GRPY: An Accurate Bead Method for Calculation of Hydrodynamic Properties of Rigid Biomacromolecules

On the importance of the diffusivity gradient term in Brownian dynamics simulations

In a recent study, Garner et al. investigated diffusion in the cytoplasm of fission yeasts, revealing vast heterogeneity in intracellular viscosity. Their conclusion was based on a combination of single-particle-tracking experiments and Brownian dynamics simulations. However, in their simulations, the diffusivity gradient term has been neglected-an assumption common in some biophysical applications but unjustified in this particular case due to spatial variations in diffusivity. Here, we aim to comment on the importance of the diffusivity gradient term and the physical consequences of not including it. We also demonstrate that omitting this term likely leads to overestimating fission yeast intracellular viscosity variance and underestimating its mean. Additionally, we propose modifications to the simulations to incorporate the gradient term.

Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Magnetically locked Janus particle clusters with orientation-dependent motion in AC electric fields

Active particles, or micromotors, locally dissipate energy to drive locomotion at small length scales. The type of trajectory is generally fixed and dictated by the geometry and composition of the particle, which can be challenging to tune using conventional fabrication procedures. Here, we report a simple, bottom-up method to magnetically assemble gold-coated polystyrene Janus particles into "locked" clusters that display diverse trajectories when stimulated by AC electric fields. The orientation of particles within each cluster gives rise to distinct modes of locomotion, including translational, rotational, trochoidal, helical, and orbital. We model this system using a simplified rigid beads model and demonstrate qualitative agreement between the predicted and experimentally observed cluster trajectories. Overall, this system provides a facile means to scalably create micromotors with a range of well-defined motions from discrete building blocks.

Beyond the US-SOMO-AF database: a new website for hydrodynamic, structural, and circular dichroism calculations on user-supplied structures

At the 25th International Analytical Ultracentrifugation Workshop and Symposium, we described the recent implementation of the UltraScan SOlution MOdeler AlphaFold (US-SOMO-AF) database, containing hydrodynamic, structural, CD calculations, and other ancillary information, performed on the entire AF v2 database of predicted protein structures, containing more than 1,000,000 entries. The scope of the US-SOMO-AF database was that of providing direct access to pre-calculated physicochemical parameters for rapid assessment against their experimentally determined counterparts to test the compatibility in solution of predicted AlphaFold structures. In the meantime, the AlphaFold consortium has extended its database of predicted structures to an astonishing > 200 million entries, making it quite impractical for their coverage in the US-SOMO-AF database. Therefore, we have created the US-SOMO-Web site, allowing the rapid calculations of all the properties, as present in the US-SOMO-AF database, on user-supplied PDB and mmCIF structures, as well as allowing direct processing of the latest AlphaFold models. Major features on the website are described, along with current limitations and potential future developments.

Estimating near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules

We developed a computationally efficient approach to approximate near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules. The proposed method relies on extremum principles for Stokes flows produced by the motion of rigid bodies. In the presence of the wall, the rate of energy dissipation is decreased relative to the unbounded fluid. In our approach, the position- and orientation-dependent mobility matrix of a body suspended near a no-slip plane is calculated numerically using a coarse-grained molecular model and the Rotne-Prager-Yamakawa description of hydrodynamics. Effects of the boundary are accounted for via Blake's image construction. The matrix components are scaled using ratios of the corresponding bulk values evaluated for the detailed representation of the molecule and its coarse-grained model, leading to accurate values of the near-wall diffusion coefficients. We assess the performance of the approach for two biomolecules at different levels of coarse-graining.

Quantitative analysis of biochemical processes in living cells at a single-molecule level: a case of olaparib-PARP1 (DNA repair protein) interactions

Quantitative description of biochemical processes inside living cells and at single-molecule levels remains a challenge at the forefront of modern instrumentation and spectroscopy. This paper demonstrates such single-cell, single-molecule analyses performed to study the mechanism of action of olaparib - an up-to-date, FDA-approved drug for germline-BRCA mutated metastatic breast cancer. We characterized complexes formed with PARPi-FL - fluorescent analog of olaparib in vitro and in cancer cells using the advanced fluorescent-based method: Fluorescence Correlation Spectroscopy (FCS) combined with a length-scale dependent cytoplasmic/nucleoplasmic viscosity model. We determined in vitro olaparib-PARP1 equilibrium constant (6.06 × 10⁸ mol L^-1). In the cell nucleus, we distinguished three states of olaparib: freely diffusing drug (24%), olaparib-PARP1 complex (50%), and olaparib-PARP1-RNA complex (26%). We show olaparib accumulation in 3D spheroids, where intracellular concentration is twofold higher than in 2D cells. Moreover, olaparib concentration was tenfold higher (506 nmol L^-1vs. 57 nmol L^-1) in cervical cancer (BRCA1 high abundance) than in breast cancer cells (BRCA1 low abundance) but with a lower toxic effect. Thus we confirmed that the amount of BRCA1 protein in the cells is a better predictor of the therapeutic effect of olaparib than its penetration into cancer tissue. Our single-molecule and single-cell approach give a new perspective of drug action in living cells. FCS provides a detailed in vivo insight, valuable in drug development and targeting.

Generalized Rotne-Prager-Yamakawa approximation for Brownian dynamics in shear flow in bounded, unbounded, and periodic domains

Inclusion of hydrodynamic interactions is essential for a quantitatively accurate Brownian dynamics simulation of colloidal suspensions or polymer solutions. We use the generalized Rotne-Prager-Yamakawa (GRPY) approximation, which takes into account all long-ranged terms in the hydrodynamic interactions, to derive the complete set of hydrodynamic matrices in different geometries: unbounded space, periodic boundary conditions of Lees-Edwards type, and vicinity of a free surface. The construction is carried out both for non-overlapping as well as for overlapping particles. We include the dipolar degrees of freedom, which allows one to use this formalism to simulate the dynamics of suspensions in a shear flow and to study the evolution of their rheological properties. Finally, we provide an open-source numerical package, which implements the GRPY algorithm in Lees-Edwards periodic boundary conditions.

Hydrodynamic effects in the capture of rod-like molecules by a nanopore

In the approach of biomolecules to a nanopore, it is essential to capture the effects of hydrodynamic anisotropy of the molecules and the near-wall hydrodynamic interactions which hinder their diffusion. We present a detailed theoretical analysis of the behaviour of a rod-like molecule attracted electrostatically by a charged nanopore. We first estimate the time scales corresponding to Brownian and electrostatic translations and reorientation. We find that Brownian motion becomes negligible at distances within the pore capture radius, and numerically determine the trajectories of the nano-rod in this region to explore the effects of anisotropic mobility. This allows us to determine the range of directions from the pore in which hydrodynamic interactions with the boundary shape the approach dynamics and need to be accounted for in detailed modelling.

The hydrodynamic motion of Nanodiscs

We present a fluorescence-based methodology for monitoring the rotational dynamics of Nanodiscs. Nanodiscs are nano-scale lipid bilayers surrounded by a helical membrane scaffold protein (MSP) that have found considerable use in studying the interactions between membrane proteins and their lipid bilayer environment. Using a long-lifetime Ruthenium label covalently attached to the Nanodiscs, we find that Nanodiscs of increasing diameter, made by varying the number of helical repeats in the MSP, display increasing rotational correlation times. We also model our system using both analytical equations that describe rotating spheroids and numerical calculations performed on atomic models of Nanodiscs. Using these methods, we observe a linear relationship between the experimentally determined rotational correlation times and those calculated from both analytical equations and numerical solutions. This work sets the stage for accurate, label-free quantification of protein-lipid interactions at the membrane surface.