Designing polymer-tethered membrane-nanoparticle composites

This thesis proposes a novel design of nanoparticles for drug delivery. By tethering a bilayer membrane vesicle to a solid nanoparticle core at its center using hydrophilic soft polymers, this structure is expected to exhibit improved stability, narrowed size distribution, and a variety of functionalization possibilities. Various aspects of this design will be examined from a theoretical perspective using physico-chemical knowledge and computer simulations. The aim is to significantly reduce the size of the fairly large parameter space and shed light on experimental protocols for how to effectively assemble such nanoparticles in the laboratory.

To study the properties of this design, coarse-grained molecular simulations are introduced in Chapter 2 as one of the major tools employed in this work, thanks to their computational efficiency and the possibility of obtaining important generic insights of the system being modeled. The general philosophy of coarse-graining (CGing) will be outlined, followed by an introduction to the CG models used in this work. Then, it will be illustrated how to connect length, energy, and time scales in CG simulations to reality. This chapter is concluded by applying the CG concepts and techniques described earlier on to obtain a CG model for PEGylated linker molecules, which is one of the two major components of the system of polymer-tethered nanocomposites studied in this work.

After the second chapter on coarse-graining, this thesis will spend three chapters focusing on either one of the two major components of the system we proposed, namely the polymeric linkers and the lipid bilayers. In Chapter 3, to understand the mechanical properties of the polymer linkers which tether the membrane vesicle to the nanoparticle core, a theoretical model for polymer brushes confined by two concentric spheres will be derived based on single-chain theories and scaling concepts. Using the CG linker model parameterized in Chapter 2, it will be demonstrated that this theoretical polymer model quantitatively predicts the force-extension relation of the polymers. This provides an efficient way to estimate both the size distribution and the stability of the tethered membrane-nanoparticle composites.

Following the chapter on polymers, this thesis will proceed to investigate the other major component in the proposed nanocomposites, namely the lipid membrane. Hence, computational methods to determine the two curvature elastic moduli in Helfrich theory, namely the bending modulus and the Gaussian curvature modulus, will be elaborated upon in the next two chapters. To be more specific, a method to measure the bending modulus by simulating membrane buckles will be proposed and validated in Chapter 4. Compared to other existed ways for measuring the bending modulus, the buckling method will turn out to be computationally efficient, and it can be applied to almost all types of membrane models.

In Chapter 5, a novel method for determining the Gaussian curvature modulus in simulations will be developed. The interplay between the bending energy and the edge tension in the membrane vesiculation process provides an efficient and robust way to pinpoint the Gaussian curvature modulus. As a comparison, another time-honored method to determine this modulus by measuring the lateral stress profile of flat bilayers is discussed. Based on the results measured in this alternative technique, as well as a comparison with the vesiculation protocol, it is argued that the stress profile method in fact fails to produce trustworthy values for the Gaussian curvature modulus. This unexpected result suggests caution when attempting to extract bilayer properties from the stress profile.

The models and knowledge which have been developed in this thesis will then be linked together in Chapter 6. The study of planar polymer-tethered bilayer membranes in this chapter serves as an intermediate step towards the membrane-nanoparticle composites in a spherical geometry. Simulations of the assembly process of tethered bilayers mimicking the rapid solvent exchange and the vesicle fusion protocols are qualitatively consistent with experimental observations found in the literature, supporting the reliability of our CG model. Moreover, the polymer theories discussed in Chapter 3 prove sufficient in semi-quantitatively describing the structural properties of such tethered membranes.

Bringing everything together, this thesis concludes with a study of the polymertethered membrane-nanoparticle composites proposed in Chapter 1. Theoretical constraints on the design parameters of this structure are first outlined and tested in simulations, with a major focus on the plausible range of the nanocomposite size. Then, a number of practical aspects regarding such nanocomposites, including their assembly process, solvent conditions, and the effect of the polydispersity in the linker chain lengths, are investigated.