Coarse-grained modelling of urea-adamantyl functionalised poly(propylene imine) dendrimersby A.F. Smeijers, A.J. Markvoort, K. Pieterse, P.A.J. Hilbers

Molecular Simulation

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Molecular Simulation

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Coarse-grained modelling of urea-adamantyl functionalised poly(propylene imine) dendrimers

A.F. Smeijers, A.J. Markvoort, K. Pieterse & P.A.J. Hilbers

To cite this article: A.F. Smeijers, A.J. Markvoort, K. Pieterse & P.A.J. Hilbers (2015): Coarsegrained modelling of urea-adamantyl functionalised poly(propylene imine) dendrimers,

Molecular Simulation, DOI: 10.1080/08927022.2015.1096359

To link to this article: http://dx.doi.org/10.1080/08927022.2015.1096359

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Molecular SiMulation, 2015 http://dx.doi.org/10.1080/08927022.2015.1096359

Coarse-grained modelling of urea-adamantyl functionalised poly(propylene imine) dendrimers

A.F. Smeijersa, A.J. Markvoorta,b, K. Pietersea,b and P.A.J. Hilbersa,b 1computational Biology, Department of Biomedical engineering, technische universiteit eindhoven, eindhoven, the netherlands.; 2institute for complex

Molecular Systems, technische universiteit eindhoven, eindhoven, the netherlands.

ABSTRACT

To investigate the behaviour of poly(propylene imine) dendrimers – and urea–adamantyl functionalised ones – in solution using molecular dynamics simulations, we developed a coarse-grained model to tackle the relatively large system sizes and time scales needed. Harmonic bond and angle potentials were derived from atomistic simulations using an iterative Boltzmann inversion scheme, modified to incorporate

Gaussian fits of the bond and angle distributions. With the coarse-grained model and accompanying force field simulations of generations 1–7 of both dendrimer types in water were performed. They compare favourably with atomistic simulations and experimental results on the basis of size, shape, monomer density, spacer back-folding and atomic form factor measurements. These results show that the structural dynamics of these dendrimers originate from flexible chains constrained by configurational and spatial requirements. Large dendrimers are more rigid and spherical, while small ones are flexible, alternatively rod-like and globular. © 2015 taylor & Francis

KEYWORDS

Molecular dynamics simulations; dendrimers; coarse graining; Boltzmann inversion

ARTICLE HISTORY received 16 January 2015 accepted 16 September 2015

CONTACT P.a.J. Hilbers p.a.j.hilbers@tue.nl 1. Introduction

Dendrimers are a class of hyperbranched polymeric macromolecules.[1,2] Short branches emanate from a multifunctional core, each an anchoring point for a next set of short branches. They are synthesised in an iterative reaction sequence. Each iteration adds another generational shell of branches, multiplying the number of reactive ends. Compared to other polymers, it is a very controlled synthesis leading to well-defined monodisperse structures. Finally the ends can be coupled to functional groups to provide specific features to the dendrimer. The large number of possible cores, branches and end groups [3–5] allows for nanoengineering of properties like size, shape, topology, flexibility and surface chemistry.

Dendrimers have been investigated using computer models for a long time. The first attempts were made using the principles of statistical models of macromolecules [6,7] to generate dendrimers with a self-avoiding walk algorithm.[8] To elucidate the dendrimer structure of an archetypal dendritic molecule, various bead-spring models have been researched using lattice Monte

Carlo algorithms [9–11] and off-lattice ones,[12–16] mostly with implicit solvent. Other models where the solvent was treated implicitly were made with molecular dynamics (MD) [17–19] and Brownian dynamics.[20–23] One improvement in detail has been including solvent particles.[24–28] Another was using atomistic MD to model specific dendrimers, but still in implicit solvent or actual vacuum. Most notable are poly(propylene imine) (PPI) in vacuum [29,30] and melt [31,32] and poly(amido amine) (PAMAM) in vacuum [33–35] and melt,[36] but also various phenyl-[37–40] and carbosilane-based [41,42] dendrimers have been modelled. As both the solvent and the dendrimer composition influence the behaviour, explicit solvent atomistic simulations have also been performed for, e.g., PPI,[43–46]

PAMAM [46–49] and carbosilane [50] dendrimers. The early simulations scarcely lasted more than 1ns, but the recent examples typically reach time scales of up to 10s of nanoseconds. Since experiments are performed with multiple dendrimers in solution and for much longer time scales, these atomistic simulations are only able to reproduce a limited portion of experimental results.

For phenomena where dendrimer–dendrimer interactions play a role, while also maintaining chemical specificity, coarse-grained simulations may provide new insight.

For some dendrimers such coarse-grained models have been published. The difference with earlier bead-spring models is that they are fitted on data obtained from atomistic simulations. The first reported coarse-grained model is a study of PAMAM engaging with a lipid bilayer.[51] The dendrimer uses repurposed lipid parameters. The same is true for a recent study of two PAMAM dendrimers interacting.[52] Another model is of stiff polyphenylene dendrimers in the melt phase,[53] where each bead represents six phenyl groups. These dendrimers have been made using a Boltzmann-inversion scheme for nonbonded interactions, and a fit of multiple Gaussians for the bonded interactions. Recently two new coarse-grained models have been published. One is a Monte Carlo model for various dendrimers [54], where the

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