Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models.

Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results.

Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes defines survival threshold in erythroid progenitor cells.

Survival or apoptosis is a binary decision in individual cells. However, at the cell-population level, a graded increase in survival of colony-forming unit-erythroid (CFU-E) cells is observed upon stimulation with erythropoietin (Epo). To identify components of Janus kinase 2/signal transducer and activator of transcription 5 (JAK2/STAT5) signal transduction that contribute to the graded population response, we extended a cell-population-level model calibrated with experimental data to study the behavior in single cells. The single-cell model shows that the high cell-to-cell variability in nuclear phosphorylated STAT5 is caused by variability in the amount of Epo receptor (EpoR):JAK2 complexes and of SHP1, as well as the extent of nuclear import because of the large variance in the cytoplasmic volume of CFU-E cells. 24-118 pSTAT5 molecules in the nucleus for 120 min are sufficient to ensure cell survival. Thus, variability in membrane-associated processes is sufficient to convert a switch-like behavior at the single-cell level to a graded population-level response.

Functional Proteomics of Breast Cancer Metabolism Identifies GLUL as Responder during Hypoxic Adaptation.

Hypoxia as well as metabolism are central hallmarks of cancer, and hypoxia-inducible factors (HIFs) and metabolic effectors are crucial elements in oxygen-compromised tumor environments. Knowledge of changes in the expression of metabolic proteins in response to HIF function could provide mechanistic insights into adaptation to hypoxic stress, tumorigenesis, and disease progression. We analyzed time-resolved alterations in metabolism-associated protein levels in response to different oxygen potentials across breast cancer cell lines. Effects on the cellular metabolism of both HIF-dependent and -independent processes were analyzed by reverse-phase protein array profiling and a custom statistical model. We revealed a strong induction of glucose transporter 1 (GLUT1) and lactate dehydrogenase A (LDHA) as well as reduced glutamate-ammonia ligase (GLUL) protein levels across all cell lines tested as consistent changes upon hypoxia induction. Low GLUL protein levels were correlated with aggressive molecular subtypes in breast cancer patient data sets and also with hypoxic tumor regions in a xenograft mouse tumor model. Moreover, low GLUL expression was associated with poor survival in breast cancer patients and with high HIF-1α-expressing patient subgroups. Our data reveal time-resolved changes in the regulation of metabolic proteins under oxygen-deprived conditions and elucidate GLUL as a strong responder to HIFs and the hypoxic environment.

Profile likelihood-based analyses of infectious disease models.

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015-2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.

Cause and cure of sloppiness in ordinary differential equation models.

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.