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Abstract:

The crossover from single-file diffusion, where the mean-square displacement scales as (x2) to approximately t(1/2), to normal Fickian diffusion, where (x2) to approximately t, is studied as a function of channel width for colloidal particles. By comparing Brownian dynamics to a hybrid molecular dynamics and mesoscopic simulation technique, we can study the effect of hydrodynamic interactions on the single file mobility and on the crossover to Fickian diffusion for wider channel widths. For disc-like particles with a steep interparticle repulsion, the single file mobilities for different particle densities are well described by the exactly solvable hard-rod model. This holds both for simulations that include hydrodynamics, as well as for those that do not. When the single file constraint is lifted, then for particles of diameter sigma and pipe of width L such that (L - 2sigma)/sigma = deltac << 1, the particles can be described as hopping past one-another in an average time t(hop). For shorter times t << t(hop) the particles still exhibit sub-diffusive behaviour, but at longer times t >> t(hop), normal Fickian diffusion sets in with an effective diffusion constant Dhop to approximately 1/ mean square root of t(hop). For the Brownian particles, t(hop) to approximately deltac(-2) when deltac << 1, but when hydrodynamic interactions are included, we find a stronger dependence than deltac(-2). We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels.

Abstract:

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures.

Abstract:

We study the self-assembly behavior of patchy particles with "proteinlike" interactions that can be considered as a minimal model for the assembly of viral capsids and other shell-like protein complexes. We thoroughly explore the thermodynamics and dynamics of self-assembly as a function of the parameters of the model and find robust assembly of all target structures considered. Optimal assembly occurs in the region of parameter space where a free energy barrier regulates the rate of nucleation, thus preventing the premature exhaustion of the supply of monomers that can lead to the formation of incomplete shells. The interactions also need to be specific enough to prevent the assembly of malformed shells, but while maintaining kinetic accessibility. Free energy landscapes computed for our model have a funnel-like topography guiding the system to form the target structure and show that the torsional component of the interparticle interactions prevents the formation of disordered aggregates that would otherwise act as kinetic traps.

Abstract:

We apply a simple model system of patchy particles to study monodisperse self-assembly using the Platonic solids as target structures. We find marked differences between the assembly behaviors of the different systems. Tetrahedra, octahedral, and icosahedra assemble easily, while cubes are more challenging and dodecahedra do not assemble. We relate these differences to the kinetics and thermodynamics of assembly, with the formation of large disordered aggregates a particular important competitor to correct assembly. In particular, the free energy landscapes of those targets that are easy to assemble are funnel-like, whereas for the dodecahedral system the landscape is relatively flat with little driving force to facilitate escape from disordered aggregates.

Abstract:

We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands: duplex hybridization, single-stranded stacking and hairpin formation, and also captures the essential structural properties of DNA: the helical pitch, persistence length and torsional stiffness of double-stranded molecules, as well as the comparative flexibility of unstacked single strands. We apply the model to calculate the detailed free-energy landscape of one full cycle of DNA 'tweezers', a simple machine driven by hybridization and strand displacement.