Fluctuation-dissipation ratios in the dynamics of self-assembly

Abstract

We consider two seemingly very different self-assembly processes: formation of viral capsids and crystallization of sticky disks. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long-term fate of the system, based on the early stages of assembly.

Collective translational and rotational Monte Carlo moves for attractive particles

“…We use N C = 1/x, with x being a random number from the uniform distribution U(0,1). The scaling of the cluster selection can be used to approximate the Brownian dynamics by collective MC moves [9,26]. Although the time is nonphysical, the gradient of the MSD is constant, defining a diffusion coefficient for each simulation in Fig.…”

“…Second, event-driven Monte Carlo [36] displaces single particles, but selects and accepts them in a way which is dynamic. It would be interesting to see how these algorithms complement the VMMC methods in capturing the kinetic and thermodynamic crossover in glassy systems [26,37]. This paper aimed to clarify the way of creating collective translational and rotational Monte Carlo moves, based on local pairwise energy changes, and to shed more light on the technical details, as well as to provide a clear validation of the algorithm.…”

“…Since links between (i,j ), i,j ∈ C, can be seen to be selected to C with the same probability in states μ and ν, relation (26) implies that…”

Controlling viral capsid assembly with templating

“…The formation of too many partial capsids can be suppressed by a slow nucleation step [48], but avoidance of both sources of kinetic frustration requires relatively weak subunitsubunit binding free energies [26,28,29,47,48,56]. Theoretical work suggests that weak binding free energies are a general requirement for successful assembly into an ordered low free energy product; binding free energies that are large compared to the thermal energy (kBT) prevent the system from 'locally' equilibrating between different metastable configurations during assembly [56,57].…”

“…Assembly rates must be restrained to avoid two forms of kinetic traps (long-lived metastable states): (a) if new intermediates form too rapidly, the pool of free subunits becomes depleted before most capsids finish assembling [12,21,26,47,48,52,53], (b) malformed structures result when additional subunits bind more rapidly than strained bonds can anneal within a partial capsid [26,28,54,55]. The formation of too many partial capsids can be suppressed by a slow nucleation step [48], but avoidance of both sources of kinetic frustration requires relatively weak subunitsubunit binding free energies [26,28,29,47,48,56]. Theoretical work suggests that weak binding free energies are a general requirement for successful assembly into an ordered low free energy product; binding free energies that are large compared to the thermal energy (kBT) prevent the system from 'locally' equilibrating between different metastable configurations during assembly [56,57].…”