Precise control of polymer coated nanopores by nanoparticle additives: Insights from computational modeling

Colloidal adsorption in planar polymeric brushes

The design of nano-functionalised membranes or channels, able to effectively adsorb pollutants in aqueous solutions, is a topic that is gaining a great deal of attention in the materials science community. With this work we explore, through a combination of scaling theories and molecular dynamics simulations, the adsorption of spherical non-deformable colloidal nanoparticles within planar polymeric brushes. Our strategy is twofold: first, we generalise the Alexander-de Gennes theory for planar homopolymeric brushes to the case of diblock copolymer brushes, then we map the adsorbing homopolymeric brushes onto a diblock copolymer system, where the adsorbed colloids and all interacting monomers are considered monomers in bad solvent and we apply the generalised scaling theory to this effective diblock copolymer. This allows the prediction of the average conformation of the grafted substrate, i.e. its average height, as a function of the amount of loaded particles, as well as the introduction of a continuous mapping between a homopolymeric brush, the fraction of loaded particles and the average height of the adsorbing substrate.

Morphology of Polymer Brushes in the Presence of Attractive Nanoparticles: Effects of Temperature

We study the role of temperature on the structure of pure polymer brushes and their mixture with attractive nanoparticles in flat and cylindrical geometries. It has previously been established that the addition of such nanoparticles causes the polymer brush to collapse and the intensity of the collapse depends on the attraction strength, the nanoparticle diameter, and the grafting density. In this work, we carry out molecular dynamics simulation under good solvent conditions to show how the collapse transition is affected by the temperature, for both plane grafted and inside-cylinder grafted brushes. We first examine the pure brush morphology and verify that the brush height is insensitive to temperature changes in both planar and cylindrical geometries, as expected for a polymer brush in a good solvent. On the other hand, for both system geometries, the brush structure in the presence of attractive nanoparticles is quite responsive to temperature changes. Generally speaking, for a given nanoparticle concentration, increasing the temperature causes the brush height to increase. A brush which contracts when nanoparticles are added eventually swells beyond its pure brush height as the system temperature is increased. The combination of two easily controlled external parameters, namely, concentration of nanoparticles in solution and temperature, allows for sensitive and reversible adjustment of the polymer brush height, a feature which could be exploited in designing smart polymer devices.

Physics of the Nuclear Pore Complex: Theory, Modeling and Experiment

The hallmark of eukaryotic cells is the nucleus that contains the genome, enclosed by a physical barrier known as the nuclear envelope (NE). On the one hand, this compartmentalization endows the eukaryotic cells with high regulatory complexity and flexibility. On the other hand, it poses a tremendous logistic and energetic problem of transporting millions of molecules per second across the nuclear envelope, to facilitate their biological function in all compartments of the cell. Therefore, eukaryotes have evolved a molecular "nanomachine" known as the Nuclear Pore Complex (NPC). Embedded in the nuclear envelope, NPCs control and regulate all the bi-directional transport between the cell nucleus and the cytoplasm. NPCs combine high molecular specificity of transport with high throughput and speed, and are highly robust with respect to molecular noise and structural perturbations. Remarkably, the functional mechanisms of NPC transport are highly conserved among eukaryotes, from yeast to humans, despite significant differences in the molecular components among various species. The NPC is the largest macromolecular complex in the cell. Yet, despite its significant complexity, it has become clear that its principles of operation can be largely understood based on fundamental physical concepts, as have emerged from a combination of experimental methods of molecular cell biology, biophysics, nanoscience and theoretical and computational modeling. Indeed, many aspects of NPC function can be recapitulated in artificial mimics with a drastically reduced complexity compared to biological pores. We review the current physical understanding of the NPC architecture and function, with the focus on the critical analysis of experimental studies in cells and artificial NPC mimics through the lens of theoretical and computational models. We also discuss the connections between the emerging concepts of NPC operation and other areas of biophysics and bionanotechnology.

Nanopore gates via reversible crosslinking of polymer brushes: a theoretical study

Polymer-brush-modified nanopores are synthetic structures inspired by the gated transport exhibited by their biological counterparts. This work theoretically analyzes how the reversible crosslinking of a polymer network by soluble species can be used to control transport through nanochannels and pores. The study was performed with a molecular theory that allows inhomogeneities in the three spatial dimensions and explicitly takes into account the size, shape and conformations of all molecular species, considers the intermolecular interactions between the polymers and the soluble crosslinkers and includes the presence of a translocating particle inside the pore. It is shown than increasing the concentration of the soluble crosslinkers in bulk solution leads to a gradual increase of its number within the pore until a critical bulk concentration is reached. At the critical concentration, the number of crosslinkers inside the pore increases abruptly. For long chains, this sudden transition triggers the collapse of the polymer brush to the center of the nanopore. The resulting structure increases the free-energy barrier that a translocating particle has to surmount to go across the pore and modifies the route of translocation from the axis of the pore to its walls. On the other hand, for short polymer chains the crosslinkers trigger the collapse of the brush to the pore walls, which reduces the translocation barrier.

Liquid and Droplet Transport in Brush-Coated Cylindrical Nanochannels: Brush-Assisted Droplet Formation

We study, by coarse-grained molecular dynamics simulations, equilibrium and flow properties of a liquid in cylindrical nanochannels, coated with polymer brushes. The parameters of the interaction potential model confer a chemical incompatibility between brush monomers and liquid particles. First, we study cylindrical channels whose radii are larger than the brush height and a continuous column of liquid forms at the center of the channel. These results are contrasted to the limiting case in which the radius of the cylinder is comparable to the brush height. In this second case, the grafted polymers interact across the channel and "close" it. We observe a train of droplets as the stable liquid morphology. The droplet size is comparable to the cylinder radius. By applying a constant body force onto the liquid, we induce a Poiseuille-like flow and investigate the morphology and flow rate as a function of driving force. Upon increasing the driving force, we encounter a nonequilibrium transition from a closed channel with slowly moving droplets to a flowing liquid thread at the center. The switching between these two states is reversible.

The Role of Cohesiveness in the Permeability of the Spatial Assemblies of FG Nucleoporins

Nuclear pore complexes (NPCs) conduct selective, bidirectional transport across the nuclear envelope. The NPC passageway is lined by intrinsically disordered proteins that contain hydrophobic phenylalanine-glycine (FG) motifs, known as FG nucleoporins (FG nups), that play the key role in the NPC transport mechanism. Cohesive interactions among the FG nups, which arise from the combination of hydrophobic, electrostatic, and other forces, have been hypothesized to control the morphology of the assemblies of FG nups in the NPC, as well as their permeability with respect to the transport proteins. However, the role of FG nup cohesiveness is still vigorously debated. Using coarse-grained polymer theory and numerical simulations, we study the effects of cohesiveness on the selective permeability of in vitro FG nup assemblies in different geometries that have served as proxies for the morphological and transport properties of the NPC. We show that in high-density FG nup assemblies, increase in cohesiveness leads to the decrease in their permeability, in accordance with the accepted view. On the other hand, the permeability of low-density assemblies is a nonmonotonic function of the cohesiveness, and a moderate increase in cohesiveness can enhance permeability. The density- and cohesiveness-dependent effects on permeability are explained by considering the free-energy cost associated with penetrating the FG nup assemblies. We discuss the implications of these findings for the organization and function of the NPC.

Controlling the Surface Properties of Binary Polymer Brush-Coated Colloids via Targeted Nanoparticles

This paper explores a novel mechanism for controlling the surface properties of polymer-coated colloids using targeted ("sticky") nanoparticles which attract monomers of certain polymer species. In our study, colloids are coated by two types of tethered polymer chains having different chemical properties. Attraction of nanoparticles to the monomers of one polymer type causes these polymer chains to contract toward the grafting surface, rendering the other type more exposed to the environment. Thus, the effective surface properties of the colloid are dominated by the intended polymer type. We use coarse-grained molecular dynamics (CGMD) simulation to demonstrate that introducing nanoparticles which interact preferentially with certain types of polymers makes it possible to switch between different surface properties of the colloid. This mechanism can in principle be exploited in drug delivery systems and self-assembly applications.

Interactions between a fluctuating polymer barrier and transport factors together with enzyme action are sufficient for selective and rapid transport through the nuclear pore complex

The nuclear pore complex, the only pathway for transport between the nucleus and cytoplasm, functions as a highly selective gate that blocks nonspecific macromolecules while allowing the rapid transport of tagged [transport factor (TF) bound] cargo up to an order of magnitude larger. The mechanism of this gate's operation is not yet fully understood and progress has been primarily hindered by the inherent complexity and multiscale nature of the problem. One needs to consider the hundreds of disordered proteins (phenylalanine glycine nucleoporins or FG nups) lining the pore, as well as their overall architecture and dynamics at the microsecond scale, while also accounting for transport at the millisecond scale across the entire pore. Here we formulate an approach that addresses transport properties over a large range of length and time scales. We do this by incorporating microscopic biophysical details, such as charge and specific TF-FG nup interactions, to compute the free energy landscape encountered by the cargo. We connect this to macroscopic transport by treating cargo translocation as a stochastic barrier crossing process and computing the current and the translocation time. We then identify distinct transport regimes (fast permeable, slow permeable, and impermeable) determined by the cargo size, TF affinity for FG nups, and the activity of the enzymes that cleave TFs from cargo. Our results, therefore provide an integrated picture of transport through the NPC, while highlighting how FG nup interactions with TFs and enzyme activity cooperate to produce selectivity and efficiency.

Gating Protein Transport in Solid State Nanopores by Single Molecule Recognition

Control of molecular translocation through nanoscale apertures is of great interest for DNA sequencing, biomolecular filters, and new platforms for single molecule analysis. However, methods for controlling the permeability of nanopores are very limited. Here, we show how nanopores functionalized with poly(ethylene glycol) brushes, which fully prevent protein translocation, can be reversibly gated to an "open" state by binding of single IgG antibodies that disrupt the macromolecular barrier. On the basis of surface plasmon resonance data we propose a two-state model describing the antibody-polymer interaction kinetics. Reversibly (weakly) bound antibodies decrease the protein exclusion height while irreversibly (strongly) bound antibodies do not. Our results are further supported by fluorescence readout from pore arrays and high-speed atomic force microscopy on single pores. This type of dynamic barrier control on the nanoscale provides new possibilities for biomolecular separation and analysis.

Polymer brushes in solid-state nanopores form an impenetrable entropic barrier for proteins

Polymer brushes are widely used to prevent the adsorption of proteins, but the mechanisms by which they operate have remained heavily debated for many decades. We show conclusive evidence that a polymer brush can be a remarkably strong kinetic barrier towards proteins by using poly(ethylene glycol) grafted to the sidewalls of pores in 30 nm thin gold films. Despite consisting of about 90% water, the free coils seal apertures up to 100 nm entirely with respect to serum protein translocation, as monitored label-free through the plasmonic activity of the nanopores. The conclusions are further supported by atomic force microscopy and fluorescence microscopy. A theoretical model indicates that the brush undergoes a morphology transition to a sealing state when the ratio between the extension and the radius of curvature is approximately 0.8. The brush-sealed pores represent a new type of ultrathin filter with potential applications in bioanalytical systems.

Adhesion and Separation of Nanoparticles on Polymer-Grafted Porous Substrates

This work explores interactions of functionalized nanoparticles (NP) with polymer brushes (PB) in a binary mixture of good and poor solvents. NP-PB systems are used in multiple applications, and we are particularly interested in the problem of chromatographic separation of NPs on polymer-grafted porous columns. This process involves NP flow through the pore channels with walls covered by PBs. NP-PB adhesion is governed by adsorption of polymer chains to NP surface and entropic repulsion caused by the polymer chain confinement between NP and the channel wall. Both factors depend on the solvent composition, variation of which causes contraction or expansion of PB. Using dissipative particle dynamics simulations in conjunction with the ghost tweezers free energy calculation technique, we examine the free energy landscapes of functionalized NPs within PB-grafted channels depending on the solvent composition at different PB grafting densities and polymer-solvent affinities. The free energy landscape determines the probability of NP location at a given distance to the surface, positions of equilibrium adhesion states, and the Henry constant that characterizes adsorption equilibrium and NP partitioning between the stationary phase of PB and mobile phase of flowing solvent. We analyze NP transport through a polymer-grafted channel and calculate the mean velocity and retention time of NP depending on the NP size and solvent composition. We find that, with the increase of the bad (poor) solvent fraction and respective PB contraction, NP separation exhibits a transition from the hydrodynamic size exclusion regime with larger NPs having shorter retention time to the adsorption regime with smaller NPs having shorter retention time. The observed reversal of the sequence of elution is reminiscent of the critical condition in polymer chromatography at which the retention time is molecular weight independent. This finding suggests the possibility of the existence of an analogous special regime in nanoparticle chromatography at which NPs with like surface properties elute together regardless of their size. The latter has important practical implications: NPs can be separated by surface chemistry rather than by their size employing the gradient mode of elution with controlled variation of solvent composition.

Investigating molecular crowding within nuclear pores using polarization-PALM

The key component of the nuclear pore complex (NPC) controlling permeability, selectivity, and the speed of nucleocytoplasmic transport is an assembly of natively unfolded polypeptides, which contain phenylalanine-glycine (FG) binding sites for nuclear transport receptors. The architecture and dynamics of the FG-network have been refractory to characterization due to the paucity of experimental methods able to probe the mobility and density of the FG-polypeptides and embedded macromolecules within intact NPCs. Combining fluorescence polarization, super-resolution microscopy, and mathematical analyses, we examined the rotational mobility of fluorescent probes at various locations within the FG-network under different conditions. We demonstrate that polarization PALM (p-PALM) provides a rich source of information about low rotational mobilities that are inaccessible with bulk fluorescence anisotropy approaches, and anticipate that p-PALM is well-suited to explore numerous crowded cellular environments. In total, our findings indicate that the NPC's internal organization consists of multiple dynamic environments with different local properties.

Protein Transport by the Nuclear Pore Complex: Simple Biophysics of a Complex Biomachine

In eukaryotic cells, transport of molecules between the nucleus and the cytoplasm is facilitated by highly selective and efficient biomachines known as nuclear pore complexes (NPCs). The structural details of NPCs vary across species, with many of their constituent proteins exhibiting relatively low sequence conservation; yet the NPC as a whole retains its general architecture and mechanism of action in all eukaryotes from yeast to humans. This functional conservation in the absence of precise molecular conservation suggests that many aspects of the NPC transport mechanism may be understood based on general biophysical considerations. Accordingly, some aspects of NPC function have been recapitulated in artificial nanochannel mimics, even though they lack certain molecular elements of the endogenous NPC. Herein, we review biophysical aspects of NPC architecture and function and cover recent progress in the field. We also review recent advances in man-made molecular filters inspired by NPCs, and their applications in nanotechnology. We conclude the review with an outlook on outstanding questions in the field and biomedical aspects of NPC transport.