Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent.

The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of Rg2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy.

Efficient single-run implementation of generalized Einstein relation to compute transport coefficients: A binary-based time sampling.

A robust and simple implementation of the generalized Einstein formulation using single equilibrium molecular dynamics simulation is introduced to compute diffusion and shear viscosity. The unique features underlying this framework are as follows: (1) The use of a simple binary-based method to sample time-dependent transport coefficients results in a uniform distribution of data on a logarithmic time scale. Although we sample "on-the-fly," the algorithm is readily applicable for post-processing analysis. Overlapping same-length segments are not sampled as they indicate strong correlations. (2) Transport coefficients are estimated using a power law fitting function, a generalization of the standard linear relation, that accurately describes the long-time plateau. (3) The use of a generalized least squares (GLS) fitting estimator to explicitly consider correlations between fitted data points results in a reliable estimate of the statistical uncertainties in a single run. (4) The covariance matrix for the GLS method is estimated analytically using the Wiener process statistics and computed variances. (5) We provide a Python script to perform the fits and automate the procedure to determine the optimal fitting domain. The framework is applied to two fluids, binary hard sphere and a Lennard-Jones near the triple point, and the validity of the single-run estimates is verified against multiple independent runs. The approach should be applicable to other transport coefficients since the diffusive limit is universal to all of them. Given its rigor and simplicity, this methodology can be readily incorporated into standard molecular dynamics packages using on-the-fly or post-processing analysis.

Virial equation of state as a new frontier for computational chemistry.

The virial equation of state (VEOS) provides a rigorous bridge between molecular interactions and thermodynamic properties. The past decade has seen renewed interest in the VEOS due to advances in theory, algorithms, computing power, and quality of molecular models. Now, with the emergence of increasingly accurate first-principles computational chemistry methods, and machine-learning techniques to generate potential-energy surfaces from them, VEOS is poised to play a larger role in modeling and computing properties. Its scope of application is limited to where the density series converges, but this still admits a useful range of conditions and applications, and there is potential to expand this range further. Recent applications have shown that for simple molecules, VEOS can provide first-principles thermodynamic property data that are competitive in quality with experiment. Moreover, VEOS provides a focused and actionable test of molecular models and first-principles calculations via comparison to experiment. This Perspective presents an overview of recent advances and suggests areas of focus for further progress.

Probabilistic computations of virial coefficients of polymeric structures described by rigid configurations of spherical particles: A fundamental extension of the ZENO program.

We describe an extension of the ZENO program for polymer and nanoparticle characterization that allows for precise calculation of the virial coefficients, with uncertainty estimates, of polymeric structures described by arbitrary rigid configurations of hard spheres. The probabilistic method of virial computation used for this extension employs a previously developed Mayer-sampling Monte Carlo method with overlap sampling that allows for a reduction of bias in the Monte Carlo averaging. This capability is an extension of ZENO in the sense that the existing program is also based on probabilistic sampling methods and involves the same input file formats describing polymer and nanoparticle structures. We illustrate the extension's capabilities, demonstrate its accuracy, and quantify the efficiency of this extension of ZENO by computing the second, third, and fourth virial coefficients and metrics quantifying the difficulty of their calculation, for model polymeric structures having several different shapes. We obtain good agreement with literature estimates available for some of the model structures considered.

The EcpD Tip Adhesin of the Escherichia coli Common Pilus Mediates Binding of Enteropathogenic E. coli to Extracellular Matrix Proteins.

The attachment of enteropathogenic Escherichia coli (EPEC) to intestinal epithelial cells is facilitated by several adhesins; however, the individual host-cell receptors for pili-mediated adherence have not been fully characterized. In this study, we evaluated the hypothesis that the E. coli common pilus (ECP) tip adhesin protein EcpD mediates attachment of EPEC to several extracellular matrix (ECM) glycoproteins (fibronectin, laminin, collagens I and IV, and mucin). We found that the ΔecpA mutant, which lacks production of the EcpA filament but retains EcpD on the surface, adhered to these glycoproteins below the wild-type levels, while the ΔecpD mutant, which does not display EcpA or EcpD, bound significantly less to these host glycoproteins. In agreement, a purified recombinant EcpD subunit bound significantly more than EcpA to laminin, fibronectin, collagens I and IV, and mucin in a dose-dependent manner. These are compelling data that strongly suggest that ECP-producing EPEC may bind to host ECM glycoproteins and mucins through the tip adhesin protein EcpD. This study highlights the versatility of EPEC to bind to different host proteins and suggests that the interaction of ECP with the host's ECM glycoproteins may facilitate colonization of the intestinal mucosal epithelium.

Brahma-Related Gene-1 (BRG1) promotes the malignant phenotype of glioblastoma cells.

Glioblastoma multiforme (GBM) is an aggressive malignant brain tumour that is resistant to existing therapeutics. Identifying signalling pathways deregulated in GBM that can be targeted therapeutically is critical to improve the present dismal prognosis for GBM patients. In this report, we have identified that the BRG1 (Brahma-Related Gene-1) catalytic subunit of the SWI/SNF chromatin remodelling complex promotes the malignant phenotype of GBM cells. We found that BRG1 is ubiquitously expressed in tumour tissue from GBM patients, and high BRG1 expression levels are localized to specific brain tumour regions. Knockout (KO) of BRG1 by CRISPR-Cas9 gene editing had minimal effects on GBM cell proliferation, but significantly inhibited GBM cell migration and invasion. BRG1-KO also sensitized GBM cells to the anti-proliferative effects of the anti-cancer agent temozolomide (TMZ), which is used to treat GBM patients in the clinic, and selectively altered STAT3 tyrosine phosphorylation and gene expression. These results demonstrate that BRG-1 promotes invasion and migration, and decreases chemotherapy sensitivity, indicating that it functions in an oncogenic manner in GBM cells. Taken together, our findings suggest that targeting BRG1 in GBM may have therapeutic benefit in the treatment of this deadly form of brain cancer.

Implementation of harmonically mapped averaging in LAMMPS, and effect of potential truncation on anharmonic properties.

Implementation of the harmonically mapped averaging (HMA) framework in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is presented for on-the-fly computations of the energy, pressure, and heat capacity of crystalline systems during canonical molecular dynamics simulations. HMA has a low central processing unit and storage requirements and is straightforward to use. As a case study, the properties of the Lennard-Jones and embedded-atom model (parameterized for nickel) crystals are computed. The results demonstrate the higher efficiency of the new class compared to the inbuilt LAMMPS classes for calculating these properties. However, HMA loses its effectiveness in systems where diffusion occurs in the crystal, and an example is presented to allow this behavior to be recognized. In addition to its improved precision, HMA is less affected by small errors introduced by having a larger time step in molecular dynamics simulations. We also present an analysis of the effect of potential truncation on anharmonic properties, and show that artifacts of truncation on the HMA averages can be eliminated simply by shifting the potential energy to zero at the truncation radius. Full properties can be obtained by adding easily computed values for the lattice and harmonic properties using the untruncated potential.

Application of the interface potential approach for studying wetting behavior within a molecular dynamics framework.

We introduce a means to implement the interface potential approach for computing wetting properties within a molecular dynamics framework. The general approach provides a means to determine the contact angle of a liquid droplet on a solid substrate in a mother vapor. We present a framework for implementing "spreading" and "drying" versions of the method within an isothermal-isobaric ensemble. Two free energy methods are considered: cumulative integration of average force profile and multistate Bennett acceptance ratio. An umbrella sampling strategy is used to restrain volume fluctuations and to ensure adequate sampling of a broad volume range. We explore implementation of the approach with the GROningen MAchine for Chemical Simulations and the Large-scale Atomic/Molecular Massively Parallel Simulator. We test the accuracy and efficiency of the method with models consisting of a monoatomic Lennard-Jones fluid in the vicinity of a structureless or atomistically detailed substrate. Our results show that one can successfully generate the drying potential within the framework pursued here. The efficiency of the method is strongly dependent upon how one handles the dynamics of the two confining walls. These decisions impact the rate of volume fluctuations, and therefore, the quality of the volume distributions collected. Our efforts to implement the spreading method with molecular dynamics alone proved unsuccessful. The rate at which the configuration space of the vapor phase evolves is insufficient. We show how one can overcome this challenge by implementing a coupled molecular dynamics/Monte Carlo approach. Finally, we show how one can determine the variation in interfacial properties with temperature and substrate strength.

Construction of the interface potential from a series of canonical ensemble simulations.

We introduce a method to construct the interface potential from a series of molecular dynamics simulations conducted within the canonical ensemble. The interface potential provides the surface excess free energy associated with the growth of a fluid film from a surface. We collect the force that the fluid exerts on the surface (disjoining pressure) at a series of film thicknesses. These force data are then integrated to obtain the interface potential. "Spreading" and "drying" versions of the general approach are considered. The spreading approach focuses on the growth of a thin liquid film from a solid substrate in a mother vapor. The drying approach focuses on the growth of a thin vapor film on a solid substrate in a mother liquid. The methods provide a means to compute the contact angle of a fluid droplet in contact with the surface. The general method is applied to two model systems: (1) a monatomic Lennard-Jones fluid in contact with atomistically detailed face centered cubic (FCC) substrate and (2) TIP4P/2005 water in contact with a rigid silica surface. For the Lennard-Jones model system, we generate results with both the drying and spreading methods at various temperatures and substrate strengths. These results are compared to those from previous simulation studies. For the water system, the drying method is used to obtain wetting properties over a range of temperatures. The water system also highlights challenges associated with application of the spreading method within the framework pursued here.

Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres.

In Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] of this series, a methodology was presented for computing the coefficients of a power series of the Helmholtz energy in reciprocal temperature, ß, through density series based on cluster integral expansions. Previously, power series in ß were evaluated by thermodynamic perturbation theory (TPT) using molecular simulation of a reference fluid. The present methodology uses cluster integrals to evaluate coefficients of the density expansion at each individual order of temperature. While Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] developed this methodology for square well (SW) spheres, the present work extends the methodology to Lennard-Jones (LJ) spheres, where the reference fluid is the Weeks-Chandler-Andersen potential. Comparisons of TPT coefficients computed from cluster integrals to those from molecular simulation show good agreement through third order in ß when coefficients are expressed with effective approximants. Notably, the agreement for LJ spheres is much better than for SW spheres although fewer coefficients of the density series (B2-B5) are available than for SW spheres (B2-B6). The coefficients for Bi(ß) of the reference fluid are shown to follow a simple relationship to the virial coefficients of hard sphere fluids, corrected for the temperature dependency of the equivalent hard sphere diameter. This lays the foundation for a correlation of the second virial coefficient of LJ spheres B2(ß) that extrapolates to infinite order in temperature. This correlation of B2(ß) provides a basis for estimating the low density limit of TPT coefficients at all orders in temperature, facilitating a recursive extrapolation formula to estimate TPT coefficients of fourth order and higher over the entire density range. The applicability of the resulting equation of state is demonstrated by computing the thermodynamic properties for LJ spheres and comparing to standard simulation results.

Molecular Calculation of the Critical Parameters of Classical Helium.

We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol·L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol·L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible; in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.

A pilot study of the performance of captive-reared delta smelt Hypomesus transpacificus in a semi-natural environment.

A captive breeding programme was developed in 2008 for delta smelt Hypomesus transpacificus in reaction to dramatic population decline over several decades. We took 526 sub-adult captive-reared delta smelt and cultured them for 200 days without providing artificial food or water quality management to assess their performance once released in the wild. The results indicated captive-reared sub-adult delta smelt could survive in a semi-natural environment with uncontrolled water quality and naturally produced wild prey through spawning and into their post spawning phase.

Comprehensive high-precision high-accuracy equation of state and coexistence properties for classical Lennard-Jones crystals and low-temperature fluid phases.

We report equilibrium molecular simulation data for the classical Lennard-Jones (LJ) model, covering all thermodynamic states where the crystal is stable, as well as fluid states near coexistence with the crystal; both fcc and hcp polymorphs are considered. These data are used to compute coexistence lines and triple points for equilibrium among the fcc, hcp, and fluid phases. All results are obtained with very high accuracy and precision such that coexistence conditions are obtained with one to two significant figures more than previously reported. All properties are computed in the limit of an infinite cutoff radius of the LJ potential and in the limit of an infinite number of atoms; furthermore, the effect of vacancy defects on the free energy of the crystals is included. Data are fit to a semi-empirical equation of state to within their estimated precision, and convenient formulas for the thermodynamic and coexistence properties are provided. Of particular interest is the liquid-vapor-fcc triple point temperature, which we compute to be 0.694 55 ± 0.000 02 (in LJ units).

Effects of thermostatting in molecular dynamics on anharmonic properties of crystals: Application to fcc Al at high pressure and temperature.

The precision and accuracy of the anharmonic energy calculated in the canonical (NVT) ensemble using three different thermostats (viz., Andersen, Langevin, and Nosé-Hoover) along with no thermostat (i.e., microcanonical, NVE) are compared via application to aluminum crystals at ≈100 GPa for temperatures up to melting (4000 K) using ab initio molecular dynamics (AIMD) simulation. In addition to the role of the thermostat, the effect of using either conventional or the recently introduced harmonically mapped averaging (HMA) method is considered. The effect of AIMD time-step size Δt on the ensemble averages gauges accuracy, while for a given Δt, the stochastic uncertainty (computed using block averaging) provides the metric for precision. We identify the rate of convergence of block averages (with respect to block size) as an important issue in this context, as it imposes a minimum simulation length required to achieve reliable statistics, and it differs considerably among the methods. We observe that HMA with a Langevin thermostat in an NVT simulation shows the best performance, from the point of view of accuracy, precision, and simulation length. In addition, we introduce a novel HMA-based ensemble average for the temperature. In application to NVE simulations, the new formulation exhibits much smaller fluctuations compared to the conventional kinetic-energy approach; however, it provides only marginal improvement in uncertainty due to strong negative correlations exhibited by the conventional form (which acts to reduce its uncertainty but also slows convergence of the block averages).

Virial Coefficients and Equations of State for Hard Polyhedron Fluids.

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on thermodynamic properties, even in moderate-density fluids. Only the second virial coefficient is known analytically for general convex shapes, so higher-order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating virial coefficients up to B4 and numerically evaluating them to B8. Using virial coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow et al. (J. Chem. Phys. 2012, 137, 204102) is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fluids of arbitrary hard convex bodies are too complicated to be described in a general way at high densities, so the high-precision state data we provide can serve as a reference for future work in calculating state data or as a basis for thermodynamic integration.

Etomica: an object-oriented framework for molecular simulation.

We describe the design of an object-oriented library of software components that are suitable for constructing simulations of systems of interacting particles. The emphasis of the discussion is on the general design of the components and how they interact, and less on details of the programming interface or its implementation. Example code is provided as an aid to understanding object-oriented programming structures and to demonstrate how the framework is applied.

Combined temperature and density series for fluid-phase properties. I. Square-well spheres.

Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(ß) η + B3(ß) η(2) + B4(ß) η(3) + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B(i)(ß) coefficients are expanded as a power series in reciprocal temperature, ß, about ß = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B(i) coefficients can be expressed in closed form as a function of ß, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the ß series. Expanding the B(i) coefficients in ß provides a correspondence between the power series in density (typically called the virial series) and the power series in ß (typically called thermodynamic perturbation theory, TPT). The coefficients of the ß series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in ß. These comparisons show good agreement at first order in ß, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in ß. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in ß appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.

Eighth to sixteenth virial coefficients of the Lennard-Jones model.

We calculated virial coefficients BN, 8 ≤ N ≤ 16, of the Lennard-Jones (LJ) model using both the Mayer-sampling Monte Carlo method and direct generation of configurations, with Wheatley's algorithm for summation of clusters. For N = 8, 24 values are reported, and for N = 9, 12 values are reported, both for temperatures T in the range 0.6 ≤ T ≤ 40.0 (in LJ units). For each N in 10 ≤ N ≤ 16, one to four values are reported for 0.6 ≤ T ≤ 0.9. An approximate functional form for the temperature dependence of BN was developed, and fits of LJ BN(T) based on this form are presented for each coefficient, 4 ≤ N ≤ 9, using new and previously reported data.

Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.