Steady-state nucleation rate and flux of composite nucleus at saddle point

Multiscale Exploration of Concentration-Dependent Amyloid-β(16-21) Amyloid Nucleation

Atomic descriptions of peptide aggregation nucleation remain lacking due to the difficulty of exploring complex configurational spaces on long time scales. To elucidate this process, we develop a multiscale approach combining a metadynamics-based method with cluster statistical mechanics to derive concentration-dependent free energy surfaces of nucleation at near-atomic resolution. A kinetic transition network of nucleation is then constructed and employed to systematically explore nucleation pathways and kinetics through stochastic simulations. This approach is applied to describe Aβ_16-21 amyloid nucleation, revealing a two-step mechanism involving disordered aggregates at millimolar concentration, and an unexpected mechanism at submillimolar concentrations that exhibits kinetics reminiscent of classical nucleation but atypical pathways involving growing clusters with structured cores wrapped by disordered surface. When this atypical mechanism is operative, critical nucleus size can be reflected by the nucleation reaction order. Collectively, our approach paves the way for a more quantitative and detailed understanding of peptide aggregation nucleation.

Nucleation and growth by diffusion under Ostwald-Freundlich boundary condition

The critical radius of a nucleus grown by diffusion in a solution is studied thermodynamically as well as kinetically. The thermodynamic growth equation called Zeldovich equation of classical nucleation theory and the kinetic diffusional growth equation combined with the Ostwald-Freundlich boundary condition lead to the same critical radius. However, it should be pointed out that the diffusional equation may lead to a kinetic critical radius that is different from the thermodynamic critical radius, thus indicating the possibility of kinetically controlling the critical radius of a nucleus.

Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency

We propose a method for identifying accurate reaction coordinates among a set of trial coordinates. The method applies to special cases where motion along the reaction coordinate follows a one-dimensional Smoluchowski equation. In these cases the reaction coordinate can predict its own short-time dynamical evolution, i.e., the dynamics projected from multiple dimensions onto the reaction coordinate depend only on the reaction coordinate itself. To test whether this property holds, we project an ensemble of short trajectory swarms onto trial coordinates and compare projections of individual swarms to projections of the ensemble of swarms. The comparison, quantified by the Kullback-Leibler divergence, is numerically performed for each isosurface of each trial coordinate. The ensemble of short dynamical trajectories is generated only once by sampling along an initial order parameter. The initial order parameter should separate the reactants and products with a free energy barrier, and distributions on isosurfaces of the initial parameter should be unimodal. The method is illustrated for three model free energy landscapes with anisotropic diffusion. Where exact coordinates can be obtained from Kramers-Langer-Berezhkovskii-Szabo theory, results from the new method agree with the exact results. We also examine characteristics of systems where the proposed method fails. We show how dynamical self-consistency is related (through the Chapman-Kolmogorov equation) to the earlier isocommittor criterion, which is based on longer paths.

Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the postcritical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the postcritical nucleus is more appropriately described in the component space. Although both the free-energy landscape and the reaction rates play decisive role to determine the kinetics of nucleation at the saddle point, the details of the free-energy landscape are irrelevant to the kinetics of the postcritical nucleus.