Nanoscale insight into silk-like protein self-assembly: effect of design and number of repeat units.

By means of replica exchange molecular dynamics simulations we investigate how the length of a silk-like, alternating diblock oligopeptide influences its secondary and quaternary structure. We carry out simulations for two protein sizes consisting of three and five blocks, and study the stability of a single protein, a dimer, a trimer and a tetramer. Initial configurations of our simulations are ß-roll and ß-sheet structures. We find that for the triblock the secondary and quaternary structures upto and including the tetramer are unstable: the proteins melt into random coil structures and the aggregates disassemble either completely or partially. We attribute this to the competition between conformational entropy of the proteins and the formation of hydrogen bonds and hydrophobic interactions between proteins. This is confirmed by our simulations on the pentablock proteins, where we find that, as the number of monomers in the aggregate increases, individual monomers form more hydrogen bonds whereas their solvent accessible surface area decreases. For the pentablock ß-sheet protein, the monomer and the dimer melt as well, although for the ß-roll protein only the monomer melts. For both trimers and tetramers remain stable. Apparently, for these the entropy loss of forming ß-rolls and ß-sheets is compensated for in the free-energy gain due to the hydrogen-bonding and hydrophobic interactions. We also find that the middle monomers in the trimers and tetramers are conformationally much more stable than the ones on the top and the bottom. Interestingly, the latter are more stable on the tetramer than on the trimer, suggesting that as the number of monomers increases protein-protein interactions cooperatively stabilize the assembly. According to our simulations, the ß-roll and ß-sheet aggregates must be approximately equally stable.

Effect of bending flexibility on the phase behavior and dynamics of rods.

We study by means of molecular and Brownian dynamics simulations the influence of bending flexibility on the phase behavior and dynamics of monodisperse hard filamentous particles with an aspect ratio of 8 and persistence lengths equal to 3 and 11 times the particle length. Although our particles are much shorter, the latter corresponds to the values for wild-type and mutant fd virus particles that have been subject of a recent experimental study, where the diffusion of these particles in the nematic and smectic-A phase was investigated by means of video fluorescence microscopy [E. Pouget, E. Grelet, and M. P. Lettinga, Phys. Rev. E 84, 041704 (2011)]. In agreement with theoretical predictions and simulations, we find that for the more flexible particles (shorter persistence length) the nematic (N) to smectic-A (Sm-A) phase transition shifts to larger values of the particle density. Interestingly, we find that for the more rigid particles (larger persistence length), the smectic layer-to-layer distance decreases monotonically with increasing density, whereas for the more flexible ones, it first increases, reaches a maximum and then decreases. For our more flexible particles, we find a smectic-B phase at sufficiently high densities. Moreover, in line with experimental observations and theoretical predictions, we find heterogeneous dynamics in the Sm-A phase, in which particles hop between the smectic layers. We compare the diffusion of our two types of particle at identical values of smectic order parameter, and find that flexibility does not change the diffusive behavior of particles along the director yet significantly slows down the diffusion perpendicular to it. In our simulations, the ratio of diffusion constants along and perpendicular to the director decreases just beyond the N-Sm-A phase transition for both our stiff and more flexible particles.

Prediction of the structure of a silk-like protein in oligomeric states using explicit and implicit solvent models.

We perform Replica Exchange Molecular Dynamics (REMD) simulations on a silk-like protein design with amino-acid sequence [(Gly-Ala)3-Gly-Glu]5 to investigate the stability of a single protein, a dimer, a trimer and a tetramer made up of these proteins starting from ß-roll and ß-sheet structures in both explicit (TIP3P) and implicit (GBSA) solvent models. Our simulation results for the implicit solvent model agree with those for the explicit solvent model for simulation times up to the longest tested, being 30 ns per replica. From this we infer that the implicit solvent model that we use is reliable, allowing us to reach much longer time scales (up to 200 ns per replica). We find that the self-assembly of fibers of these proteins in solution must be a nucleated process, involving nuclei made up of at least three monomers. We also find that the conformation of the protein changes upon assembly, i.e., there is a transition from a disordered globular state to an ordered ß-sheet structure in the self-assembled state of aggregates containing more than two monomers. This indicates that autosteric effects must be important in the polymerization of this protein, reminiscent of what is observed for ß-amyloids. Our findings are consistent with recent experimental results on a protein with an amino acid sequence similar to that of the protein we study.

Collective stringlike motion of semiflexible filamentous particles in columnar liquid crystalline phases.

We study, by means of Brownian dynamics simulations, heterogeneous dynamics in a dense columnar phase of monodisperse hard filamentous particles, and find that in a background of barely moving particles, some particles occasionally engage in a fast coherent string-type motion similar to what is observed in glassy states of isometric particles. This fast motion is triggered by the exchange of particles between two or more columns at different positions in the columns, which leads to sudden displacement of particles between these positions. The distribution of particle displacements shows a pronounced peak at one particle length. We perform our simulations with particles of different persistence lengths and find that for more flexible particles, the number of jump events increases. As the number of particles in the columns increases with system size for a given linear fraction of particles in the columns, the peak in the distribution becomes wider and, for sufficiently large systems, the peak disappears completely. This is associated with the increase in the magnitude of fluctuations in the motion of particles as the system size increases. Our simulation results explain recent experimental observations on single-particle motion in dense columnar phases in aqueous dispersions of filamentous virus particles.

Size and boundary effects on the diffusive behavior of elongated colloidal particles in a strongly confined dense dispersion.

In very recent experimental work, diffusive motion of individual particles in a dense columnar phase of colloidal suspension of filamentous virus particles probed by means of fluorescence video microscopy [S. Naderi, E. Pouget, P. Ballesta, P. van der Schoot, M. P. Lettinga, and E. Grelet, Phys. Rev. Lett. 111, 037801 (2013)]. Rare events were observed in which the minority fluorescently labeled particles engage in sudden, jump-like motion along the director. The jump length distribution turned out to be biased towards a half and a full particle length. We suggest these events may be indicative of two types of particle motion, one in which particles overtake other particles in the same column and the other where a column re-equilibrates after a particle leaves a column either to enter into another column or into a void defect on the lattice. Our Brownian dynamics simulations of a quasi one-dimensional system of semi-flexible particles, subject to a Gaussian confinement potentials mimicking the effects of the self-consistent molecular field in the columnar phase, support this idea. We find that the frequency of overtaking depends on the linear fraction of particles and the steepness of the confining potential. The re-equilibration time of a column after a particle is removed from it is much shorter than the self-diffusion timescale. For the case of large system sizes and periodic boundary conditions, overtaking events do not present themselves as full-length jumps. Only if the boundary conditions are reflecting and the system is sufficiently small, full length jumps are observed in particle trajectories. The reason is that only then the amplitude of the background fluctuations is smaller than a particle length. Increasing the bending flexibility of the particles on the one hand enhances the ability of particles to overtake each other but on the other it enhances fluctuations that wash out full jumps in particle trajectories.

Fractional hoppinglike motion in columnar mesophases of semiflexible rodlike particles.

We report on single-particle dynamics of strongly interacting filamentous fd virus particles in the liquid-crystalline columnar state in aqueous solution. From fluorescence microscopy, we find that rare, discrete events take place, in which individual particles engage in sudden, jumplike motion along the main rod axis. The jump length distribution is bimodal and centered at half- and full-particle lengths. Our Brownian dynamics simulations of hard semiflexible particles mimic our experiments and indicate that full-length jumps must be due to collective dynamics in which particles move in stringlike fashion in and between neighboring columns, while half jumps arise as a result of particles moving into defects. We find that the finite domain structure of the columnar phase strongly influences the observed dynamics.