Role of cross-links in bundle formation, phase separation and gelation of long filaments

We predict the thermodynamic and structural behavior of solutions of long cross-linked filaments. We find that at the mean field level, the entropy of self-assembled junctions induces an effective attraction between the filaments that can result in a phase separation into a connected network, in equilibrium with a dilute phase. A connected network can also be formed in a non-thermodynamic transition upon increase of the chain, or cross link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network, to anisotropic bundles of rods tightly bound by cross links, that is triggered by the interplay between the configurational entropy of the cross-link distribution among the rods, and the rotational and translational entropy of the rods.Comment: typos and graphics corrected; 6 pages 1 figur

The Immunity of Polymer-Microemulsion Networks

The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution $p(\sigma)$ of the number of polymers between a pair of droplets, and show that gel immunity decreases as the variance of $p(\sigma)$ increases. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance, and may result in a bimodal $p(\sigma)$.Comment: Corrected typo

Physical modelling of multivalent interactions in the nuclear pore complex

In the nuclear pore complex (NPC), intrinsically disordered proteins (FG Nups) along with their interactions with more globular proteins called nuclear transport receptors (NTRs) are vital to the selectivity of transport into and out of the cell nucleus. While such interactions can be modelled at different levels of coarse graining, in-vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, where the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and non-cohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion, and compare them to experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties, but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences

Effects of jamming on non-equilibrium transport times in nano-channels

Many biological channels perform highly selective transport without direct input of metabolic energy and without transitions from a 'closed' to an 'open' state during transport. Mechanisms of selectivity of such channels serve as an inspiration for creation of artificial nano-molecular sorting devices and bio-sensors. To elucidate the transport mechanisms, it is important to understand the transport on the single molecule level in the experimentally relevant regime when multiple particles are crowded in the channel. In this paper we analyze the effects of inter-particle crowding on the non-equilibrium transport times through a finite-length channel by means of analytical theory and computer simulations

Efficiency, selectivity and robustness of the nuclear pore complex transport

All materials enter or exit the cell nucleus through nuclear pore complexes (NPCs), efficient transport devices that combine high selectivity and throughput. A central feature of this transport is the binding of cargo-carrying soluble transport factors to flexible, unstructured proteinaceous filaments called FG-nups that line the NPC. We have modeled the dynamics of transport factors and their interaction with the flexible FG-nups as diffusion in an effective potential, using both analytical theory and computer simulations. We show that specific binding of transport factors to the FG-nups facilitates transport and provides the mechanism of selectivity. We show that the high selectivity of transport can be accounted for by competition for both binding sites and space inside the NPC, which selects for transport factors over other macromolecules that interact only non-specifically with the NPC. We also show that transport is relatively insensitive to changes in the number and distribution of FG-nups in the NPC, due mainly to their flexibility; this accounts for recent experiments where up to half of the total mass of the NPC has been deleted, without abolishing the transport. Notably, we demonstrate that previously established physical and structural properties of the NPC can account for observed features of nucleocytoplasmic transport. Finally, our results suggest strategies for creation of artificial nano-molecular sorting devices.Comment: 38 pages, six figure

Entropic phase separation of linked beads

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase separation mechanism of the system is extremely robust and does not depend on the particlular physical realization of the network. The discussed model applies as well to other polymer linked particle aggregates, such as nano-particles connected with short DNA linkers

Thermodynamics of Competitive Molecular Channel Transport: Application to Artificial Nuclear Pores

In an analytical model channel transport is analyzed as a function of key parameters, determining efficiency and selectivity of particle transport in a competitive molecular environment. These key parameters are the concentration of particles, solvent-channel exchange dynamics, as well as particle-in-channel- and interparticle interaction. These parameters are explicitly related to translocation dynamics and channel occupation probability. Slowing down the exchange dynamics at the channel ends, or elevating the particle concentration reduces the in-channel binding strength necessary to maintain maximum transport. Optimized in-channel interaction may even shift from binding to repulsion. A simple equation gives the interrelation of access dynamics and concentration at this transition point. The model is readily transferred to competitive transport of different species, each of them having their individual in-channel affinity. Combinations of channel affinities are determined which differentially favor selectivity of certain species on the cost of others. Selectivity for a species increases if its in-channel binding enhances the species' translocation probablity when compared to that of the other species. Selectivity increases particularly for a wide binding site, long channels, and fast access dynamics. Recent experiments on competitive transport of in-channel binding and inert molecules through artificial nuclear pores serve as a paradigm for our model. It explains qualitatively and quantitatively how binding molecules are favored for transport at the cost of the transport of inert molecules

A swollen phase observed between the liquid-crystalline phase and the interdigitated phase induced by pressure and/or adding ethanol in DPPC aqueous solution

A swollen phase, in which the mean repeat distance of lipid bilayers is larger than the other phases, is found between the liquid-crystalline phase and the interdigitated gel phase in DPPC aqueous solution. Temperature, pressure and ethanol concentration dependences of the structure were investigated by small-angle neutron scattering, and a bending rigidity of lipid bilayers was by neutron spin echo. The nature of the swollen phase is similar to the anomalous swelling reported previously. However, the temperature dependence of the mean repeat distance and the bending rigidity of lipid bilayers are different. This phase could be a precursor to the interdigitated gel phase induced by pressure and/or adding ethanol.Comment: 7 pages, 6 figure

Thermodynamics and structure of self-assembled networks

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold junctions leads to a first order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed.Comment: Submitted to Phys. Rev.