The microscopic mechanisms controlling heterogeneous ice nucleation are complex and remain poorly understood. Although good ice nucleators are generally believed to match ice lattice and to bind water, counter examples are often identified. Here we show, by advanced molecular simulations, that the heterogeneous nucleation of ice on graphitic surface is controlled by the coupling of surface crystallinity and surface hydrophilicity. Molecular level analysis reveals that the crystalline graphitic lattice with an appropriate hydrophilicity may indeed template ice basal plane by forming a strained ice layer, thus significantly enhancing its ice nucleation efficiency. Remarkably, the templating effect is found to transit from within the first contact layer of water to the second as the hydrophilicity increases, yielding an oscillating distinction between the crystalline and amorphous graphitic surfaces in their ice nucleation efficiencies. Our study sheds new light on the long-standing question of what constitutes a good ice nucleator.

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model mW, we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation.Our numerical study thus provides a strong support to the quantitative power of the theory, and allows understanding ice nucleation behaviors under the most relevant freezing conditions.

Fibrils of amyloid proteins are currently of great interest because of their involvement in various amyloid-related diseases and nanotechnological products. In a recent kinetic Monte Carlo simulation study (Cabriolu, R.; Kashchiev, D.; Auer, S. J. Chem. Phys.2012, 137, 204903), we found that our simulation data for the rate of amyloid fibril nucleation occurring by direct polymerization of monomeric protein could not be described adequately by nucleation theory. It turned out that the process occurred in a peculiar way, thus confounding the nucleation paradigm and demanding a new theoretical treatment. In the present study, we reconsider the theoretical approach to nucleation of amyloid fibrils and derive new expressions for the stationary rate of the process. As these expressions provide a remarkably good description of the simulation data, by using them we propose a theoretical dependence of the amyloid-β(40) fibril nucleation rate on the concentration of monomeric protein in the solution. This dependence reveals the existence of a threshold concentration below which the fibril nucleation in small enough solution volumes is practically arrested, and above which the process occurs vigorously, because then each monomeric protein in the solution acts as fibril nucleus. The presented expressions for the threshold concentration and for the dependence of the fibril nucleation rate on the concentration of monomeric protein can be a valuable guide in designing new therapeutic and/or technological strategies for prevention or stimulation of amyloid fibril formation.

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations. Published by AIP Publishing.

We consider the nucleation of amyloid fibrils at the molecular level when the process takes place by a direct polymerization of peptides or protein segments into β-sheets. Employing the atomistic nucleation theory (ANT), we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) composed of successively layered β-sheets. The application of this expression to a recently studied peptide system allows us to determine the size of the fibril nucleus, the fibril nucleation work, and the fibril nucleation rate as functions of the supersaturation of the protein solution. Our analysis illustrates the unique feature of ANT that the size of the fibril nucleus is a constant integer in a given supersaturation range. We obtain the ANT nucleation rate and compare it with the rates determined previously in the scope of the classical nucleation theory (CNT) and the corrected classical nucleation theory (CCNT). We find that while the CNT nucleation rate is orders of magnitude greater than the ANT one, the CCNT and ANT nucleation rates are in very good quantitative agreement. The results obtained are applicable to homogeneous nucleation, which occurs when the protein solution is sufficiently pure and/or strongly supersaturated.