Free Energy Barrier Height Research Articles

Inhibition of the Early-Stage Cross-Amyloid Aggregation of Amyloid-β and IAPP via EGCG: Insights from Molecular Dynamics Simulations.

Amyloid-β (Aβ) and islet amyloid polypeptide (IAPP) are small peptides that have the potential to not only self-assemble but also cross-assemble and form cytotoxic amyloid aggregates. Recently, we experimentally investigated the nature of Aβ-IAPP coaggregation and its inhibition by small polyphenolic molecules. Notably, we found that epigallocatechin gallate (EGCG) had the ability to reduce heteroaggregate formation. However, the precise molecular mechanism behind the reduction of heteroaggregates remains unclear. In this study, the dimerization processes of Aβ40 and IAPP peptides with and without EGCG were characterized by the enhanced sampling technique. Our results showed that these amyloid peptides exhibited a tendency to form a stable heterodimer, which represented the first step toward coaggregation. Furthermore, we also found that the EGCG regulated the dimerization process. In the presence of EGCG, well-tempered metadynamics simulation indicated a notable shift in the bound state toward a greater center of mass (COM) distance. Additionally, the presence of EGCG led to a significant increase in the free energy barrier height (∼15k B T) along the COM distance, and we observed a transition state between the bound and unbound states. Our findings also unveiled that the EGCG formed a greater number of hydrogen bonds with Aβ40, effectively obstructing the dimer formation. In addition, we carried out microseconds of all-atom conventional molecular dynamics (cMD) simulations to investigate the formation of both hetero- and homo-oligomer states by these peptides. MD simulations illustrated that EGCG played a significant role in preventing oligomer formation by reducing the content of β-sheets in the peptide. Collectively, our results offered valuable insight into the mechanism of cross-amyloid aggregation between Aβ40 and IAPP and the inhibition effect of EGCG on the heteroaggregation process.

Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach.

Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.

Solute interaction-driven and solvent interaction-driven liquid-liquid phase separation induced by molecular size difference.

We conducted molecular dynamics (MD) simulations in a binary Lennard-Jones system as a model system for molecular solutions and investigated the mechanism of liquid-liquid phase separation (LLPS), which has recently been recognized as a fundamental step in crystallization and organelle formation. Our simulation results showed that LLPS behavior varied drastically with the size ratio of solute to solvent molecules. Interestingly, increasing the size ratio can either facilitate or inhibit LLPS, depending on the combination of interaction strengths. We demonstrated that the unique behavior observed in MD simulation could be reasonably explained by the free energy barrier height calculated using our thermodynamic model based on the classical nucleation theory. Our model proved that the molecular size determines the change in number of interaction pairs through LLPS. Varying the size ratio changes the net number of solute-solvent and solvent-solvent interaction pairs that are either broken or newly generated per solute-solute pair generation, thereby inducing a complicated trend in LLPS depending on the interaction parameters. As smaller molecules have more interaction pairs per unit volume, their contribution is more dominant in the promotion of LLPS. Consequently, as the size ratio of the solute to the solvent increased, the LLPS mode changed from solute-related interaction-driven to solvent-related interaction-driven.

Acceleration of xenon kick-out exchange in a cryptophane host explained by ab initio simulation.

The degenerate exchange involving xenon and anti-cryptophane-222-(OCH2COOH)6 in basic water is studied. The reaction consists of the intrusion of a xenon atom into a cavity hosting another xenon and the escape of the latter from the cage to reach the aqueous solution. A series of constrained ab initio molecular dynamics simulations were performed according to the Blue Moon ensemble method to reconstruct the free-energy profile for the degenerate exchange reaction at ambient temperature. In addition to the estimation of the free-energy barrier height of the reaction, analysis of the trajectories provides details on its mechanism as well as on the nature of its transition state, where both Xe atoms interact through strong dispersion forces owing to moderate confinement effects.

Entropic barrier theory of polymer melting

AbstractWe present a theory of melting kinetics of semicrystalline polymers at temperatures above the equilibrium melting temperature, by accounting for conformational entropy of chains during melting. We have derived free energy landscapes for escape of individual chains from a lamella into the amorphous phase as a function of the characteristics of the initial lamella, such as the lamellar thickness, number of chain folds, fold‐ and lateral‐surface free energies, and mean energy of a monomer inside the lamella. We show that melting of lamellae is always accompanied by a free energy barrier which is entirely entropic in origin. In terms of the parameters characterizing the lamellae and the extent of superheating, closed‐form formulas are presented for the equilibrium melting temperature, driving force for crystallization, free energy barrier height, average expulsion time of a single chain from a lamella, and the melting velocity of lamellae. The present entropic barrier theory predicts that the dependence of melting velocity on superheating is nonlinear and non‐Arrhenius, in qualitative agreement with experimental observations reported in the literature. The derived formulas open an opportunity to further explore the role of various molecular features of semicrystalline polymers on their melting kinetics.

Additivity of Diene Substituent Gibbs Free Energy Contributions for Diels-Alder Reactions between Me2C=CMe2 and Substituted Cyclopentadienes.

Systematic computational studies of pericyclic Diels-Alder reactions between (H3C)2C=C(CH3)2, 1, and all permutations of substituted cyclopentadienes c-C5R1R2R3R4R5aR5b (R = H, CH3, CF3, F) allowed isolation of substitutional effects on Gibbs free energy barrier heights and reaction Gibbs free energies. "Average Substitution Gibbs Free Energy Correction" ΔG ASC# ‡/ΔG ASC# values for each substituent in each position appeared to be additive. Substituent effects on barriers showed interesting contrasts. Methyl substitution at positions 5a and 5b increased barriers significantly, while substitution at all other positions had essentially no impact. In contrast, fluoro substitution at positions 5a and 5b lowered barriers more than substitution at other positions. Trifluoromethyl substitution mixed these effects, in that substitution at positions 5a and 5b increased barriers, but substitution at other positions lowered them. Despite the variances, ΔG ASC# ‡/ΔG ASC# values allowed reliable prediction of barriers and exergonicities for reactions between 1 and highly substituted cyclopentadienes, and between 1 and cyclopentadienes with random mixtures of CH3/CF3/F substituents. ΔG ASC# ‡/ΔG ASC# values were correlated with steric considerations and quantum theory of atoms in molecules (QTAIM) calculations. Overall, the ASC values provide a resource for predicting which Diels-Alder reactions of this type should occur at rapid rates and/or give stable bicyclic products.

Understanding electrocaloric cooling of ferroelectrics guided by phase‐field modeling

AbstractWith the urgent need to explore low‐cost, high‐efficiency solid‐state refrigeration technology, the electrocaloric effects of ferroelectric materials have attracted much attention in the past decades. With the development of modern computing technology, the phase‐field method is widely used to simulate the evolution of microstructure at mesoscale and predict the properties of different types of ferroelectric materials. In this article, we review the recent progress of electrocaloric effects from phenomenological Landau thermodynamics theory to phase‐field simulation by discussing the microcosmic composition, mesoscopic domain structures, macroscopic size/shape, and external stimulus of strain/stress. More importantly, in searching for new ferroelectric electrocaloric cooling materials, it is possible to find materials whose free energy barrier height changes rapidly with temperature, such materials have a faster change rate with polarization temperature in terms of ferroelectric macroscopic properties, from them could get superior electrocaloric effects. We compile a relatively comprehensive computational design on the high performance of electrocaloric effects in different types of ferroelectrics and offer a perspective on the computational design of electrocaloric refrigeration materials at the mesoscale microstructure level.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics.

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Extraction of the spin-glass free-energy landscape from 1/f noise measurements

The $1/f$ resistance noise has been measured in thin CuMn (13.5 at.%) spin-glass films. The temperature and frequency dependence have been analyzed in terms of the landscape of free-energy barriers. This analysis provides the full barrier distribution for various thin film thicknesses between 10 nm and 80 nm. The free-energy barrier height distribution's width and energy position have been determined. Contrary to previous models with fixed shape and energy, the free-energy landscape is described by a distribution of barriers that both shifts and changes shape as the temperature is reduced. The dependence of this distribution is in contrast with recent predictions. Using the fluctuation dissipation theorem, the $1/f$ measurements connect with ${\ensuremath{\chi}}^{\ensuremath{''}}$, displaying agreement with other direct measurements of the latter.

Interactions between conducting surfaces in salt solutions.

In this work, we simulate interactions between two perfectly conducting surfaces, immersed in a salt solution. We demonstrate that these forces are quantitatively different from those between (equally charged) non-conducting surfaces. There is, for instance, a significant repulsion between net neutral surfaces. On the other hand, there are also qualitative similarities, with behaviours found with non-conducting surfaces. For instance, there is a non-monotonic dependence of the free energy barrier height, on the salt concentration, and the minimum essentially coincides with a flat profile of the apparent surface charge density (i.e. the effective net surface charge density, some distance away from the surface, when accounting for ion neutralization), outside the so-called Stern layer. These conditions can be described as "perfect surface charge neutralization". Despite observed quantitative differences, we demonstrate that it might be possible to mimic a dispersion containing charged colloidal metal particles by a simpler model system with charged non-conducting particles, using modified particle-ion interactions.

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon.

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Thin smectic liquid crystalline fibrils of chiral rodlike particles.

Inspired by recent experimental work on virus-polymer mixtures, we study the properties of thin smectic fibrils composed of chiral rodlike particles using Monte Carlo simulations. Due to the interplay between surface energy, elastic deformation energy, and entropic effects, the fibril's layers relax into a twisted state. We focus our study on the layers' twist direction and map our results to the antiferromagnetic Ising model. In this view, the chiral interaction mimics an external field that drives the layers to have the same sense of twist. Besides, we determine the free energy difference and barrier height between an alternating and a nonalternating sequence of twisted layers composed of achiral rods and find that an alternating sequence is slightly preferred. We also see that the fibrils contract on increasing the chiral interaction strength and think that further studies on self-assembled functional materials can use our results.

The Next Frontier for Designing Switchable Proteins: Rational Enhancement of Kinetics.

Designing proteins that can switch between active (ON) and inactive (OFF) conformations in response to signals such as ligand binding and incident light has been a tantalizing endeavor in protein engineering for over a decade. While such designs have yielded novel biosensors, therapeutic agents, and smart biomaterials, the response times (times for switching ON and OFF) of many switches have been too slow to be of practical use. Among the defining properties of such switches, the kinetics of switching has been the most challenging to optimize. This is largely due to the difficulty of characterizing the structures of transient states, which are required for manipulating the height of the effective free energy barrier between the ON and OFF states. We share our perspective of the most promising new experimental and computational strategies over the past several years for tackling this next frontier for designing switchable proteins.

Designed Giant Room‐Temperature Electrocaloric Effects in Metal‐Free Organic Perovskite [MDABCO](NH4)I3 by Phase–Field Simulations

AbstractAchieving a colossal room‐temperature electrocaloric effect is essential for practical solid‐state refrigeration applications with low‐cost and high‐efficiency. Here, through the design of applying external stimuli (hydrostatic pressure and misfit strain), giant room‐temperature electrocaloric effects in the bulk and thin film of metal‐free organic perovskite [MDABCO](NH4)I3 are obtained by using a combination of thermodynamic calculations and phase–field simulations. Under the hydrostatic pressure of 1 GPa, there emerges excellent room‐temperature (300 K) electrocaloric performance with the temperature change (ΔT) of 8.41 K at 30 MV m−1 and electrocaloric strength (ΔT/ΔE) of 0.63 K m MV−1 at 10 MV m−1, respectively. The prominent electrocaloric effects of MDABCO(NH4)I3 may be related to its rapid change rates of free energy barrier height. Additionally, it can be found that some stripe domains and non‐180° domain walls form in the [MDABCO](NH4)I3 bulk, which is consistent with the experimental results. This work not only provides new insights into organic perovskite [MDABCO](NH4)I3, but also guides for further developing to realize remarkable room‐temperature electrocaloric cooling.

Formation free energy of an i-mer at spinodal.

In statistical mechanics, the formation free energy of an i-mer can be understood as the Gibbs free energy change in a system consisting of pure monomers after and prior to the formation of the i-mer. For molecules interacting via Lennard-Jones potential, we have computed the formation free energy of a Stillinger i-mer [F. H. Stillinger, J. Chem. Phys. 38, 1486 (1963)] and a ten Wolde-Frenkel (tWF) [P. R. ten Wolde and D. Frenkel, J. Chem. Phys. 109, 9901 (1998)] i-mer at spinodal at reduced temperatures from 0.7 to 1.2. It turns out that the size of a critical Stillinger i-mer remains finite and its formation free energy is on the order of kBT, and the size of a critical tWF i-mer remains finite and its formation free energy is even higher. This can be explained by Binder's theory [K. Binder, Phys. Rev. A 29, 341 (1984)] that for a system, when approaching spinodal, if the Ginzburg criterion is not satisfied, a gradual transition will take place from nucleation to spinodal decomposition, where the free-energy barrier height is on the order of kBT.

Additivity of Diene Substituent Gibbs Free Energy Contributions for Diels-Alder Reactions between (F3C)2B = NMe2 and Substituted Cyclopentadienes.

Systematic computational studies of pericyclic Diels-Alder-type reactions between aminoborane (F3C)2B = N(CH3)2, 1, and all permutations of substituted cyclopentadienes c-C5R1R2R3R4R5aR5b (R = H, CH3, CF3, F) allow isolation of substitutional effects on Gibbs free energy barrier heights and reaction Gibbs free energies. The effects appear to be additive in all cases. Substitution at positions 5a and 5b always increases barriers and reaction energies, an effect explained by steric interactions between substituents and the aminoborane moiety. For cases R = CH3, regioselectivities differ from those expected from canonical organic chemistry predictions. Frontier molecular orbital calculations suggest this arises from the extreme polarization of the π interaction in 1. For cases R = CF3, the 2/3-substitution comparison accords with canon, but the 1/4-substitution comparison does not. This appears to arise from a combination of electronic and steric issues. For cases R = F, many of the reactions are exergonic, in contrast to the cases R = CH3, CF3. Additionally, fluorine substitution at positions 2 and 4 has a barrier-lowering effect. Frontier molecular orbital calculations support an orbital-based preference for formation of 2- and 4-substituted "meta" products rather than "ortho/para" products.

Effect of Ammonium Salts on the Decarboxylation of Oxaloacetic Acid in Atmospheric Particles

Oxaloacetic acid (OAA) is a 3-oxocarboxylic acid formed from the oxidation of succinic acid. OAA and other 3-oxocarboxylic acids experience a decarboxylation reaction in aqueous solutions, which can be catalyzed by ammonium and amines. This catalysis has not been studied under atmospherically relevant conditions despite previous interest in OAA in the atmosphere. To address this, 1 mM solutions of OAA were prepared with varying concentrations of ammonium sulfate, ammonium bisulfate, ammonium chloride, and sodium sulfate to simulate various atmospheric conditions. The extent of the decarboxylation was monitored using UV–visible absorption spectroscopy. OAA’s uncatalyzed decarboxylation lifetime was around 5 h. Under moderately acidic conditions representative of aerosol particles (pH = 3–4), the decarboxylation rate increased linearly with ammonium concentration up to about 2.7 M, after which additional ammonium had no effect. The effective lifetime of OAA reduced to approximately 1 h under these conditions. Density functional theory calculations support the proposed catalytic mechanism, predicting the free energy barrier height for decarboxylation to be approximately 21 kcal/mol lower after OAA has reacted with ammonium. In more acidic solutions (pH < 1), OAA’s decarboxylation was suppressed, with lifetimes of tens of hours, even in the presence of ammonium. A comparison of the decarboxylation rate with the expected rate of oxidation by OH suggests that decarboxylation will be the dominant loss mechanism for OAA, and presumably other 3-oxocarboxylic acids, in aerosol particles and cloud/fog droplets. This result explains why OAA is hard to detect in field measurements even though it is a known oxidation product of succinic acid.

Nucleation rate in the two dimensional Ising model in the presence of random impurities.

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from the Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy of the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.

Interplay of hydrophobic and hydrophilic interactions in sequence-dependent cell penetration of spontaneous membrane-translocating peptides revealed by bias-exchange metadynamics simulations

Spontaneous Membrane Translocating Peptides (SMTPs) can translocate silently across the bilayer and, thus, have the best potential to improve the delivery of therapeutic molecules to cells without toxicity. However, how their translocation mechanisms are affected by a specific peptide sequence remains poorly understood. Here, bias-exchange metadynamics simulations were employed to investigate the translocation mechanisms of five SMTPs with the same composition of amino acids (LLRLR, LRLLR, LLLRR, RLLLR, and LRLRL). Simulation results yield sequence-dependent free energy barrier using the FESs along the z-directional distance. An in-depth analysis of sequence-dependent interactions in different regions of the bilayers indicates that the free-energy barrier height of a specific sequence is resulted from the accessibility balance of isolated or clustered hydrophobic residues (L) and hydrophilic residues (R) that leads to different levels of resistance for moving of a peptide into the hydrophobic center of the membrane. At the maximal of the free-energy barrier, all peptides have a conformation parallel to the membrane surface with the barrier height determined by their affinity to the hydrophobic region. The appropriate bilayer perturbation and GDM+ pairing are beneficial for peptide translocation. These results provide an improved microscopic understanding of how peptide sequence influences the translocation efficiency and mechanism.

Investigation into electrocaloric effect of different types of ferroelectric materials by Landau-Devonshire theory

The electrocaloric effects in various types of materials, including inorganic perovskites, organic perovskites, organic polymers, molecular ferroelectrics and two-dimensional ferroelectric materials, possess great potential in realizing solid-state cooling devices due to the advantages of low-cost, high-efficiency and environmental friendly. Different ferroelectric materials have distinct characteristics in terms of phase transition and electrocaloric response. The mechanism for enhancing the electrocaloric effect currently remains elusive. Here, typical inorganic perovskite BaTiO&lt;sub&gt;3&lt;/sub&gt;, PbTiO&lt;sub&gt;3&lt;/sub&gt; and BiFeO&lt;sub&gt;3&lt;/sub&gt;, organic perovskite [MDABCO](NH&lt;sub&gt;4&lt;/sub&gt;)I&lt;sub&gt;3&lt;/sub&gt;, organic polymer P(VDF-TrFE), molecular ferroelectric ImClO&lt;sub&gt;4&lt;/sub&gt; and two-dimensional ferroelectric CuInP&lt;sub&gt;2&lt;/sub&gt;S&lt;sub&gt;6&lt;/sub&gt; are selected to analyze the origins of their electrocaloric effects based on the Landau-Devonshire theory. The temperature-dependent pyroelectric coefficients and electrocaloric performances of different ferroelectric materials indicate that the first-order phase transition material MDABCO and the second-order phase transition material ImClO&lt;sub&gt;4&lt;/sub&gt; have excellent performances for electrocaloric refrigeration. The predicted results also strongly suggest that near the phase transition point of the ferroelectric material, the variation rate of free energy barrier height with temperature contributes to the polarizability change with temperature, resulting in enhanced electrocaloric effect. This present work provides a theoretical basis and a new insight into the further development of ferroelectric materials with high electrocaloric response.