu; Fax: +1-530-754-5739; Tel: +1-530-752-6700

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3mb70259f

Received 30th June 2013,Accepted 10th December 2013

DOI: 10.1039/c3mb70259f

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MolecularBioSystems

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signaling components are affected by cancerous mutations byintroducing a mutation resulting in downregulation of TGF-breceptors through decreased initial concentration and synthesisrate of the affected species.22 Furthermore, it has been shown thatcomputational modeling can be used as a fundamental step in thedevelopment of novel pharmaceuticals.27,28

A prime example of the applicability of computationalapproaches is the epidermal growth factor receptor (EGFR)signaling pathway, which has been extensively studied usinga number of computational models to investigate both receptortrafficking and downstream signaling.29 In particular, modelsof the EGF-induced extracellular signal regulated kinase (ERK)signal transduction pathway have been successfully used tostudy the effects of oncogenic mutations,25 to assess the role ofmutation in the sensitivity of cells to an existing therapy,24 andto identify therapeutic targets and biomarkers.30 Specifically,Orton and coworkers developed a model of the ERK signaltransduction pathway and compared the signaling dynamics ofnormal and cancer cells as modeled through knockouts andmutations of signaling proteins. From this, the authorshypothesized which components of the signaling pathway weresusceptible to therapeutic intervention.25 Using similarstrategies, Hendriks et al. introduced perturbations into theirmodel to represent the effects of mutant receptors and testedpotential mechanisms by which the mutated signal dynamicsobserved experimentally differed from those of normal cells.24

Using sensitivity analysis, Lebedeva and coworkers identified anumber of potential therapeutic targets and biomarkers in thepathway.30

In addition to investigating the effects of mutations, com-putational modeling has been used to analyze how therapiesinteract with mutated signaling pathways and to propose noveltargets for therapeutic intervention in a number of systems anddiseases.31–36 Specifically, Sung and Simon compared theeffects of novel inhibitor drugs on the signaling dynamics ofthe nuclear factor-kB (NF-kB) pathway.32 Yan et al. and Araujoet al. extended this analysis in the NF-kB and EGFR pathways,respectively, to simulations of drug combinations.31,33 Inparticular, Araujo and coworkers evaluated the effects of kinaseinhibitors targeting one or two nodes in the pathway, revealingthat simultaneous administration allows for a reduction in therequired dose necessary to significantly affect the signalresponse.31 Mathematical modeling of transferrin bindingand receptor trafficking was used to successfully propose anovel mechanism to improve its drug delivery capabilities,34

which was validated with in vitro and in vivo experiments.34–36

Here we apply a comprehensive computational model of theTGF-b signal transduction pathway19 to study the signalingdynamics of mutated and normal cells treated with inhibitorydrugs or treatments. Using this model, we build upon strategiesapplied to the TGF-b signaling pathway and other systems todevelop an effective in silico approach for identifying targetableprocesses and potential intervention points that are capable ofrestoring the normal signaling dynamics to the mutated systemwhile maintaining the behavior of normal cells substantiallyunperturbed.

We have chosen the TGF-b signaling system because of itsprominent role in cancer.8 Cancer is a multistage process thatinvolves the successive failure of many control points, such ascancer cells stimulating their own growth and resisting inhibitorysignals that might otherwise stop their growth as well as theevasion of programmed cell death. Therefore, dysregulation of theTGF-b pathway in cancer cell lines is accompanied by thedysregulation of additional pathways, such as those arisingfrom K-ras oncogene mutations.37,38 There are many therapiesunder development that target the components of the TGF-bpathway.6 One of the most sought features of a therapy is theselective targeting of the mutated cells while keeping the normalcells largely unperturbed. So far there has not been a systematicapproach to identify those therapies. The in silico approach wepresent here is a first step in this direction, which can be appliedto a number of other signaling systems as a guiding tool in thetherapy development process. Subsequent aspects that wouldneed to be taken into account in the full therapy developmentinclude the differences between cell lines and tumor samples aswell as the cross-talking between different signaling pathways.

MethodsThe TGF-b pathway model

To study the dynamics of the pathway upon stimulation withTGF-b, we use the comprehensive mathematical modeldeveloped in ref. 19, which has been shown to accuratelyreproduce the behavior of human keratinocytes (HaCaT),bovine aortic endothelial cells (BAEC), and the mousemesenchymal C2C12 cell line. The model considers explicitlyreceptor trafficking, downstream signaling by intracellularSmad proteins, and negative feedback through Smad7. Signalingis initiated when a TGF-b ligand binds to its type II receptor,denoted as RII. This complex then recruits a type I receptor, oneof RI1 or RI2, forming the ligand–receptor complex C1 or C2,respectively. The ligand–receptor complexes propagate the signalupon internalization into the endosome, where C1 may bindwith cytosolic Smad1 (S1c) and C2 may bind with cytosolic Smad2(S2c) and phosphorylate the R-Smad. We use the subscripts c andn to denote cytosolic and nuclear species, respectively, and applya prefix p to phosphorylated species. pS1c and pS2c bind toSmad4 (S4c), forming the pS1S4c and pS2S4c complexes,respectively, which may translocate into the nucleus wherepS1S4n and pS2S4n then may promote the expression of Smad7(S7). This initiates a negative feedback loop in which S7 binds tothe ligand–receptor complexes (C1 or C2) at the plasmamembrane, preventing their association and phosphorylationof R-Smad proteins, and targeting them for degradation. Aschematic representation of the model is shown in Fig. 1, wherearrows indicate modeled reactions in the pathway. Reactions aremathematically represented using mass-action kinetics, whichare then combined to form the system of ordinary differentialequations (ODEs) to track the rate of change of each modeledspecies (Table S1, ESI†). Parameter values for the three cell typesare listed in Table S2 (ESI†).10,19,22,56–64

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Prior to ligand stimulation, we determine the steady statesolution for the system of ODEs (Table S1, ESI†) by setting eachtime-derivative to zero and solving the resulting linear systemof equations with the concentration of the ligand set to zerousing the ‘linalg.solve’ method in Numpy 1.6.2 (http://numpy.scipy.org). Upon ligand stimulation, we numerically solve thesystem of ODEs using the CVODE method in the SUNDIALS2.5.0 package.39 These correspond to the typical experimentalconditions that measure the response of the system to a suddenchange of the TGF-b ligand concentration from zero to asaturating value that is kept constant afterwards.

Mutation and molecular intervention simulations

In order to capture the effects of mutations in the pathway, weuse a strategy similar to that employed in ref. 22 and 31 tointroduce altered protein expression or functional mutation.Focusing on the mutations outlined in Table 1, we define amutation factor (MF) within the range [0,1] with which to reducethe parameter values associated with each mutation. Forexample, to introduce the ‘inhibited Smad4 nuclear import’mutation with a 0.1 mutation factor, we multiply k7imp andk14imp by 0.1. Similarly, we simulate the effects of a molecularintervention by introducing an intervention factor (IF) within

the range [0,1] that is multiplied with the rate constantsaffected by a particular molecular intervention.

Sensitivity analysis

We use a global sensitivity analysis to investigate how themodel responds to perturbations of individual parameters inthe parameter space.40 Concretely, we compute the derivative-based global sensitivity measures developed in ref. 41, whichsample the effects of local parameter perturbation in a largerparameter space. To compute the effects of local parameterperturbation, we use the scaled sensitivity coefficients42

given by

eki; j ¼ki; j

Cj

@Cj

@ki; j; (1)

where ki,j defines the value of the ith parameter of sample j andCj is the time integral of the model output over 24 hours afterstimulation with the ligand for the parameters of the jthsample. As model output, we examine the signaling dynamicsof both nuclear phosphorylated Smad1–Smad4 (pS1S4n) andnuclear phosphorylated Smad2–Smad4 (pS2S4n) complexessince they control the long-term effects of ligand stimulationthrough regulation of gene expression.7 To approximate thepartial derivative, we simulate the model with 0.5 percent

Fig. 1 Schematic illustration of the Smad-dependent TGF-b signaling pathway model upon stimulation with TGF-b. Arrows denote reaction steps in thepathway and are labeled with the rate constant for the reaction. Synthesis and degradation reactions are provided in the table (inset) with the notationfor the different molecular species given in the text. Expression of Smad7 is under the control of a single gene, activated by nuclear phosphorylatedSmad1–Smad4 and/or Smad2–Smad4 complexes.

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perturbations of parameter ki about its value at sample j andcalculate the finite central difference.43 For each parameter ki, wecalculate the local sensitivity coefficient eki,j

for 4000 parametervalues, i.e. j = 1,. . .,4000, by randomly sampling around its originalvalue (Table S2, ESI†) in the parameter space. Specifically, wegenerate a random variable x with a uniform distribution withinthe range [�1,1] and multiply the original parameter value by 10x.The scaled sensitivity coefficients are then used to compute theglobal sensitivity coefficient41 defined by

Gki ¼1

N

XNj¼1

eki; j2; (2)

where N is the number of samples, equal to 4000 here. Weimplemented the sensitivity analysis using Python 2.7.3 (http://www.python.org), Numpy 1.6.2 (http://numpy.scipy.org), andScipy 0.10.0.44

Molecular intervention optimization

We optimize the intervention factor IF, defined as a valuewithin the range [0,1], by fitting the simulation result of amutated cell with the specific molecular intervention to that ofa normal cell. Additionally, we fit the simulation result of thenormal cell with the molecular intervention to that of a normalcell in order to minimize the potential risk of side effects fromexposing normal cells to the molecular intervention since thegoal of our approach is to identify those molecular inter-ventions that lead to the recovery of normal behavior bymutated cells and that minimally affect the behavior of normalcells. Therefore, we define the objective function for minimizationas the least-squares error:

E ¼Xni¼1

S tið Þ �M� tið Þð Þ2þ S tið Þ � S� tið Þð Þ2� �

; (3)

where S(ti) and M(ti) are the normal and mutated cell dynamics,respectively, at the time point ti of n total time points andthe asterisk represents the corresponding dynamics with themolecular intervention. To determine the optimized interventionfactor (OIF) we first evaluate the objective function with inter-vention factors within the range [0.1,0.9] with 0.1 increments.The intervention factor with the minimum objective functionvalue becomes the starting point for a downhill simplex algorithmwith the ‘optimize.fmin’ function in Scipy 0.10.0.44 In order toimpose the bounds of [0,1] for the intervention factor, we use thetransformations described in ref. 45. Our computational imple-mentation uses Python 2.7.3 (http://www.python.org), Numpy1.6.2 (http://numpy.scipy.org), and Scipy 0.10.0.44

Results and discussionModel dynamics

To examine the ability of the model to reproduce the observedbehavior in mutated cell lines, we compare the results of thesimulation with experimental data in HaCaT cells and twopancreatic cancer cell lines, namely Colo-357 and PT45(Fig. 2). The TGF-b signaling in these cell lines has been studiedin detail in ref. 46. The results show that Colo-357 cells exhibitan epithelial phenotype, forming well-defined epithelial sheetsand expressing E-cadherin at their adherens junctions. Colo-357 cells respond to TGF-b in a way very similar to HaCaT cells,strongly inducing the expression of p21, JunB, c-Jun, Smad7,and PAI-1 mRNA within 1 hour of ligand stimulation. PT45cells, in contrast, do not present the epithelial phenotype andthe induction of p21 and JunB mRNA with TGF-b is onlytransient. Colo-357 cells, as HaCaT cells, display rapid nuclearaccumulation of phosphorylated Smad2 that is still present, butreduced 6 hours after activation. In contrast, nuclear accumu-lation of phosphorylated Smad2 in PT45 cells disappearsabruptly after 1 hour of stimulation. The kinetics of nuclearaccumulation of Smad4 was observed to be very similar to thatof phosphorylated Smad2 in both Colo-357 and PT45 cells.Using the parameters for HaCaT cells (Table S2, ESI†), themodel reproduces the normal signaling dynamics of bothnuclear phosphorylated Smad2 (Fig. 2A) and nuclear Smad4(Fig. 2D) molecular species. To simulate the dynamics ofpancreatic cancer cells Colo-357 and PT45, we introduce the‘inhibited Smad4 nuclear import’ mutation found in pancreaticcancer cell lines (Table 2) to the normal cases with a mutationfactor of MF = 0.1. As Colo-357 cells exhibit an epithelialphenotype,46 we use the model for HaCaT cells to reproducetheir signaling dynamics. By introducing the mutation, themodel results change only minimally for both nuclearphosphorylated Smad2 (Fig. 2B and Fig. S1, ESI†) and nuclearSmad4 (Fig. 2E and Fig. S1, ESI†), consistently with theexperimental data. The differences between the model andexperimental results observed in the early stages of signalingin Fig. 2B and E are attributable, as discussed in ref. 11, tothe detailed trafficking dynamics of the receptors. We usethe parameters for C2C12 cells to reproduce the PT45

Table 1 Potential targetable processes and their associated rateconstants analyzed in the optimization of the molecular interventions.The parameters associated with each process are multiplied by an inter-vention factor in the range [0,1] to simulate the process inhibition

Inhibited process Parameters

Type II receptor synthesis ksyn,RIIType I receptor synthesis ksyn,RIR-Smad synthesis ksyn,RS

Smad4 synthesis ksyn,S4

Smad7 synthesis ksyn,S7, klip,1, and klip,2

Association of TGF-b with type II receptor k1a

Association of TGF-b–type II receptorcomplex with type I receptor

k2a

Ligand–receptor complex–R-Smadassociation

k4a

R-Smad–Smad4 association k6a and k10a

R-Smad nuclear import k7imp, k12imp, and k13imp

R-Smad nuclear export k12exp

Smad4 nuclear import k7imp and k14impSmad4 nuclear export k14exp

Ligand–receptor complex–Smad7 association k20a,1 and k20a,2

Association of phospho-R-Smad–Smad4complex with DNA

KA,1 and KA,2

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dynamics as the latter also exhibits a mesenchymal pheno-type.46 The model captures the more transient signal inboth nuclear phosphorylated Smad2 (Fig. 2C) and nuclearSmad4 (Fig. 2F) species in PT45 cells as compared to C2C12dynamics without the mutation (Fig. 2A and D), as observedexperimentally.

To demonstrate that the model reproduces the observedexperimental behavior in the presence of inhibitory drugs andtreatments, we simulate the model upon stimulation withTGF-b and treatment with endocytosis inhibitors (Fig. 3 andFig. S2, ESI†) and with a phosphatase inhibitor (Fig. 4). InFig. 3, we show the results of simulating the effect of potassiumdepletion (–KCl) to inhibit clathrin-mediated endocytosis andof Nystatin to inhibit lipid raft-caveolar endocytosis on thedynamics of the ratio of phosphorylated Smad2 to totalSmad2 species in Mv1Lu cells. In this case, we use the para-meters for HaCaT cells in the model as both cells exhibit anepithelial phenotype. To simulate the effects of potassiumdepletion, we decreased the internalization and constitu-tive degradation rate constants for all receptor species

(kdeg,RII, kdeg,RI, k3int, k16deg, k18int, and k19int) with an inter-vention factor of IF = 0.15. This results in a decreased phosphory-lated Smad2 response upon TGF-b stimulation as it minimizes thepool of internalized ligand–receptor complexes to bind to Smad2(Fig. 3B). To simulate the effects of Nystatin, we decrease the rateconstants for Smad7–ligand–receptor complex association (k20a,1

and k20a,2) with an intervention factor of IF = 0.85. In contrast tothe strong effects observed for potassium depletion, Nystatintreatment results just in a slight increase in the phosphorylatedSmad2 concentration due to the inhibition of the Smad7-mediatednegative feedback loop (Fig. 3C).

The effects of phosphatase inhibition through treatmentwith sodium orthovanadate in BAEC cells are simulated bydecreasing the dephosphorylation rate constants (k8dp andk11dp) with an intervention factor of IF = 0.3. The modelreproduces a slightly more sustained phosphorylated Smad1response to TGF-b in the presence of sodium orthovanadate ascompared to normal signaling dynamics in this cell line(Fig. 4) as it eliminates one mode of negative regulation inthe pathway.

Fig. 2 Simulation of the effects of pancreatic cancer mutations on TGF-b signaling dynamics. We simulate the dynamics of the model using theparameters for HaCaT (black solid lines) and C2C12 cells (blue dashed lines) and show the results for nuclear phosphorylated Smad2 (top row; A–C) andnuclear Smad4 (bottom row; D–F) species upon stimulation with 2 ng mL�1 TGF-b at t = 0 hours. Experimental data (symbols) was quantified usingImageJ 10.252 from Western blot experiments in ref. 46 for HaCaT cells (left column; A and D) and two pancreatic cancer cell lines: Colo-357 (middlecolumn; B and E) and PT45 (right column; C and F). To simulate the dynamics of the pancreatic cancer cell lines, we use the ‘inhibited Smad4 nuclearimport’ mutation (Table 2) with a mutation factor MF = 0.1. The root-mean-square deviation (RMSD) between the model results and the experimentaldata is 0.13, 0.18, 0.16, 0.22, 0.26, and 0.18 for panels A, B, C, D, E, and F, respectively.

Table 2 Effects of cancerous TGF-b pathway mutations and their implementation in the computational model. For each mutation, the affectedparameters are multiplied by a mutation factor to capture the decreased synthesis or association rates

Mutation Disease Ref. Model alteration

TGF-b receptordownregulation

Bladder, breast,esophageal, ovarian,and prostate cancer

Levy & Hill2 Decrease receptor synthesis rate (ksyn,RII and ksyn,RI)

Smad4 downregulation Breast cancer Levy & Hill2 Decrease Smad4 synthesis rate (ksyn,S4)Smad7 downregulation Colon cancer Levy & Hill2 Decrease Smad7 synthesis rate (ksyn,S7, klip,1, and klip,2)Inhibited Smad4 nuclearimport

Pancreatic cancer Moren et al.50 Decrease nuclear import rate constant of monomeric Smad4 and phospho-R-Smad–Smad4 complexes (k7imp and k14imp)

Inhibited phospho-R-Smad–Smad4 association

Pancreatic cancer Hata et al.51 Decrease association rate constant for cytosolic andnuclear phospho-R-Smad with Smad4 (k6a and k10a)

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Computational approach for identification of potentialtherapeutic targets

As the TGF-b pathway model is capable of reproducing the effectsof both mutations and treatment with inhibitory drugs observedexperimentally, we use it as the foundation with which to demon-strate the applicability of the novel in silico approach to identifypotential therapeutic targets in intracellular networks. The differentsteps of the computational approach, summarized in Fig. 5, arediscussed in the following sections.

Step 1: identification of targetable network processes. Sev-eral strategies have been developed to specifically target bio-chemical processes that may be used here. Antisenseoligonucleotides are used to specifically inhibit protein synth-esis by binding to mRNA and preventing translation.47 In themodeled pathway, these could be used to inhibit synthesis oftype II receptors, type I receptors, R-Smads, Smad4, and Smad7.Peptide aptamers are engineered to inhibit protein–protein orprotein–DNA association by binding to the associated region of

Fig. 3 Simulation of the effects of endocytosis inhibitors on TGF-b signaling dynamics. Using the parameters for HaCaT cells, we simulate the dynamics(lines) of the system and show the results for the ratio of phosphorylated Smad2 to total Smad2 upon stimulation with 0.5 nM (12.8 ng mL�1) TGF-b att = 0 hours. Experimental Western blot data (symbols) and quantification are from ref. 53 with Mv1Lu cells. The experimental data and simulation resultsare normalized to the maximum from all three conditions. (A) The control case with no inhibitory treatment. (B) Treatment with potassium depletion(–KCl). To simulate the effects of potassium depletion, which inhibits clathrin-mediated endocytosis, we decrease internalization and constitutivedegradation rate constants for all receptor species (kdeg,RII, kdeg,RI, k3int, k16deg, k18int, and k19int) by an intervention factor IF = 0.15. (C) Treatment withNystatin. To simulate the effects of Nystatin, which inhibits lipid raft-caveolar endocytosis, we decrease the rate constants for Smad7–ligand–receptorcomplex association (k20a,1 and k20a,2) with an intervention factor IF = 0.85. The root-mean-square deviation between the model results and theexperimental data is 0.19, 0.06, and 0.06 for panels A, B, and C, respectively.

Fig. 4 Simulation of the effects of phosphatase inhibitors on TGF-b signaling dynamics. Using the parameters for BAEC cells, we simulate the dynamics(lines) of the system and show the results for phosphorylated Smad1 upon stimulation with 1 ng mL�1 TGF-b at t = 0 hours. Experimental Western blotdata (symbols) are from BAEC cells. (A) The control case with no inhibitory effects. Experimental data are from ref. 15 and 54 and quantified in ref. 15.(B) Treatment with sodium orthovanadate. To simulate the effects of sodium orthovanadate, a phosphatase inhibitor, we decrease the dephosphorylation rateconstants (k8dp and k11dp) with an intervention factor IF = 0.3. Experimental data are from ref. 54 and quantified using ImageJ 10.2.52 The root-mean-squaredeviation between the model results and the experimental data is 0.18 and 0.07 for panels A and B, respectively.

Fig. 5 Flowchart of the approach used to identify potential therapeutic targets. See text (Results section) for additional details on the four steps of theapproach.

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the protein, competing for the site with the normal bindingpartner.48 We envision that peptide aptamers could also beused to inhibit nuclear translocation by masking the sites onthe Smad proteins responsible for interacting with the nuclearpore complex or accessory proteins mediating nuclear trans-location.49 Finally, kinase inhibitors have already been developedto target the ligand–receptor complexes and inhibit phosphoryl-ation of R-Smads.9 From these strategies, we have identified a setof potential targetable processes in the TGF-b pathway and theirassociated rate constants that would be decreased upon admin-istration of the inhibitory treatment (Table 1).

Step 2: sensitivity analysis. We use a global sensitivityanalysis (see Methods section) in order to determine how themodel responds to perturbation of its parameters. Processeswith high sensitivity coefficients will be the most responsive tomolecular intervention; therefore, we use sensitivity analysis asa guiding tool for identifying targets in the pathway. Weperform the sensitivity analysis with each of the three cell linesmutated with one of the five mutations identified in cancercells (Table 2), establishing 15 cell-type-mutation combina-tions, in addition to the 3 non-mutated cases. Each mutationis simulated with a mutation factor of MF = 0.1. In Fig. 6, weshow a sample of these results, concretely those for the ‘recep-tor downregulation’ mutation. The results for the global sensi-tivity coefficients of the normal cells are included as a control tocompare with the effects of the mutation. In general, themutation decreases the sensitivity coefficients of eachparameter as compared to those for the normal cell types,suggesting an increased difficulty in perturbing processes incells with this mutation.

Step 3: sensitive target identification. In order to identifytargetable processes that may have the most significant effecton the signaling dynamics, we define as filtering criteria a lowerbound of 0.01 for the global sensitivity coefficients Gki

. Fromthis, each of the 15 cell-type-mutation combinations will have aset of sensitive parameters with values satisfying the filteringcriteria (Gki

Z 0.01). To illustrate these results, we color theparameters in Fig. 6 in three groups. Black parameters were notidentified as specifically targetable (i.e. not found in Table 1)and are not considered beyond this step. Those in red representparameters with sensitivity coefficients satisfying the filteringcriteria for at least one studied cell type for the consideredmutation (H-, B-, or C-; denoting mutated HaCaT, BAEC, orC2C12 cells, respectively). It is important to note that thesensitivity analysis assesses single parameter perturbations,but several of the potential molecular interventions consideredin Table 1 affect multiple parameters. Therefore, if at least oneparameter from the set of parameters associated with amolecular intervention in Table 1 is selected at this step, weconsider the molecular intervention as potentially effective andit passes the filtering procedure to the next step in theapproach. Parameters are colored red if within a set ofparameters for a particular intervention at least one satisfiesthe filtering criteria. Those parameters in green correspond tothe rest of cases. This is illustrated in the parameter coloring ofFig. S3 (ESI†).

Step 4: molecular intervention optimization. Using the set ofmolecular interventions filtered from the sensitivity analysis foreach cell-type-mutation combination, we optimize the inter-vention factor for each case in order to restore normal signalingdynamics to the mutated system, while maintaining the signalingdynamics of the normal system in the presence of the molecularinterventions. Fig. 7 displays the results of the optimizationroutine for all the considered cell types, mutations, and molecularinterventions.

The ‘No intervention’ case is included as a control in Fig. 7,where we evaluate the objective function (eqn (3)) without anytreatment added to the normal or mutated systems. Successfulmolecular interventions will minimize the objective functionvalue as compared to the ‘No intervention’ case for a given celltype and mutation. Mutations resulting in low values of theobjective function signify that the signaling dynamics arerobust to the perturbations introduced by that mutation inthe specific cell type. In these cases, there is no need oftargeting the system with an inhibitor because the mutatedcell exhibits similar signaling dynamics as the correspondingnormal cell. Therefore, any treatment that reduces the objectivefunction will only result in minimal change from the mutatedstate as its dynamics already closely mirrors that of the normalstate, as illustrated in Fig. 8A for the case of HaCaT cells.

By using this optimization routine, rather than relying onthe sensitivity analysis alone, we are able to ensure that targetinga particular process is capable of restoring normal signalingdynamics. For example, with the BAEC case affected by the‘Smad7 downregulation’ mutation, the R-Smad–Smad4 associationinhibition was selected as a potential molecular intervention fromthe sensitivity analysis results (Fig. 7B). However, this mutationresults in a more sustained signaling response as compared to thatof the normal system and inhibiting R-Smad–Smad4 associationincreases the signal duration further, moving in the oppositedirection than desired (Fig. 8B). Similarly, when the C2C12 casewith the ‘inhibited Smad4 nuclear import’ mutation is treated withan R-Smad synthesis inhibitor, the dynamics are unaffected ascompared to those with the mutation alone (Fig. 8C).

In Fig. 9, we show a selection of the best optimization resultsfor each cell type, which minimize the objective function(eqn (3)) in cases where the mutation has a substantial effecton the normal signaling dynamics. Furthermore, these resultsminimally impact the signaling dynamics of normal cells in thepresence of the molecular intervention, reducing the risk ofpotential side effects. In HaCaT cells, we show the effects of‘Smad7 downregulation’ identified in colon cancer (Table 2),which results in a more sustained response to TGF-b for thenuclear phosphorylated Smad2–Smad4 species than withoutthe mutation (Fig. 9A). By inhibiting type II receptor synthesiswith an optimized intervention factor of OIF = 0.063, the modeldynamics of the mutated case is restored to that of the normalcase. For the BAEC case, the ‘inhibited phospho-R-Smad–Smad4association’ mutation identified in pancreatic cancer (Table 2)results in a more permanent response to ligand stimulation forthe nuclear phosphorylated Smad1–Smad4 species (Fig. 9B). Bytreating the system with Smad4 nuclear export inhibition at the

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optimized intervention factor of OIF = 0.037, the dynamics isrestored to its normal transient response, while minimallyaffecting the normal cell case. For the C2C12 case, we mutatethe system with the ‘Smad7 downregulation’ mutation, which

increases the duration of the response to TGF-b stimulation forthe nuclear phosphorylated Smad1–Smad4 species (Fig. 9C). Byinhibiting R-Smad–Smad4 association with an optimized inter-vention factor of OIF = 0.132, the mutated-cell dynamics returns

Fig. 6 Sensitivity analysis for the ‘receptor downregulation’ mutation. We plot the results obtained for the global sensitivity coefficient Gki(eqn (2)) for each

model parameter ki upon stimulation with 45 000 molecules (1.9 ng mL�1) of TGF-b. Each column represents the result for one species (pS1S4n or pS2S4n)and one cell type. Results for normal HaCaT, BAEC, and C2C12 cells are denoted as H, B, and C, respectively. The mutated cells, with a mutation factor ofMF = 0.1, are abbreviated by appending a dash symbol (–) to the cell type character. Rows represent the results for each parameter, grouped by the modulein the pathway it represents. The heat map, generated with Matplotlib 1.1.0,55 represents the value of log10(Gki

) as the color intensities in the color key (right-hand side of the heat map); empty spaces indicate a sensitivity coefficient equal to zero or a parameter value set to zero from Table S2 (ESI†). Parameternames in black are not specifically targetable, while those colored red or green represent processes that may be specifically targeted (Table 1). Those in redrepresent parameters satisfying the filtering criteria described in the Results section, while those in green do not satisfy the filtering criteria.

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to the transient response from the normal case, while minimallyimpacting the normal C2C12 signaling dynamics.

Finally, we filter the results of the molecular interventionsoptimization routine to produce a list of potential treatmentsfor each cell-type-mutation combination (Table 3). For eachcell-type-species combination, we first determine the set ofmutations with objective functions for the ‘No intervention’

case greater than or equal to 500 for each cell type. With this, wethen determine the set of molecular interventions that minimizethe objective function below 0.3 times the ‘No intervention’ valuefrom the set of mutations for each cell-type-species combination.Although the HaCaT dynamics is only substantially responsive tothe ‘Smad7 downregulation’ mutation, this method identifiedtwo potential molecular interventions to restore normal

Fig. 7 Results of the optimization of the molecular interventions. Bars represent the objective function value (eqn (3)) using one species, mutation, andmolecular intervention for (A) HaCaT, (B) BAEC, and (C) C2C12 cells. Bars are grouped by the type of mutation and color coded with the molecularintervention used. Dots beneath an empty bar indicate that the molecular intervention was not selected as potentially effective from the sensitivityanalysis step.

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Fig. 8 Simulation results of mutations and molecular interventions with minimal or negative effects on normal signaling dynamics. Solid blue linesrepresent simulations of normal cells and solid red lines represent simulations of mutated cells with a mutation factor of MF = 0.1 upon stimulation with45 000 molecules (1.9 ng mL�1) of TGF-b at t = 0 hours. Dashed lines indicate simulations with the molecular interventions. (A) HaCaT cells with the‘Smad4 downregulation’ mutation. (B) BAEC cells with the ‘Smad7 downregulation’ mutation and treated with an R-Smad–Smad4 association inhibitorusing an intervention factor of IF = 0.1. (C) C2C12 cells with the ‘inhibited Smad4 nuclear import’ mutation and treated with an R-Smad synthesis inhibitorusing an intervention factor of IF = 0.1.

Fig. 9 Simulation results for optimal molecular interventions. Same conditions as in Fig. 8 for combinations of species, mutation, and molecularinterventions selected from the optimization routine for each cell type. (A) HaCaT cells with the ‘Smad7 downregulation’ mutation and treated with a typeII receptor synthesis inhibitor using the optimized intervention factor OIF = 0.063. (B) BAEC cells with the ‘inhibited phospho-R-Smad–Smad4association’ mutation and treated with a Smad4 nuclear export inhibitor using the optimized intervention factor OIF = 0.037. (C) C2C12 cells with the‘Smad7 downregulation’ mutation and treated with an R-Smad–Smad4 association inhibitor using the optimized intervention factor OIF = 0.132.

Table 3 Potential targetable processes identified by optimization of the molecular interventions. For each cell type and mutations that significantlyaffect the normal signaling dynamics, we show the corresponding molecular interventions that restore normal signaling dynamics to the mutated system.The entries in boldface are those used in Fig. 9

Mutation

HaCaT BAEC C2C12

Targeted process Species Targeted process Species Targeted process Species

Smad4 downregulation Type II receptorsynthesis

pS1S4n

Type I receptorsynthesis

pS1S4n

Smad4 nuclear export pS1S4n

Smad7 downregulation Type II receptor synthesis pS2S4n Type I receptorsynthesis

pS1S4n Type I receptor synthesis pS1S4n

R-Smad–Smad4association

pS2S4n Smad4 nuclear export pS1S4n Smad4 nuclear import pS1S4n

R-Smad–Smad4 association pS1S4n

Inhibited Smad4 nuclear import Type I receptorsynthesis

pS1S4n

R-Smad nuclear export pS1S4n

Smad4 nuclear export pS1S4n

Inhibited R-Smad–Smad4association

Type I receptor synthesis pS1S4n

R-Smad nuclear export pS1S4n

Smad4 nuclear export pS1S4n Receptor–R-Smadassociation

pS2S4n

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signaling dynamics to the mutated system: inhibited type IIreceptor synthesis and inhibited R-Smad–Smad4 association.For the BAEC case, this method identified a number ofmolecular interventions for four of the five mutations consideredhere, targeting receptor synthesis and R-Smad/Smad4 nucleo-cytoplasmic shuttling. The results for the C2C12 case reveal fourdistinct molecular interventions that may be used to target thesystem for two of the mutations we used in this analysis. Finally,our approach did not identify any molecular intervention for the‘TGF-b receptor downregulation’ mutation in any of theconsidered cases.

Conclusions

Effectively targeting the TGF-b signal transduction pathwayrequires a detailed dissection of the network interactionsbeyond insight gained from intuition alone. Here we havedeveloped a strategy based on computational modeling toquantitatively analyze the signaling pathway in order todetermine potential therapeutic targets. We have considered amodel that captures the precise dynamics of the system, muta-tions that affect the system parameters, and a collection ofpotentially targetable components of the pathway, such asinhibition of association or synthesis of proteins. The keyelement of the approach is the identification of molecularinterventions in the pathway that, in addition to bringingthe mutated system back to its normal dynamics, do notsubstantially affect the non-mutated system. To do so, ourapproach uses global sensitivity analysis to identify parameterswith high sensitivity coefficients and passes the molecularinterventions containing these sensitive parameters to theoptimization routine that selects the optimal strength of themolecular intervention.

We have shown the capabilities of the computationalapproach for different cell types by reproducing experimentalTGF-b signaling dynamics when the system is mutated inpancreatic cancer cells and in the presence of inhibitory drugstargeting distinct processes in the pathway. From the results ofthe molecular intervention optimization routine, we haveidentified a set of mutations that significantly affect the signalingdynamics for each cell type and a number of molecular inter-ventions that may be used to effectively target the effects of thesemutations. Interestingly, our approach identified multiple types ofmolecular interventions that can be used for a given mutation.This type of approach can generally be applied to a wide variety ofsignaling systems with characterized biochemical interactionsand mutations affecting their components to identify noveltargets for therapeutic intervention. Therefore, our methodologyprovides an efficient starting point to select potential targets forfurther experimental and clinical investigation.

Acknowledgements

This work was supported by the University of California, Davis(to LS).

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