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

AbstractIn 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 EditorThis 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

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press