Critical length of a one-dimensional nucleus

Thermal stability and secondary aggregation of self-limiting, geometrically frustrated assemblies: Chain assembly of incommensurate polybricks

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multisubunit size which results from the competition between the elastic costs of frustration within an assembly and the surface energy at its boundaries. Physical realizations-from ill-fitting particle assemblies to self-twisting protein superstructures-are capable of multiple mechanisms of escaping the cumulative costs of frustration, resulting in unlimited equilibrium assembly, including elastic modes of "shape flattening" and the formation of weak, defective bonds that screen intra-assembly stresses. Here we study a model of one-dimensional chain assembly of incommensurate "polybricks" and determine its equilibrium assembly as a function of temperature, concentration, degree of shape frustration, elasticity, and interparticle binding, notably focusing on how weakly cohesive, defective bonds give rise to strongly temperature-dependent assembly. Complex assembly behavior derives from the competition between multiple distinct local minima in the free-energy landscape, including self-limiting chains, weakly bound aggregates of self-limiting chains, and strongly bound, elastically defrustrated assemblies. We show that this scenario, in general, gives rise to anomalous multiple aggregation behavior, in which disperse subunits (stable at low concentration and high temperature) first exhibit a primary aggregation transition to self-limiting chains (at intermediate concentration and temperature) which are ultimately unstable to condensation into unlimited assembly of finite-chains through weak binding beyond a secondary aggregation transition (at low temperature and high concentration). We show that window of stable self-limitation is determined both by the elastic costs of frustration in the assembly as well as energetic and entropic features of intersubunit binding.

Absolute chemical potentials for complex molecules in fluid phases: A centroid reference for predicting phase equilibria

Solid-fluid phase equilibria are difficult to predict in simulations because bound degrees of freedom in the crystal phase must be converted to free translations and rotations in the fluid phase. Here, we avoid the solid-to-fluid transformation step by starting with chemical potentials for two reference systems, one for the fluid phase and one for the solid phase. For the solid, we start from the Einstein crystal and transform to the fully interacting molecular crystal. For the fluid phase, we introduce a new reference system, the "centroid," and then transform to gas phase molecules. We illustrate the new calculations by predicting the sublimation vapor pressure of succinic acid in the temperature range of 300 K-350 K.

Growth probability and formation time of the individual Oosawa-Kasai protein fibril

Protein fibrils are currently of great academic and practical interest because of their involvement in scores of severe human diseases and their promising use in various high-technology devices. The Oosawa-Kasai (OK) model of protein self-assembly into fibrils has been widely used to gain mechanistic insight into the process of fibril formation and growth. Here this model is employed to obtain exact and mathematically simple expressions for the probability P_{n} of an individual fibril of n protein monomers to grow to a macroscopically large size and for the mean time τ_{n} that such a fibril needs for its formation. These expressions quantify the increase of P_{n} and the decrease of τ_{n} with increasing the concentration of monomeric protein in the solution. When used for analysis of experimental P_{n} and τ_{n} data, they make it possible to determine the parameters characterizing fibril nucleation and growth in the framework of the OK model. Finally, an expression is found for the mean time of the first appearance of an n-sized fibril in the protein solution. The results obtained are applicable to the formation of other aggregates corresponding to the OK fibrils, such as the one-dimensional Kossel-Stranski crystals and Ising ferromagnets.