A theory is presented for lambda_C, the coefficient of the first-order correction in the density of the collective diffusion coefficient, for protein spheres interacting by electrostatic and adhesive forces. An extensive numerical analysis of the Stokesian hydrodynamics of two moving spheres is given so as to gauge the precise impact of lubrication forces. An effective stickiness is introduced and a simple formula for lambda_C in terms of this variable is put forward. A precise though more elaborate approximation for lambda_C is also developed. These and numerically exact expressions for lambda_C are compared with experimental data on lysozyme at pH 4.5 and a range of ionic strengths between 0.05 M and 2 M.
We develop a simple correspondence between hydrophobic surface topology of globular proteins and and an effective protein-protein adhesiveness parameter of the Baxter type. We discuss within this framework analytical interpretation of the structure factor governing static light scattering.
Using a recently developed mesoscopic theory of protein dielectrics, we have calculated the salt bridge energies, total residue electrostatic potential energies, and transfer energies into a low dielectric amyloid-like phase for 12 species and mutants of the prion protein. Salt bridges and self energies play key roles in stabilizing secondary and tertiary structural elements of the prion protein. The total electrostatic potential energy of each residue was found to be invariably stabilizing. Residues frequently found to be mutated in familial prion disease were among those with the largest ele…
We present a generic model to describe the fractal self-assembly of proteins in terms of electrostatic and hydrophobic interactions. The predictions of the model were correlated with the simulated fractals obtained using patchy diffusion-limited aggregation, and the experimentally observed Amyloid-\b{eta} (A\b{eta}) fractal self-assembly using confocal microscopy. The molecular docking was used to determine the properties of the patches on A\b{eta} oligomers. Similar patch properties were used to design the particles for simulation. In agreement with the model predictions, the free energy of f…
Bovine heart cytochrome c has been immobilized into the mesoporous silica host material SBA-15 in both its native folded and urea-unfolded state. The comparison of the two folding states' behavior casts doubt on the commonly used explanation of cytochrome c adsorption, i.e. the electrostatic interaction model. A detailed investigation of the protein binding as a function of pH and ionic strength of the buffer solution reveals the complex nature of the protein-silica interaction. Electrostatic interaction, van der Waals forces and entropic contributions by counterion release each contribute to …
A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effec…
The possibility for proteins to aggregate in different superstructures, i.e. large-scale polymorphism, has been widely observed, but an understanding of the physico-chemical mechanisms behind it is still out of reach. Here we present a theoretical model for the description of a generic aggregate formed from an ensemble of charged proteins. The model predicts the formation of multi-fractal structures with the geometry of the growth determined by the electrostatic interactions between single proteins. The model predictions are successfully verified in comparison with experimental curves for aggr…
The foaming properties, foaming capacity and foam stability, of soluble complexes of pectin and a globular protein, napin, have been investigated with a "Foamscan" apparatus. Complementary, we also used SANS with a recent method consisting in an analogy between the SANS by foams and the neutron reflectivity of films to measure in situ film thickness of foams. The effect of ionic strength, of protein concentration and of charge density of the pectin has been analysed. Whereas the foam stability is improved for samples containing soluble complexes, no effect has been noticed on the foam film thi…
Under the most common experimental conditions, the adsorption of proteins to solid surfaces is an spontaneous process that leads to a rather compact layer of randomly oriented molecules. Due to the importance of this process for the development of catalytic surfaces, a number of existing computational and experimental approaches try to predict and control the orientation of such molecules. However, and despite their own advantages, these tend to be either too expensive computationally, or oversimplified, undermining their ability to predict the most appropriate experimental conditions to maxim…
We present an approximate method for calculating the electrostatic free energy of concentrated protein solutions. Our method uses a cell model and accounts for both the coulomb energy and the entropic cost of Donnan salt partitioning. The former term is calculated by linearizing the Poisson-Boltzmann equation around a nonzero average potential, while the second term is calculated using a jellium approximation that is empirically modified to reproduce the dilute solution limit. When combined with a short-ranged binding interaction, calculated using the mean spherical approximation, our model re…
Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian Dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with gri…
A detailed study of energy differences between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps) in protein systems and water clusters is presented. Recent work questioning the applicability of Kohn-Sham density-functional theory to proteins and large water clusters (E. Rudberg, J. Phys.: Condens. Mat. 2012, 24, 072202) has demonstrated vanishing HOMO-LUMO gaps for these systems, which is generally attributed to the treatment of exchange in the functional used. The present work shows that the vanishing gap is, in fact, an electrostatic artefact of the method used t…
Gene expression and regulation rely on an apparently finely tuned set of reactions between some proteins and DNA. Such DNA-binding proteins have to find specific sequences on very long DNA molecules and they mostly do so in absence of any active process. It has been rapidly recognized that to achieve this task these proteins should be efficient at both searching (i.e. sampling fast relevant parts of DNA) and finding (i.e. recognizing the specific site). A two-mode search and variants of it have been suggested since the 70s to explain either a fast search or an efficient recognition. Combining …
We present an extended structural study of globular complexes made by mixing a positively charge protein (lysozyme) and a negatively charged polyelectrolyte (PSS). We study the influence of all the parameters that may act on the structure of the complexes (charge densities and concentration of the species, partial hydrophobicity of the polyion chain, ionic strength). The structures on a 15 scale range lying from 10Å to 1000Å are measured by SANS. Whatever the conditions, the same structure is found, based on the formation of dense globules of ~ 100Å with a neutral core and a volume fraction of…
Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In order to investigate the competition betwe…
The mechanism allowing a protein to search of a target sequence on DNA is currently described as an intermittent process composed of 3D diffusion in bulk and 1D diffusion along the DNA molecule. Due to the relevant charge of protein and DNA, electrostatic interaction should play a crucial role during this search. In this paper, we explicitly derive the mean field theory allowing for a description of the protein-DNA electrostatics in solution. This approach leads to a unified model of the search process, where 1D and 3D diffusion appear as a natural consequence of the diffusion on an extended i…
While almost any kind of face mask offers some protection against particles and pathogens of different sizes, the most efficient ones make use of a layered structure where one or more layers are electrically charged. This electret layer is essential to efficient filtration of difficult-to-capture small particles, yet the exact nature of electrostatic capture with respect to both the charge on the particles and the electret fibres as well as the effect of immediate environment remains unclear. Here, we explore in detail the electrostatic interaction between the surface of a single charged elect…
Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous co-assembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.
Electrostatics plays a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can co-assembled into functional units, such as DNA and histone proteins into nucleosomes and actin-binding protein complexes into cytoskeleton components, at appropriate ionic conditions. These cationic-anionic co-assemblies often have surface charge heterogeneities that result from the delicate balance between electrostatics and packing constraints. Despite their importance, the precise role of surface charge heterogeneities in the organization of cationic-anionic co-assemblies is not wel…
We present experiments on RBCs that flow through microcapillaries under physiological conditions. We show that the RBC clusters form as a subtle imbrication between hydrodynamics interaction and adhesion forces because of plasma proteins. Clusters form along the capillaries and macromolecule-induced adhesion contribute to their stability. However, at high yet physiological flow velocities, shear stresses overcome part of the adhesion forces, and cluster stabilization due to hydrodynamics becomes stronger. For the case of pure hydrodynamic interaction, cell-to-cell distances have a pronounced b…
A trick of the tail: how electrostatics helps a DNA repair enzyme to localize on nucleosomes
University of Lille（里尔大学）；Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN CNRS UMR8520)（电子、微电子与纳米技术研究所）；Unité de Glycobiologie Structurale et Fonctionnelle (UGSF)（结构与功能糖生物学单元）
We study the non-equilibrium dynamics of lipid membranes with proteins that actively pump ions across the membrane. We find that the activity leads to a fluctuating force distribution due to electrostatic interactions arising from variation in dielectric constant across the membrane. By applying a multipole expansion we find effects on both the tension and bending rigidity dominated parts of the membranes fluctuation spectrum. We discuss how our model compares with previous studies of force-multipole models.
Viruses self-assemble from identical capsid proteins and their genome consisting, for example, of a long single stranded (ss) RNA. For a big class of T = 3 viruses capsid proteins have long positive N-terminal tails. We explore the role played by the Coulomb interaction between the brush of positive N-terminal tails rooted at the inner surface of the capsid and the negative ss RNA molecule. We show that viruses are most stable when the total contour length of ss RNA is close to the total length of the tails. For such a structure the absolute value of the total RNA charge is approximately twice…
We present a set of Langmuir binding models in which electrostatic cooperativity effects to protein sorption is incorporated in the spirit of Guoy-Chapman-Stern models, where the global substrate (microgel) charge state is modified by bound reactants (charged proteins). Application of this approach to lysozyme sorption to oppositely charged core-shell microgels allows us to extract the intrinsic, binding affinity of the protein to the gel, which is salt-concentration independent and mostly hydrophobic in nature. The total binding affinity is found to be mainly electrostatic in nature, changes …
Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS), we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess the roles of electrostatic, hydrophobic, cation-$π$, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated 3 residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-ar…
Electrostatic interaction is the driving force for the encapsulation by virus coat proteins of nanoparticles such as quantum dots, gold particles and magnetic beads for, e.g., imaging and therapeutic purposes. In recent experimental work, Daniel et al. [ACS Nano 4 (2010), 3853-3860] found the encapsulation efficiency to sensitively depend on the interplay between the surface charge density of negatively charged gold nanoparticles and the number of positive charges on the RNA binding domains of the proteins. Surprisingly, these experiments reveal that despite the highly cooperative nature of th…
Many single-stranded (ss) RNA viruses self assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean field theory to investigate how the secondary structure of the R…
As proteins typically have charges of around 10, they will interact strongly with charged surfaces. We calculate the electrostatic contribution to the interaction of crystals of protein with charged surfaces. The surfaces repel like-charged crystals and attract oppositely-charged crystals, with free energies which can be easily several kT per protein molecule brought into contact with the surface. This means that oppositely charged surfaces can act as a nucleant, they can induce nucleation of a protein crystal by lowering the free energy barrier to heterogeneous nucleation of the crystal from …
The protein-polysaccharide combinations that lead to electrostatic complex and coacervates formation are the object of extensive research using both layer-by-layer and mixed emulsion approaches. The protein-polysaccharide conjugates demonstrated interesting physico-chemical properties as stabilizers and emulsifiers as well as texture modifiers in food products. Furthermore, they are potential optimal nutrient delivery systems. Their complex behavior due to several factors such as pH, ionic strength, concentration, heat, and mechanical treatments is the main reason behind the continuous growth …
Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase polymer concentration depending on the electrostatic interaction strength -- the ratio of the Bjerrum length to the bond length of the chain. We establish that in a wide range of polymer concentration value…
Intermolecular interactions in protein solutions in general contain many contributions. If short-range attractions dominate, the state diagram exhibits liquid-liquid phase separation (LLPS) that is metastable with respect to crystallization. In this case, the extended law of corresponding states (ELCS) suggests that thermodynamic properties are insensitive to details of the underlying interaction potential. Using lysozyme solutions, we investigate the applicability of the ELCS to the static structure factor and in how far effective colloidal interaction models can help to rationalize the phase…
The so-called extended law of corresponding states, as proposed by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)], involves a mapping of the phase behaviors of systems with short-range attractive interactions. While it has already extensively been applied to various model potentials, here we test its applicability to protein solutions with their complex interactions. We successfully map their experimentally determined metastable gas--liquid binodals, as available in the literature, to the binodals of short-range square-well fluids, as determined by previous as well as new Monte Carlo simul…
We study unbinding of multivalent cationic ligands from oppositely charged polymeric binding sites sparsely grafted on a flat neutral substrate. Our molecular dynamics (MD) simulations are suggested by single-molecule studies of protein-DNA interactions. We consider univalent salt concentrations spanning roughly a thousandfold range, together with various concentrations of excess ligands in solution. To reveal the ionic effects on unbinding kinetics of spontaneous and facilitated dissociation mechanisms, we treat electrostatic interactions both at a Debye-Hückel (DH, or `implicit' ions, i.e., …
Integral membrane proteins deform the surrounding bilayer creating long-ranged forces that influence distant proteins. These forces can be attractive or repulsive, depending on the proteins' shape, height, contact angle with the bilayer, as well as the local membrane curvature. Although interaction energies are not pairwise additive, for sufficiently low protein density, thermodynamic properties depend only upon pair interactions. Here, we compute pair interaction potentials and entropic contributions to the two-dimensional osmotic pressure of a collection of noncircular proteins. In contrast …
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic interactions and membrane curvature. Though the lateral diffusion rates of lipids on membrane of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain undetermined. Here we propose an …
Ethanol is a common protein crystallization agent, precipitant, and denaturant, but also alters the dielectric properties of solutions. While ethanol-induced unfolding is largely ascribed to its hydrophobic parts, its effect on protein phase separation and inter-protein interactions remains poorly understood. Here, the effects of ethanol and NaCl on the phase behavior and interactions of protein solutions are studied in terms of the metastable liquid-liquid phase separation (LLPS) and the second virial coefficient $B_2$ using lysozyme solutions. Determination of the phase diagrams shows that t…
Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment -- most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments…
Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-…
Deciphering Molecular Charge Anisotropy: the Case of Antibody Solutions
Lund University（隆德大学）；Sapienza University of Rome（罗马第一大学）；LINXS Institute of Advanced Neutron and X-ray Science, Lund University（隆德大学 LINXS 先进中子与X射线科学研究所）；CNR Institute of Complex Systems, Uos Sapienza（意大利国家研究委员会复杂系统研究所（萨皮恩扎分部））
We report on a joint experimental-theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series o…
We study the adsorption of charged patchy particle models (CPPMs) on a thin film of a like-charged and dense polyelectrolyte (PE) brush (of 50 monomers per chain) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined one-, and two-patched spherical globules, each of the same net charge and (nanometer) size, with mono- and multipole moments comparable to those of small globular proteins. We focus on electrostatic effects on the adsorption far away from the isoelectric point of typical proteins, i.e., wher…
The structure of DNA Binding Proteins enables a strong interaction with their specific target site on DNA. However, recent single molecule experiment reported that proteins can diffuse on DNA. This suggests that the interactions between proteins and DNA play a role during the target search even far from the specific site. It is unclear how these non-specific interactions optimize the search process, and how the protein structure comes into play. Each nucleotide being negatively charged, one may think that the positive surface of DNA-BPs should electrostatically collapse onto DNA. Here we show …
RNA/protein interactions play crucial roles in controlling gene expression. They are becoming important targets for pharmaceutical applications. Due to RNA flexibility and to the strength of electrostatic interactions, standard docking methods are insufficient. We here present a computational method which allows studying the binding of RNA molecules and charged peptides with atomistic, explicit-solvent molecular dynamics. In our method, a suitable estimate of the electrostatic interaction is used as an order parameter (collective variable) which is then accelerated using bi-directional pulling…
Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model …
Lund University（隆德大学）；University of Copenhagen（哥本哈根大学）；CNR Institute of Complex Systems, Uos Sapienza（意大利国家研究委员会复杂系统研究所，萨皮恩扎小组）；Department of Physics, Sapienza University of Rome（罗马萨皮恩扎大学物理系）；Institute of Theoretical Physics, Faculty of Physics, University of Warsaw（华沙大学物理学院理论物理研究所）；Institute of Physical Chemistry, Polish Academy of Sciences（波兰科学院物理化学研究所）；LINXS Institute of Advanced Neutron and X-ray Science, Lund University（隆德大学LINXS高级中子和X射线科学研究所）
The equilibrium phase behavior of a binary mixture of charged colloids and neutral, non-adsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with non-additive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter -- the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion …
We investigate the thermodynamics of complexation of functionalized charged nano-spheres with viral proteins. The physics of this problem is governed by electrostatic interaction between the proteins and the nano-sphere cores (screened by salt ions), but also by configurational degrees of freedom of the charged protein N-tails. We approach the problem by constructing an appropriate complexation free energy functional. On the basis of both numerical and analytical studies of this functional we construct the phase diagram for the assembly which contains the information on the assembled structure…
We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a ``sticky'' Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a …
A statistical theory is presented of the magnesium ion interacting with lysozyme under conditions where the latter is positively charged. Temporarily assuming magnesium is not noncovalently bound to the protein, I solve the nonlinear Poisson-Boltzmann equation accurately and uniformly in a perturbative fashion. The resulting expression for the effective charge, which is larger than nominal owing to overshooting, is subtle and cannot be asymptotically expanded at high ionic strengths that are practical. An adhesive potential taken from earlier work together with the assumption of possibly bound…
The molecular arrangement of lipids and proteins within biomembranes and monolayers gives rise to complex film morphologies as well as regions of distinct electrical surface potential, topographical and electrostatic nanoscale domains. To probe these nanodomains in soft matter is a challenging task both experimentally and theoretically. This work addresses the effects of cholesterol, lipid composition, lipid charge, and lipid phase on the monolayer structure and the electrical surface potential distribution. Atomic Force Microscopy (AFM) was used to resolve topographical nanodomains and Kelvin…
