Coarse-grained Brownian Dynamics 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.

Chain rotational dynamics in dilute polymer solutions and melts under shear flow

We present detailed scaling characteristics of the chain rotation dynamics in shear flow for melt and dilute linear polymer systems using extensive atomistic and coarse-grained Brownian dynamics (BD) molecular dynamics simulations, respectively. We find that the dilute systems with hydrodynamic interaction (HI) and excluded volume (EV) effects generally exhibit two distinct scaling behavior of the chain rotation time τrot between the intermediate and strong flow regimes, whereas the free-draining dilute polymer systems display a relatively simple single-scaling behavior for τrot with respect to the shear rate throughout the intermediate-to-strong flow regimes. This dynamic feature correlates with the scaling characteristics of average chain deformation and orientation of the system with respect to the flow strength. Notably, the combined HI and EV effects generally weaken the structural change of polymer chains in response to the applied flow and enhance the overall chain rotation dynamics by disturbing the chain stretch and alignment to the flow direction. Accordingly, due to the variation in the HI and EV effects (in association with chain deformation) with the flow strength, the dilute systems with HI and EV turn out to reveal relatively lower and higher scaling behaviors of τrot in the intermediate and strong flow regimes, respectively, in comparison to the corresponding free-draining systems. Despite the absence of HI and EV effects, the melt systems also exhibit two distinct scaling behaviors of τrot between the intermediate and strong flow regimes. This feature arises from the intermolecular interactions between chains, resulting in a significant influence of interchain entanglement and interchain dynamic collision on the chain rotation dynamics. It is further observed that the overall τrot scaling behavior for each system is predominantly determined by the corresponding scaling behavior of the kinematically stable (diffusive) angular regions near the flow direction, where the flow force is relatively weak. Additionally, polymer chains in kinematically unstable (convective) angular regions exhibit nearly affine chain rotation dynamics conforming to the imposed flow field, independent of the polymer concentration and chain length. This is considered to be a universal feature for general polymeric liquids in shear flow.

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.

Between Two Walls: Modeling the Adsorption Behavior of β-Glucosidase A on Bare and SAM-Functionalized Gold Surfaces.

The efficient immobilization of enzymes on surfaces remains a complex but central issue in the biomaterials field, which requires us to understand this process at the atomic level. Using a multiscale approach combining all-atom molecular dynamics and coarse-grain Brownian dynamics simulations, we investigated the adsorption behavior of β-glucosidase A (βGA) on bare and self-assembled monolayer (SAM)-functionalized gold surfaces. We monitored the enzyme position and orientation during the molecular dynamics (MD) trajectories and measured the contacts it forms with both surfaces. While the adsorption process has little impact on the protein conformation, it can nonetheless perturb its mechanical properties and catalytic activity. Our results show that compared to the SAM-functionalized surface, the adsorption of βGA on bare gold is more stable, but less specific, and more likely to disrupt the enzyme's function. This observation emphasizes the fact that the structural organization of proteins at the solid interface is a key point when designing devices based on enzyme immobilization, as one must find an acceptable stability-activity trade-off.

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.

Conformational Stability Adaptation of a Double-Stranded RNA-Binding Domain to Transfer RNA Ligand.

The double-stranded RNA-binding domain (dsRBD) is a broadly distributed domain among RNA-maturing enzymes. Although this domain recognizes dsRNA's structures via a conserved canonical structure adopting an α1-β1β2β3-α2 topology, several dsRBDs can accommodate discrete structural extensions expanding further their functional repertoire. How these structural elements engage cooperative communications with the canonical structure and how they contribute to the dsRBD's overall folding are poorly understood. Here, we addressed these issues using the dsRBD of human dihydrouridine synthase-2 (hDus2) (hDus2-dsRBD) as a model. This dsRBD harbors N- and C-terminal extensions, the former being directly involved in the recognition of tRNA substrate of hDus2. These extensions engage residues that form a long-range hydrophobic network (LHN) outside the RNA-binding interface. We show by coarse-grain Brownian dynamics that the Nt-extension and its residues F359 and Y364 rigidify the major folding nucleus of the canonical structure via an indirect effect. hDus2-dsRBD unfolds following a two-state cooperative model, whereas both F359A and Y364A mutants, designed to destabilize this LHN, unfold irreversibly. Structural and computational analyses show that these mutants are unstable due to an increase in the dynamics of the two extensions favoring solvent exposure of α2-helix and weakening the main folding nucleus rigidity. This LHN appears essential for maintaining a thermodynamic stability of the overall system and eventually a functional conformation for tRNA recognition. Altogether, our findings suggest that functional adaptability of extended dsRBDs is promoted by a cooperative hydrophobic coupling between the extensions acting as effectors and the folding nucleus of the canonical structure.

Prediction of membrane separation efficiency for hydrophobic and hydrophilic proteins : A coarse-grained Brownian dynamics simulation study.

A coarse-grained Brownian dynamics model was used to simulate two proteins of similar sizes inside model membrane pores of varying size and hydrophobicity. The two proteins, which have radii of gyration of approximately 9.5 Å in their native states, are a 36-residue hydrophilic villin head piece (HP-36) and a 40-residue hydrophobic amyloid beta (Aβ-40). From calculations of the separation factor, it is found that the two proteins are best separated using a pore radius of 15 Å and that hydrophobic pores select Aβ-40 while the hydrophilic pores preferentially pass through HP-36. In addition, it is found that a simple model based on the net hydropathy of a protein is capable of estimating the separation factor trends of other protein pairs. Together, the coarse-grained Brownian dynamics model and the simple model are fast methodologies to guide experimental membrane design and to provide insights on protein structure variations. Graphical Abstract Simulation setup and snapshots of protein in various pore sizes.

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.

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

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.

On the validity of representation of the inter-particle forces of a polymer-colloid cluster by linear springs

We have investigated the validity of the popular assumption of identical linear spring (ILS) in polymer-colloids aggregated clusters. The ILS assumption suggests that all inter-particle bonds in an aggregated cluster of polymer chains and colloid particles can be represented by identical linear springs. The assumption has been challenged by several experiments that showed the bond stiffness varies across the cluster based on the connectivity of their associated particles. Yet, the predictions of the computational models that used ILS assumption are surprisingly well-aligned with the experiments in some materials. By coupling the coarse-grain Brownian dynamics simulation to a Multi-body dynamics model, a systematic pathway for analyzing the effect of connectivity of particles on elasticity of polymer-colloids aggregated clusters is presented. ILS assumption is found to be valid for systems with a stress path formation mechanism such as close-packed polymer-colloid clusters. We found the assumption irrelevant in systems with wave-like stress distribution mechanism, such as with granular materials, sand piles and jammed systems. Keywords Mechanics; polymer-colloid clusters; Identical springs assumption.

Computational support for a scaffolding mechanism of centriole assembly.

Centrioles are essential for forming cilia, flagella and centrosomes. Successful centriole assembly requires proteins of the SAS-6 family, which can form oligomeric ring structures with ninefold symmetry in vitro. While important progress has been made in understanding SAS-6 protein biophysics, the mechanisms enabling ring formation in vivo remain elusive. Likewise, the mechanisms by which a nascent centriole forms near-orthogonal to an existing one are not known. Here, we investigate possible mechanisms of centriole assembly using coarse-grained Brownian dynamics computer simulations in combination with a rate equation approach. Our results suggest that without any external factors, strong stabilization associated with ring closure would be needed to enable efficient ring formation. Strikingly, our simulations reveal that a scaffold-assisted assembly mechanism can trigger robust ring formation owing to local cooperativity, and that this mechanism can also impart orthogonalilty to centriole assembly. Overall, our findings provide novel insights into the organizing principles governing the assembly of this important organelle.

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).

Bridging Enzymatic Structure Function via Mechanics: A Coarse-Grain Approach.

Flexibility is a central aspect of protein function, and ligand binding in enzymes involves a wide range of structural changes, ranging from large-scale domain movements to small loop or side-chain rearrangements. In order to understand how the mechanical properties of enzymes, and the mechanical variations that are induced by ligand binding, relate to enzymatic activity, we carried out coarse-grain Brownian dynamics simulations on a set of enzymes whose structures in the unbound and ligand-bound forms are available in the Protein Data Bank. Our results show that enzymes are remarkably heterogeneous objects from a mechanical point of view and that the local rigidity of individual residues is tightly connected to their part in the protein's overall structure and function. The systematic comparison of the rigidity of enzymes in their unbound and bound forms highlights the fact that small conformational changes can induce large mechanical effects, leading to either more or less flexibility depending on the enzyme's architecture and the location of its ligand-biding site. These mechanical variations target a limited number of specific residues that occupy key locations for enzymatic activity, and our approach thus offers a mean to detect perturbation-sensitive sites in enzymes, where the addition or removal of a few interactions will lead to important changes in the proteins internal dynamics.

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.

Fold and flexibility: what can proteins' mechanical properties tell us about their folding nucleus?

The determination of a protein's folding nucleus, i.e. a set of native contacts playing an important role during its folding process, remains an elusive yet essential problem in biochemistry. In this work, we investigate the mechanical properties of 70 protein structures belonging to 14 protein families presenting various folds using coarse-grain Brownian dynamics simulations. The resulting rigidity profiles combined with multiple sequence alignments show that a limited set of rigid residues, which we call the consensus nucleus, occupy conserved positions along the protein sequence. These residues' side chains form a tight interaction network within the protein's core, thus making our consensus nuclei potential folding nuclei. A review of experimental and theoretical literature shows that most (above 80%) of these residues were indeed identified as folding nucleus member in earlier studies.

Efficient Brownian dynamics simulation of DNA molecules with hydrodynamic interactions in linear flows.

The coarse-grained molecular dynamics (MD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). In this paper, an efficient algorithm is proposed to simulate the motion of a single DNA molecule in linear flows. The algorithm utilizes the integrating factor to cope with the effect of the linear flow of the surrounding fluid and applies the Metropolis method (MM) by Bou-Rabee, Donev, and Vanden-Eijnden [Multiscale Model. Simul. 12, 781 (2014)] to achieve more efficient BD simulation. Thus our method permits much larger time step size than previous methods while still maintaining the stability of the BD simulation, which is advantageous for long-time BD simulation. Our numerical results on λ-DNA agree very well with both experimental data and previous simulation results. Finally, when combined with fast algorithms such as the fast multipole method which has nearly optimal complexity in the total number of beads, the resulting method is parallelizable, scalable to large systems, and stable for large time step size, thus making the long-time large-scale BD simulation within practical reach. This will be useful for the study of membranes, long-chain molecules, and a large collection of molecules in the fluids.