Resolving the Combinatorial Complexity of Smad Protein Complex Formation and Its Link to Gene Expression

Abstract

Upon stimulation of cells with transforming growth factor β (TGF-β), Smad proteins form trimeric complexes and activate a broad spectrum of target genes. It remains unresolved which of the possible Smad complexes are formed in cellular contexts and how these contribute to gene expression. By combining quantitative mass spectrometry with a computational selection strategy, we predict and provide experimental evidence for the three most relevant Smad complexes in the mouse hepatoma cell line Hepa1-6. Utilizing dynamic pathway modeling, we specify the contribution of each Smad complex to the expression of representative Smad target genes, and show that these contributions are conserved in human hepatoma cell lines and primary hepatocytes. We predict, based on gene expression data of patient samples, increased amounts of Smad2/3/4 proteins and Smad2 phosphorylation as hallmarks of hepatocellular carcinoma and experimentally verify this prediction. Our findings demonstrate that modeling approaches can disentangle the complexity of transcription factor complex formation and its impact on gene expression.

A New Approximation Approach for Transient Differential Equation Models

“…To prevent overfitting which is recommended if a limited amount of data is available, the same time constant τ 1 ≡ τ ′ 1 for induction of the transient response and for the sustained response can be assumed. We used the resulting five-parameter transient function TF in Lucarelli et al [21] previously for analyzing the transcription of TGFβ target genes. In that application, the analyses were performed for pairs of time-courses for treated and untreated cells and the resulting time dependencies were used for clustering of genes.…”

“…These bounds should be independent of physical units, i.e., they should be invariant under scaling of the data or sampling times. Technically, bounds are also required for making reasonable initial guesses for the numerical optimization of equation (21). Moreover, setting parameter bounds strongly improves the convergence behavior in the course of numerical non-linear least squares optimization [22].…”

“…The underlying equations of the ODE models originate from the original publications and were taken from the benchmark collection [2]. The fitting has been performed based on (13), (18)- (21). The histogram in the center shows the distribution of the resulting approximation errors (15).…”

“…If constant time courses with RMSEs close to zero are omitted, the median is 0.662 for FIGURE 3 | (A) Shows six typical outcomes for fitted RTF models (blue lines) (11), (12) and ODE models (brown lines) in order to compare the outcomes of both modeling approaches for fitting of data. Fitting has been performed based on (13), (18)- (21). The black lines represent the solutions of the ODE equation models which are taken from Hass et al [2] for published parameter values and presumed as true dynamics for the simulation of the data.…”

TGF-β Signaling

“…The conformational changes triggered by the phosphorylation of the Ser-X-Ser motif on R-SMAD monomers, not only drive the dissociation from the receptor complex but they also mediate the interaction between the phosphorylated C-terminus of an activated R-SMAD and the L3 loop on the MH2 domain of SMAD4 (or another R-SMAD), thus leading to the formation of SMAD oligomers [96,104,105]. SMAD trimeric complexes can be found in different compositions: as either oligomers consisting of three activated R-SMAD monomers (that can be either homo-or heterotrimers) or as oligomers composed of either two and one, or one and two phosphorylated R-SMADs, and SMAD4 respectively [104,106,107].…”