HYDRO: a computer program for the prediction of hydrodynamic properties of macromolecules

From an obliquely falling rod in a viscous fluid to the motion of suspended magnetic bead chains that are driven by a gradient magnetic field and that make an arbitrary angle with the magnetic force vector: A Stokes flow study

In view of the growing role of magnetic particles under magnetic field influence in medical and other applications, and perforce the bead chaining, it is important to understand more generally the chain dynamics. As is well known, in the presence of a magnetic field, magnetic beads tend to form chains that are aligned with the magnetic field vector. In addition, if there is a magnetic field gradient, there will be a magnetic force acting on this chain. The main goal of the present research is to study the motion of a magnetic bead chain that makes an arbitrary angle with the magnetic force vector in the Stokes flow limit, that is, in the limit of zero Reynolds number. We used the public-domain computer program HYDRO++ to calculate the mobility matrix, which relates the magnetic force acting on the chain to the velocity of the chain, for a chain of N beads making an arbitrary angle with the magnetic force vector. Because of the presence of off-diagonal elements of the mobility matrix, as the chain is drawn in the direction of the magnetic force, it is also deflected to the side. We derived analytic solutions for this motion. Also, for bead chains moving in directions both parallel and perpendicular to their lengths, we fit three-parameter functions to solutions from HYDRO++. We found the fits to be excellent. Combining these results with the analytic solutions, we obtained expressions for the velocity components for the bead chains that provide excellent fits to HYDRO++ solutions for arbitrary angles. Finally, we apply the methodology used for the bead chain studies to the study of an obliquely falling rod in a viscous fluid and derive analytic solutions for the velocity components of the obliquely falling rod.

Modelling red blood cell optical trapping by machine learning improved geometrical optics calculations

Optically trapping red blood cells allows for the exploration of their biophysical properties, which are affected in many diseases. However, because of their nonspherical shape, the numerical calculation of the optical forces is slow, limiting the range of situations that can be explored. Here we train a neural network that improves both the accuracy and the speed of the calculation and we employ it to simulate the motion of a red blood cell under different beam configurations. We found that by fixing two beams and controlling the position of a third, it is possible to control the tilting of the cell. We anticipate this work to be a promising approach to study the trapping of complex shaped and inhomogeneous biological materials, where the possible photodamage imposes restrictions in the beam power.

Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Physics of the Nuclear Pore Complex: Theory, Modeling and Experiment

The hallmark of eukaryotic cells is the nucleus that contains the genome, enclosed by a physical barrier known as the nuclear envelope (NE). On the one hand, this compartmentalization endows the eukaryotic cells with high regulatory complexity and flexibility. On the other hand, it poses a tremendous logistic and energetic problem of transporting millions of molecules per second across the nuclear envelope, to facilitate their biological function in all compartments of the cell. Therefore, eukaryotes have evolved a molecular "nanomachine" known as the Nuclear Pore Complex (NPC). Embedded in the nuclear envelope, NPCs control and regulate all the bi-directional transport between the cell nucleus and the cytoplasm. NPCs combine high molecular specificity of transport with high throughput and speed, and are highly robust with respect to molecular noise and structural perturbations. Remarkably, the functional mechanisms of NPC transport are highly conserved among eukaryotes, from yeast to humans, despite significant differences in the molecular components among various species. The NPC is the largest macromolecular complex in the cell. Yet, despite its significant complexity, it has become clear that its principles of operation can be largely understood based on fundamental physical concepts, as have emerged from a combination of experimental methods of molecular cell biology, biophysics, nanoscience and theoretical and computational modeling. Indeed, many aspects of NPC function can be recapitulated in artificial mimics with a drastically reduced complexity compared to biological pores. We review the current physical understanding of the NPC architecture and function, with the focus on the critical analysis of experimental studies in cells and artificial NPC mimics through the lens of theoretical and computational models. We also discuss the connections between the emerging concepts of NPC operation and other areas of biophysics and bionanotechnology.

Phase behaviour in 2D assemblies of dumbbell-shaped colloids generated under geometrical confinement

The structure formation and the phase behaviour of monolayers of dumbbell-shaped colloids are explored. For this, we conduct Langmuir-Blodgett experiments at the air/water interface and conventional Brownian dynamic simulations without hydrodynamic interactions. Using Voronoi tessellations and the probability density of the corresponding shape factor of the Voronoi cells p(ζ), the influence of the area fraction φ on the structure of the monolayers is investigated. An increase of the area fraction leads to a higher percentage of domains containing particles with six nearest neighbours and a sharper progression of p(ζ). Especially in dense systems, these domains can consist of aligned particles with uniform Voronoi cells. Thus, the increase of φ enhances the order of the monolayers. Simulations show that a sufficient enhancement of φ also impacts the pair correlation function which develops a substructure in its first maxima. Furthermore, we find that reducing the barrier speed in the Langmuir-Blodgett experiments enhances the final area fraction for a given target surface pressure which, in turn, also increases the percentage of particles with six nearest neighbours and sharpens the progression of p(ζ). Overall, the experiments and simulations show a remarkable qualitative agreement which indicates a versatile way of characterising colloidal monolayers by Brownian dynamics simulations. This opens up perspectives for application to a broad range of nanoparticle-based thin film coatings and devices.

Hierarchical self-assembly and controlled disassembly of a cavitand-based host–guest supramolecular polymer

Two hierarchical aggregation modes of cavitand-based supramolecular polymers allow implementing orthogonal disassembly procedures: electrochemical reduction for linear chains and solvent-driven dissolution for bundles.

Phase Separation of Toxic Dipeptide Repeat Proteins Related to C9orf72 ALS/FTD

The expansion mutation in the C9orf72 gene is the most common known genetic cause for amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). This mutation can produce five dipeptide repeat proteins (DPRs), of which three are known to be toxic: poly-PR, poly-GR, and poly-GA. The toxicity of poly-GA is attributed to its aggregation in the cytoplasm, whereas for poly-PR and poly-GR, several toxicity pathways have been proposed. The toxicity of the DPRs has been shown to depend on their length, but the underlying molecular mechanism of this length dependence is not well understood. To address the possible role of phase separation in DPR toxicity, a one-bead-per-amino-acid (1BPA) coarse-grained molecular dynamics model is used to study the single-molecule and phase-separation properties of the DPRs. We find a strong dependence of the phase-separation behavior on both DPR length and concentration, with longer DPRs having a higher propensity to phase separate and form condensed phases with higher concentrations. The critical lengths required for phase separation (25 for poly-PR and 50 for poly-GA) are comparable to the toxicity threshold limit of 30 repeats found for the expansion mutation in patient cells, suggesting that phase separation could play an important role in DPR toxicity.

Flexible and Extended Linker Domains Support Efficient Targeting of Heh2 to the Inner Nuclear Membrane

The nuclear pore complex (NPC) is embedded in the nuclear envelope and forms the main gateway to the nuclear interior including the inner nuclear membrane (INM). Two INM proteins in yeast are selectively imported. Their sorting signals consist of a nuclear localization signal, separated from the transmembrane domain by a long intrinsically disordered (ID) linker. We used computational models to predict the dynamic conformations of ID linkers and analyzed the INM targeting efficiency of proteins with linker regions with altered Stokes radii and decreased flexibilities. We find that flexibility, Stokes radius, and the frequency at which the linkers are at an extended end-to-end distance larger than 25 nm are good predictors for the targeting of the proteins. The data are consistent with a transport mechanism in which INM targeting of Heh2 is dependent on an ID linker that facilitates the crossing of the approximately 25-nm thick NPC scaffold.

Diffusion Tensors of Arbitrary-Shaped Nanoparticles in Fluid by Molecular Dynamics Simulation

The anisotropic diffusive behavior of nanoparticles with complex shapes attracts great interest due to its potential applications in many fields ranging from bionics to aeronautic industry. Although molecular dynamics (MD) simulations are used widely to investigate nanoparticle diffusion properties, universal methods to describe the diffusion process comprehensively are still lacking. Here, we address this problem by introducing diffusion tensor as it can describe translational and rotational diffusion in three dimensions both individually and their coupling. We take carbon triple sphere suspended in argon fluid as our model system. The consistency of our results and velocity autocorrelation function(VAF) method validates our simulations. The coupling between translational and rotational diffusion is observed directly from analyzing diffusion tensor, and quantified by coupling diffusion coefficient. Our simulation reveals non-trivial effect of some factors in diffusion at nanoscale, which was not considered in previous theories. In addition to introducing an effective method to calculate the diffusion tensor in MD simulations, our work also provides insights for understanding the diffusion process of arbitrary-shaped particles in nanoengineering.

The Effect of FG-Nup Phosphorylation on NPC Selectivity: A One-Bead-Per-Amino-Acid Molecular Dynamics Study

Nuclear pore complexes (NPCs) are large protein complexes embedded in the nuclear envelope separating the cytoplasm from the nucleoplasm in eukaryotic cells. They function as selective gates for the transport of molecules in and out of the nucleus. The inner wall of the NPC is coated with intrinsically disordered proteins rich in phenylalanine-glycine repeats (FG-repeats), which are responsible for the intriguing selectivity of NPCs. The phosphorylation state of the FG-Nups is controlled by kinases and phosphatases. In the current study, we extended our one-bead-per-amino-acid (1BPA) model for intrinsically disordered proteins to account for phosphorylation. With this, we performed molecular dynamics simulations to probe the effect of phosphorylation on the Stokes radius of isolated FG-Nups, and on the structure and transport properties of the NPC. Our results indicate that phosphorylation causes a reduced attraction between the residues, leading to an extension of the FG-Nups and the formation of a significantly less dense FG-network inside the NPC. Furthermore, our simulations show that upon phosphorylation, the transport rate of inert molecules increases, while that of nuclear transport receptors decreases, which can be rationalized in terms of modified hydrophobic, electrostatic, and steric interactions. Altogether, our models provide a molecular framework to explain how extensive phosphorylation of FG-Nups decreases the selectivity of the NPC.

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

Two main problems that arise in the context of hydrodynamic bead modeling are an inaccurate treatment of bead overlaps and the necessity of using volume corrections when calculating intrinsic viscosity. We present a formalism based on the generalized Rotne-Prager-Yamakawa approximation that successfully addresses both of these issues. The generalized Rotne-Prager-Yamakawa method is shown to be highly effective for the calculation of transport properties of rigid biomolecules represented as assemblies of spherical beads of different sizes, both overlapping and nonoverlapping. We test the method on simple molecular shapes as well as real protein structures and compare its performance with other computational approaches.

Temperature dependent FCS studies using a long working distance objective: Viscosities of supercooled liquids and particle size

In this work, we describe new experimental setups for Fluorescence Correlation Spectroscopy (FCS) where a long working distance objective is used. Using these setups, FCS measurements in a broad temperature range for a small sample volume of about 50 μl can be performed. The use of specially designed cells and a dry long working distance objective was essential for avoiding temperature gradients in the sample. The performance of the new setups and a traditional FCS setup with immersion objectives is compared. The FCS data in combination with the Stokes-Einstein (SE) relation were used to obtain the values of the nanoviscosity of a fluid. We show for selected molecular van der Waals supercooled liquids that despite the fact that in these systems, a characteristic length scale can be defined, the nanoviscosity obtained from FCS is in a very good agreement with the macroscopic (rheometric) viscosity of the sample in a broad temperature range. This result corroborates the applicability of the SE relation to supercooled liquids at temperatures above 1.2 T_g. We also show that the temperature dependent size of thermoresponsive microgel particles can be determined by FCS using the designed cells and a long working distance objective in a broader size range without a need to use the correction procedure since the size correction is proportional to the square of the ratio of the hydrodynamic radius to the confocal volume size.

Enhanced Sampling of Interdomain Motion Using Map-Restrained Langevin Dynamics and NMR: Application to Pin1

Many signaling proteins consist of globular domains connected by flexible linkers that allow for substantial domain motion. Because these domains often serve as complementary functional modules, the possibility of functionally important domain motions arises. To explore this possibility, we require knowledge of the ensemble of protein conformations sampled by interdomain motion. Measurements of NMR residual dipolar couplings (RDCs) of backbone HN bonds offer a per-residue characterization of interdomain dynamics, as the couplings are sensitive to domain orientation. A challenge in reaching this potential is the need to interpret the RDCs as averages over dynamic ensembles of domain conformations. Here, we address this challenge by introducing an efficient protocol for generating conformational ensembles appropriate for flexible, multi-domain proteins. The protocol uses map-restrained self-guided Langevin dynamics simulations to promote collective, interdomain motion while restraining the internal domain motion to near rigidity. Critically, the simulations retain an all-atom description for facile inclusion of site-specific NMR RDC restraints. The result is the rapid generation of conformational ensembles consistent with the RDC data. We illustrate this protocol on human Pin1, a two-domain peptidyl-prolyl isomerase relevant for cancer and Alzheimer's disease. The results include the ensemble of domain orientations sampled by Pin1, as well as those of a dysfunctional variant, I28A-Pin1. The differences between the ensembles corroborate our previous spin relaxation results that showed weakened interdomain contact in the I28A variant relative to wild type. Our protocol extends our abilities to explore the functional significance of protein domain motions.

Mobility and settling rate of agglomerates of polydisperse nanoparticles

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO₂ agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter d_m and is compared with that from scaling laws for fractal-like agglomerates. The ratio d_m/d_g of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant d_m and mean d_p, the agglomerate settling rate, u_s, increases with increasing PP geometric standard deviation σ_p,g (polydispersity). A linear relationship between u_s and agglomerate mass to d_m ratio, m/d_m, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the u_s of agglomerates consisting of polydisperse PPs is then derived, u_s=1-ρ_fρ_pg3πμmd_m (ρ_f is the density of the fluid, ρ_p is the density of PPs, μ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates u_s by a fraction depending on σ_p,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO₂ agglomerates in water.

From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better.

Static and dynamic light scattering by red blood cells: A numerical study

Light scattering is a well-established experimental technique, which gains more and more popularity in the biological field because it offers the means for non-invasive imaging and detection. However, the interpretation of light-scattering signals remains challenging due to the complexity of most biological systems. Here, we investigate static and dynamic scattering properties of red blood cells (RBCs) using two mesoscopic hydrodynamics simulation methods—multi-particle collision dynamics and dissipative particle dynamics. Light scattering is studied for various membrane shear elasticities, bending rigidities, and RBC shapes (e.g., biconcave and stomatocyte). Simulation results from the two simulation methods show good agreement, and demonstrate that the static light scattering of a diffusing RBC is not very sensitive to the changes in membrane properties and moderate alterations in cell shapes. We also compute dynamic light scattering of a diffusing RBC, from which dynamic properties of RBCs such as diffusion coefficients can be accessed. In contrast to static light scattering, the dynamic measurements can be employed to differentiate between the biconcave and stomatocytic RBC shapes and generally allow the differentiation based on the membrane properties. Our simulation results can be used for better understanding of light scattering by RBCs and the development of new non-invasive methods for blood-flow monitoring.

Efficient shapes for microswimming: From three-body swimmers to helical flagella

We combine a general formulation of microswimmer equations of motion with a numerical bead-shell model to calculate the hydrodynamic interactions with the fluid, from which the swimming speed, power, and efficiency are extracted. From this framework, a generalized Scallop theorem emerges. The applicability to arbitrary shapes allows for the optimization of the efficiency with respect to the swimmer geometry. We apply this scheme to "three-body swimmers" of various shapes and find that the efficiency is characterized by the single-body friction coefficient in the long-arm regime, while in the short-arm regime the minimal approachable distance becomes the determining factor. Next, we apply this scheme to a biologically inspired set of swimmers that propel using a rotating helical flagellum. Interestingly, we find two distinct optimal shapes, one of which is fundamentally different from the shapes observed in nature (e.g., bacteria).

Free Diffusivity of Icosahedral and Tailed Bacteriophages: Experiments, Modeling, and Implications for Virus Behavior in Media Filtration and Flocculation

The aqueous bulk diffusivities of several near-spherical (icosahedral) and nonspherical (tailed) bacterial viruses were experimentally determined by measuring their flux across large pore membranes and using dynamic light scattering, with excellent agreement between values measured using the two techniques. For the icosahedral viruses, good agreement was also found between measured diffusivity values and values predicted with the Stokes-Einstein equation. However, when the tailed viruses were approximated as spheres, poor agreement was found between measured values and Stokes-Einstein predictions. The shape of the tailed organisms was incorporated into two modeling approaches used to predict diffusivity. Model predictions were found to be in good agreement with measured values, demonstrating the importance of the tail in the diffusive transport of these viruses. Our calculations also show that inaccurate estimates of virus diffusion can lead to significant errors when predicting diffusive contributions to flocculation and to single collector efficiency in media filtration.

Effect of shape and bending modulus on the properties of nematic lyotropic liquid crystals

Variation in the structure of the molecular aggregate associated with the increase of the TTAC concentration in the liquid crystal.

Prediction of solution properties and dynamics of RNAs by means of Brownian dynamics simulation of coarse-grained models: Ribosomal 5S RNA and phenylalanine transfer RNA

Background

The possibility of validating biological macromolecules with locally disordered domains like RNA against solution properties is helpful to understand their function. In this work, we present a computational scheme for predicting global properties and mimicking the internal dynamics of RNA molecules in solution. A simple coarse-grained model with one bead per nucleotide and two types of intra-molecular interactions (elastic interactions and excluded volume interactions) is used to represent the RNA chain. The elastic interactions are modeled by a set of Hooke springs that form a minimalist elastic network. The Brownian dynamics technique is employed to simulate the time evolution of the RNA conformations.

Results

That scheme is applied to the 5S ribosomal RNA of E. Coli and the yeast phenylalanine transfer RNA. From the Brownian trajectory, several solution properties (radius of gyration, translational diffusion coefficient, and a rotational relaxation time) are calculated. For the case of yeast phenylalanine transfer RNA, the time evolution and the probability distribution of the inter-arm angle is also computed.

Conclusions

The general good agreement between our results and some experimental data indicates that the model is able to capture the tertiary structure of RNA in solution. Our simulation results also compare quite well with other numerical data. An advantage of the scheme described here is the possibility of visualizing the real time macromolecular dynamics.

Electronic supplementary material

The online version of this article (doi:10.1186/s13628-015-0025-7) contains supplementary material, which is available to authorized users.

Zinc-induced oligomerization of zinc α2 glycoprotein reveals multiple fatty acid-binding sites

Zinc α2 glycoprotein (ZAG) is an adipokine with a class I MHC protein fold and is associated with obesity and diabetes. Although its intrinsic ligand remains unknown, ZAG binds the dansylated C11 fatty acid 11-(dansylamino)undecanoic acid (DAUDA) in the groove between the α1 and α2 domains. The surface of ZAG has approximately 15 weak zinc-binding sites deemed responsible for precipitation from human plasma. In the present study the functional significance of these metal sites was investigated. Analytical ultracentrifugation (AUC) and CD showed that zinc, but not other divalent metals, causes ZAG to oligomerize in solution. Thus ZAG dimers and trimers were observed in the presence of 1 and 2 mM zinc. Molecular modelling of X-ray scattering curves and sedimentation coefficients indicated a progressive stacking of ZAG monomers, suggesting that the ZAG groove may be occluded in these. Using fluorescence-detected sedimentation velocity, these ZAG-zinc oligomers were again observed in the presence of the fluorescent boron dipyrromethene fatty acid C16-BODIPY (4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-hexadecanoic acid). Fluorescence spectroscopy confirmed that ZAG binds C16-BODIPY. ZAG binding to C16-BODIPY, but not to DAUDA, was reduced by increased zinc concentrations. We conclude that the lipid-binding groove in ZAG contains at least two distinct fatty acid-binding sites for DAUDA and C16-BODIPY, similar to the multiple lipid binding seen in the structurally related immune protein CD1c. In addition, because high concentrations of zinc occur in the pancreas, the perturbation of these multiple lipid-binding sites by zinc may be significant in Type 2 diabetes where dysregulation of ZAG and zinc homoeostasis occurs.

Optical trapping of silver nanoplatelets

Optical trapping of silver nanoplatelets obtained with a simple room temperature chemical synthesis technique is reported. Trap spring constants are measured for platelets with different diameters to investigate the size-scaling behaviour. Experimental data are compared with models of optical forces based on the dipole approximation and on electromagnetic scattering within a T-matrix framework. Finally, we discuss applications of these nanoplatelets for surface-enhanced Raman spectroscopy.

The solution structures of two human IgG1 antibodies show conformational stability and accommodate their C1q and FcγR ligands

The human IgG1 antibody subclass shows distinct properties compared with the IgG2, IgG3, and IgG4 subclasses and is the most exploited subclass in therapeutic antibodies. It is the most abundant subclass, has a half-life as long as that of IgG2 and IgG4, binds the FcγR receptor, and activates complement. There is limited structural information on full-length human IgG1 because of the challenges of crystallization. To rectify this, we have studied the solution structures of two human IgG1 6a and 19a monoclonal antibodies in different buffers at different temperatures. Analytical ultracentrifugation showed that both antibodies were predominantly monomeric, with sedimentation coefficients s20,w (0) of 6.3-6.4 S. Only a minor dimer peak was observed, and the amount was not dependent on buffer conditions. Solution scattering showed that the x-ray radius of gyration Rg increased with salt concentration, whereas the neutron Rg values remained unchanged with temperature. The x-ray and neutron distance distribution curves P(r) revealed two peaks, M1 and M2, whose positions were unchanged in different buffers to indicate conformational stability. Constrained atomistic scattering modeling revealed predominantly asymmetric solution structures for both antibodies with extended hinge structures. Both structures were similar to the only known crystal structure of full-length human IgG1. The Fab conformations in both structures were suitably positioned to permit the Fc region to bind readily to its FcγR and C1q ligands without steric clashes, unlike human IgG4. Our molecular models for human IgG1 explain its immune activities, and we discuss its stability and function for therapeutic applications.

Probing the disordered domain of the nuclear pore complex through coarse-grained molecular dynamics simulations

The distribution of disordered proteins (FG-nups) that line the transport channel of the nuclear pore complex (NPC) is investigated by means of coarse-grained molecular dynamics simulations. A one-bead-per-amino-acid model is presented that accounts for the hydrophobic/hydrophilic and electrostatic interactions between different amino acids, polarity of the solvent, and screening of free ions. The results indicate that the interaction of the FG-nups forms a high-density, doughnut-like distribution inside the NPC, which is rich in FG-repeats. We show that the obtained distribution is encoded in the amino-acid sequence of the FG-nups and is driven by both electrostatic and hydrophobic interactions. To explore the relation between structure and function, we have systematically removed different combinations of FG-nups from the pore to simulate inviable and viable NPCs that were previously studied experimentally. The obtained density distributions show that the maximum density of the FG-nups inside the pore does not exceed 185 mg/mL in the inviable NPCs, whereas for the wild-type and viable NPCs, this value increases to 300 mg/mL. Interestingly, this maximum density is not correlated to the total mass of the FG-nups, but depends sensitively on the specific combination of essential Nups located in the central plane of the NPC.

Coarse-Grained Langevin Equation for Protein Dynamics: Global Anisotropy and a Mode Approach to Local Complexity

We utilize a multiscale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin equation for protein dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal-mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free-energy landscape of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with nuclear magnetic resonance relaxation experiments. Fundamental to this approach is the inclusion of internal dissipation, which is absent in any rigid-body hydrodynamical modeling scheme.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Multidimensional analysis of nanoparticles with highly disperse properties using multiwavelength analytical ultracentrifugation

The worldwide trend in nanoparticle technology toward increasing complexity must be directly linked to more advanced characterization methods of size, shape and related properties, applicable to many different particle systems in science and technology. Available techniques for nanoparticle characterization are predominantly focused on size characterization. However, simultaneous size and shape characterization is still an unresolved major challenge. We demonstrate that analytical ultracentrifugation with a multiwavelength detector is a powerful technique to address multidimensional nanoparticle analysis. Using a high performance optical setup and data acquisition software, information on size, shape anisotropy and optical properties were accessible in one single experiment with unmatched accuracy and resolution. A dynamic rotor speed gradient allowed us to investigate broad distributions on a short time scale and differentiate between gold nanorod species including the precise evaluation of aggregate formation. We report how to distinguish between different species of single-wall carbon nanotubes in just one experiment using the wavelength-dependent sedimentation coefficient distribution without the necessity of time-consuming purification methods. Furthermore, CdTe nanoparticles of different size and optical properties were investigated in a single experiment providing important information on structure-property relations. Thus, multidimensional information on size, density, shape and optical properties of nanoparticulate systems becomes accessible by means of analytical ultracentrifugation equipped with multiwavelength detection.

Retarded hydrodynamic properties of fractal clusters

Fractal clusters are commonly encountered when working with the stability and the aggregation of colloidal suspensions. In spite of the number of studies that have focused on their stationary hydrodynamic properties, no information is currently known on their retarded hydrodynamic properties. The objective of this work is to close this gap. Clusters with a broad range of fractal dimension values, generated via Monte-Carlo simulations have been analyzed. A rigorous model based on multipole expansion of time-dependent Stokes equations has been developed, and then the full cluster resistance matrix as a function of the frequency has been computed. An attempt has been made to extend Basset, Boussinesque and Oseen equations to fractal clusters, but it was found that the corresponding hydrodynamic radius needs to be a function of frequency. In the case of translational motion, the cluster hydrodynamic radius loses any structural information at high frequencies, becoming independent of the fractal dimension, but depending only on its mass. A simplified model, based on an extension of Kirkwood-Rieseman approach has also been developed. This allows one to perform calculations for clusters with arbitrary masses and fractal dimensions, with good accuracy and very low computational time. It is the first time that the frequency dependence of hydrodynamic properties of complex non-spherical objects has been investigated.

The Fab conformations in the solution structure of human immunoglobulin G4 (IgG4) restrict access to its Fc region: implications for functional activity

Human IgG4 antibody shows therapeutically useful properties compared with the IgG1, IgG2, and IgG3 subclasses. Thus IgG4 does not activate complement and shows conformational variability. These properties are attributable to its hinge region, which is the shortest of the four IgG subclasses. Using high throughput scattering methods, we studied the solution structure of wild-type IgG4(Ser(222)) and a hinge mutant IgG4(Pro(222)) in different buffers and temperatures where the proline substitution suppresses the formation of half-antibody. Analytical ultracentrifugation showed that both IgG4 forms were principally monomeric with sedimentation coefficients s20,w(0) of 6.6-6.8 S. A monomer-dimer equilibrium was observed in heavy water buffer at low temperature. Scattering showed that the x-ray radius of gyration Rg was unchanged with concentration in 50-250 mm NaCl buffers, whereas the neutron Rg values showed a concentration-dependent increase as the temperature decreased in heavy water buffers. The distance distribution curves (P(r)) revealed two peaks, M1 and M2, that shifted below 2 mg/ml to indicate concentration-dependent IgG4 structures in addition to IgG4 dimer formation at high concentration in heavy water. Constrained x-ray and neutron scattering modeling revealed asymmetric solution structures for IgG4(Ser(222)) with extended hinge structures. The IgG4(Pro(222)) structure was similar. Both IgG4 structures showed that their Fab regions were positioned close enough to the Fc region to restrict C1q binding. Our new molecular models for IgG4 explain its inability to activate complement and clarify aspects of its stability and function for therapeutic applications.

Role of Albumin in the Formation and Stabilization of Nanoparticle Aggregates in Serum Studied by Continuous Photon Correlation Spectroscopy and Multiscale Computer Simulations

Recently, small (<5 nm diameter) nanoparticles (NPs) have shown improved in vivo biocompatibility compared to that of larger (>10 nm) NPs. However, the fate of small NPs under physiological conditions is poorly understood and remains unexplored. Here, the long-term aggregation behavior of gold nanoparticles (AuNPs) exposed to serum proteins in a near-physiological setup is studied using continuous photon correlation spectroscopy and computer simulations. It is found that the medium, temperature, and NP concentration affect the aggregation of AuNPs, but the observed aggregates are much smaller than previously reported. Simulations show that a single layer of albumin is deposited on the NP surface, but the properties of the aggregates (size, shape, and internal structure) depend critically on the charge distribution on the proteins, which changes with the conditions of the solution. These results explain the seemingly conflicting data reported in the literature regarding the size of aggregates and the morphology of the albumin corona. The simulations suggest that controlling the concentration of NPs as well as the pH and ionic strength of the solution prior to intravenous administration may help to preserve properties of the functionalized NPs in the bloodstream.

Transport powered by bacterial turbulence

We demonstrate that collective turbulentlike motion in a bacterial bath can power and steer the directed transport of mesoscopic carriers through the suspension. In our experiments and simulations, a microwedgelike "bulldozer" draws energy from a bacterial bath of varied density. We obtain that an optimal transport speed is achieved in the turbulent state of the bacterial suspension. This apparent rectification of random motion of bacteria is caused by polar ordered bacteria inside the cusp region of the carrier, which is shielded from the outside turbulent fluctuations.

Assessing the two-body diffusion tensor calculated by the bead models

The diffusion tensor of complex macromolecules in Stokes flow is often approximated by the bead models. The bead models are known to reproduce the experimental diffusion coefficients of a single macromolecule, but the accuracy of their calculation of the whole multi-body diffusion tensor, which is important for Brownian dynamics simulations, has not been closely investigated. As a first step, we assess the accuracy of the bead model calculated diffusion tensor of two spheres. Our results show that the bead models produce very accurate diffusion tensors for two spheres where a reasonable number of beads are used and there is no bead overlap.

Hydrodynamic multibead modeling: problems, pitfalls and solutions. 3. Comparison of new approaches for improved predictions of translational properties

Modeling simple and complex biopolymers in solution requires the shapes of these molecules to be approximated by bead modeling procedures, primarily for the prediction of hydrodynamic and scattering quantities. Though several bead modeling strategies (strict, shell and filling models) and a variety of computer programs (preferably the HYDRO suite by the García de la Torre group) are available, several subtle questions remain to be answered, in particular concerning the appropriate volume correction for intrinsic viscosity computations. In this context, various versions of the HYDRO programs and different types of volume corrections, as well as the novel, alternative program ZENO of the Mansfield group, were applied to a plethora of thoroughly designed multibead models of spherical, ellipsoidal, cylindrical and prismatic shapes. A critical comparison of the results obtained reveals a variety of new aspects, useful for many future applications. Among these, application of our recently suggested "reduced volume correction" (RVC) together with specially adapted HYDRO versions and use of ZENO turned out to be highly effective, in particular when aiming at filling model strategies and using high bead numbers, a domain not fully supported by the recent HYDRO++ versions. By our approaches, the values of translational properties (diffusion coefficients, D, and intrinsic viscosities, [η]) of all multibead models applied were anticipated correctly.

Circular motion of asymmetric self-propelling particles

Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study their circular motion on a substrate and near channel boundaries. Our experimental observations are in full agreement with a theory of Brownian dynamics for asymmetric self-propelled particles, which couples their translational and orientational motion.

Conformational dynamics of the Rpt6 ATPase in proteasome assembly and Rpn14 binding

Juxtaposed to either or both ends of the proteasome core particle (CP) can exist a 19S regulatory particle (RP) that recognizes and prepares ubiquitinated proteins for proteolysis. RP triphosphatase proteins (Rpt1-Rpt6), which are critical for substrate translocation into the CP, bind chaperone-like proteins (Hsm3, Nas2, Nas6, and Rpn14) implicated in RP assembly. We used NMR and other biophysical methods to reveal that S. cerevisiae Rpt6's C-terminal domain undergoes dynamic helix-coil transitions enabled by helix-destabilizing glycines within its two most C-terminal α helices. Rpn14 binds selectively to Rpt6's four-helix bundle, with surprisingly high affinity. Loss of Rpt6's partially unfolded state by glycine substitution (Rpt6 G³⁶⁰,³⁸⁷A) disrupts holoenzyme formation in vitro, an effect enhanced by Rpn14. S. cerevisiae lacking Rpn14 and incorporating Rpt6 G³⁶⁰,³⁸⁷A demonstrate hallmarks of defective proteasome assembly and synthetic growth defects. Rpt4 and Rpt5 exhibit similar exchange, suggesting that conserved structural heterogeneity among Rpt proteins may facilitate RP-CP assembly.

Hydrodynamic modelling of protein conformation in solution: ELLIPS and HYDRO

The last three decades has seen some important advances in our ability to represent the conformation of proteins in solution on the basis of hydrodynamic measurements. Advances in theoretical modeling capabilities have been matched by commensurate advances in the precision of hydrodynamic measurements. We consider the advances in whole-body (simple ellipsoid-based) modeling—still useful for providing an overall idea of molecular shape, particularly for those systems where only a limited amount of data is available—and outline the ELLIPS suite of algorithms which facilitates the use of this approach. We then focus on bead modeling strategies, particularly the surface or shell–bead approaches and the HYDRO suite of algorithms. We demonstrate how these are providing great insights into complex issues such as the conformation of immunoglobulins and other multi-domain complexes.

Calculation of hydrodynamic properties for G-quadruplex nucleic acid structures from in silico bead models

Nucleic acids enriched in guanine bases can adopt unique quadruple helical tertiary structures known as G-quadruplexes. G-quadruplexes have emerged as attractive drug targets as many G-quadruplex-forming sequences have been discovered in functionally critical sites within the human genome, including the telomere, oncogene promoters, and mRNA processing sites. A single G-quadruplex-forming sequence can adopt one of many folding topologies, often resulting in a lack of a single definitive atomic-level resolution structure for many of these sequences and a major challenge to the discovery of G-quadruplex-selective small molecule drugs. Low-resolution techniques employed to study G-quadruplex structures (e.g., CD spectroscopy) are often unable to discern between G-quadruplex structural ensembles, while high-resolution techniques (e.g., NMR spectroscopy) can be overwhelmed by a highly polymorphic system. Hydrodynamic bead modeling is an approach to studying G-quadruplex structures that could bridge the gap between low-resolution techniques and high-resolution molecular models. Here, we present a discussion of hydrodynamic bead modeling in the context of studying G-quadruplex structures, highlighting recent successes and limitations to this approach, as well as an example featuring a G-quadruplex structure formed from the human telomere. This example can easily be adapted to the investigation of any other G-quadruplex-forming sequences.

Translational diffusion coefficients of macromolecules

The calculation of the translational diffusion coefficient of a single flexible polymer chain in dilute solution can be basically addressed either a) within the Einstein theory (calculating the time autocorrelation function of the macromolecule center of mass), or b) within the Kirkwood and Riseman theory for irreversible processes of macromolecules in solution. The equations of the latter theory can be solved employing different approximations that give rise to different values of the diffusion coefficient. In general, the value of the diffusion coefficient obtained through the different theories and approaches varies slightly depending on polymer features like flexibility. In this paper, we evaluate the most common procedures to compute the diffusion coefficient of flexible macromolecules via computer simulation and the difference between the values obtained.

The solution structure of rabbit IgG accounts for its interactions with the Fc receptor and complement C1q and its conformational stability

Solution structures for antibodies are critical to understand function and therapeutic applications. The stability of the solution structure of rabbit IgG in different buffers and temperatures was determined by analytical ultracentrifugation and X-ray and neutron scattering. Rabbit IgG showed a principally monomeric species, which is well resolved from small amounts of a dimeric species. The proportion of dimer increased with increased concentration, decreased temperature and heavy water from 8% to 25% in all buffers except for high salt (250 mM NaCl). The Guinier X-ray radius of gyration R(G) likewise increased with concentration in 137 mM NaCl buffer but was unchanged in 250 mM NaCl buffer. The Guinier neutron R(G) values increased as the temperature decreased. The X-ray and neutron distance distribution curves P(r) revealed two peaks, M1 and M2, whose positions did not change with concentration to indicate unchanged structures under all these conditions. The maximum dimension increased with concentration because of dimer formation. Constrained scattering modeling reproducibly revealed very similar asymmetric solution structures for monomeric rabbit IgG in different buffers, in which the Fab-Fc and Fab-Fab pairs were separated by maximally extended hinge structures. The dimer was best modeled by two pairs of Fab regions forming tip-to-tip contacts. The intact rabbit IgG structures explained the ability of its two ligands, the Fc receptor and complement C1q, to bind to the top of its Fc region that is fully accessible and unhindered by the Fab regions.

Oligomeric properties of adeno-associated virus Rep68 reflect its multifunctionality

The adeno-associated virus (AAV) encodes four regulatory proteins called Rep. The large AAV Rep proteins Rep68 and Rep78 are essential factors required in almost every step of the viral life cycle. Structurally, they share two domains: a modified version of the AAA(+) domain that characterizes the SF3 family of helicases and an N-terminal domain that binds DNA specifically. The combination of these two domains imparts extraordinary multifunctionality to work as initiators of DNA replication and regulators of transcription, in addition to their essential role during site-specific integration. Although most members of the SF3 family form hexameric rings in vitro, the oligomeric nature of Rep68 is unclear due to its propensity to aggregate in solution. We report here a comprehensive study to determine the oligomeric character of Rep68 using a combination of methods that includes sedimentation velocity ultracentrifugation, electron microscopy, and hydrodynamic modeling. We have determined that residue Cys151 induces Rep68 to aggregate in vitro. We show that Rep68 displays a concentration-dependent dynamic oligomeric behavior characterized by the presence of two populations: one with monomers and dimers in slow equilibrium and a second one consisting of a mixture of multiple-ring structures of seven and eight members. The presence of either ATP or ADP induces formation of larger complexes formed by the stacking of multiple rings. Taken together, our results support the idea of a Rep68 molecule that exhibits the flexible oligomeric behavior needed to perform the wide range of functions occurring during the AAV life cycle.

A variable light domain fluorogen activating protein homodimerizes to activate dimethylindole red

Novel fluorescent tools such as green fluorescent protein analogues and fluorogen activating proteins (FAPs) are useful in biological imaging for tracking protein dynamics in real time with a low fluorescence background. FAPs are single-chain variable fragments (scFvs) selected from a yeast surface display library that produce fluorescence upon binding a specific dye or fluorogen that is normally not fluorescent when present in solution. FAPs generally consist of human immunoglobulin variable heavy (V(H)) and variable light (V(L)) domains covalently attached via a glycine- and serine-rich linker. Previously, we determined that the yeast surface clone, V(H)-V(L) M8, could bind and activate the fluorogen dimethylindole red (DIR) but that the fluorogen activation properties were localized to the M8V(L) domain. We report here that both nuclear magnetic resonance and X-ray diffraction methods indicate the M8V(L) forms noncovalent, antiparallel homodimers that are the fluorogen activating species. The M8V(L) homodimers activate DIR by restriction of internal rotation of the bound dye. These structural results, together with directed evolution experiments with both V(H)-V(L) M8 and M8V(L), led us to rationally design tandem, covalent homodimers of M8V(L) domains joined by a flexible linker that have a high affinity for DIR and good quantum yields.

Solution structure of TT30, a novel complement therapeutic agent, provides insight into its joint binding to complement C3b and C3d

A novel therapeutic reagent TT30 was designed to be effective in diseases of the alternative pathway of complement such as paroxysmal nocturnal hemoglobinuria and other diseases. TT30 is constructed from the first four short complement regulator (SCR) domains of complement receptor type 2 (CR2) that bind to complement C3d, followed by the first five SCR domains of complement factor H that bind to complement C3b. In order to assess how TT30 binds to C3d and C3b, we determined the TT30 solution structure by a combination of analytical ultracentrifugation, X-ray scattering and constrained modeling. The sedimentation coefficients and radius of gyration of TT30 were unaffected by citrate or phosphate-buffered saline buffers and indicate an elongated monomeric structure with a sedimentation coefficient of 3.1 S and a radius of gyration R(G) of 6.9 nm. Molecular modeling starting from 3000 randomized TT30 conformations showed that high-quality X-ray curve fits were obtained with extended SCR arrangements, showing that TT30 has a limited degree of inter-SCR flexibility in its solution structure. The best-fit TT30 structural models are readily merged with the crystal structure of C3b to show that the four CR2 domains extend freely into solution when the five complement factor H domains are bound within C3b. We reevaluated the solution structure of the CR2-C3d complex that confirmed its recent crystal structure. This recent CR2-C3d crystal structure showed that TT30 is able to interact readily with C3d ligands in many orientations when TT30 is bound to C3b.