Building hydrodynamic bead-shell models for rigid bioparticles of arbitrary shape

Amyloid fibril length distribution from dynamic light scattering data

The study of the aggregation of amyloid proteins is challenging. A new approach to processing dynamic light scattering data was developed and tested using aggregates of the well-known model Sup35NM amyloid. After filtering and calculating the moving averages of autocorrelation functions to reduce impacts of noise, each averaged autocorrelation function is converted to the fibril length distribution via numerical modeling. The processing results were verified using atomic force and scanning electron microscopy data. Analysis of fibril length distribution changes over time gives valuable information about the aggregation process.

Hydrodynamic Steering in Protein Association Revisited: Surprisingly Minuscule Effects of Considerable Torques

We investigate the previously postulated hydrodynamic steering phenomenon, resulting from complication of molecular shapes, its magnitude and possible relevance for protein-ligand and protein-protein diffusional encounters, and the kinetics of diffusion-controlled association. We consider effects of hydrodynamic interactions in a prototypical model system consisting of a cleft enzyme and an elongated substrate, and real protein-protein complexes, that of barnase and barstar, and human growth hormone and its binding protein. The kinetics of diffusional encounters is evaluated on the basis of rigid-body Brownian dynamics simulations in which hydrodynamic interactions between molecules are modeled using the bead-shell method for detailed description of molecular surfaces, and the first-passage-time approach. We show that magnitudes of steering torques resulting from the hydrodynamic coupling of associating molecules, evaluated for the studied systems on the basis of the Stokes-Einstein type relations for arbitrarily shaped rigid bodies, are comparable with magnitudes of torques resulting from electrostatic interactions of binding partners. Surprisingly, however, unlike in the case of electrostatic torques that strongly affect the diffusional encounter, overall effects of hydrodynamic steering torques on the association kinetics, while clearly discernible in Brownian dynamics simulations, are rather minute. We explain this result as a consequence of the thermal agitation of the binding partners. Our finding is relevant for the general understanding of a wide spectrum of molecular processes in solution but there is also a more practical aspect to it if one considers the low level of shape detail of models that are usually employed to evaluate hydrodynamic interactions in particle-based Stokesian and Brownian dynamics simulations of multicomponent biomolecular systems. Results described in the current work justify, in part at least, such a low-resolution description.

Molecular Dynamics of Cyclodextrins in Water Solutions from NMR Deuterium Relaxation: Implications for Cyclodextrin Aggregation

The aggregation of the most common natural cyclodextrins (α-, β-, and γ-) in aqueous solutions is addressed by studying the CD-CD interactions using deuterium relaxation rates for deuterium labeled CDs. Relaxation times (T₁) and their corresponding relaxation rates (R₁ = 1/T₁) provide information about the rotational correlation times of CDs and serve as a proxy for solute-solute interactions. Measured T₁'s for α-, β-, and γ-CD at the lowest CD concentrations were in agreement with predictions of a hydrodynamic model for toroids, in particular with regard to the dependence of T₁ on CD size. On the other hand, the dependence of T₁'s with respect to the increase in CD concentration could not be explained by hydrodynamic or direct interaction between CD molecules, and it is suggested that there is an equilibrium between monomeric and dimeric CD to account for the observed concentration dependence. No evidence in favor of large aggregates of CDs involving a non-negligible fraction was found for the investigated CDs.

Effects of Spatially Dependent Mobilities on the Kinetics of the Diffusion-Controlled Association Derived from the First-Passage-Time Approach

Brownian dynamics (BD) simulations and the first-passage-time approach are applied to investigate diffusion-controlled association in a biologically relevant model system consisting of a fixed receptor with an elongated cavity and a capsule-like ligand that fits this cavity precisely. Before the binding at the receptor cavity, the ligand undergoes translational and rotational diffusion, either free or under the influence of electrostatic interactions with the receptor. The spatial dependence of the translational and rotational mobilities of the ligand resulting from its hydrodynamic interactions (HIs) with the receptor is accounted for in BD simulations, and an accurate numerical approach is applied for the evaluation of the spatially dependent mobility tensor of the ligand. Different magnitudes of electrostatic interactions (either attraction or repulsion) between the ligand and receptor are considered. The effective range of receptor-ligand electrostatic interactions is varied to account for their screening under different conditions of ionic strength. The effects of HIs on the kinetics of the diffusion-controlled association, evaluated for different electrostatic properties of binding partners, are thoroughly analyzed and discussed.

Mapping the Free Energy Landscape of PKA Inhibition and Activation: A Double-Conformational Selection Model for the Tandem cAMP-Binding Domains of PKA RIα

Protein Kinase A (PKA) is the major receptor for the cyclic adenosine monophosphate (cAMP) secondary messenger in eukaryotes. cAMP binds to two tandem cAMP-binding domains (CBD-A and -B) within the regulatory subunit of PKA (R), unleashing the activity of the catalytic subunit (C). While CBD-A in RIα is required for PKA inhibition and activation, CBD-B functions as a “gatekeeper” domain that modulates the control exerted by CBD-A. Preliminary evidence suggests that CBD-B dynamics are critical for its gatekeeper function. To test this hypothesis, here we investigate by Nuclear Magnetic Resonance (NMR) the two-domain construct RIα (91–379) in its apo, cAMP₂, and C-bound forms. Our comparative NMR analyses lead to a double conformational selection model in which each apo CBD dynamically samples both active and inactive states independently of the adjacent CBD within a nearly degenerate free energy landscape. Such degeneracy is critical to explain the sensitivity of CBD-B to weak interactions with C and its high affinity for cAMP. Binding of cAMP eliminates this degeneracy, as it selectively stabilizes the active conformation within each CBD and inter-CBD contacts, which require both cAMP and W260. The latter is contributed by CBD-B and mediates capping of the cAMP bound to CBD-A. The inter-CBD interface is dispensable for intra-CBD conformational selection, but is indispensable for full activation of PKA as it occludes C-subunit recognition sites within CBD-A. In addition, the two structurally homologous cAMP-bound CBDs exhibit marked differences in their residual dynamics profiles, supporting the notion that conservation of structure does not necessarily imply conservation of dynamics.

Protein Kinase A (PKA) is the major receptor for the cAMP secondary messenger in eukaryotes. This study shows how PKA's regulatory subunit dynamically samples a degenerate free energy landscape that controls affinities for the catalytic subunit and cAMP; intra-domain conformational selection by cAMP controls inter-domain interactions and PKA activation.

Cyclic adenosine monophosphate (cAMP) is a messenger molecule produced within cells to control cellular metabolism in response to external stimuli. Protein Kinase A (PKA) is the major receptor for cAMP. cAMP binds to tandem cAMP-binding domains (CBD-A and -B) within the regulatory subunits of PKA (R), unleashing the activity of the catalytic subunit (C). While CBD-A is required for C-subunit inhibition and activation, in RIα CBD-B functions as a “gatekeeper” domain that modulates the control exerted by CBD-A. However, it is not currently clear how ligand binding and dynamics of CBD-B mediate its gatekeeper function. We comparatively analyzed by Nuclear Magnetic Resonance (NMR) a two-domain construct of the regulatory subunit RIα with no ligand, with cAMP₂ bound, and the C-bound form. These data show that both CBDs can exist in a system of uncorrelated conformational selection as both can independently sample activated and inactivated states (in what is known as a nearly degenerate free energy landscape). This explains why both RIα CBDs exhibit a higher cAMP-affinity than other cAMP receptors. Once cAMP has bound, the degeneracy is lost and dissociation of the kinase subunit is promoted through a combination of intra-domain conformational selection and changes in inter-CBD orientation. The proposed model—a double-conformational selection model—provides a general framework to interpret the effect of PKA mutations that have been reported in rare human disorders such as Carney complex and Acrodysostosis.

Effects of Hydrodynamic Interactions on the Apparent 1D Mobility of a Nonspecifically Bound Protein Following a Helical Path around DNA

We investigated effects of hydrodynamic interactions on diffusivities of proteins that undergo rotation-coupled sliding along DNA. For that, we applied numerical calculations of mobility and friction tensors to systems consisting of detailed bead-shell models of DNA and proteins of different size. Using tensors that result from these calculations along with an expression for the instantaneous energy dissipation rate due to motions of a nonspecifically bound protein that follows a helical track around DNA, we evaluated apparent one-dimensional friction and mobility coefficients for model proteins. The results that we obtained indicate that hydrodynamic interactions between DNA and proteins may substantially (even several-fold) reduce the apparent one-dimensional diffusivity of proteins, when compared with results of other theoretical analyses of the rotation-coupled sliding of proteins along DNA that neglect hydrodynamic effects. Moreover, accounting for hydrodynamic effects decreases the gap between values of diffusion coefficients of proteins on DNA measured experimentally and those estimated based on theoretical calculations and analyses applied to model systems. Altogether, the current study gives insights into the significance of hydrodynamic interactions in determination of the rate of finding target sites by DNA-binding proteins.

Hydrodynamic Modeling and Its Application in AUC

The hydrodynamic parameters measured in an AUC experiment, s(20,w) and D(t)(20,w)(0), can be used to gain information on the solution structure of (bio)macromolecules and their assemblies. This entails comparing the measured parameters with those that can be computed from usually "dry" structures by "hydrodynamic modeling." In this chapter, we will first briefly put hydrodynamic modeling in perspective and present the basic physics behind it as implemented in the most commonly used methods. The important "hydration" issue is also touched upon, and the distinction between rigid bodies versus those for which flexibility must be considered in the modeling process is then made. The available hydrodynamic modeling/computation programs, HYDROPRO, BEST, SoMo, AtoB, and Zeno, the latter four all implemented within the US-SOMO suite, are described and their performance evaluated. Finally, some literature examples are presented to illustrate the potential applications of hydrodynamics in the expanding field of multiresolution modeling.

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.

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.

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.

Structural interconversions modulate activity of Escherichia coli ribonucleotide reductase

Essential for DNA biosynthesis and repair, ribonucleotide reductases (RNRs) convert ribonucleotides to deoxyribonucleotides via radical-based chemistry. Although long known that allosteric regulation of RNR activity is vital for cell health, the molecular basis of this regulation has been enigmatic, largely due to a lack of structural information about how the catalytic subunit (α(2)) and the radical-generation subunit (β(2)) interact. Here we present the first structure of a complex between α(2) and β(2) subunits for the prototypic RNR from Escherichia coli. Using four techniques (small-angle X-ray scattering, X-ray crystallography, electron microscopy, and analytical ultracentrifugation), we describe an unprecedented α(4)β(4) ring-like structure in the presence of the negative activity effector dATP and provide structural support for an active α(2)β(2) configuration. We demonstrate that, under physiological conditions, E. coli RNR exists as a mixture of transient α(2)β(2) and α(4)β(4) species whose distributions are modulated by allosteric effectors. We further show that this interconversion between α(2)β(2) and α(4)β(4) entails dramatic subunit rearrangements, providing a stunning molecular explanation for the allosteric regulation of RNR activity in E. coli.

The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems

We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work.

Hydrodynamic properties of cyclodextrin molecules in dilute solutions

Three well-known representatives of the cyclodextrin family were completely characterized by molecular hydrodynamics methods in three different solvents. For the first time the possibility of an estimation of velocity sedimentation coefficients s between 0.15 and 0.5 S by the numerical solution of the Lamm equation is shown. Comparison of the experimental hydrodynamic characteristics of the cyclodextrins with theoretical calculations for toroidal molecules allows an estimation of the thickness of the solvent layers on the surface of cyclodextrin molecules.

Intrinsic viscosity of bead models for macromolecules and nanoparticles

The calculation of the intrinsic viscosity by means of classical treatments of bead models, typically composed of a number of identical beads, presents some problems when applied to models where the beads are unequal and their number is not very large. A correction to this problem was proposed 10 years ago (García de la Torre and Carrasco in Eur Biophys J 27:549-557, 1998). This so-called volume correction, which consisted of adding a term proportional to the volume of the model, was proved to be rigorous in physico-mathematical terms, and produced improved results in some circumstances, but not always. Recently, the volume correction is being reconsidered so that with some deduced or empirical modifications, it can allow for safer predictions of the intrinsic viscosity. This paper contributes a discussion and further improvements of that correction for the intrinsic viscosity.

Association of aminoglycosidic antibiotics with the ribosomal A-site studied with Brownian dynamics

Brownian dynamics methodology was applied to simulate the encounter of aminoglycosidic antibiotics with the ribosomal A-site RNA. Studied antibiotics included neamine, neomycin, ribostamycin and paromomycin which differ in chemical structure, the number of pseudo-sugar rings and the net charge. The influence of structural, electrostatic and hydrodynamic properties of antibiotics on the kinetics of their association with the ribosomal A-site was analyzed. The computed diffusion limited rates of association are of the order of 10(10)[Formula: see text] and they weakly depend on ionic strength. Prior to binding antibiotics often slide along the RNA groove with the time scale of approximately 10 ns per base pair in case of neamine. We observed that upon forming the encounter complex aminoglycosides displace from the binding pocket up to two Mg(2+) ions.

Role of intrinsic flexibility in signal transduction mediated by the cell cycle regulator, p27 Kip1

p27(Kip1) (p27), which controls eukaryotic cell division through interactions with cyclin-dependent kinases (Cdks), integrates and transduces promitogenic signals from various nonreceptor tyrosine kinases by orchestrating its own phosphorylation, ubiquitination and degradation. Intrinsic flexibility allows p27 to act as a "conduit" for sequential signaling mediated by tyrosine and threonine phosphorylation and ubiquitination. While the structural features of the Cdk/cyclin-binding domain of p27 are understood, how the C-terminal regulatory domain coordinates multistep signaling leading to p27 degradation is poorly understood. We show that the 100-residue p27 C-terminal domain is extended and flexible when p27 is bound to Cdk2/cyclin A. We propose that the intrinsic flexibility of p27 provides a molecular basis for the sequential signal transduction conduit that regulates p27 degradation and cell division. Other intrinsically unstructured proteins possessing multiple sites of posttranslational modification may participate in similar signaling conduits.

Hydrodynamic modeling: the solution conformation of macromolecules and their complexes

Hydrodynamic bead modeling (HBM) is the representation of a macromolecule by an assembly of spheres (or beads) for which measurable hydrodynamic (and related) parameters are then computed in order to understand better the macromolecular solution conformation. An example-based account is given of the main stages in HBM of rigid macromolecules, namely: model construction, model visualization, accounting for hydration, and hydrodynamic calculations. Different types of models are appropriate for different macromolecules, according to their composition, to what is known about the molecule or according to the types of experimental data that the model should reproduce. Accordingly, the construction of models based on atomic coordinates as well as much lower resolution data (e.g., electron microscopy images) is described. Similarly, several programs for hydrodynamic calculations are summarized, some generating the most basic set of solution parameters (e.g., sedimentation and translational diffusion coefficients, intrinsic viscosity, radius of gyration, and Stokes radius) while others extend to data determined by nuclear magnetic resonance, fluorescence anisotropy, and electric birefringence methods. An insight into the topic of hydrodynamic hydration is given, together with some practical suggestions for its satisfactory treatment in the modeling context. All programs reviewed are freely available.

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.

Improved calculation of rotational diffusion and intrinsic viscosity of bead models for macromolecules and nanoparticles

The conventional Kirkwood-Riseman calculation of the hydrodynamic properties of bead models gives abnormal results for rotational quantities and the intrinsic viscosities for models with a few beads or when one bead is dominant. The reason is that beads are treated as point sources of friction. This can be remedied by introducing terms that are neglected in the conventional treatment of orders 0 and -3 in interbead distances. An alternative strategy is the cubic substitution in which each bead is replaced by a cubic array of minibeads. These procedures require a computational overload that, in the case of the intrinsic viscosity, can be avoided using an estimate of the correction due to the nonzero volume of the beads. We have found how such a correction can be estimated from the geometry of the model, and its application yields results that are within the range of typical experimental errors.

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.

Mismatch-induced DNA unbending upon duplex opening

A DNA duplex can be torn open at a specific position by introducing a branch or bulge to create an asymmetric three-way junction (TWJ). The opened duplex manifests a bent conformation (bending angle approximately 60 degrees , relative to the unopened form), which leads to a dramatic decrease in gel electrophoretic mobility. In the presence of a basepair mismatch at the opening position, the DNA backbone becomes less bent and assumes a distorted T-shaped structure, resulting in an increase in polyacrylamide gel electrophoretic mobility. Both conformational changes are confirmed using fluorescence resonance energy transfer experiments and found to be similar to the signature conformational changes of DNA duplex upon MutS protein binding. Our results imply that some structural rearrangements essential for mismatch recognition are achievable without protein interference. The gel electrophoretic mobility data for DNA TWJs with and without base mismatches correlates well with rotational diffusivity, computed by taking into account the conformational change of TWJ induced by base mismatch.

Effect of topological asymmetry on the electrophoretic mobility of branched DNA structures with and without single-base mismatches

The electrophoretic mobility of three-arm star DNA structures with varying degrees of branch length asymmetry has been investigated in polyacrylamide (PAA) hydrogels. We report the effect of single-base mismatches, adjacent to the branch point, on the mobility of branched DNA with three different arm lengths. Branched DNA structures were formed using wild-type and mutated fragments of the p53 tumor suppressor gene, which is believed to play an important role in cancer development. Branching was directed at the site of several previously characterized mutations in exon 7 of p53. At a given gel concentration, the mobility of branched DNA with fully complementary base pairing is found to increase as the degree of branch length asymmetry is increased. Ferguson analysis of the gel electrophoresis data leads to a retardation coefficient that is strongly dependent on topology. This finding can be explained in terms of a minimum molecular cross-section for each molecule. Specifically, we show that structures with the smallest molecular cross-section can access more pores in the gel, which leads to higher mobility. Our results can also be understood by considering the rotational diffusivity of branched DNA. Asymmetric DNA stars with higher calculated rotational diffusivities also have higher mobilities. When a mutated base is present in junctions with low degrees of branch length asymmetry, adjacent to the branch point, the mobility increases in comparison to the fully complementary molecules. The reason for this increased mobility is unclear, here, we propose that the mismatched base introduces additional flexibility to the arm containing the mutation leading to higher conformational freedom and enhanced mobility in gels. When a mismatched base is present in junctions with high degrees of branch length asymmetry, the opposite result is obtained. Here, the mutated species has a lower mobility. This result is argued to arise from incomplete hybridization and/or frayed ends. Finally, we have shown that by using two of the branch point oligonucleotides as probe molecules, mutations known to occur at specific sites can be detected through the mobility shift. If the sequences of the probe chains are changed in a controlled manner, the location and base of the mutant can also be determined.

Translational friction coefficients for cylinders of arbitrary axial ratios estimated by Monte Carlo simulation

Translational friction coefficients for cylinders of arbitrary axial ratios (including disks) are calculated using Monte Carlo simulation and an approximate description of the hydrodynamic interaction. The calculations indicate that the approximate description is exact for ellipsoids and this result is generalized to include cylinders, which possess the same symmetry as ellipsoids. From the result an approximate formula for the translational friction coefficient of cylinders is calculated which is compared to results from other sources.

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

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.

Backbone dynamics and thermodynamics of Borrelia outer surface protein A

Nuclear spin relaxation experiments performed at 298K, 308K and 318K are used to characterize the intramolecular dynamics and thermodynamics of outer surface protein A (OspA), a key protein in the life-cycle of Borrelia burgdorferi, the causative agent of Lyme disease. It has recently been demonstrated that OspA specifically binds to the gut of the intermediate tick host (Ixodes scapularis), and that this interaction is mediated, at least in part, by residues in the C-terminal domain of OspA that are largely inaccessible to solvent in all X-ray structures of this protein. Our analysis of 15N relaxation parameters in OspA shows that the putative-binding region contains and is surrounded by flexible residues, which could facilitate accessibility to solvent and ligands. In addition, residues with similar activation energies are clustered in a manner that suggests locally collective motions. We have used molecular modeling to show that these collective motions are consistent with a hinge-bending mechanism that exposes residues implicated in binding. Characteristic temperatures describing the energy landscape of the OspA backbone are derived from the temperature dependence of the N-H bond vector order parameters, and a comparison is made between the N and C-terminal globular domains and the unusual single-layer beta-sheet connecting them. The average characteristic temperatures in the three regions indicate that, with an increase in temperature, a larger increase in accessible conformational states occurs for N-H bond vectors in the single-layer central beta-sheet than for bond vectors in the globular N and C-terminal domains. These conformational states are accessible without disruption of hydrogen bonds, providing a conformational entropic gain, upon increase in temperature, without a significant enthalpic penalty. This increase in heat capacity may help to explain the unexpected thermal stability of the unusual single-layer beta-sheet.

Brownian dynamics simulation of rigid particles of arbitrary shape in external fields

We have developed a Brownian dynamics simulation algorithm to generate Brownian trajectories of an isolated, rigid particle of arbitrary shape in the presence of electric fields or any other external agents. Starting from the generalized diffusion tensor, which can be calculated with the existing HYDRO software, the new program BROWNRIG (including a case-specific subprogram for the external agent) carries out a simulation that is analyzed later to extract the observable dynamic properties. We provide a variety of examples of utilization of this method, which serve as tests of its performance, and also illustrate its applicability. Examples include free diffusion, transport in an electric field, and diffusion in a restricting environment.