Map conformational landscapes of intrinsically disordered proteins with polymer physics quantities.

Disordered proteins are conformationally flexible proteins that are biologically important and have been implicated in devastating diseases such as Alzheimer's disease and cancer. Unlike stably folded structured proteins, disordered proteins sample a range of different conformations that needs to be accounted for. Here, we treat disordered proteins as polymer chains, and compute a dimensionless quantity called instantaneous shape ratio (Rs), as Rs = Ree2/Rg2, where Ree is end-to-end distance and Rg is radius of gyration. Extended protein conformations tend to have high Ree compared with Rg, and thus have high Rs values, whereas compact conformations have smaller Rs values. We use a scatter plot of Rs (representing shape) against Rg (representing size) as a simple map of conformational landscapes. We first examine the conformational landscape of simple polymer models such as Random Walk, Self-Avoiding Walk, and Gaussian Walk (GW), and we notice that all protein/polymer maps lie within the boundaries of the GW map. We thus use the GW map as a reference and, to assess conformational diversity, we compute the fraction of the GW conformations (fC) covered by each protein/polymer. Disordered proteins all have high fC scores, consistent with their disordered nature. Each disordered protein accesses a different region of the reference map, revealing differences in their conformational ensembles. We additionally examine the conformational maps of the nonviral gene delivery vector polyethyleneimine at various protonation states, and find that they resemble disordered proteins, with coverage of the reference map decreasing with increasing protonation state, indicating decreasing conformational diversity. We propose that our method of combining Rs and Rg in a scatter plot generates a simple, meaningful map of the conformational landscape of a disordered protein, which in turn can be used to assess conformational diversity of disordered proteins.

Coarse-grained Simulations of the Impact of Chain Length and Stiffness on the Formation and Aggregation of Polyelectrolyte Complexes.

Polyelectrolyte complexes formed from nucleic acids and synthetic polycations have been studied because of their potential in gene delivery. Coarse-grained molecular dynamics simulations are performed to examine the impact of chain length and polyanion stiffness on polyplex formation and aggregation. Polyplexes containing single polyanion chain fall into three structural regimes depending on polyanion stiffness: flexible polyanions form collapsed complexes, semiflexible polyanions form various morphologies including toroids and hairpins, and stiff polyanions form rod-like structures. Polyplex size generally decreases as polycation length increases. Aggregation (i.e., formation of complexes containing multiple polyanions) is observed in some simulations containing multiple polyanions and an excess of short polycations. Aggregation is observed to only occur for semiflexible and stiff polyanions and is promoted by shorter polycation lengths. Simulations of short, stiff polyanions condensed by long polycations are used as a model for siRNA gene delivery complexes. These simulations show multiple polyanions are spaced out along the polycation with polyanion-polyanion interactions, usually limited to overlapping chain ends. These structures differ from aggregates of longer polyanions in which the polyanions are packed together in parallel, forming bundles.