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

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

Proteomic Profiling of Antimalarial Plasmodione Using 3-Benz(o)ylmenadione Affinity-Based Probes

Understanding the mechanisms of drug action in malarial parasites is crucial for the development of new drugs to combat infection and to counteract drug resistance. Proteomics is a widely used approach to study host-pathogen systems and to identify drug protein targets. Plasmodione is an antiplasmodial early-lead drug exerting potent activities against young asexual and sexual blood stages in vitro with low toxicity to host cells. To elucidate its molecular mechanisms, an affinity-based protein profiling (AfBPP) approach was applied to yeast and P. falciparum proteomes. New (pro-)AfBPP probes based on the 3-benz(o)yl-6-fluoro-menadione scaffold were synthesized. With optimized conditions of both photoaffinity labeling and click reaction steps, the AfBPP protocol was then applied to a yeast proteome, yielding 11 putative drug-protein targets. Among these, we found four proteins associated with oxidoreductase activities, the hypothesized type of targets for plasmodione and its metabolites, and other proteins associated with the mitochondria. In Plasmodium parasites, the MS analysis revealed 44 potential plasmodione targets that need to be validated in further studies. Finally, the localization of a 3-benzyl-6-fluoromenadione AfBPP probe was studied in the subcellular structures of the parasite at the trophozoite stage.

Synthesis and Photochemical Properties of Fluorescent Metabolites Generated from Fluorinated Benzoylmenadiones in Living Cells

This work describes the reactivity and properties of fluorinated derivatives (F-PD and F-PDO) of plasmodione (PD) and its metabolite, the plasmodione oxide (PDO). Introduction of a fluorine atom on the 2-methyl group markedly alters the redox properties of the 1,4-naphthoquinone electrophore, making the compound highly oxidizing and particularly photoreactive. A fruitful set of analytical methods (electrochemistry, absorption and emission spectrophotometry, and HRMS-ESI) have been used to highlight the products resulting from UV photoirradiation in the absence or presence of selected nucleophiles. With F-PDO and in the absence of nucleophile, photoreduction generates a highly reactive ortho-quinone methide (o-QM) capable of leading to the formation of a homodimer. In the presence of thiol nucleophiles such as β-mercaptoethanol, which was used as a model, o-QMs are continuously regenerated in sequential photoredox reactions generating mono- or disulfanylation products as well as various unreported sulfanyl products. Besides, these photoreduced adducts derived from F-PDO are characterized by a bright yellowish emission due to an excited-state intramolecular proton transfer (ESIPT) process between the dihydronapthoquinone and benzoyl units. In order to evidence the possibility of an intramolecular coupling of the o-QM intermediate, a synthetic route to the corresponding anthrones is described. Tautomerization of the targeted anthrones occurs and affords highly fluorescent stable hydroxyl-anthraquinones. Although probable to explain the intense visible fluorescence emission also observed in tobacco BY-2 cells used as a cellular model, these coupling products have never been observed during the photochemical reactions performed in this study. Our data suggest that the observed ESIPT-induced fluorescence most likely corresponds to the generation of alkylated products through reduction species, as demonstrated with the β-mercaptoethanol model. In conclusion, F-PDO thus acts as a novel (pro)-fluorescent probe for monitoring redox processes and protein alkylation in living cells.

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

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

Estimating near-wall diffusion coefficients of arbitrarily shaped rigid macromolecules

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

Nuclear pore complex acetylation regulates mRNA export and cell cycle commitment in budding yeast

Nuclear pore complexes (NPCs) mediate communication between the nucleus and the cytoplasm, and regulate gene expression by interacting with transcription and mRNA export factors. Lysine acetyltransferases (KATs) promote transcription through acetylation of chromatin‐associated proteins. We find that Esa1, the KAT subunit of the yeast NuA4 complex, also acetylates the nuclear pore basket component Nup60 to promote mRNA export. Acetylation of Nup60 recruits the mRNA export factor Sac3, the scaffolding subunit of the Transcription and Export 2 (TREX‐2) complex, to the nuclear basket. The Esa1‐mediated nuclear export of mRNAs in turn promotes entry into S phase, which is inhibited by the Hos3 deacetylase in G1 daughter cells to restrain their premature commitment to a new cell division cycle. This mechanism is not only limited to G1/S‐expressed genes but also inhibits the expression of the nutrient‐regulated GAL1 gene specifically in daughter cells. Overall, these results reveal how acetylation can contribute to the functional plasticity of NPCs in mother and daughter yeast cells. In addition, our work demonstrates dual gene expression regulation by the evolutionarily conserved NuA4 complex, at the level of transcription and at the stage of mRNA export by modifying the nucleoplasmic entrance to nuclear pores.

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

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

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.

Near-wall diffusion tensor of an axisymmetric colloidal particle

Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple functions in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.

Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations

In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.

Characterization of the mycobacterial acyl-CoA carboxylase holo complexes reveals their functional expansion into amino acid catabolism

Biotin-mediated carboxylation of short-chain fatty acid coenzyme A esters is a key step in lipid biosynthesis that is carried out by multienzyme complexes to extend fatty acids by one methylene group. Pathogenic mycobacteria have an unusually high redundancy of carboxyltransferase genes and biotin carboxylase genes, creating multiple combinations of protein/protein complexes of unknown overall composition and functional readout. By combining pull-down assays with mass spectrometry, we identified nine binary protein/protein interactions and four validated holo acyl-coenzyme A carboxylase complexes. We investigated one of these - the AccD1-AccA1 complex from Mycobacterium tuberculosis with hitherto unknown physiological function. Using genetics, metabolomics and biochemistry we found that this complex is involved in branched amino-acid catabolism with methylcrotonyl coenzyme A as the substrate. We then determined its overall architecture by electron microscopy and found it to be a four-layered dodecameric arrangement that matches the overall dimensions of a distantly related methylcrotonyl coenzyme A holo complex. Our data argue in favor of distinct structural requirements for biotin-mediated γ-carboxylation of α−β unsaturated acid esters and will advance the categorization of acyl-coenzyme A carboxylase complexes. Knowledge about the underlying structural/functional relationships will be crucial to make the target category amenable for future biomedical applications.

Tuberculosis is deadly human disease caused by infection with the bacterium Mycobacterium tuberculosis. This pathogen has a complex metabolism with many genes required for the synthesis of components of its unique cell envelope. We have investigated a family of closely related genes coding for different acyl CoA carboxylase enzyme complexes with previously unexplained genetic redundancy that have been thought to have an involvement in the synthesis of these cell envelope components. We identified five functional multienzyme complexes. Of the two complexes with hitherto unknown function we chose to investigate, one specifically and to our surprise it is required for the degradation of the amino acid leucine. To our knowledge this is the first demonstration that mycobacteria have a specific pathway for leucine degradation and thus broaden the functional diversity associated with acyl CoA carboxylase coding genes.

Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering

In this article we extend recent experimental developments [Rogers et al., Phys. Rev. Lett., 2012, 109, 098305] by providing a suitable theoretical framework for the derivation of exact expressions for the first cumulant (initial decay rate) of the correlation function measured in Evanescent Wave Dynamic Light Scattering (EWDLS) experiments. We focus on a dilute suspension of optically anisotropic spherical Brownian particles diffusing near a planar hard wall. In such a system, translational and rotational diffusion are hindered by hydrodynamic interactions with the boundary which reflects the flow incident upon it, affecting the motion of colloids. The validity of the approximation by the first cumulant for moderate times is assessed by juxtaposition to Brownian dynamics simulations, and compared with experimental results. The presented method for the analysis of experimental data allows the determination of penetration-depth-averaged rotational diffusion coefficients of spherical colloids at low density.

One-particle correlation function in evanescent wave dynamic light scattering

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.

Rotational diffusion of spherical colloids close to a wall

There is currently no experimental technique available to probe spatially resolved rotational diffusion of nanoparticles in the vicinity of a wall. We present the first experimental study of rotational diffusion of small spherical colloids, using dynamic evanescent wave scattering. A setup is used where the wave vector components parallel and perpendicular to the wall can be varied independently, and an expression is derived for the first cumulant of the intensity correlation function in VH evanescent wave geometry for optically anisotropic spheres. The experimental results are in agreement with theoretical predictions that take particle-wall hydrodynamic interactions into account.

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.

High-frequency viscosity and generalized Stokes-Einstein relations in dense suspensions of porous particles

We study the high-frequency limiting shear viscosity, η∞, of colloidal suspensions of uncharged porous particles. An individual particle is modeled as a uniformly porous sphere with the internal solvent flow described by the Debye-Bueche-Brinkman equation. A precise hydrodynamic multipole method with a full account of many-particle hydrodynamic interactions encoded in the HYDROMULTIPOLE program extended to porous particles, is used to calculate η∞ as a function of porosity and concentration. The second-order virial expansion for η∞ is derived, and its range of applicability assessed. The simulation results are used to test the validity of generalized Stokes-Einstein relations between η∞ and various short-time diffusion coefficients, and to quantify the accuracy of a simplifying cell model calculation of η∞. An easy-to-use generalized Saitô formula for η∞ is presented which provides a good description of its porosity and concentration dependence.

The intensity correlation function in evanescent wave scattering

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.

Dynamics of permeable particles in concentrated suspensions

We calculate short-time diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluid-phase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMULTIPOLE program, results are presented for the hydrodynamic function, H(q) , sedimentation coefficient, and self-diffusion coefficients with a full account of many-body hydrodynamic interactions. While self-diffusion and sedimentation are strongly permeability dependent, the wave-number dependence of the hydrodynamic function can be reduced by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed.

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction phi. For low rod concentrations, the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of phi with the slope alpha proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two-body hydrodynamic interactions are calculated using the so-called bead model in which the rod of aspect ratio p is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to p=1000. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than 5% from the model with filling. An analytical expression for alpha as a function of p is derived in the limit of very long rods. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.

Hydrodynamic interactions between spheres in a viscous fluid with a flat free surface or hard wall

Hydrodynamic interactions between spheres immersed in a low-Reynolds-number fluid flow close to a flat free surface or hard wall are investigated. The spheres may have different or equal radii, and may be separated from the boundary or at contact with the free surface. A simple and useful expression is derived for the propagator (Green operator) connecting centers of two spheres. In the derivation, the method of images and the displacement theorems are used. Symmetry of the displacement operators is explicitly shown. The significance of these results in efficient Stokesian and Brownian dynamics simulations is outlined. An example of an application is shown.

Variational theory of average-atom and superconfigurations in quantum plasmas

Models of screened ions in equilibrium plasmas with all quantum electrons are important in opacity and equation of state calculations. Although such models have to be derived from variational principles, up to now existing models have not been fully variational. In this paper a fully variational theory respecting virial theorem is proposed-all variables are variational except the parameters defining the equilibrium, i.e., the temperature T, the ion density ni and the atomic number Z. The theory is applied to the quasiclassical Thomas-Fermi (TF) atom, the quantum average atom (QAA), and the superconfigurations (SC) in plasmas. Both the self-consistent-field (SCF) equations for the electronic structure and the condition for the mean ionization Z* are found from minimization of a thermodynamic potential. This potential is constructed using the cluster expansion of the plasma free energy from which the zero and the first-order terms are retained. In the zero order the free energy per ion is that of the quantum homogeneous plasma of an unknown free-electron density n0 = Z* ni occupying the volume 1/ni. In the first order, ions submerged in this plasma are considered and local neutrality is assumed. These ions are considered in the infinite space without imposing the neutrality of the Wigner-Seitz (WS) cell. As in the Inferno model, a central cavity of a radius R is introduced, however, the value of R is unknown a priori. The charge density due to noncentral ions is zero inside the cavity and equals en0 outside. The first-order contribution to free energy per ion is the difference between the free energy of the system "central ion+infinite plasma" and the free energy of the system "infinite plasma." An important part of the approach is an "ionization model" (IM), which is a relation between the mean ionization charge Z* and the first-order structure variables. Both the IM and the local neutrality are respected in the minimization procedure. The correct IM in the TF case is found to be Z-Z*= integral d3 r[n(r)-n0], where n(r) is the first-order electron density. It is shown that in the QAA case the same IM has to be used and that other IMs lead to unphysical solutions. With this IM R becomes in both cases (TF and QAA) equal to the WS radius and the variational calculation leads to SCF equations in an infinite plasma while n0 (or equivalently Z*) is to be found from the condition integral d3r theta(r-R)Vel(r)=0, where theta denotes Heaviside function and Vel(r) is the SCF electrostatic potential. In the SC case results are similar except that averages over all superconfigurations appear. In the TF case the condition for n0 gives the neutrality of the WS sphere and one gets the classical TF ion-in-cell average atom. The situation is different in the QAA and in the SC cases in which the cavity is not neutral and the SCF potential Vel(r) is not zero outside the cavity. Due to the fully variational character of our approach the expression for the thermodynamic pressure in all cases does not require any numerical differentiation and is consistent with the virial theorem.

Motion of spheres along a fluid-gas interface

A system of many spherical particles, suspended in a quiescent fluid and touching a planar free fluid-gas interface, is considered. Stick fluid boundary conditions at the sphere surfaces are assumed. The free surface boundary conditions are taken into account with the use of the method of images. For such a quasi-two-dimensional system, the one-sphere resistance operator is calculated numerically. Moreover, the corresponding friction and mobility tensors are constructed from irreducible multipole expansion. Finally, the long-distance terms of the two-sphere mobility tensor are evaluated explicitly up to the order of 1/r3, where r is the interparticle distance. Experiments which have motivated this work are outlined.

Memory effects in collective dynamics of Brownian suspensions

We obtain macroscopic equations for average suspension velocity and particle current in a Brownian suspension valid on long time scales for which the memory effects are important. The coefficients in these equations depend solely on local properties of the medium. This formalism allows one to obtain well-defined theoretical expressions for transport coefficients, free of the integrals diverging with the size of the system. As an example, the expression for long-time collective diffusion coefficient is derived and the memory contribution to this coefficient is estimated.

Long-time tails in the solid-body motion of a sphere immersed in a suspension

Long-time tails in the translational and rotational motion of a sphere immersed in a suspension of spherical particles are discussed on the basis of the linear, time-dependent Stokes equations of hydrodynamics. It is argued that the coefficient of the t(-3/2) long-time tail of translational motion depends only on the effective mass density and shear viscosity of the suspension. A similar expression holds for the coefficient of the t(-5/2) long-time tail of rotational motion. In particular, the long-time tails are independent of the sphere radius, and therefore the expressions hold also for a particle of the suspension. On account of the fluctuation-dissipation theorem the long-time tails of the velocity autocorrelation function and the angular velocity autocorrelation function of interacting Brownian particles are also given by these expressions.