Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform.
ABSTRACT: The second virial coefficient, B2, measures a protein solution's deviation from ideal behavior. It is widely used to predict or explain solubility, crystallization condition, aggregation propensity, and critical temperature for liquid-liquid phase separation. B2 is determined by the interaction energy between two protein molecules and, specifically, by the integration of the Mayer f-function in the relative configurational space (translation and rotation) of the two molecules. Simple theoretical models, such as one attributed to Derjaguin, Landau, Verwey, and Overbeek (DLVO), can fit the dependence of B2 on salt concentrations. However, model parameters derived often are physically unrealistic and hardly transferable from protein to protein. Previous B2 calculations incorporating atomistic details were done with limited sampling in the configurational space, due to enormous computational cost. Our FMAP method, based on fast Fourier transform, can considerably accelerate such calculations, and here we adapt it to calculate B2 values for proteins represented at the atomic level in implicit solvent. After tuning of a single parameter in the energy function, FMAPB2 predicts well the B2 values for lysozyme and other proteins over wide ranges of solvent conditions (salt concentration, pH, and temperature). The method is available as a web server at http://pipe.rcc.fsu.edu/fmapb2 .
Project description:The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.
Project description:Aqueous colloidal suspensions, both man-made and natural, are part of our everyday life. The applicability of colloidal suspensions, however, is limited by the range of conditions over which they are stable. Here we report a novel type of highly monodisperse raspberry-like colloids, which are prepared in a single-step synthesis that relies on simultaneous dispersion and emulsion polymerisation. The resulting raspberry colloids behave almost like hard spheres. In aqueous solutions, such prepared raspberries show unexpected stability against aggregation over large variations of added salt concentrations without addition of stabilisers. We present simple Derjaguin-Landau-Verwey-Overbeek (DLVO) calculations performed on raspberry-like and smooth colloids showing that this stability results from our raspberries' unique morphology, which extends our understanding of colloidal stability against salting. Further, the raspberries' stability facilitates the formation of superspheres and thin films in which the raspberry colloids self-assemble into hexagonally close-packed photonic crystals with exquisite reproducibility.
Project description:Recombinantly engineered bacterial outer membrane vesicles (OMVs) are promising vaccine delivery vehicles. The diversity of exogenous antigens delivered by OMVs can be enhanced by induced fusion of OMV populations. To date there are no reports of induced fusion of bacterial OMVs. Here we measure the pH and salt-induced aggregation and fusion of OMVs and analyze the processes against the Derjaguin-Landau-Verwey-Overbeek (DLVO) colloidal stability model. Vesicle aggregation and fusion kinetics were investigated for OMVs isolated from native E. coli (Nissle 1917) and lipopolysaccharide (LPS) modified E. coli (ClearColi) strains to evaluate the effect of lipid type on vesicle aggregation and fusion. Electrolytes and low pHs induced OMV aggregation for both native and modified LPS constructs, approaching a calculated fusion efficiency of ~25% (i.e. ~1/4 of collision events lead to fusion). However, high fusion efficiency was achieved for Nissle OMVs solely with decreased pH as opposed to a combination of low pH and increased divalent counterion concentration for ClearColi OMVs. The lipid composition of the OMVs from Nissle negatively impacted fusion in the presence of electrolytes, causing higher deviations from DLVO-predicted critical coagulation concentrations with monovalent counterions. The outcome of the work is a defined set of conditions under which investigators can induce OMVs to fuse and make various combinations of vesicle compositions.
Project description:Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.
Project description:The self-assembly of nanoparticles on substrates is relevant for a variety of applications such as plasmonics, sensing devices and nanometer-sized electronics. We investigate the deposition of 60 nm spherical Au nanoparticles onto silicon dioxide (SiO2) substrates by changing the chemical treatment of the substrate and by that altering the surface charge. The deposition is characterized by scanning electron microscopy (SEM). Kelvin probe force microscopy (KPFM) was used to characterize the surface workfunction. The underlying physics involved in the deposition of nanoparticles was described by a model based on Derjaguin-Landau-Verwey-Overbeek (DLVO) theory combined with random sequential adsorption (RSA). The spatial statistical method Ripley's K-function was used to verify the DLVO-RSA model (ERSA). The statistical results also showed that the adhered particles exhibit a short-range order at distances below ~300 nm. This method can be used in future research to predict the deposition densities of charged nanoparticles onto charged surfaces.
Project description:Controlling interactions between proteins and nanoparticles in electrolyte solutions is crucial for advancing biological sciences and biotechnology. The assembly of charged nanoparticles (NPs) and proteins in aqueous solutions can be directed by modifying the salt concentration. High concentrations of monovalent salt can induce the solubilization or crystallization of NPs and proteins. By using a multiscale coarse-grained molecular dynamics approach, we show that, due to ionic correlations in the electrolyte, NPs pairs at high monovalent salt concentrations interact via remarkably strong long-range attractions or repulsions, which can be split into three regimes depending on the surface charge densities of the NPs. NPs with zero-to-low surface charge densities interact via a long-range attraction that is stronger and has a similar range to the depletion attraction induced by polymers with radius of gyrations comparable to the NP diameter. On the other hand, moderately charged NPs with smooth surfaces as well as DNA-functionalized NPs with no possibility of hybridization between them interact via a strong repulsion of range and strength larger than the repulsion predicted by models that neglect ionic correlations, including the Derjaguin-Landau-Vervey-Overbeek (DLVO) model. Interactions between strongly charged NPs (>2 e/nm2), both types smooth and DNA-functionalized NPs, show an attractive potential well at intermediate-to-high salt concentrations, which demonstrates that electrolytes can induce aggregation of strongly charged NPs. Our work provides an improved understanding of the role of ionic correlations in NP assembly and design rules to utilize the salting-out process to crystallize NPs.
Project description:The effects of pH and electrolyte concentration on protein-protein interactions in lysozyme and chymotrypsinogen solutions were investigated by static light scattering (SLS) and small-angle neutron scattering (SANS). Very good agreement between the values of the virial coefficients measured by SLS and SANS was obtained without use of adjustable parameters. At low electrolyte concentration, the virial coefficients depend strongly on pH and change from positive to negative as the pH increases. All coefficients at high salt concentration are slightly negative and depend weakly on pH. For lysozyme, the coefficients always decrease with increasing electrolyte concentration. However, for chymotrypsinogen there is a cross-over point around pH 5.2, above which the virial coefficients decrease with increasing ionic strength, indicating the presence of attractive electrostatic interactions. The data are in agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO)-type modeling, accounting for the repulsive and attractive electrostatic, van der Waals, and excluded volume interactions of equivalent colloid spheres. This model, however, is unable to resolve the complex short-ranged orientational interactions. The results of protein precipitation and crystallization experiments are in qualitative correlation with the patterns of the virial coefficients and demonstrate that interaction mapping could help outline new crystallization regions.
Project description:Little is known about the influence of nanoconfinement on calcium carbonate mineralization. Here, colloidal probe atomic force microscopy is used to confine the calcite-solution interface with a silica microsphere and to measure Derjaguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO forces as a function of the calcium concentration, also after charge reversal of both surfaces occurs. Through the statistical analysis of the oscillatory component of a strong hydration force, the subnanometer interfacial structure of the confined atomically flat calcite is resolved in aqueous solution. By applying a mechanical work, both water and hydrated counterions are squeezed out from the nanoconfined solution, leaving the calcite surface more negatively charged than the analogous unconfined surfaces. Layer size and applied work allow a distinction between the hydration states of the counterions in the Stern layer; we propose counterions to be inner- and outer-sphere calcium ions, with a population of inner-sphere calcium ions larger than on unconfined calcite surfaces. It is also shown that the composition of the nanoconfined solution can be tuned by varying calcium concentration. This is a fundamental study of DLVO and hydration forces, and of their connection, on atomically flat calcite. More broadly, our work scrutinizes the greatly unexplored relation between surface science and confined mineralization, with implications for diverse areas of inquiry, such as nanoconfined biomineralization, CO2 sequestration in porous aquifers, and pressure solution and crystallization in confined hydrosystems.
Project description:Given the lack of a complete and comprehensive library of microbial reference genomes, determining the functional profile of diverse microbial communities is challenging. The available functional analysis pipelines lack several key features: (i) an integrated alignment tool, (ii) operon-level analysis, and (iii) the ability to process large datasets.Here we introduce our open-sourced, stand-alone functional analysis pipeline for analyzing whole metagenomic and metatranscriptomic sequencing data, FMAP (Functional Mapping and Analysis Pipeline). FMAP performs alignment, gene family abundance calculations, and statistical analysis (three levels of analyses are provided: differentially-abundant genes, operons and pathways). The resulting output can be easily visualized with heatmaps and functional pathway diagrams. FMAP functional predictions are consistent with currently available functional analysis pipelines.FMAP is a comprehensive tool for providing functional analysis of metagenomic/metatranscriptomic sequencing data. With the added features of integrated alignment, operon-level analysis, and the ability to process large datasets, FMAP will be a valuable addition to the currently available functional analysis toolbox. We believe that this software will be of great value to the wider biology and bioinformatics communities.
Project description:The thermodynamic properties of protein solutions are determined by the molecular interactions involving both solvent and solute molecules. A quantitative understanding of the relationship would facilitate more systematic procedures for manipulating the properties in a process environment. In this work the molecular basis for the osmotic second virial coefficient, B22, is studied; osmotic effects are critical in membrane transport, and the value of B22 has also been shown to correlate with protein crystallization behavior. The calculations here account for steric, electrostatic, and short-range interactions, with the structural and functional anisotropy of the protein molecules explicitly accounted for. The orientational dependence of the protein interactions is seen to have a pronounced effect on the calculations; in particular, the relatively few protein-protein configurations in which the apposing surfaces display geometric complementarity contribute disproportionately strongly to B22. The importance of electrostatic interactions is also amplified in these high-complementarity configurations. The significance of molecular recognition in determining B22 can explain the correlation with crystallization behavior, and it suggests that alteration of local molecular geometry can help in manipulating protein solution behavior. The results also have implications for the role of protein interactions in biological self-organization.