Supplementary data are available at Bioinformatics online.

As interactions between the immune system and tumour cells are governed by a complex network of cell–cell interactions, knowing the specific immune cell composition of a solid tumour may be essential to predict a patient’s response to immunotherapy. Here, we analyse in depth how to derive the cellular composition of a solid tumour from bulk gene expression data by mathematical deconvolution, using indication-specific and cell type-specific reference gene expression profiles (RGEPs) from tumour-derived single-cell RNA sequencing data. We demonstrate that tumour-derived RGEPs are essential for the successful deconvolution and that RGEPs from peripheral blood are insufficient. We distinguish nine major cell types, as well as three T cell subtypes. Using the tumour-derived RGEPs, we can estimate the content of many tumours associated immune and stromal cell types, their therapeutically relevant ratios, as well as an improved gene expression profile of the malignant cells.

As interactions between the immune system and tumour cells are governed by a complex network of cell-cell interactions, knowing the specific immune cell composition of a solid tumour may be essential to predict a patient's response to immunotherapy. Here, we analyse in depth how to derive the cellular composition of a solid tumour from bulk gene expression data by mathematical deconvolution, using indication-and cell type-specific reference gene expression profiles (RGEPs) from tumour-derived single-cell RNA sequencing data. We demonstrate that tumour-derived RGEPs are essential for the successful deconvolution and that RGEPs from peripheral blood are insufficient. We distinguish nine major cell types as well as three T cell subtypes. As the ratios of CD4+, CD8+ and regulatory T cells have been shown to predict overall survival, we extended our analysis to include the estimation of prognostic ratios that may enable the application in a clinical setting. Using the tumour derived RGEPs, we can estimate, for the first time, the content of cancer associated fibroblasts, endothelial cells and the malignant cells in a patient sample by a deconvolution approach. In addition, improved tumour cell gene expression profiles can be obtained by this method by computationally removing contamination from non-malignant cells. Given the difficulty around sample preparation and storage to obtain high quality single-cell RNA-seq data in the clinical context, the presented method represents a computational solution to derive the cellular composition of a tissue sample.

Lung cancer, with its most prevalent form non-small-cell lung carcinoma (NSCLC), is one of the leading causes of cancer-related deaths worldwide, and is commonly treated with chemotherapeutic drugs such as cisplatin. Lung cancer patients frequently suffer from chemotherapy-induced anemia, which can be treated with erythropoietin (EPO). However, studies have indicated that EPO not only promotes erythropoiesis in hematopoietic cells, but may also enhance survival of NSCLC cells. Here, we verified that the NSCLC cell line H838 expresses functional erythropoietin receptors (EPOR) and that treatment with EPO reduces cisplatin-induced apoptosis. To pinpoint differences in EPO-induced survival signaling in erythroid progenitor cells (CFU-E, colony forming unit-erythroid) and H838 cells, we combined mathematical modeling with a method for feature selection, the L1 regularization. Utilizing an example model and simulated data, we demonstrated that this approach enables the accurate identification and quantification of cell type-specific parameters. We applied our strategy to quantitative time-resolved data of EPO-induced JAK/STAT signaling generated by quantitative immunoblotting, mass spectrometry and quantitative real-time PCR (qRT-PCR) in CFU-E and H838 cells as well as H838 cells overexpressing human EPOR (H838-HA-hEPOR). The established parsimonious mathematical model was able to simultaneously describe the data sets of CFU-E, H838 and H838-HA-hEPOR cells. Seven cell type-specific parameters were identified that included for example parameters for nuclear translocation of STAT5 and target gene induction. Cell type-specific differences in target gene induction were experimentally validated by qRT-PCR experiments. The systematic identification of pathway differences and sensitivities of EPOR signaling in CFU-E and H838 cells revealed potential targets for intervention to selectively inhibit EPO-induced signaling in the tumor cells but leave the responses in erythroid progenitor cells unaffected. Thus, the proposed modeling strategy can be employed as a general procedure to identify cell type-specific parameters and to recommend treatment strategies for the selective targeting of specific cell types.

Since the publication of Leonor Michaelis and Maude Menten's paper on the reaction kinetics of the enzyme invertase in 1913, molecular biology has evolved tremendously. New measurement techniques allow in vivo characterization of the whole genome, proteome or transcriptome of cells, whereas the classical enzyme essay only allows determination of the two Michaelis–Menten parameters V and Km. Nevertheless, Michaelis–Menten kinetics are still commonly used, not only in the in vitro context of enzyme characterization but also as a rate law for enzymatic reactions in larger biochemical reaction networks. In this review, we give an overview of the historical development of kinetic rate laws originating from Michaelis–Menten kinetics over the past 100 years. Furthermore, we briefly summarize the experimental techniques used for the characterization of enzymes, and discuss web resources that systematically store kinetic parameters and related information. Finally, describe the novel opportunities that arise from using these data in dynamic mathematical modeling. In this framework, traditional in vitro approaches may be combined with modern genome‐scale measurements to foster thorough understanding of the underlying complex mechanisms.

Motivation: Cellular information processing can be described mathematically using differential equations. Often, external stimulation of cells by compounds such as drugs or hormones leading to activation has to be considered. Mathematically, the stimulus is represented by a time-dependent input function.Parameters such as rate constants of the molecular interactions are often unknown and need to be estimated from experimental data, e.g. by maximum likelihood estimation. For this purpose, the input function has to be defined for all times of the integration interval. This is usually achieved by approximating the input by interpolation or smoothing of the measured data. This procedure is suboptimal since the input uncertainties are not considered in the estimation process which often leads to overoptimistic confidence intervals of the inferred parameters and the model dynamics.Results: This article presents a new approach which includes the input estimation into the estimation process of the dynamical model parameters by minimizing an objective function containing all parameters simultaneously. We applied this comprehensive approach to an illustrative model with simulated data and compared it to alternative methods. Statistical analyses revealed that our method improves the prediction of the model dynamics and the confidence intervals leading to a proper coverage of the confidence intervals of the dynamic parameters. The method was applied to the JAK-STAT signaling pathway.Availability: MATLAB code is available on the authors' website http://www.fdmold.uni-freiburg.de/~schelker/.Contact: max.schelker@fdm.uni-freiburg.deSupplementary Information: Additional information is available at Bioinformatics Online.

After endocytic uptake, influenza viruses transit early endosomal compartments and eventually reach late endosomes. There, the viral glycoprotein hemagglutinin (HA) triggers fusion between endosomal and viral membrane, a critical step that leads to release of the viral segmented genome destined to reach the cell nucleus. Endosomal maturation is a complex process involving acidification of the endosomal lumen as well as endosome motility along microtubules. While the pH drop is clearly critical for the conformational change and membrane fusion activity of HA, the effect of intracellular transport dynamics on the progress of infection remains largely unclear. In this study, we developed a comprehensive mathematical model accounting for the first steps of influenza virus infection. We calibrated our model with experimental data and challenged its predictions using recombinant viruses with altered pH sensitivity of HA. We identified the time point of virus-endosome fusion and thereby the diffusion distance of the released viral genome to the nucleus as a critical bottleneck for efficient virus infection. Further, we concluded and supported experimentally that the viral RNA is subjected to cytosolic degradation strongly limiting the probability of a successful genome import into the nucleus.

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