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.

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.].

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.

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.

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.

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.

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

Unlabelled: 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).