Kinetics of RNA-LNP delivery and protein expression.

Lipid nanoparticles (LNPs) employing ionizable lipids are the most advanced technology for delivery of RNA, most notably mRNA, to cells. LNPs represent well-defined core-shell particles with efficient nucleic acid encapsulation, low immunogenicity and enhanced efficacy. While much is known about the structure and activity of LNPs, less attention is given to the timing of LNP uptake, cytosolic transfer and protein expression. However, LNP kinetics is a key factor determining delivery efficiency. Hence quantitative insight into the multi-cascaded pathway of LNPs is of interest to elucidate the mechanism of delivery. Here, we review experiments as well as theoretical modeling of the timing of LNP uptake, mRNA-release and protein expression. We describe LNP delivery as a sequence of stochastic transfer processes and review a mathematical model of subsequent protein translation from mRNA. We compile probabilities and numbers obtained from time resolved microscopy. Specifically, live-cell imaging on single cell arrays (LISCA) allows for high-throughput acquisition of thousands of individual GFP reporter expression time courses. The traces yield the distribution of mRNA life-times, expression rates and expression onset. Correlation analysis reveals an inverse dependence of gene expression efficiency and transfection onset-times. Finally, we discuss why timing of mRNA release is critical in the context of codelivery of multiple nucleic acid species as in the case of mRNA co-expression or CRISPR/Cas gene editing.

Erratum: Publisher Correction: Multi-experiment nonlinear mixed effect modeling of single-cell translation kinetics after transfection.

[This corrects the article DOI: 10.1038/s41540-018-0079-7.].

Community-driven roadmap for integrated disease maps.

The Disease Maps Project builds on a network of scientific and clinical groups that exchange best practices, share information and develop systems biomedicine tools. The project aims for an integrated, highly curated and user-friendly platform for disease-related knowledge. The primary focus of disease maps is on interconnected signaling, metabolic and gene regulatory network pathways represented in standard formats. The involvement of domain experts ensures that the key disease hallmarks are covered and relevant, up-to-date knowledge is adequately represented. Expert-curated and computer readable, disease maps may serve as a compendium of knowledge, allow for data-supported hypothesis generation or serve as a scaffold for the generation of predictive mathematical models. This article summarizes the 2nd Disease Maps Community meeting, highlighting its important topics and outcomes. We outline milestones on the roadmap for the future development of disease maps, including creating and maintaining standardized disease maps; sharing parts of maps that encode common human disease mechanisms; providing technical solutions for complexity management of maps; and Web tools for in-depth exploration of such maps. A dedicated discussion was focused on mathematical modeling approaches, as one of the main goals of disease map development is the generation of mathematically interpretable representations to predict disease comorbidity or drug response and to suggest drug repositioning, altogether supporting clinical decisions.

Multi-experiment nonlinear mixed effect modeling of single-cell translation kinetics after transfection.

Single-cell time-lapse studies have advanced the quantitative understanding of cellular pathways and their inherent cell-to-cell variability. However, parameters retrieved from individual experiments are model dependent and their estimation is limited, if based on solely one kind of experiment. Hence, methods to integrate data collected under different conditions are expected to improve model validation and information content. Here we present a multi-experiment nonlinear mixed effect modeling approach for mechanistic pathway models, which allows the integration of multiple single-cell perturbation experiments. We apply this approach to the translation of green fluorescent protein after transfection using a massively parallel read-out of micropatterned single-cell arrays. We demonstrate that the integration of data from perturbation experiments allows the robust reconstruction of cell-to-cell variability, i.e., parameter densities, while each individual experiment provides insufficient information. Indeed, we show that the integration of the datasets on the population level also improves the estimates for individual cells by breaking symmetries, although each of them is only measured in one experiment. Moreover, we confirmed that the suggested approach is robust with respect to batch effects across experimental replicates and can provide mechanistic insights into the nature of batch effects. We anticipate that the proposed multi-experiment nonlinear mixed effect modeling approach will serve as a basis for the analysis of cellular heterogeneity in single-cell dynamics.

The symmetry of the Kepler problem, the inverse Ligon-Schaaf mapping and the Birkhoff conjecture.

The Ligon-Schaaf regularization (LS mapping) was introduced in 1976 and has been used several times. However, we are not aware of any direct usage of the inverse mapping, perhaps since it appears at first sight to be quite complex, involves the use of a transcendental equation (referred to as the generalized Kepler equation) that cannot be solved in closed form, and lacks smoothness near the collision point. Here, we provide some insight into the significance of this equation, along with a very simple derivation and confirmation of the inverse LS mapping. Then we use numerical methods to investigate three applications: 1) solutions of the Kepler function, 2) calculation of orbits including time-of-flight data based on the Delaunay Hamiltonian, and 3) numerical evidence for the Birkhoff conjecture for the circular restricted 3-body problem.

GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models.

Motivation: Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results: We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models. Availability and implementation: GenSSI 2.0 is an open-source MATLAB toolbox and available at https://github.com/genssi-developer/GenSSI. Contact: thomas.ligon@physik.uni-muenchen.de or jan.hasenauer@helmholtz-muenchen.de. Supplementary information: Supplementary data are available at Bioinformatics online.

Multi-level kinetic model of mRNA delivery via transfection of lipoplexes.

Recent work on the use of mRNA lipoplexes for gene delivery demonstrates the need for a mathematical model that simulates and predicts kinetics and transfection efficiency. The small copy numbers involved make it necessary to use stochastic models and include statistical analysis of the variation observed in the experimental data. The modeling requirements are further complicated by the multi-level nature of the problem, where mRNA molecules are contained in lipoplexes, which are in turn contained in endosomes, where each of these entities displays a behavior of its own. We have created a mathematical model that reproduces both the time courses and the statistical variance observed in recent experiments using single-cell tracking of GFP expression after transfection. By applying a few key simplifications and assumptions, we have limited the number of free parameters to five, which we optimize to match five experimental determinants by means of a simulated annealing algorithm. The models demonstrate the need for modeling of nested species in order to reproduce the shape of the dose-response and expression-level curves.

Single-cell mRNA transfection studies: delivery, kinetics and statistics by numbers.

In artificial gene delivery, messenger RNA (mRNA) is an attractive alternative to plasmid DNA (pDNA) since it does not require transfer into the cell nucleus. Here we show that, unlike for pDNA transfection, the delivery statistics and dynamics of mRNA-mediated expression are generic and predictable in terms of mathematical modeling. We measured the single-cell expression time-courses and levels of enhanced green fluorescent protein (eGFP) using time-lapse microscopy and flow cytometry (FC). The single-cell analysis provides direct access to the distribution of onset times, life times and expression rates of mRNA and eGFP. We introduce a two-step stochastic delivery model that reproduces the number distribution of successfully delivered and translated mRNA molecules and thereby the dose-response relation. Our results establish a statistical framework for mRNA transfection and as such should advance the development of RNA carriers and small interfering/micro RNA-based drugs. FROM THE CLINICAL EDITOR: This team of authors established a statistical framework for mRNA transfection by using a two-step stochastic delivery model that reproduces the number distribution of successfully delivered and translated mRNA molecules and thereby their dose-response relation. This study establishes a nice connection between theory and experimental planning and will aid the cellular delivery of mRNA molecules.