Finite-Size Effects in Simulations of Peptide/Lipid Assembly

System size effects on the free energy landscapes from molecular dynamics of phase-separating bilayers

The "lipid raft" hypothesis proposes that cell membranes contain distinct domains of varying lipid compositions, where "rafts" of ordered lipids and cholesterol coexist with disordered lipid regions. Experimental and theoretical phase diagrams of model membranes have revealed multiple coexisting phases. Molecular dynamics (MD) simulations can also capture spontaneous phase separation of bilayers. However, these methods merely determine the sign of the free energy change upon phase separation-whether or not it is favorable-but not the amplitude. Recently, we developed a workflow to compute the free energy of phase separation from MD simulations using the weighted ensemble method. However, while theoretical treatments generally focus on infinite systems and experimental measurements on mesoscopic to macroscopic systems, MD simulations are comparatively small. Therefore, if we are to put the results of these calculations into the appropriate context, we need to understand the effects the finite size of the simulation has on the computed free energy landscapes. In this study, we investigate this phenomenon by computing free energy profiles for a model phase-separating system as a function of system size, ranging from 324 to 10 110 lipids. The results suggest that, within the limits of statistical uncertainty, bulk-like behavior emerges once the systems contain roughly 4000 lipids.

Microscopically segregated ligand distribution in co-assembled peptide-amphiphile nanofibers

Peptide amphiphiles (PAs) self-assemble into cylindrical nanofibers with applications in protein purification, tissue engineering, and regenerative medicine. For these applications, functionalized PAs are often co-assembled with oppositely charged filler PAs. Finding the conditions at which these fibers are homogeneously mixed or segregated is crucial for the required application. We co-assemble negative C12VVEE fillers and positive C12VVKK-OEG4-Z33 ligands, which are important for antibody purifications. Our results show that the ligands tend to cluster and locally segregate in the fiber surfaces. The Z33s are overall neutral and form large aggregates in bulk solution due to short range attractions. However, full segregation of the C12VVKK-OEG4-Z33 is not observed in the cylindrical surface due to the electrostatic penalty of forming large domains of similarly charged molecules. This is commensurate with previous theoretical predictions, showing that the competition between short-range attractive interactions and long-range electrostatic repulsions leads to pattern formation in cylindrical surfaces. This work offers valuable insight into the design of functionalized nanofibers for various biomedical and chemical applications.

Ion-Induced PIP2 Clustering with Martini3: Modification of Phosphate-Ion Interactions and Comparison with CHARMM36

Phosphatidylinositol 4,5-bisphosphate (PIP2) is a critical lipid for cellular signaling. The specific phosphorylation of the inositol ring controls protein binding as well as clustering behavior. Two popular models to describe ion-mediated clustering of PIP2 are Martini3 (M3) and CHARMM36 (C36). Molecular dynamics simulations of PIP2-containing bilayers in solutions of potassium chloride, sodium chloride, and calcium chloride, and at two different resolutions are performed to understand the aggregation and the model parameters that drive it. The average M3 clusters of PIP2 in bilayers of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine and PIP2 bilayers in the presence of K+, Na+, or Ca2+ contained 2.2, 2.6, and 6.4 times more PIP2 than C36 clusters, respectively. Indeed, the Ca2+-containing systems often formed a single large aggregate. Reparametrization of the M3 ion-phosphate Lennard-Jones interaction energies to reproduce experimental osmotic pressure of sodium dimethyl phosphate (DMP), K[DMP], and Ca[DMP]2 solutions, the same experimental target as C36, yielded comparably sized PIP2 clusters for the two models. Furthermore, C36 and the modified M3 predict similar saturation of the phosphate groups with increasing Ca2+, although the coarse-grained model does not capture the cooperativity between K+ and Ca2+. This characterization of the M3 behavior in the presence of monovalent and divalent ions lays a foundation to study cation/protein/PIP2 clustering.

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.