pyPESTO: a modular and scalable tool for parameter estimation for dynamic models.

SUMMARY: Mechanistic models are important tools to describe and understand biological processes. However, they typically rely on unknown parameters, the estimation of which can be challenging for large and complex systems. pyPESTO is a modular framework for systematic parameter estimation, with scalable algorithms for optimization and uncertainty quantification. While tailored to ordinary differential equation problems, pyPESTO is broadly applicable to black-box parameter estimation problems. Besides own implementations, it provides a unified interface to various popular simulation and inference methods. AVAILABILITY AND IMPLEMENTATION: pyPESTO is implemented in Python, open-source under a 3-Clause BSD license. Code and documentation are available on GitHub (https://github.com/icb-dcm/pypesto).

Posterior marginalization accelerates Bayesian inference for dynamical models of biological processes.

Bayesian inference is an important method in the life and natural sciences for learning from data. It provides information about parameter and prediction uncertainties. Yet, generating representative samples from the posterior distribution is often computationally challenging. Here, we present an approach that lowers the computational complexity of sample generation for dynamical models with scaling, offset, and noise parameters. The proposed method is based on the marginalization of the posterior distribution. We provide analytical results for a broad class of problems with conjugate priors and show that the method is suitable for a large number of applications. Subsequently, we demonstrate the benefit of the approach for applications from the field of systems biology. We report an improvement up to 50 times in the effective sample size per unit of time. As the scheme is broadly applicable, it will facilitate Bayesian inference in different research fields.

Integrative modelling of reported case numbers and seroprevalence reveals time-dependent test efficiency and infectious contacts.

Mathematical models have been widely used during the ongoing SARS-CoV-2 pandemic for data interpretation, forecasting, and policy making. However, most models are based on officially reported case numbers, which depend on test availability and test strategies. The time dependence of these factors renders interpretation difficult and might even result in estimation biases. Here, we present a computational modelling framework that allows for the integration of reported case numbers with seroprevalence estimates obtained from representative population cohorts. To account for the time dependence of infection and testing rates, we embed flexible splines in an epidemiological model. The parameters of these splines are estimated, along with the other parameters, from the available data using a Bayesian approach. The application of this approach to the official case numbers reported for Munich (Germany) and the seroprevalence reported by the prospective COVID-19 Cohort Munich (KoCo19) provides first estimates for the time dependence of the under-reporting factor. Furthermore, we estimate how the effectiveness of non-pharmaceutical interventions and of the testing strategy evolves over time. Overall, our results show that the integration of temporally highly resolved and representative data is beneficial for accurate epidemiological analyses.

Assessment of Prediction Uncertainty Quantification Methods in Systems Biology.

Biological processes are often modelled using ordinary differential equations. The unknown parameters of these models are estimated by optimizing the fit of model simulation and experimental data. The resulting parameter estimates inevitably possess some degree of uncertainty. In practical applications it is important to quantify these parameter uncertainties as well as the resulting prediction uncertainty, which are uncertainties of potentially time-dependent model characteristics. Unfortunately, estimating prediction uncertainties accurately is nontrivial, due to the nonlinear dependence of model characteristics on parameters. While a number of numerical approaches have been proposed for this task, their strengths and weaknesses have not been systematically assessed yet. To fill this knowledge gap, we apply four state of the art methods for uncertainty quantification to four case studies of different computational complexities. This reveals the trade-offs between their applicability and their statistical interpretability. Our results provide guidelines for choosing the most appropriate technique for a given problem and applying it successfully.

Combining gene expression analysis of gastric cancer cell lines and tumor specimens to identify biomarkers for anti-HER therapies-the role of HAS2, SHB and HBEGF.

BACKGROUND: The standard treatment for patients with advanced HER2-positive gastric cancer is a combination of the antibody trastuzumab and platin-fluoropyrimidine chemotherapy. As some patients do not respond to trastuzumab therapy or develop resistance during treatment, the search for alternative treatment options and biomarkers to predict therapy response is the focus of research. We compared the efficacy of trastuzumab and other HER-targeting drugs such as cetuximab and afatinib. We also hypothesized that treatment-dependent regulation of a gene indicates its importance in response and that it can therefore be used as a biomarker for patient stratification. METHODS: A selection of gastric cancer cell lines (Hs746T, MKN1, MKN7 and NCI-N87) was treated with EGF, cetuximab, trastuzumab or afatinib for a period of 4 or 24 h. The effects of treatment on gene expression were measured by RNA sequencing and the resulting biomarker candidates were tested in an available cohort of gastric cancer patients from the VARIANZ trial or functionally analyzed in vitro. RESULTS: After treatment of the cell lines with afatinib, the highest number of regulated genes was observed, followed by cetuximab and trastuzumab. Although trastuzumab showed only relatively small effects on gene expression, BMF, HAS2 and SHB could be identified as candidate biomarkers for response to trastuzumab. Subsequent studies confirmed HAS2 and SHB as potential predictive markers for response to trastuzumab therapy in clinical samples from the VARIANZ trial. AREG, EREG and HBEGF were identified as candidate biomarkers for treatment with afatinib and cetuximab. Functional analysis confirmed that HBEGF is a resistance factor for cetuximab. CONCLUSION: By confirming HAS2, SHB and HBEGF as biomarkers for anti-HER therapies, we provide evidence that the regulation of gene expression after treatment can be used for biomarker discovery. TRIAL REGISTRATION: Clinical specimens of the VARIANZ study (NCT02305043) were used to test biomarker candidates.

HER2 Expression, Test Deviations, and Their Impact on Survival in Metastatic Gastric Cancer: Results From the Prospective Multicenter VARIANZ Study.

PURPOSE: Trastuzumab is the only approved targeted drug for first-line treatment of human epidermal growth factor receptor 2-positive (HER2+) metastatic gastric cancer (mGC). However, not all patients respond and most eventually progress. The multicenter VARIANZ study aimed to investigate the background of response and resistance to trastuzumab in mGC. METHODS: Patients receiving medical treatment for mGC were prospectively recruited in 35 German sites and followed for up to 48 months. HER2 status was assessed centrally by immunohistochemistry and chromogenic in situ hybridization. In addition, HER2 gene expression was assessed using qPCR. RESULTS: Five hundred forty-eight patients were enrolled, and 77 had HER2+ mGC by central assessment (14.1%). A high deviation rate of 22.7% between central and local test results was seen. Patients who received trastuzumab for centrally confirmed HER2+ mGC (central HER2+/local HER2+) lived significantly longer as compared with patients who received trastuzumab for local HER2+ but central HER2- mGC (20.5 months, n = 60 v 10.9 months, n = 65; hazard ratio, 0.42; 95% CI, 8.2 to 14.4; P < .001). In the centrally confirmed cohort, significantly more tumor cells stained HER2+ than in the unconfirmed cohort, and the HER2 amplification ratio was significantly higher. A minimum of 40% HER2+ tumor cells and a HER2 amplification ratio of ≥ 3.0 were calculated as optimized thresholds for predicting benefit from trastuzumab. CONCLUSION: Significant discrepancies in HER2 assessment of mGC were found in tumor specimens with intermediate HER2 expression. Borderline HER2 positivity and heterogeneity of HER2 expression should be considered as resistance factors for HER2-targeting treatment of mGC. HER2 thresholds should be reconsidered. Detailed reports with quantification of HER2 expression and amplification levels may improve selection of patients for HER2-directed treatment.

COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling.

Epidemiological models are widely used to analyze the spread of diseases such as the global COVID-19 pandemic caused by SARS-CoV-2. However, all models are based on simplifying assumptions and often on sparse data. This limits the reliability of parameter estimates and predictions. In this manuscript, we demonstrate the relevance of these limitations and the pitfalls associated with the use of overly simplistic models. We considered the data for the early phase of the COVID-19 outbreak in Wuhan, China, as an example, and perform parameter estimation, uncertainty analysis and model selection for a range of established epidemiological models. Amongst others, we employ Markov chain Monte Carlo sampling, parameter and prediction profile calculation algorithms. Our results show that parameter estimates and predictions obtained for several established models on the basis of reported case numbers can be subject to substantial uncertainty. More importantly, estimates were often unrealistic and the confidence/credibility intervals did not cover plausible values of critical parameters obtained using different approaches. These findings suggest, amongst others, that standard compartmental models can be overly simplistic and that the reported case numbers provide often insufficient information for obtaining reliable and realistic parameter values, and for forecasting the evolution of epidemics.

PEtab-Interoperable specification of parameter estimation problems in systems biology.

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been-so far-no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.

Correction to: Determining the effects of trastuzumab, cetuximab and afatinib by phosphoprotein, gene expression and phenotypic analysis in gastric cancer cell lines.

An amendment to this paper has been published and can be accessed via the original article.

Determining the effects of trastuzumab, cetuximab and afatinib by phosphoprotein, gene expression and phenotypic analysis in gastric cancer cell lines.

BACKGROUND: Gastric cancer is the fifth most frequently diagnosed cancer and the third leading cause of cancer death worldwide. The molecular mechanisms of action for anti-HER-family drugs in gastric cancer cells are incompletely understood. We compared the molecular effects of trastuzumab and the other HER-family targeting drugs cetuximab and afatinib on phosphoprotein and gene expression level to gain insights into the regulated pathways. Moreover, we intended to identify genes involved in phenotypic effects of anti-HER therapies. METHODS: A time-resolved analysis of downstream intracellular kinases following EGF, cetuximab, trastuzumab and afatinib treatment was performed by Luminex analysis in the gastric cancer cell lines Hs746T, MKN1, MKN7 and NCI-N87. The changes in gene expression after treatment of the gastric cancer cell lines with EGF, cetuximab, trastuzumab or afatinib for 4 or 24 h were analyzed by RNA sequencing. Significantly enriched pathways and gene ontology terms were identified by functional enrichment analysis. Furthermore, effects of trastuzumab and afatinib on cell motility and apoptosis were analyzed by time-lapse microscopy and western blot for cleaved caspase 3. RESULTS: The Luminex analysis of kinase activity revealed no effects of trastuzumab, while alterations of AKT1, MAPK3, MEK1 and p70S6K1 activations were observed under cetuximab and afatinib treatment. On gene expression level, cetuximab mainly affected the signaling pathways, whereas afatinib had an effect on both signaling and cell cycle pathways. In contrast, trastuzumab had little effects on gene expression. Afatinib reduced average speed in MKN1 and MKN7 cells and induced apoptosis in NCI-N87 cells. Following treatment with afatinib, a list of 14 genes that might be involved in the decrease of cell motility and a list of 44 genes that might have a potential role in induction of apoptosis was suggested. The importance of one of these genes (HBEGF) as regulator of motility was confirmed by knockdown experiments. CONCLUSIONS: Taken together, we described the different molecular effects of trastuzumab, cetuximab and afatinib on kinase activity and gene expression. The phenotypic changes following afatinib treatment were reflected by altered biological functions indicated by overrepresentation of gene ontology terms. The importance of identified genes for cell motility was validated in case of HBEGF.

Model-based analysis of response and resistance factors of cetuximab treatment in gastric cancer cell lines.

Targeted cancer therapies are powerful alternatives to chemotherapies or can be used complementary to these. Yet, the response to targeted treatments depends on a variety of factors, including mutations and expression levels, and therefore their outcome is difficult to predict. Here, we develop a mechanistic model of gastric cancer to study response and resistance factors for cetuximab treatment. The model captures the EGFR, ERK and AKT signaling pathways in two gastric cancer cell lines with different mutation patterns. We train the model using a comprehensive selection of time and dose response measurements, and provide an assessment of parameter and prediction uncertainties. We demonstrate that the proposed model facilitates the identification of causal differences between the cell lines. Furthermore, our study shows that the model provides predictions for the responses to different perturbations, such as knockdown and knockout experiments. Among other results, the model predicted the effect of MET mutations on cetuximab sensitivity. These predictive capabilities render the model a basis for the assessment of gastric cancer signaling and possibly for the development and discovery of predictive biomarkers.

Self-Amplifying Pulsatile Protein Dynamics without Positive Feedback.

Many proteins exhibit dynamic activation patterns in the form of irregular pulses. Such behavior is typically attributed to a combination of positive and negative feedback loops in the underlying regulatory network. However, the presence of positive feedbacks is difficult to demonstrate unequivocally, raising the question of whether stochastic pulses can arise from negative feedback only. Here, we use the protein kinase A (PKA) system, a key regulator of the yeast pulsatile transcription factor Msn2, as a case example to show that irregular pulses of protein activity can arise from a negative feedback loop alone. Simplification to two variables reveals that a combination of zero-order ultrasensitivity, timescale separation between the activator and the repressor, and an effective delay in the feedback are sufficient to amplify a perturbation into a pulse. The same circuit topology can account for both activation and inactivation pulses, pointing toward a general mechanism of stochastic pulse generation.