Kinetic Energy Landscape Research Articles

Non-equilibrium crystallization pathways of manganese oxides in aqueous solution

Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. Without a precise understanding of which metastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become a trial-and-error process. Here, we construct a theoretical framework to reveal the nanoscale and metastable energy landscapes of Pourbaix (E-pH) diagrams, providing quantitative insights into the size–dependent thermodynamics of metastable oxide nucleation and growth in water. By combining this framework with classical nucleation theory, we interrogate how solution conditions influence the multistage oxidation pathways of manganese oxides. We calculate that even within the same stability region of a Pourbaix diagram, subtle variations in pH and redox potential can redirect a non-equilibrium crystallization pathway through different metastable intermediates. Our theoretical framework offers a predictive platform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesis of target materials.

Two-Dimensional van der Waals Epitaxy Kinetics in a Three-Dimensional Perovskite Halide

The exploration of emerging materials physics and prospective applications of two-dimensional materials greatly relies on the growth control of their thickness, phases, morphologies, and film–substrate interactions. Though substantial progress has been made for the development of two-dimensional films from conventional layered bulky materials, particular challenges remain for obtaining ultrathin, single crystalline, dislocation-free films from intrinsically non-van der Waals-type three-dimensional materials. In this report, with the successful demonstration of single crystalline ultrathin large-scale perovskite halide material, we reveal and identify the favorable role of weak van der Waals film–substrate interaction on the nucleation and growth of the two-dimensional morphology out of nonlayered materials compared to conventional epitaxy. We also show how the bonding nature of the three-dimensional material itself affects the kinetic energy landscape of ultrathin film growth. By studying the formation of fractal perovskites assisted with Monte Carlo simulations, we demonstrate that the competition between the van der Waals diffusion and surface free energy of the perovskite leads to film thickening, suggesting that extra strategies such as surface passivation may be needed for the growth of monolayer and few-layer films.

Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous Solution: Comparing Computational Chemistry and NMR Data

A computational protocol utilizing density functional theory calculations, including Poisson-Boltzmann implicit solvent and free energy corrections, is applied to study the thermodynamic and kinetic energy landscape of glycolaldehyde in solution. Comparison is made to NMR measurements of dissolved glycolaldehyde, where the initial dimeric ring structure interconverts among several species before reaching equilibrium where the hydrated monomer is dominant. There is good agreement between computation and experiment for the concentrations of all species in solution at equilibrium, that is, the calculated relative free energies represent the system well. There is also relatively good agreement between the calculated activation barriers and the estimated rate constants for the hydration reaction. The computational approach also predicted that two of the trimers would have a small but appreciable equilibrium concentration (>0.005 M), and this was confirmed by NMR measurements. Our results suggest that while our computational protocol is reasonable and may be applied to quickly map the energy landscape of more complex reactions, knowledge of the caveats and potential errors in this approach need to be taken into account.

Periodic Forces Trigger a Complex Mechanical Response in Ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.

The Anisotropic Response of Ubiquitin Unfolded by Periodic Forces

Biological forces govern essential molecular processes in all living organisms. Many cellular forces, e.g. those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to repetitive mechanical information. The small protein ubiquitin is found in all eukaryotes and serves as cellular signaling tag e.g. in the forceful degradation of misfolded proteins. Here, we probed the nano-mechanical stability of single and multimeric ubiquitins unfolded by periodic forces. Using coarse-grained molecular dynamics simulations, we were able to model repetitive forces with periods about two orders of magnitude longer than the relaxation time of the protein. We found that even a moderate periodic force weakened ubiquitin and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. Our results also showed that the dynamic response of a small protein can be complex with transient refolding of secondary structures and an increasing importance of local interactions in asymmetric protein stability. We tested the geometry dependence of ubiquitin's mechanical stability and found that the ubiquitin linkage involved in protein degradation is remarkably insensitive to periodic forces. These observations are qualitatively and quantitatively explained using kinetic energy landscape models which can be in turn used to predict the dynamic response of proteins. Our results are also discussed in light of dynamic single-molecule measurements and physiological forces. We believe that our work provides first steps towards a theoretical framework to better understand dynamic and cellular protein biomechanics and biological force generation.We have been supported by a grant N202 0852 33 of the Ministry of Science and Higher Education in Poland (to P.S.) and a fellowship of the European Molecular Biology Organization (to H.J.).