Quantitatie modeling and analysis of the transforming growth factor β signaling pathway Seung-Wook hung, Fayth L. Miles, arlton R. ooper, Mary. Farach-arson, and Babatunde A. Ogunnaike Uniersity of Delaware, Newark, DE, USA Introduction Transforming growth factor-β (TGF-β) proteins are members of a superfamily of secreted okines that control a dierse array of cellular processes including cell proliferation, differentiation, motility, adhesion, angiogenesis, apoptosis, and immune sureillance. The TGF-β signaling cascade begins when extracellular TGF-β binds to and brings together Type I and Type II TGF-β receptor serine/threonine kinases on the cell surface, whereby the Type II receptor phosphorylates and actiates the Type I receptor. The actiated Type I receptor, in turn, propagates the signal through phosphorylation of receptor-bound (R-)Smad transcription factors (Smad2/3 and Smad/5/8). The actiated R-Smads form hetero-oligomers with Smad4 and rapidly translocate into the leus, undergoing continuous leooplasmic shuttling by interacting with the lear pore complex. Once in the leus, the actiated Smad complexes bind to specific promoters and ultimately regulate expression of target genes, generating approximately fie hundred gene responses in a cell- and context-specific manner, 2. The TGF-β signaling pathway has become an attractie but problematic target for oncology drug deelopment because of its apparently paradoxical roles in tumorigenesis and metastasis. In normal and early phase tumorigenic epithelial cells, TGF-β functions as a potent tumor suppressor primarily by inducing cell cycle arrest and apoptosis. Howeer, in the intermediate and late stages of carcinogenesis, tumor cells become resistant to the growth inhibitory effects of TGF-β and show eleated expression of TGF-β. The ligand is oerexpressed in clinical cancer samples, with increasing leels correlating with poor clinical outcomes. The role of TGF-β therefore appears to become one of tumor promotion, apparently supporting growth, suberting the immune system, and also facilitating, inasion, epithelial to mesenchymal transition (EMT), and angiogenesis. This finding has created the widely held perception that TGF-β acts as a tumor promoter in adanced tumorigenesis and metastasis 3. Although it is known that most cancer cell lines representing the entire spectrum of tumor progression hae actie TGF-β signaling pathways, detailed mechanisms of how a single stimulus, TGF-β, induces such a dierse array of responses during cancer progression are not known. This is primarily due to the complexity of the signaling cascade system in which a ariety of signaling components changing dynamically oer different time scales interact with one another. Since quantitatie understanding and analysis of such a complex regulatory circuit are not possible ia qualitatie human intuition alone, mathematical descriptions that lead to predictie models are necessary. To improe our understanding of complex TGF-β signaling quantitatiely, we hae deeloped a comprehensie, dynamic model of the canonical TGF-β pathway ia Smad transcription factors, based on the most up-to-date information aailable in the literature. Through simulation and model analysis, our model proides insight into the signal-response relationship between the binding of TGF-β to its receptor at the cell surface and the actiation of downstream effectors in the signaling cascade. In particular, we use the model to carry out
in-silico mutations from which we generate seeral hypotheses regarding potential mechanisms for how TGF-β s tumor-suppressie roles may appear to morph into tumorpromoting roles. Model Formulation Our model incorporates the following essential molecular processes: (i) sequential actiation of receptors induced by TGF-β; (ii) receptor internalization to endosomes and recycling; (iii) R-Smad phosphorylation by receptor complex; (i) R-Smad-Smad4 complex formation in the oplasm and leus; () leooplasmic shuttling of Smads; (i) dissociation and dephosphorylation of actiated Smads; (ii) constitutie and ligand-induced degradation of proteins; and (iii) protein synthesis. The components of the oerall TGF-β signaling pathway as featured in our model are depicted in Figure. The resulting model is a system of 7 non-linear ordinary differential equations (ODEs) with 37 kinetic parameters arising from chemical reactions represented by mass action kinetics (Table ). Figure. Schematic representation of the pathway components in the model.
Table. Model Equations = k a[ TGFβ [ RII k d [ TGFβ : RII = k 3 = k 3int [ R [ R : S2 5 5cat in = k2a[ TGFβ : RII[ RI k2d [ R = k R [ S2 k [ R : S2 2 4 4a[ in 4d in = k [ ps2 [ S4 k6 [ ps2s4 6 6a d = k [ ps2s4 = k [ ps2s4 7 7imp = k [ S2S4 9 9d = k imp[ S4 kexp[ S4 3 = k3syn k3deg[ RI = k k S4 5 5syn 5deg[ = k [ ps2 7 7imp ' 9 9dp = k [ RII 2 2int k 2rec[ RII in 8 8dp 0 = k0imp[ S2 k0 exp[ S2 2 = k2syn k2 deg[ RII = k k S2 4 4syn 4deg[ = + 6 = k ( k6deg k6lid )[ R [ ps2 [ S4 k8 = k [ ps 2 = k [ ps 2 = k 23 [ R 23rec in [ ps2s4 8 8a d 20 20lid = k [ RI k [ RI 22 22int 22rec in RII R S2 TGFβ : RII = = + 2 2 + 23 2 R in = 2 3 6 = 3 4 + 5 23 = 4 0 + 4 = 5 6 7 ps2 RI = R in : S2 ps2s4 2 + 3 = = 6 4 22 7 5 + 23 ps2s4 S4 S2S4 = 7 8 + 8 = 8 9 9 0 9 S4 S2 = = 9 + 8 = 6 + = 5 7 8 9 20 RIIin RIin = 2 = 22 ps2 + + The approach to obtain model parameter alues is summarized as follows:. Initial Rough Estimation: Seeral kinetic parameter alues were determined through an extensie literature search; some were computed using aailable in itro experimental data; we also used physical constraints to determine others. The remaining unknown parameters were proided with initial estimates and reasonable upper and lower bounds by comparison with similar circumstances in the literature (e.g. similar steps in preious models or other signaling pathway models) and from known physical limitations (e.g. the diffusion-limited rates, 0 8-0 9 M - s - ).
2. Parametric Sensitiity Analysis: To identify which parameters are the most important and which must therefore be estimated most precisely, using the set of initial estimates determined in Step aboe, we performed local parameter sensitiity analysis to determine the effect of parametric changes on the set of fie system responses of interest for which experimental measurements are aailable (i.e. total Smad2 in the leus and the oplasm 4, total phosphorylated Smad2 in the leus and the oplasm 4, 5, and total Smad4 in the leus 4 ). The computations are based on the following expression for the normalized sensitiity coefficient (NS): p j yi ( t, p) NSij ( t) =, i =,2,..., 5; j =,..., 37 yi p j p where y and p respectiely denote the system response ariables and kinetic parameters. A total of 3 parameters were selected to be estimated more precisely because of their high sensitiity coefficients and/or because we had little or no confidence in their initial alues. 3. Least Squares Fitting to Data: We fit our model predictions simultaneously to corresponding in itro experimental data from the literature, ia local minimization of the sum of squared residual errors: * 2 min R( p) = ( yi ( t, p) yi ( t)) i 2 where y i (t,p) and y * i (t) denote, respectiely, model predictions for a gien trial of parameter alues, p, and the corresponding experimental measurements, for each measured ariable, i. The experimental data used for the cure-fitting are time courses of (i) total Smad2 in the leus 4, (ii) total Smad2 in the oplasm 4, (ii) total phosphorylated Smad2 in the leus 5, (i) total phosphorylated Smad2 in the oplasm 4, and () total Smad4 in the leus 4. 4. Identifiability: We performed a practical identifiability analysis to determine whether the unknown parameters of the postulated model can be uniquely estimated from the aailable data, following Birtwistle et al. 6. Briefly, approximate local confidence interals for the parameter set are gien by, N N S t p T I i = tα / 2 ( Z Z) ii N N t where N t and N p respectiely denote the number of experimental data time points and the N number of parameters to be estimated; t N t p α / 2 is the Student s t-distribution statistic ealuated with N t -N p degrees of freedom, at confidence leel 00(- α)%, (with α as the tail area probability typically set at 0.05 to yield a 95% confidence leel); S is the sum of squared errors, and Z is the model sensitiity matrix ealuated at the current parameter alues. The i th parameter is said to be practically locally identifiable only if the magnitude of its approximate confidence interal is less than a specified tolerance i.e. I < ε. 5. Identifiable Parameter Estimate Refinement: Estimated alues for identifiable parameters were further refined by repeating Step 4 (local identifiability test) followed by Step 3 (local least squares estimation). After obtaining the best estimates of this subset of parameters, we carried out a final least squares estimation of the entire parameter set. p i i
Results and Discussion To help understand quantitatiely which aspects of the pathway most affect the system behaior, we carried out parameter sensitiity analysis for lear psmad2-smad4 complex, which is necessary for TGF-β-induced transcriptional regulation. Figure 2 shows normalized sensitiity coefficients as a function of time for the 0 most important parameters. The most important features of this plot are summarized as follows: () Immediately after ligand stimulation, the output ariable is strongly affected by four of this set of most sensitie parameters: in order of importance, these are k 4a (binding of Smad2 to actie receptors), k 3int (internalization of receptor complexes), k 7imp (lear import of psmad2-smad4), and k 2a (complex formation of actiated TβRII and TβRI). (2) On the other hand, in the mid- to longer time interal after ligand stimulation, the following parameters become more important: in order of importance, these are k 8a (association of lear psmad2 and Smad4), and k 8d (dissociation of lear psmad2-smad4), k exp (lear export of Smad4), k 20lid (ligandinduced degradation of psmad2), k imp (lear import of Smad4), k 23rec (recycling of internalized receptor complexes), k 3int (internalization of receptor complexes), and k 4a (binding of Smad2 to actie receptors). 0.8 Normalized Sensitiity oefficient (NS) 0.6 0.4 0.2 0-0.2-0.4-0.6 k 2a k 3int k 4a k 7imp k imp k exp k 8a k 8d k 20lid k 23rec -0.8 0 2 4 6 8 0 2 Time (hr) Figure 2. Model parameter sensitiities for select parameters with the greatest influence on phosphorylated Smad2-Smad4 complex in the leus. These results hae biologically important consequences. In particular, the increasing nature of the sensitiity coefficients of k 8a and k 8d oer time shows that both the formation of psmad2-smad4 complex in the leus and its dissolution are crucial for lear retention of these complexes. To examine how ariations in Smad complex formation in the leus
affects lear accumulation of actiated Smad complexes, we aried the rate of association between lear psmad2 and Smad4 (k 8a ) 0-fold. Figure 3 shows that while rapid formation of the complex between lear psmad2 and Smad4 induces prolonged and enhanced lear accumulation of psmad2-smad4 complex, slow binding of psmad2 and Smad4 leads to shortened and attenuated retention of psmad2 complex in the leus. Thus, these results imply that the lear complex formation step plays an important role in regulating the intensity and duration of TGF-β-targeted transcriptional actiities through psmad2 complexes. More importantly, the results imply that psmad2 complex-mediated response to TGF-β stimulation may be significantly attenuated by competitie inhibition or by interference from other lear molecules that also hae high affinity for either psmad2 or Smad4. This inhibitory action ultimately gies rise to a significant reduction in the rate of association between these proteins. Taken together, these results reeal that the step of complex formation between psmad2 and Smad4 is closely associated with modulation of TGF-β-induced signal patterns..6 Relatie oncentration of ps2s4.4.2 0.8 0.6 0.4 ontrol Fast. association of psmad2 and Smad4 Slow. association of psmad2 and Smad4 0.2 0 0 2 4 6 8 0 2 4 6 8 20 Time (hr) Figure 3. The effect of ariations in the rate of lear psmad2-smad4 association To help understand how cancer cells can become resistant to the tumor-suppressor effects of TGF-β, but, at the same time, remain responsie to the tumor-promoter effects, we inestigated the effect on the TGF-β signaling system of abnormal alterations (e.g. mutations, deletions, downregulation, etc.) in receptors, using a 0-fold reduction in the initial leels and production rate of both Type I and Type II receptors to represent cancerous conditions. First, Figure 4 indicates that the amount of TGF-β needed to produce a saturated Smad-mediated response in cancer cells is far higher than that in healthy cells. Specifically, while the response for normal cells is essentially saturated with pm of TGF-β (with higher doses producing essentially the same response), at least 0 pm of TGF-β is required before the Smad-mediated response begins to approach saturation. This is, of course, a direct effect of the reduction in
the number of functional receptors in cancer cells which renders them less responsie to TGFβ stimulation. But this finding also indicates an important characteristic of cancerous cells: to elicit lear Smad-mediated actiity generally requires more TGF-β than normal. 0.9 Relatie oncentration of ps2s4 Nuc 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. Normal ell ancerous ell 0 0-2 0-0 0 0 0 2 TGF-β dose (pm) Figure 4. The effect of different concentrations of TGF-β on the maximum responses of actiated lear Smad2-Smad4 complex in normal cells (blue circles) and in cancerous cells (red triangles). Next, a head-to-head comparison of normal ersus cancerous cell responses reeals that the sharp drop in the leel of functional receptors in cancer cells leads to a marked decrease in the actiity of lear psmad complexes (Figure 5). ompared to the normal cell response, the peak actiity of lear psmad complexes in cancer cells was reduced by 65%, with the steady-state actiity also remaining comparatiely low. Interestingly, a reduction in the leel of receptors also slowed lear psmad responses. While lear psmads in the normal system reached maximum actiity in 55 min, their actiity under a cancerous condition peaked at 86 min. Taken together, these results indicate generally that a reduction in the leel of functional TGF-β receptors in cancer cells may lead to attenuated and slower TGF-βstimulated signaling responses ia Smad2. The specific implications of the model predictions in Figures 4 and 5 reeal some potentially important findings about TGF-β and cancer cells: (i) cancer cells require higher than normal leels of TGF-β in order to elicit significantly attenuated (and much slower) lear Smad-mediated actiity; (ii) but een the increased leels of TGF-β will neer be able to produce Smad-mediated responses that will be anywhere close to normal because of the saturation effect.
Relatie oncentration of ps2s4 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Normal ancerous 0. 0 0 2 3 4 5 6 7 8 9 0 Time (hr) Figure 5. In silico mutation results: Responses of lear psmad-smad4 complex to 0-fold reduction in initial leels and protein synthesis rate constants of both Type I and Type II receptors. As shown aboe ia simulation, cancer cells may hae attenuated TGF-β-stimulated Smad pathway responses. ancer cells hae been confirmed experimentally to be resistant to the antiproliferatie effect of TGF-β, while showing typical pro-oncogenic responses. Such behaior may be explained in part by the following threshold hypothesis : in response to TGFβ, growth-inhibitory genes require higher threshold leels of lear Smad actiity for their expression than genes associated with pro-oncogenic and pro-metastatic effects. In other words, under normal conditions, or in the early stage of cancer progression, the antiproliferatie responses to TGF-β are predominant oer pro-oncogenic responses. This is because the transcriptional actiity of lear psmad is high enough to induce anti-growth gene expression. Howeer, as cancer progresses, this transcriptional actiity may decline significantly and thereby hardly exceed the threshold necessary for the expression of growthinhibition genes. Meanwhile, genes related to tumor-promoting effects may be relatiely insensitie to the attenuation of the transcriptional actiity by Smads, so that the expression of such genes remains approximately unchanged een under cancerous conditions. As a consequence, the dominance of tumor suppressor genes oer the tumor-promoter genes may be blunted in cancer cells. We beliee that further inestigation into differences in the temporal profiles of gene expression and thresholds of anti-growth and pro-oncogenic genes induced by TGF-β will proide some clues regarding the putatie dual effects of TGF-β.
onclusion In this work we hae presented a comprehensie computational model of the TGF-β signaling pathway that describes how an extracellular signal of TGF-β ligand is sensed by receptors and transmitted into the leus through intracellular Smad proteins. The model yields quantitatie insight into how TGF-β-induced responses can be modulated and regulated. The model also allows us to predict possible dynamic behaior of the Smad-mediated pathway in abnormal cells, and proides clues regarding possible mechanisms for explaining the seemingly contradictory roles of TGF-β during cancer progression. We beliee that incorporation of the effect of crosstalk among other important signaling cascades and detailed gene expression mechanisms into the current model will facilitate better understanding of the TGF-β paradox in cancer. References. Shi, Y., and J. Massague. 2003. Mechanisms of TGF-β signaling from cell membrane to the leus. ell 3:685-700. 2. Feng, X. H., and R. Derynck. 2005. Specificity and ersatility in TGF-β signaling through Smads. Annu Re ell De Biol 2:659-693. 3. Pardali, K., and A. Moustakas. 2007. Actions of TGF-β as tumor suppressor and prometastatic factor in human cancer. Biochim Biophys Acta 775:2-62. 4. Pierreux,. E., F. J. Nicolas, and. S. Hill. 2000. Transforming growth factor β- independent shuttling of Smad4 between the oplasm and leus. Mol ell Biol 20:904-9054. 5. Inman, G. J., F. J. Nicolas, and. S. Hill. 2002. Nucleooplasmic shuttling of Smads 2, 3, and 4 permits sensing of TGFβ receptor actiity. Mol ell 0:283-294. 6. Birtwistle, M. R., M. Hatakeyama, N. Yumoto, B. A. Ogunnaike, J. B. Hoek, and B. N. Kholodenko. 2007. Ligand-dependent responses of the ErbB signaling network: experimental and modeling analyses. Mol Syst Biol 3:44.