Adsorption and encapsulation of flexible polyelectrolytes in charged spherical vesicles

Free energy calculations shed light on the nuclear pore complex's selective barrier nature

The nuclear pore complex (NPC) is the exclusive gateway for traffic control across the nuclear envelope. Although smaller cargoes (less than 5-9 nm in size) can freely diffuse through the NPC, the passage of larger cargoes is restricted to those accompanied by nuclear transport receptors (NTRs). This selective barrier nature of the NPC is putatively associated with the intrinsically disordered, phenylalanine-glycine repeat-domains containing nucleoporins, termed FG-Nups. The precise mechanism underlying how FG-Nups carry out such an exquisite task at high throughputs has, however, remained elusive and the subject of various hypotheses. From the thermodynamics perspective, free energy analysis can be a way to determine cargo's transportability because the traffic through the NPC must be in the direction of reducing the free energy. In this study, we developed a computational model to evaluate the free energy composed of the conformational entropy of FG-Nups and the energetic gain associated with binding interactions between FG-Nups and NTRs and investigated whether these physical features can be the basis of NPC's selectivity. Our results showed that the reduction in conformational entropy by inserting a cargo into the NPC increased the free energy by an amount substantially greater than the thermal energy (≫kBT), whereas the free energy change was negligible ( Collapse

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MESH Headings

• Active Transport, Cell Nucleus
• Entropy
• Nuclear Pore/metabolism
• Nuclear Pore Complex Proteins/metabolism
• Phenylalanine/metabolism

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Affiliation(s)

Atsushi Matsuda Molecular Cell Biomechanics Laboratory, Departments of Bioengineering and Mechanical Engineering, University of California Berkeley, Berkeley, California
Mohammad R K Mofrad Molecular Cell Biomechanics Laboratory, Departments of Bioengineering and Mechanical Engineering, University of California Berkeley, Berkeley, California; Molecular Biophysics and Integrative Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California.

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Theory and experiment of chain length effects on the adsorption of polyelectrolytes onto spherical particles: the long and the short of it

We study here the role of polyelectrolyte chain length, that is number of repeat units (mers), in the competitive adsorption of a simple model polyanion, poly(acrylic acid), onto 85 nm spherical silica particles capped with a model polycation, poly(allylamine hydrochloride). Performing fluorescence spectroscopy experiments, we measured chain-length dependence of dilute aqueous polyelectrolyte adsorption, at full surface coverage, onto an oppositely charged polyelectrolyte overtop spherical silica nanoparticles (10-3 g L-1). Preferential adsorption was determined by comparing the characteristic fluorescence intensities of the two fluorophore-labeled and narrowly disperse polyacrylic acid samples (NMA-PAA450k and Dan-PAA2k) of 450k- and 2k-molecular weight (6250- and 28-mers), respectively. To compare and validate experimental results, a lattice model was developed for computing the probabilities of the different arrangements of two polymer chain lengths of polyacrylic acid on the surface of the silica nanosphere. We then determined which numbers of long and short adsorbed chains corresponded to the most configurations in our model. Both spectroscopic experiment results and the combinatorial model demonstrated that there is an entropic preference for complete adsorption of the longer 450k polyacrylic acid chain vs. 2k. This study provides insights on entropy driven chain-length dependence of polyelectrolyte adsorption onto spherical nanoparticle surfaces for directing and optimizing their layer-by-layer self-assembly in organic films.

Conformational properties of complexes of poly(propylene imine) dendrimers with linear polyelectrolytes in dilute solutions

This study investigates the conformational properties of complexes of poly(propylene imine) dendrimers with a linear polyelectrolyte (LPE) at neutral pH in an aqueous solution via molecular dynamics simulations. Various conformational properties, such as the atomic density profile, counterion density distribution, charge distribution, cavity volume, and the static structure factor are studied as a function of the charge and chain length of the LPE. The lower generation dendrimer complexes encapsulate the shorter linear PE chains, while the longer PE chains are adsorbed on the dendrimer surface that screen the surface charge and prevent the penetration of the counterions and water molecules. However, the overall charge of the higher generation dendrimers is not neutralized by the charge of the PE chains, which results in chloride counterion penetration within the dendrimers. The adsorption of the PE chains on the dendrimers is also verified from the charge distribution of the dendrimer-PE complexes. The charge on the lower generation dendrimer complexes is overcompensated by the longer PE chains resulting in an overall negative charge on the complexes, while the PE chains do not completely neutralize the charge of the higher generation dendrimers and produce positively charged complexes. The results of the structure factor indicate a conformational transition of the dendrimer-PE complexes from a dense compact structure to an open one with an increase in the PE chain length. This transition is characterized by an increase in the cavity volume in dendrimers with an increase in the PE chain length.

Critical adsorption of multiple polyelectrolytes onto a nanosphere: splitting the adsorption-desorption transition boundary

Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.

Manipulation of Confined Polyelectrolyte Conformations through Dielectric Mismatch

We demonstrate that a highly charged polyelectrolyte confined in a spherical cavity undergoes reversible transformations between amorphous conformations and a four-fold symmetry morphology as a function of dielectric mismatch between the media inside and outside the cavity. Surface polarization due to dielectric mismatch exhibits an extra "confinement" effect, which is most pronounced within a certain range of the cavity radius and the electrostatic strength between the monomers and counterions and multivalent counterions. For cavities with a charged surface, surface polarization leads to an increased amount of counterions adsorbed in the outer side, further compressing the confined polyelectrolyte into a four-fold symmetry morphology. The equilibrium conformation of the chain is dependent upon several key factors including the relative permittivities of the media inside and outside the cavity, multivalent counterion concentration, cavity radius relative to the chain length, and interface charge density. Our findings offer insights into the effects of dielectric mismatch in packaging and delivery of polyelectrolytes across media with different relative permittivities. Moreover, the reversible transformation of the polyelectrolyte conformations in response to environmental permittivity allows for potential applications in biosensing and medical monitoring.

Critical adsorption of periodic and random polyampholytes onto charged surfaces

How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration.