Polymer brush-induced depletion interactions and clustering of membrane proteins.

We investigate the effect of mobile polymer brushes on proteins embedded in biological membranes by employing both Asakura-Oosawa type of theoretical model and coarse-grained molecular dynamics simulations. The brush polymer-induced depletion attraction between proteins changes non-monotonically with the size of brush. The depletion interaction, which is determined by the ratio of the protein size to the grafting distance between brush polymers, increases linearly with the brush size as long as the polymer brush height is shorter than the protein size. When the brush height exceeds the protein size, however, the depletion attraction among proteins is slightly reduced. We also explore the possibility of the brush polymer-induced assembly of a large protein cluster, which can be related to one of many molecular mechanisms underlying recent experimental observations of integrin nanocluster formation and signaling.

Aggregation of flexible polyelectrolytes: Phase diagram and dynamics.

Similarly charged polymers in solution, known as polyelectrolytes, are known to form aggregated structures in the presence of oppositely charged counterions. Understanding the dependence of the equilibrium phases and the dynamics of the process of aggregation on parameters such as backbone flexibility and charge density of such polymers is crucial for insights into various biological processes which involve biological polyelectrolytes such as protein, DNA, etc. Here, we use large-scale coarse-grained molecular dynamics simulations to obtain the phase diagram of the aggregated structures of flexible charged polymers and characterize the morphology of the aggregates as well as the aggregation dynamics, in the presence of trivalent counterions. Three different phases are observed depending on the charge density: no aggregation, a finite bundle phase where multiple small aggregates coexist with a large aggregate and a fully phase separated phase. We show that the flexibility of the polymer backbone causes strong entanglement between charged polymers leading to additional time scales in the aggregation process. Such slowing down of the aggregation dynamics results in the exponent, characterizing the power law decay of the number of aggregates with time, to be dependent on the charge density of the polymers. These results are contrary to those obtained for rigid polyelectrolytes, emphasizing the role of backbone flexibility.

Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent.

We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length lB, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain Rg on lB characterized by Rg ∼ l. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.

Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes.

We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius R_{g} on the reduced Bjerrum length ℓ_{B} and find two different regimes. In the first one, called a weak electrostatic regime, R_{g}∼ℓ_{B}^{-1/2}, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find R_{g}∼ℓ_{B}^{-1/5}. To explain the novel regime we modify the counterion-fluctuation theory.

Aggregation dynamics of rigid polyelectrolytes.

Similarly charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of such rigid polyelectrolytes are studied using large scale molecular dynamics simulations. We find that the morphology of the aggregates depends on the value of the charge density of the polymers. For values close to the critical value, the shape of the aggregates is cylindrical with height equal to the length of a single polyelectrolyte chain. However, for larger values of charge, the linear extent of the aggregates increases as more and more polymers aggregate. In both the cases, we show that the number of aggregates decrease with time as power laws with exponents that are not numerically distinguishable from each other and are independent of charge density of the polymers, valency of the counterions, density, and length of the polyelectrolyte chain. We model the aggregation dynamics using the Smoluchowski coagulation equation with kernels determined from the molecular dynamics simulations and justify the numerically obtained value of the exponent. Our results suggest that once counterions condense, effective interactions between polyelectrolyte chains short-ranged and the aggregation of polyelectrolytes are diffusion-limited.