Exploring the Design Rules for Efficient Membrane-Reshaping Nanostructures

In this study, we investigate the role of the surface patterning of nanostructures for cell membrane reshaping. To accomplish this, we combine an evolutionary algorithm with coarse-grained molecular dynamics simulations and explore the solution space of ligand patterns on a nanoparticle that promote efficient and reliable cell uptake. Surprisingly, we find that in the regime of low ligand number the best-performing structures are characterized by ligands arranged into long one-dimensional chains that pattern the surface of the particle. We show that these chains of ligands provide particles with high rotational freedom and they lower the free energy barrier for membrane crossing. Our approach reveals a set of nonintuitive design rules that can be used to inform artificial nanoparticle construction and the search for inhibitors of viral entry.

Figure 1

Combining molecular dynamics and an evolutionary algorithm. (a) Graphical representation of the MD-EA scheme developed here. (b) The nanoparticle is covered by 72 ligands, of which $N$ are active (in blue, represented as “1” in the nanoparticle “genome”) and can bind the membrane. (c) Example designs from three different generations along with a snapshot from the last time step of their simulation runs.

Figure 2

Performance of the evolved nanoparticles. (a) The normalized population fitness for three examples of the active ligand number $N$ and ligand-membrane interaction $\epsilon$. The error bars represent the standard error of the mean fitness over the population of 80 individuals in one realization of the EA-MD algorithm. Fluctuations in this mean are to be expected, as not all mutations are beneficial. (b) The fraction of the entire population that successfully crossed the membrane at various values of $N$ and $\epsilon$. In the region around $N\epsilon \approx 200kT$ (marked with boxes), the population is made up of a mixed collection of budding and nonbudding particles. In the extreme of very high $N$ and high $\epsilon$, the particle often tears the membrane and simulations cannot be equilibrated (see Supplemental Material [5]).

Figure 3

Structural analysis of the evolved particles. (a) Examples of evolved nanoparticle designs. (b) The patterns of ligands on the particle are converted into a network. (c) The average normalized graph density (upper panel) and the average normalized subgraph size (bottom panel) for the budding and nonbudding particles across the whole population. The insets show sample particles in each subpopulation. The error bars represent the standard error of the mean.

Figure 4

Explaining successful designs. (a) The rotational mean square displacement of the budding and nonbudding population ($\epsilon =11kT$, $N=22$). The error bars represent the standard error of the mean for each subpopulation. The inset shows a sample rotational trajectory for one ligand on one particle from each subpopulation, while the top panel shows the count of the budding events. (b) Free energy as a function of a membrane wrapping for two sample particles from the budding and nonbudding populations ($\epsilon =11kT$, $N=22$). The insets show each particle at their free energy minima.