Coarse-grained Brownian Dynamics Simulations Research Articles

Predicting reaction behavior of tethered polymers in shear flow.

Kinetics of force-mediated chemical reactions of end-tethered polymers with varying chain length N in varying shear rate flow γ̇ are explored via coarse-grained Brownian dynamics simulations. At fixed γ̇, force F along a polymer increases linearly with N as previously predicted; however, contrary to existing theory, the F(N) slope increases for N above a transition length that exhibits minimal dependence on γ̇. Force profiles are used in a stochastic model of a force-mediated reaction to compute the time for x percent of a polymer population to experience a reaction, tx. Observations are insensitive to the selected value of x in that tx data for varying N and γ̇ can be consistently collapsed onto a single curve via appropriate scaling, with one master curve for systems below the transition N (small N) and another for those above (large N). Different force scaling for small and large N results in orders of magnitude difference in force-mediated reaction kinetics as represented by the population response time. Data presented illustrate the possibility of designing mechano-reactive polymer populations with highly controlled response to flow across a range in γ̇.

The structure of cellulose nanofibril networks at low concentrations and their stabilizing action on colloidal particles

The structure and dynamics of networks formed by rod-shaped particles can be indirectly investigated by measuring the diffusion of spherical tracer particles. This method was used to characterize cellulose nanofibril (CNF) networks in both dispersed and arrested states, the results of which were compared with coarse-grained Brownian dynamics simulations. At a CNF concentration of 0.2 wt% a transition was observed where, below this concentration tracer diffusion is governed by the increasing macroscopic viscosity of the dispersion. Above 0.2 wt%, the diffusion of small particles (20–40 nm) remains viscosity controlled, while particles (100–500 nm) become trapped in the CNF network. Sedimentation of silica microparticles (1–5 μm) in CNF dispersions was also determined, showing that sedimentation of larger particles is significantly affected by the presence of CNF. At concentrations of 0.2 wt%, the sedimentation velocity of 5 μm particles was reduced by 99 % compared to pure water.

Cascades of unfolding transitions in amphiphilic molecular brushes.

Using a combination of self-consistent field theory with coarse-grained Brownian dynamics simulations, we studied mechanical unfolding of an amphiphilic molecular brush in a solvent that was poor for the side chains but good for the main chain of the brush. In striking contrast to earlier theoretical predictions [O. V. Borisov and A. Halperin, Europhys. Lett. 34, 657 (1996)] made for amphiphilic graft copolymers, we discovered that in a partially unfolded molecular brush, a globular core co-exists, at equilibrium, with a necklace of smaller sized intra-molecular micelles, each comprising a few side chains connected by stretched main chain strands (bridges). A progressive increase in the main chain end-to-end distance of the brush triggers a sequence of discrete events of generation of new intramolecular micelles, giving rise to a sawtooth pattern in the restoring force-deformation curve.

Single molecule analysis of structural fluctuations in DNA nanostructures.

DNA origami is an excellent tool for building complex artificial nanostructures. Functionalization of these structures provides the possibility of precise organization of matter at the nanoscale. In practice, efforts in this endeavour can be impeded by electrostatic repulsion or other dynamics at the molecular scale, resulting in uncompliant local structures. Using single molecule FRET microscopy combined with coarse-grained Brownian dynamics simulations, we investigated here the local structure around the lid of a DNA origami box, which can be opened by specific DNA keys. We found that FRET signals for the closed box depend on buffer ion concentrations and small changes to the DNA structure design. Simulations provided a view of the global and local structure and showed that the distance between the box wall and lid undergoes fluctuations. These results provide methods to vizualise and improve the local structure of three-dimensional DNA origami assemblies and offer guidance for exercising control over placement of chemical groups and ligands.

Structure and dynamics of a self-propelled semiflexible filament

We investigate structural and dynamical properties of a self-propelled filament using coarse-grained Brownian dynamics simulations. A self-propulsion force is applied along the bond vectors, i.e., tangent to the filament and their locations are considered in two different manners. In case one, force is applied to all beads of the filament, which is termed as homogeneous self-propulsion. Here, we obtain a monotonic decrease in the flexibility of the filament with P\'eclet number. Hence, radius of gyration also displays the same trend. Moreover, the radius of gyration of the filament shows universal dependence for various bending rigidities with flexure number. The effective diffusivity of the filament shows enhancement with the active force and it increases linearly with force and bending rigidity. In case two, self-propulsion force is applied only to few bond vectors. The location of active forces is chosen in a periodic manner starting from the tail of the filament and leaving the front end without force. In this case, filament acquires various structures such as rod-like, helical, circular, and folded states. The transition from several states is understood in terms of tangent-tangent correlation, bending energy and torsional order parameter. The helical state is identified through a crossover from exponential to oscillatory behavior of the tangent-tangent correlation. A sudden increase in the bending energy separates a helical to a folded states of the filament.

Electrostatics of Nanoparticle-Wall Interactions within Nanochannels: Role of Double-Layer Structure and Ion-Ion Correlations.

We perform computational investigations of the electrolyte-mediated interactions of charged nanoparticles with the walls of nanochannels. We investigate the role of discrete ion effects, valence, and electrolyte strength on nanoparticle–wall interactions. We find for some of the multivalent charge regimes that the like-charged nanoparticles and walls can have attractive interactions. We study in detail these interactions and the free-energy profile for the nanoparticle–wall separation. We find there are energy barriers and energy minima giving preferred nanoparticle locations in the channel near the center and at a distance near to but separated from the channel walls. We characterize contributions from surface overcharging, condensed layers, and overlap of ion double layers. We perform our investigations using coarse-grained particle-level simulations with Brownian dynamics, classical density functional theory, and the mean-field Poisson–Boltzmann theory. We discuss the implications of our results for phenomena in nanoscale devices.

Nonmonotonic DNA-length-dependent mobility in pluronic gels.

Two-dimensional electrophoresis was used to analyze the mobility of DNA fragments in micellar gels of pluronic F127 (EO_{100}PO_{70}EO_{100}) and pluronic P123 (EO_{20}PO_{70}EO_{20}). The 20-3500 base pair DNA fragments were separated by size first in agarose gels, and then in pluronic gels at room temperature. In agarose gels, the DNA mobility decreases monotonically with increasing DNA length. In pluronic gels, however, the mobility varies nonmonotonically according to fragment lengths that are strongly correlated with the diameter of the spherical micelles. Brownian dynamics (BD) simulations with short-ranged intra-DNA hydrodynamic interactions were performed to numerically calculate the length-dependent mobility in pluronic lattices. The rising and falling trends, as well as the oscillations of mobility, were captured by the coarse-grained BD simulations. Molecular dynamics simulations in pluronic F127, with explicitly modeled micelle coronas, justified that the hydrodynamic interactions mediated by the complex fluid of hydrated poly(ethylene oxide) are a possible reason for the initial rise of mobility with DNA length.

Striking the Balance between Selectivity and Efficiency: An Integrative Model of Nucleocytoplasmic Transport

Macromolecular traffic through the nuclear pore complex (NPC) occurs by either passive or facilitated diffusion. While passive diffusion rates are believed to decrease dramatically beyond the approximately 30-60 kDa size threshold, facilitated diffusion, which is mediated by soluble nuclear transport receptors (NTRs), proceeds rapidly even for large macromolecular assemblies such as intact ribosomal subunits. To study the mechanism by which the NPC facilitates rapid facilitated diffusion while maintaining an effective barrier to the passive diffusion of large macromolecules, we created a model of transport dynamics that integrates data from multiple empirical and theoretical sources: small-angle x-ray scattering, nuclear magnetic resonance spectroscopy, electron tomography, dynamic light scattering, atomistic simulations, and additional datasets available from the literature. In both our model and in independent fluorescence recovery after photobleaching (FRAP) measurements, we show that the barrier to passive diffusion is much softer than previously thought, and completely lacks a well-defined size cutoff at 30-60 kDa. Coarse-grained Brownian Dynamics simulations replicate these results, and indicate that this gradual decrease in passive diffusion rates with molecular weight is consistent with an entropic gating mechanism, in which repulsive forces are set out by the crowded and highly dynamic FG repeat domains that fill the central channel of the NPC. In facilitated diffusion, we show that cargo-bound NTRs counter these repulsive forces by utilizing a unique dynamic interaction mechanism with the FG repeats, transitioning between weakly- and strongly-interacting states, thereby sliding and exchanging between proximal FG repeats. This ‘slide-and-exchange’ interaction mechanism is reminiscent of the sliding of transcription factors on DNA molecules. Our results highlight the direct role of the disorder within FG repeats in nucleocytoplasmic transport, and resolve the apparent conflict between the selectivity and speed of transport.

Investigation of Structural Dynamics of Enzymes and Protonation States of Substrates Using Computational Tools.

This review discusses the use of molecular modeling tools, together with existing experimental findings, to provide a complete atomic-level description of enzyme dynamics and function. We focus on functionally relevant conformational dynamics of enzymes and the protonation states of substrates. The conformational fluctuations of enzymes usually play a crucial role in substrate recognition and catalysis. Protein dynamics can be altered by a tiny change in a molecular system such as different protonation states of various intermediates or by a significant perturbation such as a ligand association. Here we review recent advances in applying atomistic molecular dynamics (MD) simulations to investigate allosteric and network regulation of tryptophan synthase (TRPS) and protonation states of its intermediates and catalysis. In addition, we review studies using quantum mechanics/molecular mechanics (QM/MM) methods to investigate the protonation states of catalytic residues of β-Ketoacyl ACP synthase I (KasA). We also discuss modeling of large-scale protein motions for HIV-1 protease with coarse-grained Brownian dynamics (BD) simulations.

The effect of bending stiffness on scaling laws for the size of colloidal nanosheets

Using coarse-grained Brownian dynamics simulations, we study the relationship between hydrodynamic radius ( and the lateral size ( of dispersed nanosheets. Our simulation results show that the bending modulus of the nanosheets has a significant impact on the exponent of this power-law relationship between the radius of gyration (and thus and The exponent can vary from 0.17 to 1. This sheds light on the interpretation of dynamic light scattering (DLS) measurements, such that DLS data can capture both nanosheet lateral size and modulus (which is, in turn, affected by nanosheet thickness).

Polymer glass transition occurs at the marginal rigidity point with connectivity z* = 4.

We re-examine the physical origin of the polymer glass transition from the point of view of marginal rigidity, which is achieved at a certain average number of mechanically active intermolecular contacts per monomer. In the case of polymer chains in a melt/poor solvent, each monomer has two neighbors bound by covalent bonds and also a number of central-force contacts modelled by the Lennard-Jones (LJ) potential. We find that when the average number of contacts per monomer (covalent and non-covalent) exceeds the critical value z* ≈ 4, the system becomes solid and the dynamics arrested - a state that we declare the glass. Coarse-grained Brownian dynamics simulations show that at sufficient strength of LJ attraction (which effectively represents the depth of quenching, or the quality of solvent) the polymer globule indeed crosses the threshold of z*, and becomes a glass with a finite zero-frequency shear modulus, G∝ (z-z*). We verify this by showing the distinction between the 'liquid' polymer droplet at z < z*, which changes shape and adopts the spherical conformation in equilibrium, and the glassy 'solid' droplet at z > z*, which retains its shape frozen at the moment of z* crossover. These results provide a robust microscopic criterion to tell the liquid apart from the glass for the linear polymers.

Computer Simulations of Viral Capsid Assembly with Patchy Particle Model

Most viruses use the power of self-assembly to protect and transport their genomic material with the help of a protein capsid. Different computational approaches have been employed to understand the dynamics of the assembly pathway, ranging from molecular dynamics simulations with atomistic detail through Brownian dynamics simulations with coarse-grained interactions to statistical or thermodynamic approaches without any explicit representation of space. We have used coarse-grained Brownian dynamics simulations of a patchy particle model to represent the physically correct assembly dynamics in time and space and at the same time to achieve sufficiently long simulation times to study the statistics of complete capsid self-assembly. In particular, we have developed algorithms that account for the anisotropic translational and rotational diffusion of assembly intermediates and ensure detailed balance for reversible patchy particle models (Klein et al., J. Chem. Phys. 140:184112, 2014). We report on studies of two biologically important questions that can be addressed only in such a computer time-efficient framework: the role of event-driven reactivity in capsid self-assembly (Baschek et al., BMC Biophysics 5:22, 2012) and the role of the rate of capsomere addition (Boettcher et al., preprint 2014). We find that hierarchical assembly is more favorable than direct assembly in the case of stable bonds and that slower capsomere supply is more favorable in order to attain a steady state of continuous capsid assembly.

Modeling of enhanced catalysis in multienzyme nanostructures: effect of molecular scaffolds, spatial organization, and concentration.

Colocalized multistep enzymatic reaction pathways within biological catabolic and metabolic processes occur with high yield and specificity. Spatial organization on membranes or surfaces may be associated with increased efficiency of intermediate substrate transfer. Using a new Brownian dynamics package, GeomBD, we explored the geometric features of a surface-anchored enzyme system by parallel coarse-grained Brownian dynamics simulations of substrate diffusion over microsecond (μs) to millisecond (ms) time scales. We focused on a recently developed glucose oxidase (GOx), horseradish peroxidase (HRP), and DNA origami-scaffold enzyme system, where the H2O2 substrate of HRP is produced by GOx. The results revealed and explained a significant advantage in catalytic enhancement by optimizing interenzyme distance and orientation in the presence of the scaffold model. The planar scaffold colocalized the enzymes and provided a diffusive barrier that enhanced substrate transfer probability, becoming more relevant with increasing interenzyme distance. The results highlight the importance of protein geometry in the proper assessment of distance and orientation dependence on the probability of substrate transfer. They shed light on strategies for engineering multienzyme complexes and further investigation of enhanced catalytic efficiency for substrate diffusion between membrane-anchoring proteins.

A Coarse-Grained Model for Polyglutamine Aggregation Modulated by Amphipathic Flanking Sequences

The aggregation of proteins with expanded polyglutamine (polyQ) tracts is directly relevant to the formation of neuronal intranuclear inclusions in Huntington’s disease. In vitro studies have uncovered the effects of flanking sequences as modulators of the driving forces and mechanisms of polyQ aggregation in sequence segments associated with HD. Specifically, a seventeen-residue amphipathic stretch (N17) that is directly N-terminal to the polyQ tract in huntingtin decreases the overall solubility, destabilizes nonfibrillar aggregates, and accelerates fibril formation. Published results from atomistic simulations showed that the N17 module reduces the frequency of intermolecular association. Our reanalysis of these simulation results demonstrates that the N17 module also reduces interchain entanglements between polyQ domains. These two effects, which are observed on the smallest lengthscales, are incorporated into phenomenological pair potentials and used in coarse-grained Brownian dynamics simulations to investigate their impact on large-scale aggregation. We analyze the results from Brownian dynamics simulations using the framework of diffusion-limited cluster aggregation. When entanglements prevail, which is true in the absence of N17, small spherical clusters and large linear aggregates form on distinct timescales, in accord with in vitro experiments. Conversely, when entanglements are quenched and a barrier to intermolecular associations is introduced, both of which are attributable to N17, the timescales for forming small species and large linear aggregates become similar. Therefore, the combination of a reduction of interchain entanglements through homopolymeric polyQ and barriers to intermolecular associations appears to be sufficient for providing a minimalist phenomenological rationalization of in vitro observations regarding the effects of N17 on polyQ aggregation.

Debye Screening Effect on Scaling Behavior of Longest Relaxation Time of Biological Polyelectrolyte Chain

The scaling relationship of the longest relaxation time of a single chain of semiflexible biological polyelectrolyte has been investigated by performing well-established coarse-grained Brownian dynamics simulations. Two kinds of longest relaxation times were estimated from time-sequences of chain trajectories, and their behaviors were interpreted by applying the scaling law for different molecular weights of polyelectrolyte and Debye lengths. The scaling exponents for longest stress relaxation and rotational relaxation are found in the ranges of 1.67-1.79 and 1.65-1.81, respectively, depending on the physicochemical interaction of electrostatic Debye screening. The scaling exponent increases with decreasing screening effect, which is a special feature of polyelectrolytes differing from neutral polymers. It revealed that the weak screening allows a polyelectrolyte chain to follow the behavior in good solvent due to the strong electrostatic repulsion between beads.

Molecule-Centered Method for Accelerating the Calculation of Hydrodynamic Interactions in Brownian Dynamics Simulations Containing Many Flexible Biomolecules

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman's Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor.

Coarse-grained Brownian dynamics simulations of protein translocation through nanopores

A crucial process in biological cells is the translocation of newly synthesized proteins across cell membranes via integral membrane protein pores termed translocons. Recent improved techniques now allow producing artificial membranes with pores of similar dimensions of a few nm as the translocon system. For the translocon system, the protein has to be unfolded, whereas the artificial pores are wide enough so that small proteins can pass through even when folded. To study how proteins permeate through such membrane pores, we used coarse-grained Brownian dynamics simulations where the proteins were modeled as single beads or bead-spring polymers for both folded and unfolded states. The pores were modeled as cylindrical holes through the membrane with various radii and lengths. Diffusion was driven by a concentration gradient created across the porous membrane. Our results for both folded and unfolded configurations show the expected reciprocal relation between the flow rate and the pore length in agreement with an analytical solution derived by Brunn et al. [Q. J. Mech. Appl. Math. 37, 311 (1984)]. Furthermore, we find that the geometric constriction by the narrow pore leads to an accumulation of proteins at the pore entrance, which in turn compensates for the reduced diffusivity of the proteins inside the pore.

Nonequilibrium Simulations of Lamellae Forming Block Copolymers under Steady Shear: A Comparison of Dissipative Particle Dynamics and Brownian Dynamics

Nonequilibrium simulations of lamellae-forming block copolymers are investigated by means of theoretically informed coarse-grained Brownian dynamics simulations and dissipative particle dynamics. T...

Conformational transition of polyelectrolyte chains extending over the de Gennes regime in slitlike nanochannels

The confinement-induced conformational transitions of the polyelectrolyte chain are characterized with the coarse-grained Brownian dynamics simulations and the blob theory. Submicron-sized biopolymer xanthan is chosen as a model polyelectrolyte taking into account both flexible and semiflexible chains for comparison. Confined flexible and semiflexible chains exhibit a nonmonotonic variation in size in weak confinements, where the relative radius of gyration shows a dip and then increases when decreasing the channel width. The rigid chain, realized at low screening, exhibits a sigmoidal transition without minima in size. Major attention should be on the dependence of scaling law exponents on the screening effect of the solution in the moderate confinement of the de Gennes regime. Our findings are expected to provide useful information and new insight into the confined polyelectrolytes when relevant micro/nanochannels are designed and fabricated.

Thermal fluctuations of haemoglobin from different species: adaptation to temperature via conformational dynamics

Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits.