Molecular Dynamics Study of Structure, Folding, and Aggregation of Poly-PR and Poly-GR Proteins.

Poly-proline-arginine (poly-PR) and poly-glycine-arginine (poly-GR) proteins are believed to be the most toxic dipeptide repeat (DPR) proteins that are expressed by the hexanucleotide repeat expansion mutation in C9ORF72, which are associated with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) diseases. Their structural information and mechanisms of toxicity remain incomplete, however. Using molecular dynamics simulation and all-atom model of proteins, we study folding and aggregation of both poly-PR and poly-GR. The results indicate formation of double-helix structure during the aggregation of poly-PR into dimers, whereas no stable aggregate is formed during the aggregation of poly-GR; the latter only folds into α-helix and double-helix structures that are similar to those formed in the folding of poly-glycine-alanine (poly-GA) protein. Our findings are consistent with the experimental data indicating that poly-PR and poly-GR are less likely to aggregate because of the hydrophilic arginine residues within their structures. Such characteristics could, however, in some respect facilitate migration of the DPR proteins between and within cells and, at the same time, give proline residues the benefits of activating the receptors that regulate ionotropic effect in neurons, resulting in death or malfunction of neurons because of the abnormal increase or decrease of the ion transmission. This may explain the neurotoxicities of poly-PR and poly-GR associated with many neurodegenerative diseases. To our knowledge, this is the first molecular dynamics simulation of the phenomena involving poly-PR and poly-GR proteins.

Efficient Transport Between Disjoint Nanochannels by a Water Bridge.

Water channels are important to new purification systems, osmotic power harvesting in salinity gradients, hydroelectric voltage conversion, signal transmission, drug delivery, and many other applications. To be effective, water channels must have structures more complex than a single tube. One way of building such structures is through a water bridge between two disjoint channels that are not physically connected. We report on the results of extensive molecular dynamics simulation of water transport through such bridges between two carbon nanotubes separated by a nanogap. We show that not only can pressurized water be transported across a stable bridge, but also that (i) for a range of the gap's width l_{g} the bridge's hydraulic conductance G_{b} does not depend on l_{g}, (ii) the overall shape of the bridge is not cylindrical, and (iii) the dependence of G_{b} on the angle between the axes of two nonaligned nanochannels may be used to tune the flow rate between the two.

Molecular dynamics study of structure, folding, and aggregation of poly-glycine-alanine (Poly-GA).

Poly-glycine-alanine (poly-GA) proteins are widely believed to be one of the main toxic dipeptide repeat molecules associated with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia diseases. Using discontinuous molecular dynamics simulation and an all-atom model of the proteins, we study folding, stability, and aggregation of poly-GA. The results demonstrate that poly-GA is an aggregation-prone protein that, after a long enough time, forms ß-sheet-rich aggregates that match recent experiment data and that two unique helical structures are formed very frequently, namely, ß-helix and double-helix. The details of the two structures are analyzed. The analysis indicates that such helical structures are stable and share the characteristics of both α-helices and ß-sheets. Molecular simulations indicate that identical phenomena also occur in the aggregation of poly-glycine-arginine (poly-GR). Therefore, we hypothesize that proteins of type (GX)n in which X may be any non-glycine amino acid and n is the repeat length may share the same folding structures of ß-helix and double-helix and that it is the glycine in the repeat that contributes the most to this characteristic. Molecular dynamics simulation with continuous interaction potentials and explicit water molecules as the solvent supports the hypothesis. To our knowledge, this is the first molecular dynamics simulation of the phenomena involving poly-GA and poly-GR proteins.

Dynamics of proteins aggregation. II. Dynamic scaling in confined media.

In this paper, the second in a series devoted to molecular modeling of protein aggregation, a mesoscale model of proteins together with extensive discontinuous molecular dynamics simulation is used to study the phenomenon in a confined medium. The medium, as a model of a crowded cellular environment, is represented by a spherical cavity, as well as cylindrical tubes with two aspect ratios. The aggregation process leads to the formation of ß sheets and eventually fibrils, whose deposition on biological tissues is believed to be a major factor contributing to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, and amyotrophic lateral sclerosis diseases. Several important properties of the aggregation process, including dynamic evolution of the total number of the aggregates, the mean aggregate size, and the number of peptides that contribute to the formation of the ß sheets, have been computed. We show, similar to the unconfined media studied in Paper I [S. Zheng et al., J. Chem. Phys. 145, 134306 (2016)], that the computed properties follow dynamic scaling, characterized by power laws. The existence of such dynamic scaling in unconfined media was recently confirmed by experiments. The exponents that characterize the power-law dependence on time of the properties of the aggregation process in spherical cavities are shown to agree with those in unbounded fluids at the same protein density, while the exponents for aggregation in the cylindrical tubes exhibit sensitivity to the geometry of the system. The effects of the number of amino acids in the protein, as well as the size of the confined media, have also been studied. Similarities and differences between aggregation in confined and unconfined media are described, including the possibility of no fibril formation, if confinement is severe.

Effect of the geometry of confining media on the stability and folding rate of α -helix proteins.

Protein folding in confined media has attracted wide attention over the past 15 years due to its importance to both in vivo and in vitro applications. It is generally believed that protein stability increases by decreasing the size of the confining medium, if the medium's walls are repulsive, and that the maximum folding temperature in confinement is in a pore whose size D 0 is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 135, 125101 (2011)], we showed that, contrary to the current theoretical predictions, the maximum folding temperature occurs in larger pores for smaller α-helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an α-helical native state that contain the ß structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding temperature T f on the size D of a confined medium occurs in larger media for larger proteins is correct only in spherical geometry, whereas the opposite is true in the two other geometries that we study. Also studied is the effect of the strength of the interaction between the confined media's walls and the proteins. If the walls are only weakly or moderately attractive, a complex behavior emerges that depends on the size of the confining medium.

Static and dynamic properties of supercooled water in small nanotubes.

The static and dynamic properties of water in small silicon-carbide and carbon nanotubes have been studied over the temperature range 100 K-298 K, using extensive molecular dynamics simulations. The computed properties include the radial distribution function, the cage correlation function, the space-time autocorrelation function, the velocity autocorrelation function, and the self-diffusivity. They all indicate that, under the conditions that we study, water does not freeze in small nanotubes; the Stokes-Einstein relation breaks down, and the self-diffusivity exhibits a transition around 230 K, very close to 228 K, the temperature at which a fragile-to-strong dynamic crossover is supposed to happen. The cage correlation function C(t) decays according to a stretched-exponential function, C(t) ∼ exp[ - (t/τ)(ß)], where τ is a relaxation time and ß is a topological exponent.

Dynamics of proteins aggregation. I. Universal scaling in unbounded media.

It is well understood that in some cases proteins do not fold correctly and, depending on their environment, even properly-folded proteins change their conformation spontaneously, taking on a misfolded state that leads to protein aggregation and formation of large aggregates. An important factor that contributes to the aggregation is the interactions between the misfolded proteins. Depending on the aggregation environment, the aggregates may take on various shapes forming larger structures, such as protein plaques that are often toxic. Their deposition in tissues is a major contributing factor to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, amyotrophic lateral sclerosis, and prion. This paper represents the first part in a series devoted to molecular simulation of protein aggregation. We use the PRIME, a meso-scale model of proteins, together with extensive discontinuous molecular dynamics simulation to study the aggregation process in an unbounded fluid system, as the first step toward MD simulation of the same phenomenon in crowded cellular environments. Various properties of the aggregates have been computed, including dynamic evolution of aggregate-size distribution, mean aggregate size, number of peptides that contribute to the formation of ß sheets, number of various types of hydrogen bonds formed in the system, radius of gyration of the aggregates, and the aggregates' diffusivity. We show that many of such quantities follow dynamic scaling, similar to those for aggregation of colloidal clusters. In particular, at long times the mean aggregate size S(t) grows with time as, S(t) ∼ tz, where z is the dynamic exponent. To our knowledge, this is the first time that the qualitative similarity between aggregation of proteins and colloidal aggregates has been pointed out.

First principles-based multiparadigm, multiscale strategy for simulating complex materials processes with applications to amorphous SiC films.

Progress has recently been made in developing reactive force fields to describe chemical reactions in systems too large for quantum mechanical (QM) methods. In particular, ReaxFF, a force field with parameters that are obtained solely from fitting QM reaction data, has been used to predict structures and properties of many materials. Important applications require, however, determination of the final structures produced by such complex processes as chemical vapor deposition, atomic layer deposition, and formation of ceramic films by pyrolysis of polymers. This requires the force field to properly describe the formation of other products of the process, in addition to yielding the final structure of the material. We describe a strategy for accomplishing this and present an example of its use for forming amorphous SiC films that have a wide variety of applications. Extensive reactive molecular dynamics (MD) simulations have been carried out to simulate the pyrolysis of hydridopolycarbosilane. The reaction products all agree with the experimental data. After removing the reaction products, the system is cooled down to room temperature at which it produces amorphous SiC film, for which the computed radial distribution function, x-ray diffraction pattern, and the equation of state describing the three main SiC polytypes agree with the data and with the QM calculations. Extensive MD simulations have also been carried out to compute other structural properties, as well the effective diffusivities of light gases in the amorphous SiC film.

Physics-informed and data-driven discovery of governing equations for complex phenomena in heterogeneous media.

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition software and hardware are providing vast amounts of data for various complex phenomena that occur in heterogeneous media, ranging from those in atmospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse multiscale and multiphysics phenomena that contain elements of stochasticity or heterogeneity, and to generate large volumes of numerical data for them. Thus, given a heterogeneous system with annealed or quenched disorder in which a complex phenomenon occurs, how should one analyze and model the system and phenomenon, explain the data, and make predictions for length and time scales much larger than those over which the data were collected? We divide such systems into three distinct classes. (i) Those for which the governing equations for the physical phenomena of interest, as well as data, are known, but solving the equations over large length scales and long times is very difficult. (ii) Those for which data are available, but the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on the data, or that the number of degrees of freedom of the system is so large that deriving the complete equations is very difficult, if not impossible, as a result of which one must develop the governing equations with reduced dimensionality. (iii) In the third class are systems for which large amounts of data are available, but the governing equations for the phenomena of interest are not known. Several classes of physics-informed and data-driven approaches for analyzing and modeling of the three classes of systems have been emerging, which are based on machine learning, symbolic regression, the Koopman operator, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation combined with a neural network, and stochastic optimization and analysis. This perspective describes such methods and the latest developments in this highly important and rapidly expanding area and discusses possible future directions.

Cross-correlation function for accurate reconstruction of heterogeneous media.

Porous media, heterogeneous materials, and biological tissues are examples of ubiquitous disordered systems, the understanding of which and any physical phenomenon in them entails having an accurate model. We show that a new reconstruction method based on a cross-correlation function and a one-dimensional raster path provides an accurate description of a wide variety of such materials and media. The reconstruction uses a single 2D slice of data to reconstruct an entire 3D medium. Seventeen examples are reconstructed accurately, as indicated by two connectivity functions that we compute for them. The reconstruction method may be used for both unconditioned and conditioned problems, and is highly efficient computationally.

Percolation and conductivity in evolving disordered media.

Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the networks' bonds remains constant throughout the entire process. There are, however, many important problems in which the conductance of the bonds evolves over time and does not remain constant. Examples include clogging, dissolution and precipitation, and catalytic processes in porous materials, as well as the deformation of a porous medium by applying an external pressure or stress to it that reduces the size of its pores. We introduce two percolation models to study the evolution of the conductivity of such networks. The two models are related to natural and industrial processes involving clogging, precipitation, and dissolution processes in porous media and materials. The effective conductivity of the models is shown to follow known power laws near the percolation threshold, despite radically different behavior both away from and even close to the percolation threshold. The behavior of the networks close to the percolation threshold is described by critical exponents, yielding bounds for traditional percolation exponents. We show that one of the two models belongs to the traditional universality class of percolation conductivity, while the second model yields nonuniversal scaling exponents.

Data-driven discovery of the governing equations for transport in heterogeneous media by symbolic regression and stochastic optimization.

With advances in instrumentation and the tremendous increase in computational power, vast amounts of data are becoming available for many complex phenomena in macroscopically heterogeneous media, particularly those that involve flow and transport processes, which are problems of fundamental interest that occur in a wide variety of physical systems. The absence of a length scale beyond which such systems can be considered as homogeneous implies that the traditional volume or ensemble averaging of the equations of continuum mechanics over the heterogeneity is no longer valid and, therefore, the issue of discovering the governing equations for flow and transport processes is an open question. We propose a data-driven approach that uses stochastic optimization and symbolic regression to discover the governing equations for flow and transport processes in heterogeneous media. The data could be experimental or obtained by microscopic simulation. As an example, we discover the governing equation for anomalous diffusion on the critical percolation cluster at the percolation threshold, which is in the form of a fractional partial differential equation, and agrees with what has been proposed previously.

Interpreting water demands of forests and grasslands within a new Budyko formulation of evapotranspiration using percolation theory.

The relationship between carbon cycle and water demand is key to understanding global climate change, vegetation productivity, and predicting the future of water resources. The water balance, which enumerates the relative fractions of precipitation P that run off, Q, or are returned to the atmosphere through evapotranspiration, ET, links drawdown of atmospheric carbon with the water cycle through plant transpiration. Our theoretical description based on percolation theory proposes that dominant ecosystems tend to maximize drawdown of atmospheric carbon in the process of growth and reproduction, thus providing a link between carbon and water cycles. In this framework, the only parameter is the fractal dimensionality df of the root system. Values of df appear to relate to the relative roles of nutrient and water accessibility. Larger values of df lead to higher ET values. Known ranges of grassland root fractal dimensions predict reasonably the range of ET(P) in such ecosystems as a function of aridity index. Forests with shallower root systems, should be characterized by a smaller df and, therefore, ET that is a smaller fraction of P. The prediction of ET/P using the 3D percolation value of df matches rather closely results deemed typical for forests based on a phenomenology already in common use. We test predictions of Q with P against data and data summaries for sclerophyll forests in southeastern Australia and the southeastern USA. Applying PET data from a nearby site constrains the data from the USA to lie between our ET predictions for 2D and 3D root systems. For the Australian site, equating cited "losses" with PET underpredicts ET. This discrepancy is mostly removed by referring to mapped values of PET in that region. Missing in both cases is local PET variability, more important for reducing data scatter in southeastern Australia, due to the greater relief.

Molecular dynamics simulation of pressure-driven water flow in silicon-carbide nanotubes.

Many properties of silicon carbide (SiC) nanotubes, such as their high mechanical strength and resistance to corrosive environments, are superior to those of their carboneous counterparts, namely, carbon nanotubes (CNTs) and, therefore, SiC nanotubes can be a viable alternative to CNTs in a variety of applications. We employ molecular dynamics simulations to examine flow of water in SiC nanotubes and to study the differences and similarities with the same phenomenon in the CNTs. The simulations indicate that SiC nanotubes always provide larger flow enhancements than those reported for the CNTs. Moreover, a given flow enhancement in SiC nanotubes requires an applied pressure gradient that is at least an order of magnitude smaller than the corresponding value in a CNT of the same size.

Confinement in nanopores can destabilize α-helix folding proteins and stabilize the ß structures.

Protein folding in confined media has attracted wide attention over the past decade due to its importance in both in vivo and in vitro applications. Currently, it is generally believed that protein stability increases by decreasing the size of the confining medium, if its interaction with the confining walls is repulsive, and that the maximum folding temperature in confinement occurs for a pore size only slightly larger than the smallest dimension of the folded state of a protein. Protein stability in pore sizes, very close to the size of the folded state, has not however received the attention that it deserves. Using detailed, 0.3-ms-long molecular dynamics simulations, we show that proteins with an α-helix native state can have an optimal folding temperature in pore sizes that do not affect the folded-state structure. In contradiction to the current theoretical explanations, we find that the maximum folding temperature occurs in larger pores for smaller α-helices. In highly confined pores the free energy surface becomes rough, and a new barrier for protein folding may appear close to the unfolded state. In addition, in small nanopores the protein states that contain the ß structures are entropically stabilized, in contrast to the bulk. As a consequence, folding rates decrease notably and the free energy surface becomes rougher. The results shed light on many recent experimental observations that cannot be explained by the current theories, and demonstrate the importance of entropic effects on proteins' misfolded states in highly confined environments. They also support the concept of passive effect of chaperonin GroEL on protein folding by preventing it from aggregation in crowded environment of biological cells, and provide deeper clues to the α → ß conformational transition, believed to contribute to Alzheimer's and Parkinson's diseases. The strategy of protein and enzyme stabilization in confined media may also have to be revisited in the case of tight confinement. For in silico studies of protein folding in confined media, use of non-Go potentials may be more appropriate.

Elastic moduli of body-centered cubic lattice near rigidity percolation threshold: Finite-size effects and evidence for first-order phase transition.

Extensive numerical simulations of rigidity percolation with only central forces in large three-dimensional lattices have indicated that many of their topological properties undergo a first-order phase transition at the rigidity percolation threshold p_{ce}. In contrast with such properties, past numerical calculations of the elastic moduli of the same lattices had provided evidence for a second-order phase transition. In this paper we present the results of extensive simulation of rigidity percolation in large body-centered cubic (bcc) lattices, and show that as the linear size L of the lattice increases, the elastic moduli close to p_{ce} decrease in a stepwise, discontinuous manner, a feature that is absent in lattices with L<30. The number and size of such steps increase with L. As p_{ce} is approached, long-range, nondecaying orientational correlations are built up, giving rise to compact, nonfractal clusters. As a result, we find that the backbone of the lattice at p_{ce} is compact with a fractal dimension D_{bb}≈3. The absence of fractal, scale-invariant clusters, the hallmark of second-order phase transitions, together with the stairwise behavior of the elastic moduli, provide strong evidence that, at least in bcc lattices, many of the topological properties of rigidity percolation as well as its elastic moduli may undergo a first-order phase transition at p_{ce}. In relatively small lattices, however, the boundary effects interfere with the nonlocal nature of the rigidity percolation. As a result, only when such effects diminish in large lattices does the true nature of the phase transition emerge.

Retraction: Phase transitions, percolation, fracture of materials, and deep learning [Phys. Rev. E 102, 011001(R) (2020)].

Retraction of DOI: 10.1103/PhysRevE.102.011001.

Graphyne-3: a highly efficient candidate for separation of small gas molecules from gaseous mixtures.

Two-dimensional nanosheets, such as the general family of graphenes have attracted considerable attention over the past decade, due to their excellent thermal, mechanical, and electrical properties. We report on the result of a study of separation of gaseous mixtures by a model graphyne-3 membrane, using extensive molecular dynamics simulations and density functional theory. Four binary and one ternary mixtures of H[Formula: see text], CO[Formula: see text], CH[Formula: see text] and C[Formula: see text]H[Formula: see text] were studied. The results indicate the excellence of graphyne-3 for separation of small gas molecules from the mixtures. In particular, the H[Formula: see text] permeance through the membrane is on the order of [Formula: see text] gas permeation unit, by far much larger than those in other membranes, and in particular in graphene. To gain deeper insights into the phenomenon, we also computed the density profiles and the residence times of the gases near the graphyne-3 surface, as well as their interaction energies with the membrane. The results indicate clearly the tendency of H[Formula: see text] to pass through the membrane at high rates, leaving behind C[Formula: see text]H[Formula: see text] and larger molecules on the surface. In addition, the possibility of chemisorption is clearly ruled out. These results, together with the very good mechanical properties of graphyne-3, confirm that it is an excellent candidate for separating small gas molecules from gaseous mixtures, hence opening the way for its industrial use.

Molecular dynamics simulations of adsorption and diffusion of gases in silicon-carbide nanotubes.

Silicon carbide nanotubes (SiCNTs) are new materials with excellent properties, such as high thermal stability and mechanical strength, which are much improved over those of their carboneous counterparts, namely, carbon nanotubes (CNTs). Gas separation processes at high temperatures and pressures may be improved by developing mixed-matrix membranes that contain SiCNTs. Such nanotubes are also of interest in other important processes, such as hydrogen production and its storage, as well as separation by supercritical adsorption. The structural parameters of the nanotubes, i.e., their diameter, curvature, and chirality, as well as the interaction strength between the gases and the nanotubes' walls, play a fundamental role in efficient use of the SiCNTs in such processes. We employ molecular dynamics simulations in order to examine the adsorption and diffusion of N(2), H(2), CO(2), CH(4), and n-C(4)H(10) in the SiCNTs, as a function of the pressure and the type of the nanotubes, namely, the zigzag, armchair, and chiral tubes. The simulations indicate the strong effect of the nanotubes' chirality and curvature on the pressure dependence of the adsorption isotherms and the self-diffusivities. Detailed comparison is made between the results and those for the CNTs. In particular, we find that the adsorption capacity of the SiCNTs for hydrogen is higher than the CNTs' under the conditions that we have studied.

Molecular origin of sliding friction and flash heating in rock and heterogeneous materials.

It is generally believed that earthquakes occur when faults weaken with increasing slip rates. An important factor contributing to this phenomenon is the faults' dynamic friction, which may be reduced during earthquakes with high slip rates, a process known as slip-rate weakening. It has been hypothesized that the weakening phenomenon during fault slip may be activated by thermal pressurization of pores' fluid and flash heating, a microscopic phenomenon in which heat is generated at asperity contacts due to high shear slip rates. Due to low thermal conductivity of rock, the heat generated at the contact points or surfaces cannot diffuse fast enough, thus concentrating at the contacts, increasing the local contact temperature, and reducing its frictional shear strength. We report the results of what we believe to be the first molecular scale study of the decay of the interfacial friction force in rock, observed in experiemntal studies and attributed to flash heating. The magnitude of the reduction in the shear stress and the local friction coefficients have been computed over a wide range of shear velocities V. The molecular simulations indicate that as the interfacial temperature increases, bonds between the atoms begin to break, giving rise to molecular-scale fracture that eventually produces the flash heating effect. The frequency of flash heating events increases with increasing sliding velocity, leaving increasingly shorter times for the material to relax, hence contributing to the increased interfacial temperature. If the material is thin, the heat quickly diffuses away from the interface, resulting in sharp decrease in the temperature immediately after flash heating. The rate of heat transfer is reduced significantly with increasing thickness, keeping most of the heat close to the interface and producing weakened material. The weakening behavior is demonstrated by computing the stress-strain diagram. For small strain rates there the frictional stress is essentially independent of the materials' thickness. As the strain rate increases, however, the dependence becomes stronger. Specifically, the stress-strain diagrams at lower velocities V manifest a pronounced strength decrease over small distances, whereas they exhibit progressive increase in the shear stress at higher V, which is reminiscent of a transition from ductile behavior at high velocities to brittle response at low velocities.