Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses

We show theoretically and experimentally a mechanismbehind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input-output characteristics (the dose-response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose-response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose-response obtained experimentally

Ligand-Specific c-Fos Expression Emerges from the Spatiotemporal Control of ErbB Network Dynamics

SummaryActivation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell-fate decisions, although signals propagate through shared pathways. Using mathematical modeling and experimental approaches, we unravel how HRG and EGF generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands

Ligand-dependent responses of the ErbB signaling network: experimental and modeling analyses

Deregulation of ErbB signaling plays a key role in the progression of multiple human cancers. To help understand ErbB signaling quantitatively, in this work we combine traditional experiments with computational modeling, building a model that describes how stimulation of all four ErbB receptors with epidermal growth factor (EGF) and heregulin (HRG) leads to activation of two critical downstream proteins, extracellular-signal-regulated kinase (ERK) and Akt. Model analysis and experimental validation show that (i) ErbB2 overexpression, which occurs in approximately 25% of all breast cancers, transforms transient EGF-induced signaling into sustained signaling, (ii) HRG-induced ERK activity is much more robust to the ERK cascade inhibitor U0126 than EGF-induced ERK activity, and (iii) phosphoinositol-3 kinase is a major regulator of post-peak but not pre-peak EGF-induced ERK activity. Sensitivity analysis leads to the hypothesis that ERK activation is robust to parameter perturbation at high ligand doses, while Akt activation is not

Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics

Tyrosine kinase inhibitors (TKIs) are highly potent cancer therapeutics that have been linked with serious cardiotoxicity, including left ventricular dysfunction, heart failure, and QT prolongation. TKI-induced cardiotoxicity is thought to result from interference with tyrosine kinase activity in cardiomyocytes, where these signaling pathways help to control critical processes such as survival signaling, energy homeostasis, and excitation–contraction coupling. However, mechanistic understanding is limited at present due to the complexities of tyrosine kinase signaling, and the wide range of targets inhibited by TKIs. Here, we review the use of TKIs in cancer and the cardiotoxicities that have been reported, discuss potential mechanisms underlying cardiotoxicity, and describe recent progress in achieving a more systematic understanding of cardiotoxicity via the use of mechanistic models. In particular, we argue that future advances are likely to be enabled by studies that combine large-scale experimental measurements with Quantitative Systems Pharmacology (QSP) models describing biological mechanisms and dynamics. As such approaches have proven extremely valuable for understanding and predicting other drug toxicities, it is likely that QSP modeling can be successfully applied to cardiotoxicity induced by TKIs. We conclude by discussing a potential strategy for integrating genome-wide expression measurements with models, illustrate initial advances in applying this approach to cardiotoxicity, and describe challenges that must be overcome to truly develop a mechanistic and systematic understanding of cardiotoxicity caused by TKIs

Linear approaches to intramolecular Förster Resonance Energy Transfer probe measurements for quantitative modeling

Numerous unimolecular, genetically-encoded Forster Resonance Energy Transfer (FRET) probes for monitoring biochemical activities in live cells have been developed over the past decade. As these probes allow for collection of high frequency, spatially resolved data on signaling events in live cells and tissues, they are an attractive technology for obtaining data to develop quantitative, mathematical models of spatiotemporal signaling dynamics. However, to be useful for such purposes the observed FRET from such probes should be related to a biological quantity of interest through a defined mathematical relationship, which is straightforward when this relationship is linear, and can be difficult otherwise. First, we show that only in rare circumstances is the observed FRET linearly proportional to a biochemical activity. Therefore in most cases FRET measurements should only be compared either to explicitly modeled probes or to concentrations of products of the biochemical activity, but not to activities themselves. Importantly, we find that FRET measured by standard intensity-based, ratiometric methods is inherently non-linear with respect to the fraction of probes undergoing FRET. Alternatively, we find that quantifying FRET either via (1) fluorescence lifetime imaging (FLIM) or (2) ratiometric methods where the donor emission intensity is divided by the directly-excited acceptor emission intensity (denoted R<sub>alt</sub>) is linear with respect to the fraction of probes undergoing FRET. This linearity property allows one to calculate the fraction of active probes based on the FRET measurement. Thus, our results suggest that either FLIM or ratiometric methods based on R<sub>alt</sub> are the preferred techniques for obtaining quantitative data from FRET probe experiments for mathematical modeling purpose

A Mechanistic Beta-Binomial Probability Model for mRNA Sequencing Data.

A main application for mRNA sequencing (mRNAseq) is determining lists of differentially-expressed genes (DEGs) between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softwares use different models and assumptions to analyze mRNAseq data. Here, we propose a mechanistic justification to model mRNAseq as a binomial process, with data from technical replicates given by a binomial distribution, and data from biological replicates well-described by a beta-binomial distribution. We demonstrate good agreement of this model with two large datasets. We show that an emergent feature of the beta-binomial distribution, given parameter regimes typical for mRNAseq experiments, is the well-known quadratic polynomial scaling of variance with the mean. The so-called dispersion parameter controls this scaling, and our analysis suggests that the dispersion parameter is a continually decreasing function of the mean, as opposed to current approaches that impose an asymptotic value to the dispersion parameter at moderate mean read counts. We show how this leads to current approaches overestimating variance for moderately to highly expressed genes, which inflates false negative rates. Describing mRNAseq data with a beta-binomial distribution thus may be preferred since its parameters are relatable to the mechanistic underpinnings of the technique and may improve the consistency of DEG analysis across softwares, particularly for moderately to highly expressed genes

Analysis of copy number loss of the ErbB4 receptor tyrosine kinase in glioblastoma.

Current treatments for glioblastoma multiforme (GBM)-an aggressive form of brain cancer-are minimally effective and yield a median survival of 14.6 months and a two-year survival rate of 30%. Given the severity of GBM and the limitations of its treatment, there is a need for the discovery of novel drug targets for GBM and more personalized treatment approaches based on the characteristics of an individual's tumor. Most receptor tyrosine kinases-such as EGFR-act as oncogenes, but publicly available data from the Cancer Cell Line Encyclopedia (CCLE) indicates copy number loss in the ERBB4 RTK gene across dozens of GBM cell lines, suggesting a potential tumor suppressor role. This loss is mutually exclusive with loss of its cognate ligand NRG1 in CCLE as well, more strongly suggesting a functional role. The availability of higher resolution copy number data from clinical GBM patients in The Cancer Genome Atlas (TCGA) revealed that a region in Intron 1 of the ERBB4 gene was deleted in 69.1% of tumor samples harboring ERBB4 copy number loss; however, it was also found to be deleted in the matched normal tissue samples from these GBM patients (n = 81). Using the DECIPHER Genome Browser, we also discovered that this mutation occurs at approximately the same frequency in the general population as it does in the disease population. We conclude from these results that this loss in Intron 1 of the ERBB4 gene is neither a de novo driver mutation nor a predisposing factor to GBM, despite the indications from CCLE. A biological role of this significantly occurring genetic alteration is still unknown. While this is a negative result, the broader conclusion is that while copy number data from large cell line-based data repositories may yield compelling hypotheses, careful follow up with higher resolution copy number assays, patient data, and general population analyses are essential to codify initial hypotheses prior to investing experimental resources

Schematic of the General mRNAseq Process.

<p>There are three main steps depicted here, from top to bottom. First is obtaining RNA samples, which contain full length transcripts. Different samples are denoted by different color circles, and transcripts by straight lines within those circles. We highlight one transcript blue to enable following it through the process. Next, library preparation converts the transcripts in each sample to a library of fragments that can be sequenced. Finally, the libraries are sequenced by choosing fragments from the library, and the number of reads that align to particular transcripts are counted for the readout of expression.</p

Differential p-values for Negative Binomial vs. Beta-Binomial Dispersion Methods.

<p>Each panel reflects a comparison of p-values for beta binomial-based dispersion or negative binomial-based dispersion generated from the UMI count data, CTRL vs SOR (A-C), or the Gierlinski data, WT vs ∆snf2 (D-F). Each panel is a scatter plot of the base-10 logarithm of the maximum normalized mean (maximum of the CTRL mean or SOR mean for UMI or the WT mean or ∆snf2 mean for Gierlinski) against the difference in base-10 logarithm of the corresponding p-values being compared for each gene. Color indicates density of points. The top row compares the beta binomial formulation versus DESeq2 (A,D). The second row compares beta binomial versus EdgeR (B,E). The third row compares EdgeR and DESeq2 (C,F).</p

Mean-Variance Relationship for Raw and Normalized mRNAseq Data.

<p>Each column of three panels reflects one of the following datasets tested: LINCS UMI (A-B) and Gierlinski WT (D-F). The two remaining datasets are shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0157828#pone.0157828.s002" target="_blank">S2 Fig</a>. For each column of three panels, the first panel (A,D) shows the CV² fit (solid blue line) and Least Squares fit (dashed green line) to the raw data points plotting mean vs variance (black x’s). The second panel (B,E) shows the same fits for the normalized data. The third panel (C,F) shows the respective R² values for the CV² and Least Squares (LS) fits for the raw and normalized data.</p