Accelerating Solvent Dynamics with Replica Exchange for Improved Free Energy Sampling.

Molecular reactions in solution typically involve solvent exchange; for example, a surface must partly desolvate for a molecule to adsorb onto it. When these reactions are simulated, slow solvent dynamics can limit the sampling of configurations and reduce the accuracy of free energy estimates. Here, we combine Hamiltonian replica exchange (HREX) with well-tempered metadynamics (WTMD) to accelerate the sampling of solvent configurations orthogonal to the collective variable space. We compute the formation free energy of a carbonate vacancy in the calcite-water interface and find that the combination of WTMD with HREX significantly improves the sampling relative to WTMD without HREX.

Dissipation production in a closed two-level quantum system as a test of the irreversibility of the dynamics.

Irreversible behavior in open stochastic dynamical systems is quantified by stochastic entropy production, a property that measures the difference in likelihoods of forward and subsequent backward system evolution. But for a closed system, governed by deterministic dynamics, such an approach is not appropriate. Instead, we can consider the difference in likelihoods of forward and "obverse" behavior: the latter being a backward trajectory initiated at the same time as the forward trajectory. Such a comparison allows us to define "dissipation production," an analog of stochastic entropy production. It quantifies the breakage of a property of the evolution termed "obversibility" just as stochastic entropy production quantifies a breakage of reversibility. Both are manifestations of irreversibility. In this study we discuss dissipation production in a quantum system. We consider a simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors, and we provide numerical results to illustrate the ideas. We consider cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production, and hence identify conditions under which the system displays time-asymmetric average behavior: an arrow of time.

Polyamines Promote Aragonite Nucleation and Generate Biomimetic Structures.

Calcium carbonate biomineralization is remarkable for the ability of organisms to produce calcite or aragonite with perfect fidelity, where this is commonly attributed to specific anionic biomacromolecules. However, it is proven difficult to mimic this behavior using synthetic or biogenic anionic organic molecules. Here, it is shown that cationic polyamines ranging from small molecules to large polyelectrolytes can exert exceptional control over calcium carbonate polymorph, promoting aragonite nucleation at extremely low concentrations but suppressing its growth at high concentrations, such that calcite or vaterite form. The aragonite crystals form via particle assembly, giving nanoparticulate structures analogous to biogenic aragonite, and subsequent growth yields stacked aragonite platelets comparable to structures seen in developing nacre. This mechanism of polymorph selectivity is captured in a theoretical model based on these competing nucleation and growth effects and is completely distinct from the activity of magnesium ions, which generate aragonite by inhibiting calcite. Profiting from these contrasting mechanisms, it is then demonstrated that polyamines and magnesium ions can be combined to give unprecedented control over aragonite formation. These results give insight into calcite/aragonite polymorphism and raise the possibility that organisms may exploit both amine-rich organic molecules and magnesium ions in controlling calcium carbonate polymorph.

Calcite Kinks Grow via a Multistep Mechanism.

The classical model of crystal growth assumes that kinks grow via a sequence of independent adsorption events where each solute transitions from the solution directly to the crystal lattice site. Here, we challenge this view by showing that some calcite kinks grow via a multistep mechanism where the solute adsorbs to an intermediate site and only transitions to the lattice site upon the adsorption of a second solute. We compute the free energy curves for Ca and CO3 ions adsorbing to a large selection of kink types, and we identify kinks terminated both by Ca ions and by CO3 ions that grow in this multistep way.

Calcite Kinetics for Spiral Growth and Two-Dimensional Nucleation.

Calcite crystals grow by means of molecular steps that develop on {10.4} faces. These steps can arise stochastically via two-dimensional (2D) nucleation or emerge steadily from dislocations to form spiral hillocks. Here, we determine the kinetics of these two growth mechanisms as a function of supersaturation. We show that calcite crystals larger than ∼1 µm favor spiral growth over 2D nucleation, irrespective of the supersaturation. Spirals prevail beyond this length scale because slow boundary layer diffusion creates a low surface supersaturation that favors the spiral mechanism. Sub-micron crystals favor 2D nucleation at high supersaturations, although diffusion can still limit the growth of nanoscopic crystals. Additives can change the dominant mechanism by impeding spiral growth or by directly promoting 2D nucleation.

Stochastic thermodynamics in a non-Markovian dynamical system.

The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme involves coupling the system to an environment-typically a source of Markovian noise that affects the dynamics of the system. Here we extend this framework to consider a non-Markovian environment, one whose dynamics have memory and which create additional correlations with the system variables, and illustrate this with a selection of simple examples. Such an environment produces a rich variety of behavior. In particular, for a case of thermal relaxation, the distributions of entropy produced under the non-Markovian dynamics differ from the equivalent case of Markovian dynamics only by a delay time. When a time-dependent external work protocol is turned on, the system's correlations with the environment can either assist or hinder its approach to equilibrium, and affect its production of entropy, depending on the coupling strength between the system and environment.

Positively Charged Additives Facilitate Incorporation in Inorganic Single Crystals.

Incorporation of guest additives within inorganic single crystals offers a unique strategy for creating nanocomposites with tailored properties. While anionic additives have been widely used to control the properties of crystals, their effective incorporation remains a key challenge. Here, we show that cationic additives are an excellent alternative for the synthesis of nanocomposites, where they are shown to deliver exceptional levels of incorporation of up to 70 wt % of positively charged amino acids, polymer particles, gold nanoparticles, and silver nanoclusters within inorganic single crystals. This high additive loading endows the nanocomposites with new functional properties, including plasmon coupling, bright fluorescence, and surface-enhanced Raman scattering (SERS). Cationic additives are also shown to outperform their acidic counterparts, where they are highly active in a wider range of crystal systems, owing to their outstanding colloidal stability in the crystallization media and strong affinity for the crystal surfaces. This work demonstrates that although often overlooked, cationic additives can make valuable crystallization additives to create composite materials with tailored composition-structure-property relationships. This versatile and straightforward approach advances the field of single-crystal composites and provides exciting prospects for the design and fabrication of new hybrid materials with tunable functional properties.

Critical Step Length as an Indicator of Surface Supersaturation during Crystal Growth from Solution.

The surface processes that control crystal growth from solution can be probed in real-time by in situ microscopy. However, when mass transport (partly) limits growth, the interfacial solution conditions are difficult to determine, precluding quantitative measurement. Here, we demonstrate the use of a thermodynamic feature of crystal surfaces-the critical step length-to convey the local supersaturation, allowing the surface-controlled kinetics to be obtained. Applying this method to atomic force microscopy measurements of calcite, which are shown to fall within the regime of mixed surface/transport control, unites calcite step velocities with the Kossel-Stranski model, resolves disparities between growth rates measured under different mass transport conditions, and reveals why the Gibbs-Thomson effect in calcite departs from classical theory. Our approach expands the scope of in situ microscopy by decoupling quantitative measurement from the influence of mass transport.

Crowding-induced phase separation of nuclear transport receptors in FG nucleoporin assemblies.

The rapid (<1 ms) transport of biological material to and from the cell nucleus is regulated by the nuclear pore complex (NPC). At the core of the NPC is a permeability barrier consisting of intrinsically disordered phenylalanine-glycine nucleoporins (FG Nups). Various types of nuclear transport receptors (NTRs) facilitate transport by partitioning in the FG Nup assembly, overcoming the barrier by their affinity to the FG Nups, and comprise a significant fraction of proteins in the NPC barrier. In previous work (Zahn et al., 2016), we revealed a universal physical behaviour in the experimentally observed binding of two well-characterised NTRs, Nuclear Transport Factor 2 (NTF2) and the larger Importin-ß (Imp-ß), to different planar assemblies of FG Nups, with the binding behaviour defined by negative cooperativity. This was further validated by a minimal physical model that treated the FG Nups as flexible homopolymers and the NTRs as uniformly cohesive spheres. Here, we build upon our original study by first parametrising our model to experimental data, and next predicting the effects of crowding by different types of NTRs. We show how varying the amounts of one type of NTR modulates how the other NTR penetrates the FG Nup assembly. Notably, at similar and physiologically relevant NTR concentrations, our model predicts demixed phases of NTF2 and Imp-ß within the FG Nup assembly. The functional implication of NTR phase separation is that NPCs may sustain separate transport pathways that are determined by inter-NTR competition.

Magnesium-rich nanoprecipitates in calcite: atomistic mechanisms responsible for toughening in Ophiocoma wendtii.

The brittlestar Ophiocoma wendtii is theorised to employ a technique already used in metallurgy in order to optimise the mechanical properties of calcitic microlenses within their skeletons. These microlenses contain arrays of Mg-rich nanoprecipitates, which are proposed to inhibit crack propagation through the compression of the local host lattice. Here, we employ classical molecular dynamics in order to study the effects of Mg-rich nanoprecipitates on lattice strain, stress distributions and crack propagation in calcite. Our quantitative results on lattice strain and stress induced on the host matrix are compatible with empirical estimates. Simulations of crack propagation demonstrate that the inclusion of a Mg-rich region results in an increase in stress required to fracture the crystal, as well as higher residual stress in the fractured crystal. This is the result of an inhomogeneous stress distribution causing a more disordered fracture, as well as deflections of the crack away from the lowest energy (10.4) surface. The results agree with the proposal that the compression of the host lattice inhibits propagation, and offer insight into other mechanisms through which the nanoprecipitates affect crack propagation.

Intrinsically disordered nuclear pore proteins show ideal-polymer morphologies and dynamics.

In the nuclear pore complex, intrinsically disordered nuclear pore proteins (FG Nups) form a selective barrier for transport into and out of the cell nucleus, in a way that remains poorly understood. The collective FG Nup behavior has long been conceptualized either as a polymer brush, dominated by entropic and excluded-volume (repulsive) interactions, or as a hydrogel, dominated by cohesive (attractive) interactions between FG Nups. Here we compare mesoscale computational simulations with a wide range of experimental data to demonstrate that FG Nups are at the crossover point between these two regimes. Specifically, we find that repulsive and attractive interactions are balanced, resulting in morphologies and dynamics that are close to those of ideal polymer chains. We demonstrate that this property of FG Nups yields sufficient cohesion to seal the transport barrier, and yet maintains fast dynamics at the molecular scale, permitting the rapid polymer rearrangements needed for transport events.

Phase-field method for epitaxial kinetics on surfaces.

We present a procedure for simulating epitaxial growth based on the phase-field method. We consider a basic model in which growth is initiated by a flux of atoms onto a heated surface. The deposited atoms diffuse in the presence of this flux and eventually collide to form islands which grow and decay by the attachment and detachment of migrating atoms at their edges. Our implementation of the phase-field method for this model includes uniform deposition, isotropic surface diffusion, and stochastic nucleation (in both space and time), which creates islands whose boundaries evolve as the surface atoms "condense" into and "evaporate" from the islands. Computations using this model in the submonolayer regime, prior to any appreciable coalescence of islands, agree with the results of kinetic Monte Carlo (KMC) simulations for the coverage-dependence of adatom and island densities and island-size distributions, for both reversible and irreversible growth. The scaling of the island density, as obtained from homogeneous rate equations, agrees with KMC simulations for irreversible growth and for reversible growth for varying deposition flux at constant temperature. For reversible growth with varying temperature but constant flux, agreement relies on an estimate of the formation energy of the critical cluster. Taken together, our results provide a comprehensive analysis of the phase-field method in the submonolayer regime of epitaxial growth, including the verification of the main scaling laws for adatoms and island densities and the scaling functions for island-size distributions, and point to the areas where the method can be extended and improved.

Ethylene decomposition on Ir(111): initial path to graphene formation.

The complete mechanism behind the thermal decomposition of ethylene (C2H4) on Ir(111), which is the first step of graphene growth, is established for the first time employing a combination of experimental and theoretical methods. High-resolution X-ray photoelectron spectroscopy was employed, along with calculations of core level binding-energies, to identify the surface species and their evolution as the surface temperature is increased. To understand the experimental results, we have developed a reaction sequence between the various CnHm species, from ethylene to C monomers and dimers, based on ab initio density functional calculations of all the energy barriers and the Arrhenius prefactors for the most important processes. The resulting temperature evolution of all species obtained from the simulated kinetics of ethylene decomposition agrees with photoemission measurements. The molecular dissociation mechanism begins with the dehydrogenation of ethylene to vinylidene (CH2C), which is then converted to acetylene (CHCH) by the removal and addition of an H atom. The C-C bond is then broken to form methylidyne (CH), and in the same temperature range a small amount of ethylidyne (CH3C) is produced. Finally methylidyne dehydrogenates to produce C monomers that are available for the early stage nucleation of the graphene islands.

Maximum entropy principle for stationary states underpinned by stochastic thermodynamics.

The selection of an equilibrium state by maximizing the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of incomplete information. But such a framework can be more compelling if it is underpinned by dynamical arguments, and we show how this can be provided by stochastic thermodynamics, where an explicit link is made between the production of entropy and the stochastic dynamics of a system coupled to an environment. The separation of entropy production into three components allows us to select a stationary state by maximizing the change, averaged over all realizations of the motion, in the principal relaxational or nonadiabatic component, equivalent to requiring that this contribution to the entropy production should become time independent for all realizations. We show that this recovers the usual equilibrium probability density function (pdf) for a conservative system in an isothermal environment, as well as the stationary nonequilibrium pdf for a particle confined to a potential under nonisothermal conditions, and a particle subject to a constant nonconservative force under isothermal conditions. The two remaining components of entropy production account for a recently discussed thermodynamic anomaly between over- and underdamped treatments of the dynamics in the nonisothermal stationary state.

Stochastic entropy production arising from nonstationary thermal transport.

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behavior of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behavior and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremization, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.

Work relations for a system governed by Tsallis statistics.

We derive analogs of the Jarzynski equality and Crooks relation to characterize the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.

Coagulation kinetics beyond mean field theory using an optimised Poisson representation.

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

Surface thermodynamics of planar, cylindrical, and spherical vapour-liquid interfaces of water.

The test-area (TA) perturbation approach has been gaining popularity as a methodology for the direct computation of the interfacial tension in molecular simulation. Though originally implemented for planar interfaces, the TA approach has also been used to analyze the interfacial properties of curved liquid interfaces. Here, we provide an interpretation of the TA method taking the view that it corresponds to the change in free energy under a transformation of the spatial metric for an affine distortion. By expressing the change in configurational energy of a molecular configuration as a Taylor expansion in the distortion parameter, compact relations are derived for the interfacial tension and its energetic and entropic components for three different geometries: planar, cylindrical, and spherical fluid interfaces. While the tensions of the planar and cylindrical geometries are characterized by first-order changes in the energy, that of the spherical interface depends on second-order contributions. We show that a greater statistical uncertainty is to be expected when calculating the thermodynamic properties of a spherical interface than for the planar and cylindrical cases, and the evaluation of the separate entropic and energetic contributions poses a greater computational challenge than the tension itself. The methodology is employed to determine the vapour-liquid interfacial tension of TIP4P/2005 water at 293 K by molecular dynamics simulation for planar, cylindrical, and spherical geometries. A weak peak in the curvature dependence of the tension is observed in the case of cylindrical threads of condensed liquid at a radius of about 8 Å, below which the tension is found to decrease again. In the case of spherical drops, a marked decrease in the tension from the planar limit is found for radii below ∼ 15 Å; there is no indication of a maximum in the tension with increasing curvature. The vapour-liquid interfacial tension tends towards the planar limit for large system sizes for both the cylindrical and spherical cases. Estimates of the entropic and energetic contributions are also evaluated for the planar and cylindrical geometries and their magnitudes are in line with the expectations of our simple analysis.

Free energies of molecular clusters determined by guided mechanical disassembly.

The excess free energy of a molecular cluster is a key quantity in models of the nucleation of droplets from a metastable vapor phase; it is often viewed as the free energy arising from the presence of an interface between the two phases. We show how this quantity can be extracted from simulations of the mechanical disassembly of a cluster using guide particles in molecular dynamics. We disassemble clusters ranging in size from 5 to 27 argonlike Lennard-Jones atoms, thermalized at 60 K, and obtain excess free energies, by means of the Jarzynski equality, that are consistent with previous studies. We only simulate the cluster of interest, in contrast to approaches that require a series of comparisons to be made between clusters differing in size by one molecule. We discuss the advantages and disadvantages of the scheme and how it might be applied to more complex systems.

Nanoscale stiffness topography reveals structure and mechanics of the transport barrier in intact nuclear pore complexes.

The nuclear pore complex (NPC) is the gate for transport between the cell nucleus and the cytoplasm. Small molecules cross the NPC by passive diffusion, but molecules larger than ∼5 nm must bind to nuclear transport receptors to overcome a selective barrier within the NPC. Although the structure and shape of the cytoplasmic ring of the NPC are relatively well characterized, the selective barrier is situated deep within the central channel of the NPC and depends critically on unstructured nuclear pore proteins, and is therefore not well understood. Here, we show that stiffness topography with sharp atomic force microscopy tips can generate nanoscale cross-sections of the NPC. The cross-sections reveal two distinct structures, a cytoplasmic ring and a central plug structure, which are consistent with the three-dimensional NPC structure derived from electron microscopy. The central plug persists after reactivation of the transport cycle and resultant cargo release, indicating that the plug is an intrinsic part of the NPC barrier. Added nuclear transport receptors accumulate on the intact transport barrier and lead to a homogenization of the barrier stiffness. The observed nanomechanical properties in the NPC indicate the presence of a cohesive barrier to transport and are quantitatively consistent with the presence of a central condensate of nuclear pore proteins in the NPC channel.