Ronald G. Larson

The MARTINI Coarse-Grained Force Field: Extension to Proteins

Many biologically interesting phenomena occur on a time scale that is too long to be studied by atomistic simulations. These phenomena include the dynamics of large proteins and self-assembly of biological materials. Coarse-grained (CG) molecular modeling allows computer simulations to be run on length and time scales that are 2-3 orders of magnitude larger compared to atomistic simulations, providing a bridge between the atomistic and the mesoscopic scale. We developed a new CG model for proteins as an extension of the MARTINI force field. Here, we validate the model for its use in peptide-bilayer systems. In order to validate the model, we calculated the potential of mean force for each amino acid as a function of its distance from the center of a dioleoylphosphatidylcholine (DOPC) lipid bilayer. We then compared amino acid association constants, the partitioning of a series of model pentapeptides, the partitioning and orientation of WALP23 in DOPC lipid bilayers and a series of KALP peptides in dimyristoylphosphatidylcholine and dipalmitoylphosphatidylcholine (DPPC) bilayers. A comparison with results obtained from atomistic models shows good agreement in all of the tests performed. We also performed a systematic investigation of the partitioning of five series of polyalanine-leucine peptides (with different lengths and compositions) in DPPC bilayers. As expected, the fraction of peptides partitioned at the interface increased with decreasing peptide length and decreasing leucine content, demonstrating that the CG model is capable of discriminating partitioning behavior arising from subtle differences in the amino acid composition. Finally, we simulated the concentration-dependent formation of transmembrane pores by magainin, an antimicrobial peptide. In line with atomistic simulation studies, disordered toroidal pores are formed. In conclusion, the model is computationally efficient and effectively reproduces peptide-lipid interactions and the partitioning of amino acids and peptides in lipid bilayers.

The centrosomal protein nephrocystin-6 is mutated in Joubert syndrome and activates transcription factor ATF4

The molecular basis of nephronophthisis, the most frequent genetic cause of renal failure in children and young adults, and its association with retinal degeneration and cerebellar vermis aplasia in Joubert syndrome are poorly understood. Using positional cloning, we here identify mutations in the gene CEP290 as causing nephronophthisis. It encodes a protein with several domains also present in CENPF, a protein involved in chromosome segregation. CEP290 (also known as NPHP6) interacts with and modulates the activity of ATF4, a transcription factor implicated in cAMP-dependent renal cyst formation. NPHP6 is found at centrosomes and in the nucleus of renal epithelial cells in a cell cycle–dependent manner and in connecting cilia of photoreceptors. Abrogation of its function in zebrafish recapitulates the renal, retinal and cerebellar phenotypes of Joubert syndrome. Our findings help establish the link between centrosome function, tissue architecture and transcriptional control in the pathogenesis of cystic kidney disease, retinal degeneration, and central nervous system development.

The rheology of dilute solutions of flexible polymers: Progress and problems

Recent progress toward understanding the rheology of dilute solutions of flexible polymers is reviewed, emphasizing experimental results from flows imaging single deoxyribonucleic acid (DNA) molecules and filament-stretching rheometry of dilute polystyrene Boger fluids, as well as Brownian dynamics (BD) simulations of these flows. The bead-spring and bead-rod models are presented, the range of their applicability discussed, and methods presented for inclusion of hydrodynamics interactions, excluded volume, and other physical effects within BD simulations. After reviewing and updating work in the linear viscoelastic regime, the primary focus shifts to the more complex nonlinear regime. While BD predictions of the conformations of 20 to 100 micron long DNA molecules in strong shear and extensional flows has been in good to excellent agreement with the corresponding experiments, predictions of the polystyrene dilute solution rheometry data have been hit or miss, with poorer results obtained for the higher mo...

Brownian dynamics simulations of single DNA molecules in shear flow

We present the results of Brownian dynamics simulations of a series of different polymer models which have been used to examine the recent experimental findings of Smith et al. (1999) who studied the dynamics of a single DNA molecule in steady shear flow. The steady average extension at various Weissenberg numbers (Wi) is shown to be well predicted by multimode nonlinear models. Quite surprisingly, the normalized average extension x/L asymptotes to less than 1/2 even for extremely large Wi and we discuss this result on a physical basis. The probability density function of molecular extension at various values of Wi using the Kramer’s chain and the finitely extensible nonlinear elastic dumbbell suggests that the number of internal modes is important in a model designed to capture the dynamics of a real DNA molecule. Three different frequency regimes in the power spectral density observed at finite Wi in the experiments are shown to arise from the coupling of the Brownian fluctuations in the gradient direct...

Nonadditivity of nanoparticle interactions.

Solutions for nanoparticle solutions Nanoparticle interactions in solution affect their binding to biomolecules, their electronic properties, and their packing into larger crystals. However, the theories that describe larger colloidal particles fail for nanoparticles, because the interactions do not add together linearly. Nanoparticles also have complex shapes and are closer in size to the solvent molecules. Silvera Batista et al. review approaches that can treat the nonadditive nature of nanoparticle interactions, resulting in a more complete understanding of nanoparticles in solution. Science, this issue p. 10.1126/science.1242477 BACKGROUND Interactions between inorganic nanoparticles (NPs) are central to a wide spectrum of physical, chemical, and biological phenomena. An understanding of these interactions is essential for technological implementation of nanoscale synthesis and engineering of self-organized NP superstructures with various dimensionalities, collective properties at the nanoscale, and predictive biological responses to NPs. However, the quantitative description of NP forces encounters many obstacles not present, or not as severe, for microsize particles (µPs). These difficulties are revealed in multiple experimental observations that are, unfortunately, not fully recognized as of yet. Inconsistencies in the accounting of NP interactions are observed across all material platforms that include ceramic, semiconductor, and metallic NPs; crystalline and amorphous NPs; as well as dispersions of inorganic, organic, and biological nanomaterials. Such systematic deviations of theoretical predictions from reality point to the generality of such phenomena for nanoscale matter. Here we analyze the sources of these inconsistencies and chart a course for future research that might overcome these challenges. ADVANCES Nanoparticle interactions are often described by classical colloidal theories developed for µPs. However, several foundational assumptions of these theories, while tolerable for microscale dispersions, fail for NPs. For example, the sizes of ions, solvent molecules, and NPs can be within one order of magnitude of each other, which inherently disallows continuum approximations. Fluctuations of ionic atmospheres, ion-specific effects, enhanced NP anisometry, and multiscale collective effects become essential for accurate accounting of NP interactions. The nonuniformity of the stabilizing layer adds another essential contradistinction. When the particle size becomes smaller than a few tens of nanometers and the gaps between particles become smaller than a few nanometers, nonadditivity of electrostatic (Vel), van der Waals (VvdW), hydrophobic (Vhph), and other potentials (V′) emerges. In fact, it becomes impossible to cleanly decompose the potential of mean force (PMF) for the interaction of two NPs into separate additive contributions from these interactions—as in, e.g., classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [V(r) = Vel(r)+ VvdW(r)+ Vhph(r)+ V′(r)]—due to the coupled structural dynamics of neighboring NPs and surrounding media. Experimentally, the nonadditivity of NP interactions was observed long ago as an unusually high colloidal stability of NP dispersions, defying all reasonable predictions based on DLVO and other classical theories. It also manifests itself in paradoxical phase behavior, self-assembly into sophisticated superstructures, complex collective behavior, enigmatic toxicology, and protein-mimetic behavior of inorganic NPs. Molecular dynamics simulations of PMFs computed for NP pairs confirm the nonadditivity of van der Waals and electrostatic interactions for nanometer-scale separations. OUTLOOK Further work in the field of NP interactions should perhaps embrace NPs as strongly correlated reconfigurable systems with diverse physical elements and multiscale coupling processes, which will require new experimental and theoretical tools. Meanwhile, several heuristic rules identified in this Review can be helpful for discriminating between the systems in which mean-field theories can and cannot be applied. These precepts can guide qualitative thinking about NP interactions, stimulate further research into NP interactions, and aid in their design for applications. Though it is the crux of nonadditivity, the similarity in size between the ions and molecules composing the solvent medium and the NP offers a silver lining: it makes atomic simulations of their interactions increasingly practical as computer speed increases. The direct determination of the PMF by atomistic simulation bypasses the enumeration of individual forces and therefore resolves the nonadditivity problem. In fact, NPs present a favorable system for atomistic simulations because solid inorganic cores have many fewer degrees of freedom than flexible organic chains. Improvements in force fields are necessary to adequately account for intermolecular interactions, entropic contributions, dispersion interactions between atoms, high polarizability of inorganic materials, and quantum confinement effects. Evolving experimental tools that can accurately examine interactions at the nanoscale should help to validate the simulations and stimulate improvement of relevant force fields. In fact, new opportunities for better understanding of the electronic origin of classical interactions are likely as the rapidly improving capabilities in synthesis, simulations, and imaging converge at the scale of NPs. Schematics of hydrated ions, a NP, and a µP, demonstrating the structural uniqueness and discreteness of NPs. Nonadditivity of NP interactions stems from the size similarity of reconfigurable structural elements of NPs (i.e., surface ligands, ionic atmosphere, adsorbed molecules, etc.) and the surrounding media, leading to their strongly coupled dynamics. The high polarizability and faceting that are typical of NPs—as well as collective multibody effects at atomic, molecular, and nanometer scales—lead to the enhancement of nonadditivity and result in interdependence of electrostatic, van der Waals, hydrophobic, and other forces. Understanding interactions between inorganic nanoparticles (NPs) is central to comprehension of self-organization processes and a wide spectrum of physical, chemical, and biological phenomena. However, quantitative description of the interparticle forces is complicated by many obstacles that are not present, or not as severe, for microsize particles (μPs). Here we analyze the sources of these difficulties and chart a course for future research. Such difficulties can be traced to the increased importance of discreteness and fluctuations around NPs (relative to μPs) and to multiscale collective effects. Although these problems can be partially overcome by modifying classical theories for colloidal interactions, such an approach fails to manage the nonadditivity of electrostatic, van der Waals, hydrophobic, and other interactions at the nanoscale. Several heuristic rules identified here can be helpful for discriminating between additive and nonadditive nanoscale systems. Further work on NP interactions would benefit from embracing NPs as strongly correlated reconfigurable systems with diverse physical elements and multiscale coupling processes, which will require new experimental and theoretical tools. Meanwhile, the similarity between the size of medium constituents and NPs makes atomic simulations of their interactions increasingly practical. Evolving experimental tools can stimulate improvement of existing force fields. New scientific opportunities for a better understanding of the electronic origin of classical interactions are converging at the scale of NPs.

Definitions of entanglement spacing and time constants in the tube model

Numerous papers have recently appeared in the literature presenting quantitative comparisons of experimental linear viscoelastic data to the most recent versions of “tube” models for entangled polymer melts and solutions. Since these tube models are now being used for quantitative, rather than just qualitative, predictions, it has become important that numerical prefactors for the time constants that appear in these theories be evaluated correctly using literature data for the parameters (i.e., density, plateau modulus, etc.) that go into the theories. However, in the literature two definitions of the entanglement spacing in terms of plateau modulus have been presented, and confusion between these has produced numerous errors in the recent literature. In addition, two different definitions of the “equilibration time,” a fundamental time constant, have also appeared, creating additional potential for confusion. We therefore, carefully review the alternative definitions and clarify the values of the prefactors that must be used for the different definitions, in the hope of helping future authors to avoid such errors.

Coarse-Grained Molecular Dynamics Studies of the Concentration and Size Dependence of Fifth- and Seventh-Generation PAMAM Dendrimers on Pore Formation in DMPC Bilayer

We have performed molecular dynamics (MD) simulations of multiple copies of unacetylated G5 and G7 and acetylated G5 dendrimers in dimyristoylphosphatidylcholine bilayers with explicit water using the coarse-grained model developed by Marrink et al. (J. Phys. Chem. B 2007, 111, 7812) with the inclusion of long-range electrostatics. When initially clustered together near the bilayer, neutral acetylated dendrimers aggregate, whereas cationic unacetylated dendrimers do not aggregate, but separate from each other, similar to the observations from atomic force microscopy by Mecke et al. (Chem. Phys. Lipids 2004, 132, 3). The bilayers interacting with unacetylated dendrimers of higher concentration are significantly deformed and show pore formation on the positively curved portions, while acetylated dendrimers are unable to form pores. Unacetylated G7 dendrimers bring more water molecules into the pores than do unacetylated G5 dendrimers. These results agree qualitatively with experimental results showing that significant cytoplasmic-protein leakage is produced by unacetylated G7 dendrimers at concentrations as low as 10 nM, but only at a much higher concentration of 400 nM for unacetylated G5 dendrimers (Bioconjugate Chem. 2004, 15, 774). This good qualitative agreement indicates that the effect on pore formation of the concentration and size of large nanoparticles can be studied through coarse-grained MD simulations, provided that long-range electrostatic interactions are included.

Comparing Experimental and Simulated Pressure-Area Isotherms for DPPC

Although pressure-area isotherms are commonly measured for lipid monolayers, it is not always appreciated how much they can vary depending on experimental factors. Here, we compare experimental and simulated pressure-area isotherms for dipalmitoylphosphatidylcholine (DPPC) at temperatures ranging between 293.15 K and 323.15 K, and explore possible factors influencing the shape and position of the isotherms. Molecular dynamics simulations of DPPC monolayers using both coarse-grained (CG) and atomistic models yield results that are in rough agreement with some of the experimental isotherms, but with a steeper slope in the liquid-condensed region than seen experimentally and shifted to larger areas. The CG lipid model gives predictions that are very close to those of atomistic simulations, while greatly improving computational efficiency. There is much more variation among experimental isotherms than between isotherms obtained from CG simulations and from the most refined simulation available. Both atomistic and CG simulations yield liquid-condensed and liquid-expanded phase area compressibility moduli that are significantly larger than those typically measured experimentally, but compare well with some experimental values obtained under rapid compression.

A constitutive model for the prediction of ellipsoidal droplet shapes and stresses in immiscible blends

We report a phenomenological constitutive model with no adjustable parameters appropriate for the transient behavior of droplets and blends. The time evolution of the droplet anisotropy tensor during droplet relaxation under quiescent conditions is described using a frame-invariant formulation that approximately imposes constancy of droplet volume. The Doi–Ohta theory [J. Chem. Phys. 95, 1242 (1991)] is then adapted to transient flows in which breakup and coalescence do not occur by replacing the Doi–Ohta relaxation terms with this relaxation description. Model predictions are compared to results of visualization of single droplets in step shear and startup of steady shear and to measurement of concentrated blend rheology in step shear and startup of steady shear. The model quantitatively described the relaxation after step strain of single droplets to axisymmetric and then to isotropic shapes. With the inclusion of the rational ellipsoidal closure for affine deformation [Wetzel and Tucker, Int. J. Multip...

Modeling hydrodynamic interaction in Brownian dynamics: Simulations of extensional flows of dilute solutions of DNA and polystyrene

Abstract We describe a method to include full hydrodynamic interactions (HI) using the Rotne–Prager tensor into the bead–spring model without excluded-volume interactions in a way suitable for Brownian dynamics (BD) simulations of the transient nonlinear rheological properties of dilute polymer solutions. First, we develop a scheme to determine the HI parameter h∗ and bead radius “a” that keeps the number of beads N modest at high molecular weight and yet matches the bead–spring model to the “real” polymer both in its longest relaxation time or diffusivity near equilibrium and in the drag on the chain at full extension, the latter being estimated by a formula of Batchelor. Second, we compare three different numerical integration methods, namely an explicit Euler’s method, a semi-implicit Newton’s method and a semi-implicit predictor–corrector method, and conclude that the predictor–corrector method is the best one available now, because of its ability to use larger time-steps and the relatively low computational expense for each step. Third, we perform simulations for two different macromolecules, namely λ-phage DNA and high molecular weight polystyrene (PS). We find that we can model λ-phage DNA with full HI with only 10 beads, and find that HI has negligible effect on extensional-flow behavior because of DNA’s expanded configuration even at rest, and therefore, its small value of h ∗ =0.03 . For PS in a theta solvent, however, molecular configurations are much more compact, and to avoid bead overlap we must keep h ∗ . This requires the use of more beads, at least N=20 for a molecular weight of 2 million, even if we drop the requirement that we match the longest relaxation time. Surprisingly, despite our inability to match the experimental longest relaxation time with a limited number of beads, excellent agreement with experimental filament-stretching strain–stress data is obtained except for the plateau Trouton ratio for PS of molecular weight of 2 million at various Weissenberg numbers. The inclusion of HI eliminates the “lag”, the delay in growth of the Trouton ratio relative to experimental data, seen in earlier simulations.