As a polycation with diverse applications in biomedical and environmental engineering, polyethylenimine (PEI) can be synthesized with varying degrees of branching, polymerization, and can exist in different protonation states. There have been some interests in molecular modeling of PEI at all‐atom or coarse‐grained (CG) levels, but present CG models are limited to linear PEIs. Here we present the methodology to systematically categorize bond lengths, bond angles and dihedral angles, which allows us to model branched PEIs. The CG model was developed under the Martini scheme based on eight ~600 Da PEIs, with four different degree of branching at two different protonation states. Comparison of the CG model with all‐atom simulations shows good agreement for both local (distributions for bonded interactions) and global (end‐to‐end distance, radius of gyration) properties, with and without salt. Compatibility of the PEI model with other CG bio‐molecules developed under the Martini scheme will allow for large‐scale simulations of many PEI‐enabled processes. © 2018 Wiley Periodicals, Inc.

Polyethylenimine (PEI)–DNA nanoparticles (NPs) have shown a lot of potential in gene delivery. The N/P ratio, the ratio between the total number of amines in PEIs and total number of phosphates in DNAs, is an essential factor determining the efficacy of delivery. In this work, the aggregation of PEIs and DNAs under different N/P ratios is studied using large-scale coarse-grained simulations under the Martini framework. At very low N/P ratio, the aggregation of DNAs is limited, and as the N/P ratio increases, the NPs change from a loose linear structure to a compact branched structure. Such a transition in the mode of aggregation is caused by the different alignments of PEIs with DNA backbones prior to aggregation, which dictates their ability to serve as polycation bridges. Except for very large NPs at high N/P ratios, the charge of a NP is proportional to the number of DNAs in it. Their ratio allows for the definition of an intrinsic property called specific repulsion, which controls the characteristics of the steady-state size distribution of NPs: unimodal for strong specific repulsion, bimodal for moderate specific repulsion, and more or less uniform for weak specific repulsion. Understanding the mechanism behind DNA–PEI NP formation helped us propose a two-step process to generate NPs that are more compact and closer to being spherical.

Correction of calculation errors in the original article led to the change of bead type for the unprotonated beads in the coarse-grained polyethylenimine model. The original model was still of good quality while the updated model showed better performance in describing the interaction between polyethylenimine and DNA.The authors found errors in the partitioning free energy of ethylamine between water and different organic solvents. We apologize for any inconvenience this may have caused. Errors are reported and corrected below, and their consequences on the results are discussed.The model presented in our original article [1] is still deemed to be of good quality; in fact, all bonded parameters remain unchanged after the correction. Meanwhile, the model can be further improved by suggesting a change to the bead type for the uncharged polyethylenimine (PEI) beads. Below references [2][3][4][5][6][7][8] correspond to references [55], [67], [66], [61], [58], [56] and [63] respectively in the original article. [1]Following the Martini methodology [2] , the bead type for uncharged PEI beads was determined in our original article [1] by considering a) the hydration free energy of the molecular analogue, ethylamine; and b) the partitioning free energy of ethylamine between water and different organic solvents. Marrink et al. [2] provided the partitioning free energies of Martini beads "between water and a number of organic phases", which should be interpreted as the free energy required to move a bead from organic solvent to water. Abraham et al. [3] reported "water-chloroform partition coefficients", denoted as logP chl , for different solutes. The free energy change associated with the partition coefficient, ΔG = − 2.303 RTlogP chl , should be interpreted as the free energy required to move a solute from water to chloroform. Duffy et al. [4] reported partition coefficients in the form of "logP(hexadecane/gas), logP(octanol/gas), logP(water/gas), and logP(octanol/water)". The free energy change calculated from the partition coefficients,

Non-viral gene delivery using polyethylenimine (PEI) has shown tremendous promise as a therapeutic technique. Through the formation of nanoparticles (NPs), PEIs protect genetic material such as DNA from degradation. Escape of the NPs from endosomes and lysosomes is facilitated by PEI's buffering capacity over a wide range of pH. However, little is known about the effects of endosomal acidification on the morphology of the NPs. In this work, large-scale coarse-grained simulations performed to mimic endosomal acidification reveal that NPs undergo a resizing process that is highly dependent on the N/P ratio (ratio of PEI nitrogen to DNA phosphate) at which they are prepared. With a low N/P ratio, NPs further aggregate after endosomal acidification, whereas with a high N/P ratio they dissociate. The mechanisms behind such NP resizing and its consequences on endosomal escape and nuclear trafficking are discussed. Based on the findings, suggestions are made on the PEI architecture that may enhance NP dissociation driven by endosomal acidification.

Fluorescence microscopy allows the visualization of live cells and their components, but even with advances in super-resolution microscopy, atomic resolution remains unattainable. Contrarily, molecular simulations can access atomic resolution, but comparison with experimental microscopy images has not been possible. In this work, a novel in silico fluorescence microscopy technique is proposed, which uses the physics-based point spread function to generate images from molecular simulations. The method allows the resolution of molecular simulation to be reduced and made comparable to experiments, enabling direct cross-comparison between in silico and experimental images. Simulation of a DNA-polyethylenimine gene delivery system is used to demonstrate the production of in silico images with a different optical axis, object focal planes, exposure time, color combinations, resolution, brightness, and amount of out-of-focus fluorescence. These images bridge the distinct worlds of molecular simulation and experimental fluorescence microscopy by generating new knowledge from direct cross-validation, determining equivalence of properties extracted from molecular simulation and experimental images, assessing and developing algorithms for experimental image analysis, etc. The technique presented here can also be used as a standalone visualization tool for molecular simulation and lays the foundation for other in silico microscopy methods.