Macromolecular Crowding: How Shape and Interactions Affect Diffusion

The long time self-diffusion of highly charged colloidal particles consisting of polybutylacrylate was studied employing pulsed field gradient NMR (PFGNMR) and Brownian dynamics (BD) simulations. The potential parameters for the Yukawa interaction potential used in the BD simulations were derived from the static structure factor measured by means of light scattering. The long time self-diffusion coefficients resulting from NMR and BD were compared for different ionic strengths, which cause a screening of the interaction potential due to stray ions. Increasing the ionic strength of the colloidal suspensions, we observed a phase transition from a crystalline to a liquidlike structure. Whereas at high salt concentrations both long time diffusion coefficients agree within a few percent, at intermediate ionic strengths the values measured via PFGNMR are by a factor of 2 higher than those predicted by the BD simulation. This deviation is explained by hydrodynamic interactions which are expected to enhance long time self-diffusion and which are not taken into account in our BD algorithm.

Brownian Dynamics Simulations of Aldolase Binding Glyceraldehyde 3-Phosphate Dehydrogenase and the Possibility of Substrate Channeling

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.

We use a combination of Brownian dynamics (BD) simulation results and deep learning (DL) strategies for the rapid identification of large structural changes caused by missense mutations in intrinsically disordered proteins (IDPs). We used ∼6500 IDP sequences from MobiDB database of length 20-300 to obtain gyration radii from BD simulation on a coarse-grained single-bead amino acid model (HPS2 model) used by us and others [Dignon, G. L. PLoS Comput. Biol. 2018, 14, e1005941,Tesei, G. Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2111696118,Seth, S. J. Chem. Phys. 2024, 160, 014902] to generate the training sets for the DL algorithm. Using the gyration radii ⟨Rg⟩ of the simulated IDPs as the training set, we develop a multilayer perceptron neural net (NN) architecture that predicts the gyration radii of 33 IDPs previously studied by using BD simulation with 97% accuracy from the sequence and the corresponding parameters from the HPS model. We now utilize this NN to predict gyration radii of every permutation of missense mutations in IDPs. Our approach successfully identifies mutation-prone regions that induce significant alterations in the radius of gyration when compared to the wild-type IDP sequence. We further validate the prediction by running BD simulations on the subset of identified mutants. The neural network yields a (104-106)-fold faster computation in the search space for potentially harmful mutations. Our findings have substantial implications for rapid identification and understanding of diseases related to missense mutations in IDPs and for the development of potential therapeutic interventions. The method can be extended to accurate predictions of other mutation effects in disordered proteins.

We have elucidated the feasibility of trapping magnetic rod-like particles that flow in a cylindrical pipe in terms of a non-uniform magnetic field. We have performed Brownian dynamics (BD) simulations in order to clarify the influence that various factors have on the attachment or trapping characteristics of magnetic rod-like particles to the poles. The employment of a local linearisation approximation enables us to apply the BD method that was fully-developed for a simple shear flow to the present Hagen-Poiseuille flow. In the case of a sufficiently small magnetic interaction between the particles, numerous rod-like particles may attach to the magnetic poles if the influence of a non-uniform magnetic field is sufficiently more dominant than that of the flow field, otherwise, the particles flow away along the centreline of the cylindrical pipe. If the magnetic interactions are sufficiently more dominant than both the flow field and the non-uniform magnetic field, the particles aggregate to form densely-packed clusters that flow away along the centreline area of the pipe without being trapped at the poles. In the situation of insufficient magnetic interactions, thin chain-like clusters may be formed from several anchored particles trapped to the poles and incline in the downstream direction.

Absolute Protein-Protein Association Rate Constants from Flexible, Coarse-Grained Brownian Dynamics Simulations: The Role of Intermolecular Hydrodynamic Interactions in Barnase-Barstar Association

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4×106 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Multiscale Modeling of Microtubules and Actin Filaments

We have studied an excited state proton transfer (ESPT) from the cationic "super" photoacid N-methyl 6-hydroxyquinolinium perfluorobutane sulfonate to non-aqueous solvents using picosecond and nanosecond time-resolved fluorescence spectroscopy. Upon the photoinduced adiabatic deprotonation from the hydroxyl moiety, a quinolinium zwitterion with a highly anisotropic charge distribution is formed. Due to the complexity of the resultant photodissociated system, the typical description of the reversible ESPT within the framework of the Spherically Symmetric Diffusion Problem (SSDP) is not possible. Additional complications are caused by the presence of a counteranion particle which affects the proton mobility. To better understand the ESPT process, we have performed extensive Brownian dynamics (BD) simulations of this three-body system as a tool to reveal the nature of the nonstationary interaction potentials and to elucidate the role of a counterion in the diffusion and reactive properties of the proton. Moreover, our results demonstrated that the anisotropy of the potential force can be taken into account after adapting this force for use in the SSDP. The results of both BD simulations and SSDP calculation with the adapted force field were used to fit the experimental kinetics of this three-body problem adequately.

Utility of Brownian dynamics simulations in chemistry and biology: A comprehensive review.

The Paths to Specific vs Nonspecific Sequence Recognition

<p>The use of computational simulation to study the dynamics and interactions of macromolecules has become an important tool in the field of biochemistry. A common method to perform these simulations is to use all-atom explicit-solvent molecular dynamics (MD). However, due to the limitations in computational power currently available, this method is not practical for simulating large-scale biomolecular systems on long timescales. An alternative is to perform implicit-solvent Brownian dynamics (BD) simulations using a coarse grained (CG) model that allows for increased computational efficiency. However, if simulations using the CG model are not realistic, then the gain in computational efficiency from using a CG model is not worthwhile.</p> <p>This thesis describes the derivation of a set of bonded and nonbonded CG potential functions for use in implicit-solvent BD simulations of proteins derived from all-atom explicit-solvent MD simulations of amino acids. To determine which force field and water model to use in the MD simulations, Chapter II describes 1 Μs all-atom explicit-solvent MD simulations of glycine, asparagine, phenylalanine, and valine solutions at 50, 100, 200 and 300 mg/ml concentrations performed using eight different force field and water model combinations. To evaluate the accuracy of the force fields at high solute concentrations, the density, viscosity, and dielectric increments of the four amino acids were calculated from the simulations and compared to experimental results. Additionally, the change in the strength of hydrophobic and electrostatic interactions with increasing solute concentration was calculated for each force field and water model combination. As a result of this study, the Amber ff99SB-ILDN force field and TIP4P-Ew explicit-solvent water model were chosen for all subsequent MD simulations. Chapter III describes the derivation of CG bonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of each of the twenty amino acids, including a separate simulation for protonated histidine. The angle and dihedral probability distributions sampled during the MD simulations were used to optimize the bonded potential functions using the iterative Boltzmann inversion (IBI) method. Chapter IV describes the derivation of CG nonbonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of every possible pairing of the amino acids (231 different systems). The radial distribution functions calculated from these MD simulations were used to optimize a set of nonbonded CG potential functions using the IBI method. The optimized set of bonded and nonbonded potential functions, which is termed COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins), quantitatively reproduced all of the calculated MD distributions. To determine if COFFDROP would be useful for simulations of bimolecular systems, Chapter V describes the testing of the transferability of the force field. First, COFFDROP was used to simulate concentrated amino acid solutions. The clustering of the solutes in these simulations was directly compared with results from corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. Next, BD simulations of 9.2 mM solutions of the small protein villin headpiece were performed. The proteins aggregated during these simulations, which is in agreement with results from MD simulation but in disagreement with experiment. After scaling the strength of COFFDROP's nonbonded potential functions by a factor of 0.8 and rerunning the BD simulations, the amount of aggregation was comparable to experimental observations. Based on these results, COFFDROP is likely to be applicable in CG BD simulations of large, highly concentrated, biomolecular systems.</p>

Brownian Dynamics Theory for Predicting Internal and External Blockages of Tetraethylammonium in the KcsA Potassium Channel

Brownian dynamics (BD) has been applied as a comprehensive tool to model sedimentation and diffusion of nanoparticles in analytical ultracentrifugation (AUC) experiments. In this article, we extend the BD algorithm by considering space-dependent diffusion and solvent compressibility. With this, the changes in the sedimentation and diffusion coefficient from altered solvent properties at increased pressures are accurately taken into account. Moreover, it is demonstrated how the concept of space-dependent diffusion is employed to describe concentration-dependent sedimentation and diffusion coefficients, in particular, through the Gralen coefficient and the second virial coefficient. The influence of thermodynamic nonideality on diffusional properties can be accurately simulated and agree with well-known evaluation tools. BD simulations for sedimentation equilibrium and sedimentation velocity (SV) AUC experiments including effects of hydrodynamic and thermodynamic nonideality are validated by global evaluation in SEDANAL. The interplay of solvent compressibility and retrieved nonideality parameters can be studied utilizing BD. Finally, the second virial coefficient is determined for lysozyme from SV AUC experiments and BD simulations and compared to membrane osmometry. These results are in line with DLVO theory. In summary, BD simulations are established for the validation of nonideal sedimentation in AUC providing a sound basis for the evaluation of complex interactions even in polydisperse systems.

This chapter provides the background theory and a practical protocol for performing Brownian dynamics simulation of peptides. Brownian dynamics simulation represents a complementary approach to Monte Carlo and molecular dynamics methods. Unlike Monte Carlo methods, it could provide dynamical information in a timescale longer than the momentum relaxation time. On the other hand, it is faster than molecular dynamics by approximating the solvent by a continuum and by operating in the over-damped limit. This chapter introduces the use of the University of Houston Brownian Dynamics (UHBD) program [1, 2] to perform Brownian dynamics simulation on peptides.