Mathematical model of early Reelin-induced Src family kinase-mediated signaling

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.

Realistic simulation of time-course measurements in systems biology

In systems biology, the analysis of complex nonlinear systems faces many methodological challenges. For the evaluation and comparison of the performances of novel and competing computational methods, one major bottleneck is the availability of realistic test problems. We present an approach for performing realistic simulation studies for analyses of time course data as they are typically measured in systems biology. Since the design of experiments in practice depends on the process of interest, our approach considers the size and the dynamics of the mathematical model which is intended to be used for the simulation study. To this end, we used 19 published systems biology models with experimental data and evaluated the relationship between model features (e.g., the size and the dynamics) and features of the measurements such as the number and type of observed quantities, the number and the selection of measurement times, and the magnitude of measurement errors. Based on these typical relationships, our novel approach enables suggestions of realistic simulation study designs in the systems biology context and the realistic generation of simulated data for any dynamic model. The approach is demonstrated on three models in detail and its performance is validated on nine models by comparing ODE integration, parameter optimization, and parameter identifiability. The presented approach enables more realistic and less biased benchmark studies and thereby constitutes an important tool for the development of novel methods for dynamic modeling.

Fast-forward breeding for a food-secure world

Crop production systems need to expand their outputs sustainably to feed a burgeoning human population. Advances in genome sequencing technologies combined with efficient trait mapping procedures accelerate the availability of beneficial alleles for breeding and research. Enhanced interoperability between different omics and phenotyping platforms, leveraged by evolving machine learning tools, will help provide mechanistic explanations for complex plant traits. Targeted and rapid assembly of beneficial alleles using optimized breeding strategies and precise genome editing techniques could deliver ideal crops for the future. Realizing desired productivity gains in the field is imperative for securing an adequate future food supply for 10 billion people.

Hepatic stellate cells: current state and open questions

This review article summarizes 20 years of our research on hepatic stellate cells within the framework of two collaborative research centers CRC575 and CRC974 at the Heinrich Heine University. Over this period, stellate cells were identified for the first time as mesenchymal stem cells of the liver, and important functions of these cells in the context of liver regeneration were discovered. Furthermore, it was determined that the space of Disse - bounded by the sinusoidal endothelium and hepatocytes - functions as a stem cell niche for stellate cells. Essential elements of this niche that control the maintenance of hepatic stellate cells have been identified alongside their impairment with age. This article aims to highlight previous studies on stellate cells and critically examine and identify open questions and future research directions.

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.

Mathematical Biology: Expand, Expose, and Educate!

Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this specialized training. This article examines the need to expand, expose, and educate others about mathematical biology. To support field expansion, we give several recommendations of ways to integrate mathematics applied curricula to attract broader student interest. With this exposure-whether it is led by an individual, a department, a university, or researchers in mathematical biology-each can help to promote a base knowledge and appreciation of the field. In order to encourage the next generation of researchers to consider mathematical biology, we highlight current interdisciplinary programs, share popular mathematical tools, and present some thoughts on ways to support a thriving and inclusive mathematical biology community for years to come.

Benchmark problems for dynamic modeling of intracellular processes

Motivation

Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A multitude of computational approaches, e.g. for parameter estimation or uncertainty analysis have been developed within recent years. However, many of these approaches lack proper testing in application settings because a comprehensive set of benchmark problems is yet missing.

Results

We present a collection of 20 benchmark problems in order to evaluate new and existing methodologies, where an ODE model with corresponding experimental data is referred to as problem. In addition to the equations of the dynamical system, the benchmark collection provides observation functions as well as assumptions about measurement noise distributions and parameters. The presented benchmark models comprise problems of different size, complexity and numerical demands. Important characteristics of the models and methodological requirements are summarized, estimated parameters are provided, and some example studies were performed for illustrating the capabilities of the presented benchmark collection.

Availability and implementation

The models are provided in several standardized formats, including an easy-to-use human readable form and machine-readable SBML files. The data is provided as Excel sheets. All files are available at https://github.com/Benchmarking-Initiative/Benchmark-Models, including step-by-step explanations and MATLAB code to process and simulate the models.

Supplementary information

Supplementary data are available at Bioinformatics online.