String Method Research Articles

Water cavitation from ambient to high temperatures

Predicting cavitation has proved a formidable task, particularly for water. Despite the experimental difficulty of controlling the sample purity, there is nowadays substantial consensus on the remarkable tensile strength of water, on the order of −120 MPa at ambient conditions. Recent progress significantly advanced our predictive capability which, however, still considerably depends on elaborate fitting procedures based on the input of external data. Here a self-contained model is discussed which is shown able to accurately reproduce cavitation data for water over the most extended range of temperatures for which accurate experiments are available. The computations are based on a diffuse interface model which, as only inputs, requires a reliable equation of state for the bulk free energy and the interfacial tension. A rare event technique, namely the string method, is used to evaluate the free-energy barrier as the base for determining the nucleation rate and the cavitation pressure. The data allow discussing the role of the Tolman length in determining the nucleation barrier, confirming that, when the size of the cavitation nuclei exceed the thickness of the interfacial layer, the Tolman correction effectively improves the predictions of the plain Classical Nucleation Theory.

Can One Predict a Drop Contact Angle?

AbstractThe study of wetting phenomena is of great interest due to the multifaceted technological applications of hydrophobic and hydrophilic surfaces. The theoretical approaches proposed by Wenzel and later by Cassie and Baxter to describe the behavior of a droplet of water on a rough solid are extensively used and continuously updated to characterize the apparent contact angle of a droplet. However, the equilibrium hypothesis implied in these models means that they are not always predictive of experimental contact angles due to the strong metastabilities typically occurring in the wetting of heterogeneous surfaces. A predictive scheme for contact angles is thus urgently needed both to characterize a surface by contact angle measurements and to design super‐hydrophobic and ‐oleophobic surfaces with the desired properties, for example, contact angle hysteresis. In this work, a combination of Monte Carlo simulation and the string method is employed to calculate the free energy profile of a liquid droplet deposited on a pillared surface. For the analyzed surfaces, it is shown that there is only one minimum of the free energy that corresponds to the superhydrophobic wetting state while the wet state can present multiple minima. Furthermore, when the surface roughness decreases the amount of local minima observed in the free energy profile increases. The presented approach clarifies the origin of contact angle hysteresis providing quantitative tools for understanding and controlling wetting at structured surfaces.

Structural and energetic analysis of metastable intermediate states in the E1P–E2P transition of Ca2+-ATPase

Sarcoplasmic reticulum (SR) Ca2+-ATPase transports two Ca2+ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca2+, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca2+ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca2+ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca2+ ions and protons when the Ca2+ ions are released toward the SR lumen.

Prediction of multiple dry-wet transition pathways with a mesoscale variational approach.

Water fluctuates in a hydrophobic confinement, forming multiple dry and wet hydration states through evaporation and condensation. Transitions between such states are critical to both thermodynamics and kinetics of solute molecular processes, such as protein folding and protein-ligand binding and unbinding. To efficiently predict such dry-wet transition paths, we develop a hybrid approach that combines a variational implicit solvation model, a generalized string method for minimum free-energy paths, and the level-set numerical implementation. This approach is applied to three molecular systems: two hydrophobic plates, a carbon nanotube, and a synthetic host molecule Cucurbit[7]uril. Without an explicit description of individual water molecules, our mesoscale approach effectively captures multiple dry and wet hydration states, multiple dry-wet transition paths, such as those geometrically symmetric and asymmetric paths, and transition states, providing activation energy barriers between different states. Further analysis shows that energy barriers depend on mesoscopic lengths, such as the separation distance between the two plates and the cross section diameter of the nanotube, and that the electrostatic interactions strongly influence the dry-wet transitions. With the inclusion of solute atomic motion, general collective variables as reaction coordinates, and the finite-temperature string method, together with an improved treatment of continuum electrostatics, our approach can be further developed to sample an ensemble of transition paths, providing more accurate predictions of the transition kinetics.

String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor.

The kinetics of a dynamical system comprising two metastable states is formulated in terms of a finite-time propagator in phase space (position and velocity) adapted to the underdamped Langevin equation. Dimensionality reduction to a subspace of collective variables yields familiar expressions for the propagator, committor, and steady-state flux. A quadratic expression for the steady-state flux between the two metastable states can serve as a robust variational principle to determine an optimal approximate committor expressed in terms of a set of collective variables. The theoretical formulation is exploited to clarify the foundation of the string method with swarms-of-trajectories, which relies on the mean drift of short trajectories to determine the optimal transition pathway. It is argued that the conditions for Markovity within a subspace of collective variables may not be satisfied with an arbitrary short time-step and that proper kinetic behaviors appear only when considering the effective propagator for longer lag times. The effective propagator with finite lag time is amenable to an eigenvalue-eigenvector spectral analysis, as elaborated previously in the context of position-based Markov models. The time-correlation functions calculated by swarms-of-trajectories along the string pathway constitutes a natural extension of these developments. The present formulation provides a powerful theoretical framework to characterize the optimal pathway between two metastable states of a system.

Impact of Molecular Asymmetry of Block Copolymers on the Stability of Defects in Aligned Lamellae

The stability of prototypical dislocation defects occurring in the ordered lamellar morphologies of block copolymers is of particular interest for both practical applications and fundamental research. Here, we study the impact of the segregation strength, compositional asymmetry, and architectural asymmetry on the evolution kinetics of single dislocation as well as the stability of its derivative disconnection defect occurring in the lamellar morphologies formed by AB diblock and AB2 miktoarm star copolymers using self-consistent field theory coupled with the string method and single-chain-in-mean-field simulations. Our results indicate that the segregation strength generally increases the stability of the two defects, whereas the two other factors of asymmetry lower the stability of the single dislocation and significantly enhance the stability of the single disconnection due to the effect of spontaneous curvature. In particular, the single disconnection becomes metastable and can survive for a long period at intermediate segregation and thus may be promisingly applicable for the fabrication of regularly broken lines.

The Role of Conserved Residues in the DEDDh Motif: the Proton-Transfer Mechanism of HIV-1 RNase H

RNase H is a prototypical example for two-metal-ion catalysis in enzymes. An RNase H activity cleaving the ribonucleic acid (RNA) backbone of a DNA/RNA hybrid is present not only in important drug targets, such as the HIV-1 reverse transcriptase, but also in many other nucleases, such as Homo sapiens (Hs) and Escherichia coli (Ec) RNase H or, notably, in enzymes that are part of the CRISPR gene editing molecular machinery. Despite its importance, the reaction mechanism uncovering the proton-transfer events is not yet understood. In particular, it is not known, which group is the proton donor for the leaving group. Moreover, several different proton acceptors were proposed, and the exact identity of the proton acceptor is also elusive. Here, we revisit the mechanism for RNAse H, whereby we find that the highly conserved Glu residue of the DDE motif acts as a proton donor via a mechanism further stabilized by the 2′O atom of the sugar. Additionally, we also describe an alternative proton-transfer mechanism via a conserved catalytic His residue to deprotonate the attacking water molecule. Furthermore, our quantum mechanics/molecular mechanics (QM/MM) calculations combining Hamiltonian replica exchange with a finite-temperature string method provide an accurate free-energy profile for the reaction catalyzed by the HIV-1 RNase H. Our reported pathway is consistent with kinetic data obtained for mutant HIV-1, Hs, and Ec RNase H, with the calculated pKa values of the DEDD residues and with crystallographic studies. The overall reaction barrier of ∼19 kcal mol–1, encountered in the phosphate-cleavage step, matches the slow experimental rate of ∼1–100 min–1. Additionally, using molecular dynamics (MD) calculations, we sample the recently identified binding site for a third transient divalent metal ion in the vicinity of the scissile phosphate in the product complex. Our results account for the experimental observation of a third metal ion facilitating product release in an Aquifex aeolicus RNase III crystal structure and the Bh RNase H in crystallo reaction. Taken together, we provide a molecular mechanism of the nuclease catalytic reaction that is likely common for the broad family of two-metal-ion catalytic phosphate-cleaving enzymes with a DDE motif.

Optimizing String Method's Reproducibility Using Generalized Solute Tempering Replica Exchange.

Obtaining accurate and reproducible free energies from molecular simulations is somewhat tricky due to incomplete knowledge of crucial slow degrees of freedom leading to hidden barriers that can stymie sampling. Employing a sufficiently large number of collective variables (CV) and ensuring ergodic sampling in orthogonal CV space, perhaps via tempering methods, can reduce these issues to some extent. For complex systems with high-dimensional free energy landscapes, both these approaches become computationally expensive. For high-dimensional landscapes, efficient exploration can be enabled by using temperature-accelerated MD (TAMD) and identification and characterization of minimum free energy pathways connecting minima can be found by using the string method (SM). Both TAMD and SM use mean-force estimates from finite MD simulations and are thus susceptible to sampling restrictions from hidden variables. A recent development in parallel tempering methods, "generalized replica exchange solute tempering" (gREST), can enhance sampling at a reasonable computational cost with its flexibility to target very specific "solutes" which can include arbitrary independent variables. Considering the advantages of both methods, we implement gREST-enabled TAMD and SM. By considering two different collective variable representations of the pentapeptide neurotransmitter met-enkephalin, we show that both gREST-enabled TAMD and SM yield more accurate and reproducible free energy predictions than TAMD and SM alone. Given the moderate computational cost of gREST compared with other replica-exchange methods, gREST-enabled SM represents a more attractive method for characterizing free energy minima and pathways among them for a large variety of systems.

Voltage Regulation and Power Consumption Analysis of LED Driver using Switched String Method

This paper discusses an AC/DC buck converter-based LED driver to reduce the voltage from 230VAC to 12VDC with a few strings of LEDs. This led driver is designed with a cost-effective circuit because using a single inductor, single inductor multiple-output (SIMO) can reduce the number of components, control the current independently and precisely on each LED string simultaneously, compared to using an inductor on each LED string. To control current and voltage, PWM (Pulse Width Modulation) control is used as a MOSFET signal switch. This MOSFET calculates the duty cycle so that the desired DC output according to the LED specifications can be realized. The circuit was analyzed using PSpice software. The test based on the duty cycle shows that the highest output voltage is obtained with a work cycle of 10% resulting in a voltage of 5.9V and a current of 32.4mA. Meanwhile, achieving the output value based on the led specification with a voltage of 12V and a maximum current of 31mA has been achieved at a duty cycle of 4.7%. This AC/DC buck converter circuit not only lowers the voltage but can overcome dimming and provide a uniform light output on each LED with an output voltage of 12VDC. The experimental results show that this AC/DC buck converter circuit has been tested and can be applied to the Led driver system.

Analysis of Charged Peptide Loop-Flipping across a Lipid Bilayer Using the String Method with Swarms of Trajectories.

The hydrophobic core of the lipid bilayer is conventionally considered a barrier to the translocation of charged species such that the translocation of even single ions occurs on long time scales. In contrast, experiments have revealed that some materials, including peptides, proteins, and nanoparticles, can translocate multiple charged moieties across the bilayer on experimentally relevant time scales. Understanding the molecular mechanisms underlying this behavior is challenging because resolving corresponding free-energy landscapes with molecular simulation techniques is computationally expensive. To address this challenge, we use atomistic molecular dynamics simulations with the swarms-of-trajectories (SOT) string method to analyze charge translocation pathways across single-component lipid bilayers as a function of multiple collective variables. We first demonstrate that the SOT string method can reproduce the free-energy barrier for the translocation of a charged lysine amino acid analogue in good agreement with the literature. We then obtain minimum free-energy pathways for the translocation, or flipping, of charged peptide loops across the lipid bilayer by utilizing trajectories from prior temperature-accelerated molecular dynamics (TAMD) simulations as initial configurations. The corresponding potential of mean force calculations reveal that the protonation of a central membrane-exposed aspartate residue substantially reduces the free-energy barrier for flipping charged loops by modulating the water content of the bilayer. These results provide new insight into the thermodynamics underlying loop-flipping processes and highlight how the combination of TAMD and the SOT string method can be used to understand complex charge translocation mechanisms.

Massively Parallel GPU-Accelerated String Method for Fast and Accurate Prediction of Molecular Diffusivity in Nanoporous Materials

The diffusivity of guest molecules in nanoporous materials is instrumental for practical applications ranging from gas separation to catalysis and energy storage. Conventional methods to predict di...

Exploring the Minimum-Energy Pathways and Free-Energy Profiles of Enzymatic Reactions with QM/MM Calculations.

Understanding molecular mechanisms of enzymatic reactions is of vital importance in biochemistry and biophysics. Here, we introduce new functions of hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in the GENESIS program to compute the minimum-energy pathways (MEPs) and free-energy profiles of enzymatic reactions. For this purpose, an interface in GENESIS is developed to utilize a highly parallel electronic structure program, QSimulate-QM (https://qsimulate.com), calling it as a shared library from GENESIS. Second, algorithms to search the MEP are implemented, combining the string method (E et al. J. Chem. Phys. 2007, 126, 164103) with the energy minimization of the buffer MM region. The method implemented in GENESIS is applied to an enzyme, triosephosphate isomerase, which converts dihyroxyacetone phosphate to glyceraldehyde 3-phosphate in four proton-transfer processes. QM/MM-molecular dynamics simulations show performances of greater than 1 ns/day with the density functional tight binding (DFTB), and 10-30 ps/day with the hybrid density functional theory, B3LYP-D3. These performances allow us to compute not only MEP but also the potential of mean force (PMF) of the enzymatic reactions using the QM/MM calculations. The barrier height obtained as 13 kcal mol-1 with B3LYP-D3 in the QM/MM calculation is in agreement with the experimental results. The impact of conformational sampling in PMF calculations and the level of electronic structure calculations (DFTB vs B3LYP-D3) suggests reliable computational protocols for enzymatic reactions without high computational costs.

The Transition Pathway Between the Closed and Open States of Insulin Degrading Enzyme Shows Two Distinct Motions: Rotation Around a Hinge and Grinding Between Two Domains

Insulin Degrading Enzyme (IDE) is involved in the degradation of insulin, amylin, and glucagon, peptides key in controlling blood glucose level. IDE has two ∼55 kDa homologous N- and C-terminal domains (IDE-N and IDE-C), each containing two homologous subdomains (D1 and D2 for IDE-N and D3 and D4 for IDE-C). For IDE to degrade its substrates, both IDE-N and IDE-C must come together for the catalytic cleft to assume a closed conformation. To investigate the mechanism through which IDE transitions between its closed and open conformations, we combined closed state crystal structures with open state CryoEM structures to run molecular dynamics simulations following the string method with swarms of trajectories and bias-exchange umbrella sampling protocols. Our analysis shows that IDE undergoes two distinct modes of motion when opening: a rotation about the hinge joining IDE-N to IDE-C (termed the hinge motion), and a rotation about the dihedral angle between the plane containing D1, D2, and D3 and the plane containing D2, D3, and D4 (termed the grinding motion). This observation matches well with multiple-body analysis performed in Relion used to deduce the protein's motion from available CryoEM data. Whereas the hinge opening motion remains relatively constant throughout the trajectory, the grinding motion appears to stop and restart. Our free energy profile constructed from MD simulations also reveals that IDE passes through a minimum energy state near its closed conformation, and our analysis suggests that this could be attributed to π-π interaction between residues W495 and F218. Our simulations and analysis provide detailed insight into the physical mechanism for the conformational transition between the closed and open states of IDE.

Conformational Transition Pathway of GkPOT

GkPOT, a Proton-Coupled coupled Oligopeptide Transporter transporter (POTs) from Geobacillus Kaustophilus, is among the symporter members of the Major Facilitator Superfamily (MFS) of transporters. Functional and structural analysis of various POTs suggest that the uptake of small peptides and peptide- like molecules to the cell across the cell membrane, via the alternating access mechanism, utilizes an inward directed proton electrochemical gradient the source of energy for their active symport function. The transition between the inward-facing (IF) and outward-facing (OF) conformations is important in understanding the structural relationship between large-scale protein conformational changes and substrate translocation that has often times remained elusive due to the short time scales of molecular dynamics simulations (MD) limitations of computational and experimental effort techniques. Using an extensive set of enhanced sampling techniques, we have characterized the conformational transition pathway of GkPOT. We have aimed at describing the large-scale conformational changes between the IF and OF states while in the presence and absence of substrate (dialanine peptide). Nonequlibrium pulling simulations were initiated from the known inward facing IF conformation and steered the system toward the unknown outward facing OF conformation using orientation based collective variables defined on different transmembrane helices. The transition pathways are far from equilibrium and are smoothed with string method with swarms of trajectories (SMwST), thus generating microseconds of biased and unbiased simlulations. Free energy profiles of the conformational transition pathways were obtained from a novel maximum-likelihood estimation method. Our results indicate that the presence of ligand significantly changes the conformational landscape with respect to the apo system which contains a greater degree of conformational variability.

Impact of Architecture of Symmetric Block Copolymers on the Stability of a Dislocation Defect

Increasing the excess free energy (ΔFd) and lowering the free-energy barrier (ΔFb) of a defect are very critical for the preparation of defect-free ordered structures from the self-assembly of block copolymers. It is well known that chain architecture is one of the most useful variables for controlling the self-assembly of block copolymers. In this work, we have investigated ΔFd and ΔFb of a prototypical dislocation defect in the melts of various symmetric [AB]n linear and AnBn star copolymers (n = 2, 3, and 4) using self-consistent field theory together with the string method. We compare the magnitudes of ΔFd and ΔFb between these different copolymers in two cases: equal χN/n and unified equivalent degree of segregation. In the case of equal χN/n, [AB]n linear copolymers have a much lower ΔFd and ΔFb than AB diblock, while AnBn star copolymers have a significantly higher ΔFd but only slightly higher ΔFb. In the other case, ΔFd and ΔFb of [AB]n linear copolymers are lower and higher than those of AB diblock, respectively, but the differences decrease with increasing n. In contrast, ΔFd of AnBn star copolymers is slightly higher or comparable to that of AB diblock, and ΔFb is significantly lower than that of AB diblock. Moreover, ΔFb of AnBn continues to decrease as n increases. Our results lead to an important conclusion that AnBn star copolymers are desired by the directed self-assembly to produce defect-free stripes.

Current status and development trends of efficient oil production testing technology

Oil production testing is a critical tool to understand reservoir properties and well producibility. The development of oil production testing technology in China has mainly gone through three phases: conventional oil production testing phase, oil production testing phase, and integrated oil production testing phase. Currently, domestic and overseas oilfields are still adopting the traditional oil production testing method, which contains plenty of repetitive processes that cost longer operating time, higher operating cost, formation damage caused by excessive high-density fluid, and many other shortcomings. Also, the difficulties of oil production testing in the deep and ultra-deep well under HPHT conditions are significant. Analyzing the development trend of oil production testing, there are two main topics identified: oil production testing for separated layer via one trip string and Pad-free oil production testing method. The oil production testing for separated layer via one trip string was developed for testing formations where lamination and thin layers are presented and causing interference among the testing layers. The Pad-free oil production testing methodology was developed for testing wells that fail to obtain reservoir fluid properties due to the formation damage caused by a high fluid density pad. This paper is aiming to summarize and analyze the most advanced oil production testing technology worldwide and innovations had been made to the oil production testing field, hopefully inspired researchers to develop possible future uses and further improvements in efficiency. Facing the challenges of low gas prices, only continuous innovation in technology and the upgradation of tools and equipment can achieve the goal of improving quality and increasing efficiency.

Construction of a Minimum Energy Path for the VT Flash Model by the String Method Coupled with the Exponential Time Differencing Scheme

Construction of a Minimum Energy Path for the VT Flash Model by the String Method Coupled with the Exponential Time Differencing Scheme

Where are those lipid nano rings?

Highly curved toroidal micelles with diameters as small as 100 nm have been successfully constructed by self-assembly of amphiphilic block copolymers. These structures may have potential applications in gene or drug delivery. Experimental observations suggest that toroidal micelles likely originate from spherical or disc-like micelles which are tricked into forming toroidal micelles upon external stimuli (‘smart’ materials). Since self-assembly of polymeric and lipid surfactants is guided by the same physical principles, we hypothesize that ‘smart’ lipid surfactants can be equivalently tricked into forming highly curved toroidal micelles that are tenfold smaller (≃10 nm diameter). Paradoxically, these ‘nano rings’ have never been observed. Using coarse-grained molecular dynamics (MD) simulations in conjunction with a state-of-the-art free energy calculation method (a string method), we illustrate how a thermo-responsive lipid surfactant is able to form toroidal micelles. These micelles originate from disc-like micelles that are spontaneously perforated upon heat shocking, thereby supporting a longstanding hypothesis on the possible origin of polymeric toroidal micelle phases observed in experiments. We illustrate that kinetically stable ‘nano rings’ are substantially shorter lived than their tenfold larger polymeric analogs. The estimated life-time (milliseconds) is in fact similar to the characteristic breaking time of the corresponding worm-like micelle. Finally, we resolve the characteristic finger print which ‘nano rings’ leave in time-resolved X-ray spectra and illustrate how the uptake of small DNA fragments may enhance their stability. Despite a shared kinetics of self-assembly, length scale dependent differences in the life-time of surfactant phases can occur when phases are kinetically rather than thermodynamically stable. This results in the apparent absence or presence of toroidal micelle phases on different length scales. Our theoretical work precisely illustrates that the universality of surfactants nevertheless remains conserved even at different length scales.

Investigating nucleation of phase transitions in rod-coil block copolymers

It is known that the nucleation of liquid crystal polymers with orientation interactions can reduce the energy barrier during the polymer crystallization. In this work, we combine the SCFT and string method to explore the nucleation and liquid crystal behavior of rod-coil block copolymers. By examining nucleation transitions from cylinders with different directions to lamellae, we obtain the information of critical nuclei for the first time, including the volume, shape and energy barrier. We further investigate the impacts of orientation interactions along different transition paths. The results show that if the cylinder and lamellae have inconsistent directions, the nucleation will occur with relatively longer transition path and multiple reorientations, and thus leading to higher energy barrier. Nucleation under different Flory-Huggins interactions and nucleation via precursory metastable structures are investigated, and compared with the classical nucleation theory. This work develops the nucleation studies for complex block copolymers with segment orientations, which is helpful for understanding the nucleation of liquid crystal polymers.

Finding Reaction Pathways and Transition States: r-ARTn and d-ARTn as an Efficient and Versatile Alternative to String Approaches.

Finding transition states and diffusion pathways is essential to understand the evolution of materials and chemical reactions. Such characterization is hampered by the heavy computation costs associated with exploring energy landscapes at ab initio accuracy. Here, we revisit the activation-relaxation technique (ARTn) to considerably reduce its costs when used with the density functional theory and propose three adapted versions of the algorithm to efficiently (i) explore the energy landscape of complex materials with the knowledge of a single minimum (ARTn); (ii) identify a transition state when two minima or a guess transition state is given (refining ART or r-ART); and (iii) reconstruct complex pathways between two given states (directed ART or d-ART). We show the application of these three variants on benchmark examples and on various complex defects in silicon. For the latter, the presented improvements to ART lead to much more precise transition states while being 2 to 6 times faster than the commonly used string methods such as the climbing image nudged elastic band method (CI-NEB).