Brownian dynamics simulation of protein folding: a study of the diffusion-collision model

The dynamic aspects of protein folding are described by a series of diffusion-collision steps involving structural units (microdomains) of various sizes that combine to form the protein in its native state. A method is introduced for obtaining the rate constants for the basic diffusion-collision step by use of Brownian dynamics. The method is applied to an investigation of the folding dynamics of two α-helices connected by a flexible (random-coil) polypeptide chain. The results of this full three-dimensional treatment are compared with simplified model calculations for the diffusion-collision step. Of particular interest are the nature of the collision dynamics and the role of the intervening peptide chain.     

Molecular dynamics simulation and essential dynamics study of mutated plastocyanin: structural, dynamical and functional effects of a disulfide bridge insertion at the protein surface

A molecular dynamics simulation (1.1 ns) at 300 K, of fully hydrated Ile21Cys, Glu25Cys plastocyanin mutant has been performed to investigate the structural, dynamical and functional effects of a disulfide bridge insertion at the surface of the protein. A detailed analysis of the root mean square fluctuations, H-bonding pattern and dynamical cross-correlation map has been performed. An essential dynamics method has also been applied as complementary analysis to identify concerted motions (essential modes), that could be relevant to the electron transfer function. The results have been compared with those previously obtained for wild-type plastocyanin and have revealed that the mutant shows a different pattern of H-bonds, with several interactions lost and a higher flexibility, especially around the electron transfer copper site. The analysis of dynamical cross-correlation map and of essential modes, has shown that the mutant performs different functional concerted motions, which might be related to the binding recognition with its electron transfer partners in comparison with the wild-type protein.     

Brownian dynamics simulation of DNA condensation.

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.     

Brownian dynamics simulations of probe and self-diffusion in concentrated protein and DNA solutions.

We have developed a Brownian dynamics algorithm for simulating probe and self-diffusion in concentrated solutions of DNA and protein. In these simulations, proteins are represented as spheres with radii given by their hydrodynamic radii, while DNA is modeled as a wormlike chain of hydrodynamically equivalent spherical frictional elements. The molecular interaction potentials employed by the program allow for intramolecular stretching and bending motions of the DNA chains, short-range Lennard-Jones interactions, and long-range electrostatic interactions. To test the program, we have carried out simulations of bovine serum albumin (BSA) probe diffusion and DNA self-diffusion in solutions of short-chain DNA as a function of both DNA concentration and solution ionic strength. In addition, we report on simulations of BSA self-diffusion as a function of BSA concentration and ionic strength. Based on a comparison to available experimental data, we find that our simulations accurately predict these transport properties under conditions of physiological salt concentration and predict the stronger concentration dependence observed at lower salt concentrations. These results are discussed in light of the nature of the intermolecular interactions in such systems and the approximations and limitations of the simulation algorithm.     

Molecular dynamics simulations of human alpha-lactalbumin: changes to the structural and dynamical properties of the protein at low pH.

Two 700-ps molecular dynamics simulations of human alpha-lactalbumin have been compared. Both were initiated from an X-ray structure determined at pH 6.5. One simulation was designed to represent native conditions and the other the protein in solution at pH 2.0 without a bound calcium ion. The low pH conditions were modelled by protonating the aspartate, glutamate, and histidine side chains and the protein C-terminus. Significant changes were observed for the C-terminal region of the sequence in the simulation at low pH. Most notably an alpha-helix, helix D, and the C-terminal 3(10) helix were substantially disrupted relative to the simulation at high pH. These perturbations to the native fold are similar to those observed in an X-ray structure of alpha-lactalbumin at pH 4.2. In addition, larger fluctuations about side chain torsion angles were observed in the low pH simulation than in that corresponding to the higher pH. These structural and dynamical changes might be representative of the early stages of the transition to the molten-globule state of the protein known to be formed under low pH conditions in solution.     

Adhesion of nanoparticles to vesicles: a Brownian dynamics simulation

We studied the interaction of bilayer vesicles and adhesive nanoparticles using a Brownian dynamics simulation. The nanoparticles are simple models of proteins or colloids. The adhering nanoparticle induces the morphological change of the vesicle: budding, formation of two vesicles in which only outer monolayers are connected, and fission. We also show that the nanoparticle promotes the fusion process: fusion-pore opening from a stalk intermediate, a neck-like structure that only connects outer monolayers of two vesicles. The nanoparticle bends the stalk, and induces the pore opening.     

Brownian dynamics simulation of restricted rotational diffusion.

The restricted rotational diffusion of an axially symmetric particle is simulated by the Brownian dynamics technique. In addition to the wobbling-in-a-cone model, several continuous potentials are considered. The particle studied is particularly simple: a sphere anchored to a point fixed in space. However, presenting the results in a convenient, reduced form, they are valid for any axially symmetric particle. From simulated rotational trajectories, we calculate (P2(cos alpha] as a function of t, where alpha is the angle between two orientations separated by time t and P2 is the second Legendre polynomial. This correlation function is closely related to time-resolved electro-optic and spectroscopic properties. Simulated results for the cone model are in excellent agreement with the quasiexact results of Lipari and Szabo (1981, J. Chem. Phys., 75:2971-2976). Thus we confirm the good performance of the simulation technique and the validity of our working conditions. Novel results are presented for continuous restricting potentials, V(theta). The (P2) results for V = 1/2K theta 2 and V = Q(1 - cos theta) are practically the same if K and Q are chosen so tht the long-time (P2) values coincide. Thus, the quadratic potential seems to be a good representation of any monotonically increasing potential. However, for an uniaxial potential such as V = Csin2 theta, the decay is appreciably faster. The (P2) decays simulated for the continuous potentials are analyzed by the monoexponential version of the cone model. We found that such an analysis produces an overestimation of the true rotational diffusion coefficient of approximately 15% only, although for uniaxial potentials the error may be larger.     

Brownian dynamics simulation of nucleosome formation and disruption under stretching

Using a Brownian dynamics simulation, we numerically studied the interaction of DNA with histone and proposed an octamer-rotation model to describe the process of nucleosome formation. Nucleosome disruption under stretching was also simulated. The theoretical curves of extension versus time as well as of force versus extension are consistent with previous experimental results.     

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants.The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues.Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.     

Self-assembly of two-patch particles in solution: a Brownian dynamics simulation study

We study the self-assembly behaviour of two-patch particles with D_∞h symmetry by using Brownian dynamics simulations. The self-assembly process of two-patch particles with diverse patch coverage in two selective solvent conditions is investigated. The patchy particles in a solvent that is bad for patches but good for matrix form linear thread-like structures with low patch coverage, whereas they form 3D network structures with relatively high patch coverage on surface. For patchy particles in a solvent which is good for patches but bad for body, monolayer structures are obtained at high patch coverage, and some cluster structures emerge when surface patch coverage is low.     

Molecular dynamics simulations of the Cx26 hemichannel: evaluation of structural models with Brownian dynamics

The recently published crystal structure of the Cx26 gap junction channel provides a unique opportunity for elucidation of the structure of the conductive connexin pore and the molecular determinants of its ion permeation properties (conductance, current-voltage [I-V] relations, and charge selectivity). However, the crystal structure was incomplete, most notably lacking the coordinates of the N-terminal methionine residue, which resides within the pore, and also lacking two cytosolic domains. To allow computational studies for comparison with the known channel properties, we completed the structure. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) simulations of the completed and the published Cx26 hemichannel crystal structure indicate that the pore is too narrow to permit significant ion flux. The GCMC/BD simulations predict marked inward current rectification and almost perfect anion selectivity, both inconsistent with known channel properties. The completed structure was refined by all-atom molecular dynamics (MD) simulations (220 ns total) in an explicit solvent and POPC membrane system. These MD simulations produced an equilibrated structure with a larger minimal pore diameter, which decreased the height of the permeation barrier formed by the N terminus. GCMC/BD simulations of the MD-equilibrated structure yielded more appropriate single-channel conductance and less anion/cation selectivity. However, the simulations much more closely matched experimentally determined I-V relations when the charge effects of specific co- and posttranslational modifications of Cx26 previously identified by mass spectrometry were incorporated. We conclude that the average equilibrated structure obtained after MD simulations more closely represents the open Cx26 hemichannel structure than does the crystal structure, and that co- and posttranslational modifications of Cx26 hemichannels are likely to play an important physiological role by defining the conductance and ion selectivity of Cx26 channels. Furthermore, the simulations and data suggest that experimentally observed heterogeneity in Cx26 I-V relations can be accounted for by variation in co- and posttranslational modifications.     

Molecular dynamics simulation of dimeric and monomeric forms of human prion protein: insight into dynamics and properties

A central theme in prion protein research is the detection of the process that underlies the conformational transition from the normal cellular prion form (PrP(C)) to its pathogenic isoform (PrP(Sc)). Although the three-dimensional structures of monomeric and dimeric human prion protein (HuPrP) have been revealed by NMR spectroscopy and x-ray crystallography, the process underlying the conformational change from PrP(C) to PrP(Sc) and the dynamics and functions of PrP(C) remain unknown. The dimeric form is thought to play an important role in the conformational transition. In this study, we performed molecular dynamics (MD) simulations on monomeric and dimeric HuPrP at 300 K and 500 K for 10 ns to investigate the differences in the properties of the monomer and the dimer from the perspective of dynamic and structural behaviors. Simulations were also undertaken with Asp178Asn and acidic pH, which is known as a disease-associated factor. Our results indicate that the dynamics of the dimer and monomer were similar (e.g., denaturation of helices and elongation of the beta-sheet). However, additional secondary structure elements formed in the dimer might result in showing the differences in dynamics and properties between the monomer and dimer (e.g., the greater retention of dimeric than monomeric tertiary structure).     

Bimolecular reaction simulation using Weighted Ensemble Brownian dynamics and the University of Houston Brownian Dynamics program

We discuss here the implementation of the Weighted Ensemble Brownian (WEB) dynamics algorithm of Huber and Kim in the University of Houston Brownian Dynamics (UHBD) suite of programs and its application to bimolecular association problems. WEB dynamics is a biased Brownian dynamics (BD) algorithm that is more efficient than the standard Northrup-Allison-McCammon (NAM) method in cases where reaction events are infrequent because of intervening free energy barriers. Test cases reported here include the Smoluchowski rate for association of spheres, the association of the enzyme copper-zinc superoxide dismutase with superoxide anion, and the binding of the superpotent sweetener N-(p-cyanophenyl)-N'-(diphenylmethyl)-guanidinium acetic acid to a monoclonal antibody fragment, NC6.8. Our results show that the WEB dynamics algorithm is a superior simulation method for enzyme-substrate reaction encounters with large free energy barriers.     

A systematic molecular dynamics simulation study of temperature dependent bilayer structural properties

Although lipid force fields (FFs) used in molecular dynamics (MD) simulations have proved to be accurate, there has not been a systematic study on their accuracy over a range of temperatures. Motivated by the X-ray and neutron scattering measurements of common phosphatidylcholine (PC) bilayers (Ku?erka et al. BBA. 1808: 2761, 2011), the CHARMM36 (C36) FF accuracy is tested in this work with MD simulations of six common PC lipid bilayers over a wide range of temperatures. The calculated scattering form factors and deuterium order parameters from the C36 MD simulations agree well with the X-ray, neutron, and NMR experimental data. There is excellent agreement between MD simulations and experimental estimates for the surface area per lipid, bilayer thickness (D_B), hydrophobic thickness (D_C), and lipid volume (V_L). The only minor discrepancy between simulation and experiment is a measure of (D_B − D_HH) / 2 where D_HH is the distance between the maxima in the electron density profile along the bilayer normal. Additional MD simulations with pure water and heptane over a range of temperatures provide explanations of possible reasons causing the minor deviation. Overall, the C36 FF is accurate for use with liquid crystalline PC bilayers of varying chain types and over biologically relevant temperatures.     

Temperature dependence of protein dynamics: computer simulation analysis of neutron scattering properties

The temperature dependence of the internal dynamics of an isolated protein, bovine pancreatic trypsin inhibitor, is examined using normal mode analysis and molecular dynamics (MD) simulation. It is found that the protein exhibits marked anharmonic dynamics at temperatures of approximately 100-120 K, as evidenced by departure of the MD-derived average mean square displacement from that of the harmonic model. This activation of anharmonic dynamics is at lower temperatures than previously detected in proteins and is found in the absence of solvent molecules. The simulation data are also used to investigate neutron scattering properties. The effects are determined of instrumental energy resolution and of approximations commonly used to extract mean square displacement data from elastic scattering experiments. Both the presence of a distribution of mean square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean square displacement obtained.     

Mechanisms of DNA separation in entropic trap arrays: a Brownian dynamics simulation

Using Brownian dynamics simulations, we study the migration of long charged chains in an electrophoretic microchannel device consisting of an array of microscopic entropic traps with alternating deep regions and narrow constrictions. Such a device has been designed and fabricated recently by Han and Craighead [Science 288 (2000) 1026] for the separation of DNA molecules. Our simulation reproduces the experimental observation that the mobility increases with the length of the DNA. A detailed data analysis allows to identify the reasons for this behavior. Two distinct mechanisms contribute to slowing down shorter chains. One has been described earlier by Han and Craighead [Science 288 (2000) 1026]: the chains are delayed at the entrance of the constriction and escape with a rate that increases with chain length. The other, actually dominating mechanism is here reported for the first time: some chains diffuse out of their main path into the corners of the box, where they remain trapped for a long time. The probability that this happens increases with the diffusion constant, i.e., the inverse chain length.     

Sarcoplasmic reticulum: structural determinants and protein dynamics

The sarcoplasmic reticulum is a unique organelle found in muscle cells that is dedicated to the regulation of Ca(2+) homeostasis and activation of myofilament contraction. The functional requirement for an efficient and synchronous activation of Ca(2+) release from the SR, following the depolarization of the plasma membrane, accounts for the complex three-dimensional organization of internal membranes observed in muscle cells and for the localization of proteins at specific sites of the SR. Recent advancements in understanding the molecular basis of SR structure and function have greatly increased our understanding of muscle cellular physiology and biology. Parallel work has revealed that several human diseases affecting skeletal and cardiac tissues are linked to either mutations or altered post-translational modifications of SR proteins.     

Topological and dynamical properties of Azurin anchored to a gold substrate as investigated by molecular dynamics simulation

A classical molecular dynamics study of the electron transfer protein azurin, covalently bound to a gold substrate through its native disulphide group, is carried out at full hydration. With the aim of investigating the effects on the protein structure and dynamics as induced by the presence of an electric field, simulations are performed on neutral, positively and negatively charged substrates. A number of parameters, such as the average structure, the root mean square deviations and fluctuations, the intraprotein hydrogen bonds and solvent accessible surface of the protein, are monitored during 10 ns of run. The orientation, the height and the lateral size of the protein, with respect to the substrate are evaluated and compared with the experimental data obtained by scanning probe nanoscopies. The electron transfer properties between the copper redox center and the disulphide bridge bound to the substrate are investigated and briefly discussed.     

Structural and dynamical correlations in PfHGXPRT oligomers: A molecular dynamics simulation study

PfHGXPRT is a key enzyme involved in purine nucleotide salvage pathway of the malarial parasite, Plasmodium falciparum. Atomistic molecular dynamics simulations have been performed on two types of PfHGXPRT dimers (D1 and D3) and its tetramer in their apo and ligand-bound states. A significant event in the catalytic cycle is the dynamics of a gate that provides access for the ligand molecules to the reaction center. The gate is formed by loops II and IV, the former being the most flexible. Large amplitude conformational changes have been observed in active site loop II. Upon complete occupancy of the active site, loop II gets stabilized due to specific interactions between its residues and the ligand molecules. Remote loop, X, is seen to be less fluxional in the D3 dimer than in D1 which is rationalized as due to the greater number of inter-subunit contacts in the former. The presence of ligand molecules in subunits of the tetramer further reduces the flexibility of loop X epitomizing a communication between this region and the active sites in the tetramer. These observations are in accordance with the outcomes of several experimental investigations. Participation of loop X in the oligomerization process has also been discerned. Between the two types of dimers in solution, D1 tetramerizes readily and thus would not be present as free dimers. We conjecture an equilibrium to exist between D3 and the tetramer in solution; upon binding of the ligand molecules to the D3 dimer, this equilibrium shifts toward the tetramer.