Calculation of the solution properties of flexible macromolecules: methods and applications

Determination of 2D Particle Size Distributions in Plasmonic Nanoparticle Colloids via Analytical Ultracentrifugation: Application to Gold Bipyramids

Multidimensional particle properties determine the product properties in numerous advanced applications. Accurate and statistically meaningful measurements of complex particles and their multidimensional distributions are highly challenging but strongly needed. 2D particle size distributions of plasmonic nanoparticles of complex regular shape can be obtained from analytical ultracentrifugation experiments via the optical back coupling method. A workflow for the calculation of frictional properties of arbitrarily shaped nanoparticles was developed based on bead shell models and applied to gold bipyramids with a pentagonal cross-section. The obtained 2D particle length-diameter distributions and the reduced cumulative 1D length and diameter distributions were compared to transmission electron microscopy measurements. While we find very good agreement for most measurements, the obtained length and diameter distributions were shifted by a few nanometers for some samples. Transmission electron microscopy, energy-dispersive X-ray spectroscopy, electron tomography, and finite element modeling indicate that the shift originated from a slight mismatch between the assumed shape of the simulated perfect bipyramids and the real particle shape and composition due to the presence of silver in the particles. This study demonstrates the feasibility of the applied techniques for complex shape analysis of nanoparticle ensembles with unmatched particle count numbers.

Influence of isoform-specific Ras lipidation motifs on protein partitioning and dynamics in model membrane systems of various complexity

The partitioning of the lipidated signaling proteins N-Ras and K-Ras4B into various membrane systems, ranging from single-component fluid bilayers, binary fluid mixtures, heterogeneous raft model membranes up to complex native-like lipid mixtures (GPMVs) in the absence and presence of integral membrane proteins have been explored in the last decade in a combined chemical-biological and biophysical approach. These studies have revealed pronounced isoform-specific differences regarding the lateral distribution in membranes and formation of protein-rich membrane domains. In this context, we will also discuss the effects of lipid head group structure and charge density on the partitioning behavior of the lipoproteins. Moreover, the dynamic properties of N-Ras and K-Ras4B have been studied in different model membrane systems and native-like crowded milieus. Addition of crowding agents such as Ficoll and its monomeric unit, sucrose, gradually favors clustering of Ras proteins in forming small oligomers in the bulk; only at very high crowder concentrations association is disfavored.

Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies

Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.

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.

Size and conformational features of ErbB2 and ErbB3 receptors: a TEM and DLS comparative study

ErbB2 and ErbB3 receptors belong to the epidermal growth factor receptor family. The members of this family are able to form homo- and heterodimers that trigger diverse downstream signalling concerned to multiple cellular events. In the absence of a ligand, ErbB3 adopts a characteristic tethered conformation, which differs from ErbB2 extended conformation. In this work, transmission electron microscopy (TEM) and dynamic light scattering (DLS) have been used to characterize the conformational features and the size of ErBb2 and ErbB3 receptors. Two main objectives are presented. The first one is to evaluate the use of TEM as a tool for structural studies for this family of receptors. The low molecular weight of these proteins represents a challenging purpose for TEM studies. The other one is to search for a relationship between the results obtained by TEM and those obtained for the hydrodynamic size measured by DLS. This comparison has allowed us to identify the conformational differences of the receptors and to anticipate the use of these experimental techniques for the study of the ligand activated heterodimerization, a process related to a significant number of human malignancies.

Global fit and structure optimization of flexible and rigid macromolecules and nanoparticles from analytical ultracentrifugation and other dilute solution properties

The calculation of hydrodynamic and other solution properties from structural information (size and shape or flexibility) of macromolecules and nanoparticles is feasible thanks to existing theories and computational tools. Here we review our recent advances in the inverse problem of extracting structural information from those properties. The concepts of equivalent radii and ratios of radii are particularly useful in global-fitting structural analysis, when one has to treat simultaneously with various properties, eventually for a series of samples. Based on the equivalent radii or their ratios, we define target functions that measure the adequacy of a given structure to fit a set of experimental properties. Structural determination is carried out by minimization of those target functions. We review a variety of examples. Some of them refer to the simple, yet important models like ellipsoids, cylinders and wormlike chains, whose structure is determined by optimization of the model parameters. In other, more complex cases, properties are calculated with computational tools like programs in the HYDRO suite. We have devised other tools to make the structure optimization from the results of those calculations in a quite direct, simple and systematic manner.

Characterization of polyelectrolyte features in polysaccharide systems and mucin

This review elucidates several aspects on the behavior of charged polysaccharides and mucin. Viscosification of dilute aqueous solutions of hyaluronan (HA) occurs in the course of time at low shear flow, whereas shear thinning as time evolves is found at moderate shear rates. Hydrogen bonds and electrostatic interaction play an important role for the emergence of these features. No time effect of the viscosity is observed for semidilute HA solutions. A degradation of HA is observed at low and high pH and this effect continues over long times, and it is only in the approximate interval 5<pH<10 that HA is stable. Small angle neutron scattering (SANS) measurements on semidilute aqueous solutions of mucin at pH=7 reveal a fractal dimension of 1.4, and the effect of temperature is insignificant on the fractal structure. This suggests that the mucin chains on a semi-local dimensional scale are rod-like. From various experimental methods on solutions of mucin it was found that at pH values around 2 (uncharged polymer), the intensive hydrophobic interactions lead to large association complexes, whereas at pH>>2 the negative charges suppress the tendency of forming associations. At pH<2, the mucin chains are compressed and they are decorated by some positive charges. In the semidilute regime, a fragmented network is developed. The intense association in semidilute solutions of mucin at pH=2 is further supported by the results from rheo-small angle light scattering measurements. Effects of ionic strength on the radius of gyration (R(g)) for dilute solutions of HA (pH=7) and positively charged hydroxyethylcellulose (HEC(+)) are studied with the aid of Monte Carlo simulations, and essential features of the polyelectrolyte effect on R(g) are captured in the computer simulation. Strong interactions are observed in aqueous mixtures of an anionic polysaccharide (HEC(-)) and an oppositely charged surfactant (cetyltrimethylammonium bromide; CTAB); this gives rise to extensive associations and macroscopic phase separation is approached. The massive association complexes are disclosed in the SANS experiments by a pronounced upturn in the scattered intensity at low values of the wave vector.

A self-consistent description of the conformational behavior of chemically denatured proteins from NMR and small angle scattering

Characterization of the conformational properties of unfolded proteins is essential for understanding the mechanisms of protein folding and misfolding. This information is also fundamental to determining the relationship between flexibility and function in the highly diverse families of intrinsically disordered proteins. Here we present a self-consistent model of conformational sampling of chemically denatured proteins in agreement with experimental data reporting on long-range distance distributions in unfolded proteins using small-angle x-ray scattering and nuclear magnetic resonance pulse-field gradient-based measurements. We find that standard statistical coil models, selected from folded protein databases with secondary structural elements removed, need to be refined to correct backbone dihedral angle sampling of denatured proteins, although they appear to be appropriate for intrinsically disordered proteins. For denatured proteins, pervasive increases in the sampling of more-extended regions of Ramachandran space {50 degrees Collapse

Key Words Collapse

MESH Headings

• Computer Simulation
• Databases, Protein
• Models, Chemical
• Nuclear Magnetic Resonance, Biomolecular
• Protein Conformation
• Protein Denaturation
• Protein Folding
• Protein Structure, Secondary
• Scattering, Small Angle

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Affiliation(s)

Pau Bernadó Institute for Research in Biomedicine, c/ Baldiri Reixac, Barcelona, Spain
Martin Blackledge Protein Dynamics and Flexibility, Institut de Biologie Structurale, UMR 5075, Commissariat à l'Énergie Atomique-Centre National de la Recherche Scientifique-Université Joseph Fourier, Grenoble, France

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Solution conformation of wild-type and mutant IgG3 and IgG4 immunoglobulins using crystallohydrodynamics: possible implications for complement activation

We have employed the recently described crystallohydrodynamic approach to compare the time-averaged domain orientation of human chimeric IgG3wt (wild-type) and IgG4wt as well as two hinge mutants of IgG3 and an IgG4S331P (mutation from serine to proline at position 331, EU numbering) mutant of IgG4. The approach involves combination of the known shape of the Fab and Fc regions from crystallography with hydrodynamic data for the Fab and Fc fragments and hydrodynamic and small angle x-ray scattering data for the intact IgG structures. In this way, ad hoc assumptions over hydration can be avoided and model degeneracy (uniqueness problems) can be minimized. The best fit model for the solution structure of IgG3wt demonstrated that the Fab regions are directed away from the plane of the Fc region and with a long extended hinge region in between. The best fit model of the IgG3m15 mutant with a short hinge (and enhanced complement activation activity) showed a more open, but asymmetric structure. The IgG3HM5 mutant devoid of a hinge region (and also devoid of complement-activation activity) could not be distinguished at the low-resolution level from the structure of the enhanced complement-activating mutant IgG3m15. The lack of inter-heavy-chain disulphide bond rather than a significantly different domain orientation may be the reason for the lack of complement-activating activity of the IgG3HM5 mutant. With IgG4, there are significant and interesting conformational differences between the wild-type IgG4, which shows a symmetric structure, and the IgG4S331P mutant, which shows a highly asymmetric structure. This structural difference may explain the ability of the IgG4S331P mutant to activate complement in stark contrast to the wild-type IgG4 molecule which is devoid of this activity.

Equivalent radii and ratios of radii from solution properties as indicators of macromolecular conformation, shape, and flexibility

The equivalent radius for any solution property is the radius of a spherical particle having the same value of solution property as that of the macromolecule under consideration. Equivalent radii for different properties present a dependence on size and shape that are more similar than the values of the properties themselves. Furthermore, the ratios of equivalent radii of two properties depend on the conformation (shape or flexibility), but not on the absolute sizes. We define equivalent radii and their ratios, and describe their evaluation for some common models of rigid and flexible macromolecules. Using radii and ratios, we have devised procedures to fit macromolecular models to experimental properties, allowing the determination of the model parameters. Using these quantities, we can construct target functions for an equilibrated, unbiased optimization. The procedures, which have been implemented in public-domain computer programs, are illustrated for rigid, globular proteins, and the rodlike tobacco mosaic virus, and for semiflexible, wormlike heparin molecules.

Dynamic electro-optic properties of macromolecules and nanoparticles in solution: A review of computational and simulation methodologies

This paper reviews some theories, and computational and simulation procedures available for the calculation of the time-course of electro-optic properties of particles in solution. For rigid particles, the time evolution of the properties is directly related to their rotational diffusion; therefore, the computational procedures for the calculation of hydrodynamic properties find a direct application in electro-optics. Several of such computational procedures, based on bead models, are reviewed. For flexible particles, the simultaneous effects the external field and the flexibility can be treated with Brownian dynamics simulation. We illustrate the various procedures, with applications to rigid bent rods and flexible, wormlike or hinged rods, trying to show how the absence or presence of flexibility, and its kind, influences the dynamic electro-optic properties, which are therefore valuable sources of information about the conformation of macromolecules and nanoparticles.

Purification, analysis, and crystal structure of integrins

Integrins are large modular cell-surface receptors that regulate almost every aspect of cellular function through bidirectional signals transmitted across the lipid bilayer. Regulation of integrin activity is accomplished by complex and still incompletely understood biochemical pathways that modify integrin ligand binding, clustering, trafficking, and signaling functions. The dynamic tertiary and quaternary changes required to channel some of these activities have hampered, until recently, the crystal structure determination of these heterodimeric receptors. In this chapter, we review the methods used to purify and characterize these proteins biophysically and functionally, and to derive their three-dimensional structures.

Organization of human interferon gamma-heparin complexes from solution properties and hydrodynamics

Heparan sulfate (HS) recognizes a variety of proteins, one of which is the pleiotropic cytokine IFN-gamma, and as such modulates many biological processes. IFN-gamma is a homodimer with a well-defined core and two flexible C-termini that constitute HS binding domains. We show here using molecular modeling that an extended IFN-gamma structure overlaps a HS fragment of 16 disaccharides (16 nm). Since a 21-24-disaccharide HS fragment was experimentally defined as the minimum size that interacts with IFN-gamma [Lortat-Jacob, H., Turnbull, J. E., and Grimaud, J. A. (1995) Biochem. J. 310 (Part 2), 497-505], this raises the question of the complexe organization. We combine analytical ultracentrifugation, size exclusion chromatography, and hydrodynamic bead modeling to characterize the complexes formed in solution with heparin oligosaccharides. For oligosaccharides of 14 and 20 nm, two types of complexes are formed with one IFN-gamma and one or two heparin molecules. Complexes consisting of two IFN-gamma and one or two heparin molecules are present for a fragment of 25 nm and aggregates for a fragment of 35 nm. The complexes are rather compact and can be formed without major conformational changes of the partners. The complex pattern of interaction is related to the size of the partners and their multiple binding possibilities. These various possibilities suggest networks of interactions at the crowded surface of the cells. Hydrodynamic methods used here proved to be very efficient tools for describing protein-HS complexes that, due to the intrinsic heterogeneity and flexibility of the partners, are otherwise very difficult to analyze.

Conformation of the HIV-1 Gag protein in solution

A single multi-domain viral protein, termed Gag, is sufficient for assembly of retrovirus-like particles in mammalian cells. We have purified the human immunodeficiency virus type 1 (HIV-1) Gag protein (lacking myristate at its N terminus and the p6 domain at its C terminus) from bacteria. This protein is capable of assembly into virus-like particles in a defined in vitro system. We have reported that it is in monomer-dimer equilibrium in solution, and have described a mutant Gag protein that remains monomeric at high concentrations in solution. We report that the mutant protein retains several properties of wild-type Gag. This mutant enabled us to analyze solutions of monomeric protein. Hydrodynamic studies on the mutant protein showed that it is highly asymmetric, with a frictional ratio of 1.66. Small-angle neutron scattering (SANS) experiments confirmed its asymmetry and yielded an R(g) value of 34 A. Atomic-level structures of individual domains within Gag have previously been determined, but these domains are connected in Gag by flexible linkers. We constructed a series of models of the mutant Gag protein based on these domain structures, and tested each model computationally for its agreement with the experimental hydrodynamic and SANS data. The only models consistent with the data were those in which Gag was folded over, with its N-terminal matrix domain near its C-terminal nucleocapsid domain in three-dimensional space. Since Gag is a rod-shaped molecule in the assembled immature virion, these findings imply that Gag undergoes a major conformational change upon virus assembly.

Crystallohydrodynamics of protein assemblies: Combining sedimentation, viscometry, and x-ray scattering

Crystallohydrodynamics describes the domain orientation in solution of antibodies and other multidomain protein assemblies where the crystal structures may be known for the domains but not the intact structure. The approach removes the necessity for an ad hoc assumed value for protein hydration. Previous studies have involved only the sedimentation coefficient leading to considerable degeneracy or multiplicity of possible models for the conformation of a given protein assembly, all agreeing with the experimental data. This degeneracy can be considerably reduced by using additional solution parameters. Conformation charts are generated for the three universal (i.e., size-independent) shape parameters P (obtained from the sedimentation coefficient or translational diffusion coefficient), nu (from the intrinsic viscosity), and G (from the radius of gyration), and calculated for a wide range of plausible orientations of the domains (represented as bead-shell ellipsoidal models derived from their crystal structures) and after allowance for any linker or hinge regions. Matches are then sought with the set of functions P, nu, and G calculated from experimental data (allowing for experimental error). The number of solutions can be further reduced by the employment of the D max parameter (maximum particle dimension) from x-ray scattering data. Using this approach we are able to reduce the degeneracy of possible solution models for IgG3 to a possible representative structure in which the Fab domains are directed away from the plane of the Fc domain, a structure in accord with the recognition that IgG3 is the most efficient complement activator among human IgG subclasses.

Large-amplitude fast motions in double-stranded DNA driven by solvent thermal fluctuations

The nature of the internal dynamics of double-stranded DNA in aqueous environment remains to be established. We consider the motions to stem from thermal fluctuations/dissipations of the harmonic modes of beads (bases and sugars) in a cylindrical geometry that are tracked through the stochastic Langevin trajectories; these are characterized by parameters obtained from published data. The present approach has allowed a comparative study of the dynamics for DNA lengths in the range of 20-600 base pairs. For this range, we find that rotational motions about directions parallel to the helix axis (opening, twist) and perpendicular to it (propeller-twist, roll) contribute significantly to the dynamics. For a 20-mer at a solvent viscosity of 1 cP, the calculated fluorescence anisotropy profile exhibits a fast decay in the subnanosecond range due to large-amplitude fluctuations at the mesoscopic level. This feature reproduces the experimental behavior well, and suggests a possible way for the initiation of biological processes: they may be suddenly triggered on this scale through the occurrence of favorable thermal fluctuations. This analysis also reveals that, as is the case for a 20-mer, the dynamics of longer N-mers are dominated by internal motions, and are modulated by the viscosity of the solvent, in agreement with our previous experimental observations. Moreover, the model indicates that occurrence of partially concerted rotations of the bases due to thermal fluctuations can possibly be sustained over a DNA length of the order of 100 A at 1 ns, suggesting a possible mechanism for action-at-a-distance in transcription.

SOMO (SOlution MOdeler) differences between X-Ray- and NMR-derived bead models suggest a role for side chain flexibility in protein hydrodynamics

Reduced numbers of frictional/scattering centers are essential for tractable hydrodynamic and small-angle scattering data modeling. We present a method for generating medium-resolution models from the atomic coordinates of proteins, basically by using two nonoverlapping spheres of differing radii per residue. The computed rigid-body hydrodynamic parameters of BPTI, RNase A, and lysozyme models were compared with a large database of critically assessed experimental values. Overall, very good results were obtained, but significant discrepancies between X-ray- and NMR-derived models were found. Interestingly, they could be accounted for by properly considering the extent to which highly mobile surface side chains differently affect translational/rotational properties. Models of larger structures, such as fibrinogen fragment D and citrate synthase, also produced consistent results. Foremost among this method's potential applications is the overall conformation and dynamics of modular/multidomain proteins and of supramolecular complexes. The possibility of merging data from high- and low-resolution structures greatly expands its scope.

Solution Structure and Backbone Dynamics of the KH-QUA2 Region of the Xenopus STAR/GSG Quaking Protein

The Quaking protein belongs to the family of STAR/GSG domain RNA-binding proteins and is involved in multiple cell signalling and developmental processes in vertebrates, including the formation of myelin. Heteronuclear NMR methods were used to determine the solution structure of a 134 residue fragment spanning the KH and QUA2 homology regions of the Quaking protein from Xenopus laevis (pXqua) in the absence of RNA. The protein is shown to adopt an extended type I KH domain fold that is connected to a structured alpha-helix in the C-terminal QUA2 region by means of a highly flexible linker. A comparison with the solution structure of the related protein splicing factor 1 (SF1) indicates that most aspects of the RNA-binding interface are conserved in pXqua, although the "variable loop" region that follows the second beta-strand possesses two additional alpha-helices. The structure of pXqua provides an appropriate template for building models of important homologues, such as GLD-1 and Sam68. Measurements of the (15)N relaxation parameters of pXqua confirm that the polypeptide backbone of the QUA2 region is more dynamic than that of the KH portion, and that the C-terminal helix is partially structured in the absence of RNA. By comparison with a random coil reference state, the nascent structure in the QUA2 region is estimated to contribute 15.5kJmol(-1) to the change in conformational free energy that occurs on forming a complex with RNA. Since STAR/GSG proteins may regulate alternative splicing by competing with SF1 in the nucleus for specific branch-point sequences that signal intronic RNA, the formation of secondary structure in the QUA2 region in the unbound state of pXqua has important functional consequences.

Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: A computer simulation study

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.

Hydrodynamic Models and Computational Methods for NMR Relaxation

Interpretation of NMR relaxation data of macromolecules is based on the analysis of their dynamic behavior in solution. For quasirigid molecules, in addition to a minor, separable contribution from local mobility, the main contribution corresponds to the overall rotational diffusion of the complete molecule. Therefore, theoretical descriptions and computational methodologies for hydrodynamic calculations, which yield the full, anisotropic rotational diffusion tensor of rigid molecules, are extremely helpful in the analysis of NMR relaxation. Recent approaches allow realistic predictions of the rotational diffusion tensor from structures at atomic detail. This enables measured relaxation rates and structural models to be compared. Such a comparison (1) provides an independent test of the structural model, (2) provides a framework for the interpretation of local motion, even for highly anisotropic systems, (3) provides a simple method for the detection of additional sources of relaxation, such as chemical exchange, and (4) provides a sensitive method for the detection of nonspecific aggregation or oligomer formation. Although hydrodynamic calculations usually assume a rigid structure, Brownian dynamics simulations extend their range of applications to flexible multidomain structures. Hydrodynamic applications are not restricted to globular proteins. Small DNA fragments, which could be otherwise considered cylindrical objects, can also be treated with atomic detail using the same methodology used for proteins.