Three-dimensional lattice Monte Carlo simulations of model proteins. IV. Proteins at an oil-water interface

Lattice Monte Carlo simulations describe the adsorption of protein-like heteropolymer chains at an oil/water interface. The heteropolymers are designed sequences of 27 and 64 amino acid-type lattice sites taken from a 20-letter alphabet. We use our recently suggested energy scale to model oil and water. We investigate the effect of the oil parameters on adsorption properties of a single chain and on the aggregation of adsorbed chains while keeping the water parameters fixed to their optimum values found previously. By varying the oil parameters, we can cause a large range of adsorption behavior: from no adsorption to reversible adsorption to irreversible adsorption. We compare adsorption at a liquid/solid interface to that at a liquid/liquid interface. A liquid interface leads to stronger adsorption and denaturation than a solid interface with the same water and oil interaction parameters. We propose "optimal" oil parameters and use them to study multichain adsorption at a liquid interface.     

Three-dimensional Monte Carlo simulations of intracellular diffusion and reaction of signaling proteins

We show that the Monte Carlo technique makes it possible to perform three-dimensional simulations of intracellular protein-mediated signal transduction with realistic ratio of the rates of protein diffusion and association with genes. Specifically, we illustrate that in the simplest case when the protein degradation and phosphorylation/dephosphorylation are negligible the distribution of the first passage time for this process is close to exponential provided that the number of target genes is between 1 and 100.     

A new method for generating volume changes in isobaric-isothermal Monte Carlo simulations of flexible molecules

A novel method has been developed to generate volume fluctuations as required in isobaric-isothermal Monte Carlo simulations of flexible (or semi-flexible) chain molecules. While conventional global volume moves entail symmetric changes of the simulation box size, in the new method proposed here, volume changes consist of one-dimensional fluctuations of one of two sections of the system. One of the two sections is a thin slab where all molecular rearrangements are restrained to occur. A deterministric method has been implemented to reposition the molecular segments contained within the slab after a volume change is proposed. The performance of the new method is examined by studying the evolution towards equilibrium of homopolymer hard-core systems upon application of a step increase in the pressure. The new method is shown to be an order of magnitude faster than conventional methods in attaining the equilibrium density of our test systems.     

Monte Carlo simulations of low background detectors

An implementation of the Electron Gamma Shower 4 code (EGS4) has been developed to allow convenient simulation of typical gamma ray measurement systems. Coincidence gamma rays, beta spectra, and angular correlations have been added to adequately simulate a complete nuclear decay and provide corrections to experimentally determined detector efficiencies. This code has been used to strip certain low-background spectra for the purpose of extremely low-level assay. Monte Carlo calculations of this sort can be extremely successful since low background detectors are usually free of significant contributions from poorly localized radiation sources, such as cosmic muons, secondary cosmic neutrons, and radioactive construction or shielding materials. Previously, validation of this code has been obtained from a series of comparisons between measurements and blind calculations. An example of the application of this code to an exceedingly low background spectrum stripping will be presented.Pacific Northwest Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract DE-AC06-76RLO 1830.     

Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Interaction of polyanions with basic proteins, 2(a) : influence of complexing polyanions on the thermo-aggregation of oligomeric enzymes

The ability of synthetic polyanions to suppress thermo-aggregation of the oligomeric enzymes (glyceraldehyde-3-phosphate dehydrogenase, lactate dehydrogenase, and aspartate aminotransferase) has been established. The ability of the polyanions to reduce the thermo-aggregation increased in the order poly(methacrylic acid) < poly(acrylic acid) < sodium poly(styrene sulphonate), which agreed well with the increase, in the same order, of the charge density of the chains. The lengthening of the chains, as well as the rise in their relative content, resulted in an increase of the ability to reduce thermo-aggregation, mentioned above. Complete prevention of the enzyme aggregation was achieved when highly charged polyanions of a relatively high degree of polymerization were used in a concentration sufficient to solubilize the protein. Complexing with the polyanions prevented thermo-aggregation of the enzymes, but not their thermo-denaturation. The adverse effect of the complexing polyanions on the catalytic activity was reduced by the addition of a synthetic polycation, which resulted in a significant reactivation (up to 40%) of the enzyme. The possibility of preventing the thermo-aggregation of enzyme molecules and then partly restoring the enzyme activity, appears to be of particular interest when studying the aggregation mechanism of proteins that are prone to form the amyloid structures responsible for the development of neurodegenerative diseases like Alzheimer's disease, bovine spongiform encephalopathy and Huntington disease. This finding can also be considered as an important step in the creation of artificial chaperones.     

Monte carlo simulations of proteins at constant pH with generalized born solvent,flexible sidechains,and an effective dielectric boundary

Titratable residues determine the acid/base behavior of proteins, strongly influencing their function; in addition, proton binding is a valuable reporter on electrostatic interactions. We describe a method for pK_a calculations, using constant‐pH Monte Carlo (MC) simulations to explore the space of sidechain conformations and protonation states, with an efficient and accurate generalized Born model (GB) for the solvent effects. To overcome the many‐body dependency of the GB model, we use a “Native Environment” approximation, whose accuracy is shown to be good. It allows the precalculation and storage of interactions between all sidechain pairs, a strategy borrowed from computational protein design, which makes the MC simulations themselves very fast. The method is tested for 12 proteins and 167 titratable sidechains. It gives an rms error of 1.1 pH units, similar to the trivial “Null” model. The only adjustable parameter is the protein dielectric constant. The best accuracy is achieved for values between 4 and 8, a range that is physically plausible for a protein interior. For sidechains with large pK_a shifts, ≥2, the rms error is 1.6, compared to 2.5 with the Null model and 1.5 with the empirical PROPKA method. © 2013 Wiley Periodicals, Inc.     

Determination of the isoelectric point of proteins by capillary isoelectric focusing

Different ways of determining isoelectric points (pI) of proteins in capillary isoelectric focusing are reviewed here. Due to the impossibility of direct pH measurements in the liquid phase, such assessments have to rely on the use of pI markers. Different types of pI markers have been described: dyes, fluorescently labelled peptides, sets of proteins of known pI values. It appears that, perhaps, the best system is a set of 16 synthetic peptides, trimers to hexamers, made to contain each a Trp residue for easy detection at 280 nm. By a careful blend of acidic (Asp, Glu), mildly basic, with pK around neutrality (His), and basic (Lys, Arg) amino acids, it is possible to obtain a series of pI markers with pI values quite evenly distributed along the pH scale, possessing good buffering capacity and conductivity around their pI values and thus focusing as sharp peaks. Another approach to pI determination is the monitoring of the current during mobilization: this allows, with the aid of known pI markers, to calibrate the system with a pI/current graph. Pitfalls and common errors in pI determinations are reviewed here and guidelines given for minimizing such errors in pI estimation.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Monte Carlo simulations of cross-linked polyelectrolyte gels with oppositely charged macroions

The volume and structural changes upon replacement of oppositely charged network counterions for oppositely charged macroions in cross-linked polyelectrolyte gels have been investigated by Monte Carlo simulations using a coarse-grained model. Initially, the gel deswells, but after an approximately equivalent amount of macroions, the gel starts to swell again. The deswelling effect is greatest for small and highly charged macroions. The role of different network properties on the deswelling has also been examined. The initial deswelling is understood in terms of a replacement of confined counterions with macroions, thereby reducing the osmotic pressure originating from the counterions. At these conditions, macroions are located near network nodes with various degrees of network chains wrapping them. At charge equivalence, a profound change in the network structure has appeared. At these conditions, the cohesive electrostatic interaction and the excluded volume effect of the macroions strongly influence the equilibrium volume of the gel. Our model system reproduces many characteristic experimental observations of polyelectrolyte gels containing oppositely charged surfactants.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Fast protein structure prediction using Monte Carlo simulations with modal moves

Using normal modes to generate torsion space moves in Monte Carlo simulations of peptides and proteins is not a new idea; nevertheless, despite its power it has not received widespread application. We show that such a "Modal Monte Carlo" approach is an efficient tool for ab initio predictions of small-protein structures. We apply this method to the Trp cage, a 20-residue polypeptide designed to fold rapidly into a structure that includes tertiary contacts, despite its short length. We achieve a high-quality ab initio structure prediction in about 2 orders of magnitude less computation time than state of the art molecular dynamics techniques.     

Optimization of 89Zr production using Monte Carlo simulations

Zirconium-89 (⁸⁹Zr) can be produced in a cyclotron by focusing the proton beam on an yttrium-89 (⁸⁹Y) foil target. Optimal combination of beam energy and target assembly configuration enables maximum production of ⁸⁹Zr while minimizing the formation of contaminant nuclides such as ⁸⁸Zr and ⁸⁸Y to allow efficient and effective radiopharmaceutical labeling. Accurate modeling of the proton beam and the target is therefore an essential step to assure the best beam and target specification. We used the radiation transport code MCNPX to simulate the transport of protons through the irradiation assembly and the nuclear reaction code TALYS to obtain the production cross sections of various nuclides from proton-⁸⁹Y reactions. Results from simulating the irradiation of 14 mm diameter targets with aluminum (Al) degrader at 19.8 mA for 1 h suggested that the 0.15 mm thick one would produce 227 MBq while the 0.3 mm thick one would produce 413 MBq of ⁸⁹Zr with less than 1 % uncertainty. These results show excellent agreement with experimental work in literature. This work provides the basis for further experimental and theoretical assessments of the use of ⁸⁹Zr as radiopharmaceutical labels.     

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.     

Monte Carlo simulations of two-dimensional hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, lambda (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class-contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Monte Carlo simulations of segregation in Pt-Re catalyst nanoparticles

We have investigated the segregation of Pt atoms to the surfaces of Pt-Re nanoparticles using the Monte Carlo method and modified embedded-atom method potentials that we have developed for Pt-Re alloys. The Pt(75)Re(25) nanoparticles (containing from 586 to 4,033 atoms) are assumed to have disordered fcc configurations and cubo-octahedral shapes (terminated by [111] and [100] facets), while the Pt(50)Re(50) and Pt(25)Re(75) nanoparticles (containing from 587 to 4,061 atoms) are assumed to have disordered hcp configurations and truncated hexagonal bipyramidal shapes (terminated by [0001] and [1011] facets). We predict that due to the segregation process the equilibrium Pt-Re nanoparticles would achieve a core-shell structure, with a Pt-enriched shell surrounding a Pt-deficient core. For fcc cubo-octahedral Pt(75)Re(25) nanoparticles, the shells consist of almost 100 at. % of Pt atoms. Even in the shells of hcp truncated hexagonal bipyramidal Pt(50)Re(50) nanoparticles, the concentrations of Pt atoms exceed 85 at. % (35 at. % higher than the overall concentration of Pt atoms in these nanoparticles). Most prominently, all Pt atoms will segregate to the surfaces in the hcp truncated hexagonal bipyramidal Pt(25)Re(75) nanoparticles containing less than 1000 atoms. We also find that the Pt atoms segregate preferentially to the vertex sites, less to edge sites, and least to facet sites on the shell of Pt-Re nanoparticles.