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 grid-based approaches alone. Here, we develop a treatment of both hydrodynamic and electrostatic interactions to include the presence of surfaces by modeling grid-based and long-range interactions. We describe its application to simulate the self-association and many-molecule adsorption of the well-characterized protein Hen Egg-White Lysozyme to mica-like and silica-like surfaces. We find that the computational model can recover a number of experimental observables of the adsorption process and provide insights into their determinants. The computational model is implemented in the Simulation of Diffusional Association (SDA) software package.
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…
In this paper, we propose a Generalized Langevin Equation (GLE)-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (non instantaneous) component modeled respectively through a Dirac delta function and a three-parameter Mittag-Leffler type function. By imposing a specific relationship between the parameters of the three-parameters Mittag-Leffler function, the different dynamical regimes, namely ballistic, subdiffusive and Brownian, as well as the crossover from one regime to another…
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 …
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…
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…
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 …
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…
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…
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…
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 lambd…
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…
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…
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…
Protein function and activity are a consequence of its three-dimensional structure. Single particle analysis of cryogenic electron micrographs has radically changed structural biology allowing atomic reconstruction of almost any type of proteins. While such an approach provides snapshots of three-dimensional structural information that can be correlated with function, the new frontier of protein structural biology is in the fourth dimension, time. Here we propose the use of liquid phase electron microscopy to expand structural biology into dynamic studies. We apply here single particle analysi…
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.
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…
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…
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…
Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex or the actin cytoskeleton is strongly determined by their spatial structure. Moreover it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positio…
Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years discoveries of many facets of the ubiquitous Brownian motion has revolutionized our fundamental understanding of the role of {\it thermal fluctuations} in the exotic structures and complex dynamics exhibited by soft matter like, for example, colloids, gels, etc. The domain of Brownian motion transcends the traditional disciplinary boundaries of physics and has become an area of …
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 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., …
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…
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-…
We describe a method to simulate the dynamics of charged colloidal particles suspended in a liquid containing dissociated ions and salt ions. Regimes of prime current interest are those of large volume fraction of colloids, highly charged particles and low salt concentrations. A description which is tractable under these conditions is obtained by treating the small dissociated and salt ions as continuous fields, while keeping the colloidal macroions as discrete particles. For each spatial configuration of the macroions, the electrostatic potential arising from all charges in the system is dete…
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…
Assemblies of allosteric proteins, nano-scale Brownian computers, are the principle information processing devices in biology. The troponin C-troponin I (TnC-TnI) complex, the Ca$^{2+}$-sensitive regulatory switch of the heart, is a paradigm for Brownian computation. TnC and TnI specialize in sensing (reading) and reporting (writing) tasks of computation. We have examined this complex using a newly developed phenomenological model of allostery. Nearest-neighbor-limited interactions among members of the assembly place previously unrecognized constrains the topology of the system's free energy l…
Small angle neutron scattering intensity distributions taken from cytochrome C and lysozyme protein solutions show a rising intensity at very small wave vector, Q, which can be interpreted in terms of the presence of a weak long-range attraction between protein molecules. This interaction has a range several times that of the diameter of the protein molecule, much greater than the range of the screened electrostatic repulsion. We show evidence that this long-range attraction is closely related to the type of anion present and ion concentration in the solution.
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）
Herein, we examined the dependence of protein adsorption on the nanoparticle surface in the presence of functional groups. Our UV-visible spectrophotometry, transmission electron microscopy, infrared spectroscopy and dynamic light scattering measurements evidently suggested that the functional groups play an important role in the formation of nanoparticle-protein corona. We found that uncoated and surfactant-free silver nanoparticles derived from a laser ablation process promoted a maximum protein (bovine serum albumin) coating due to increased changes in entropy. On the other hand, BSA displa…
The Kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers which can probe individual molecules, there has been an increasing interest in understanding the mechanisms by which motor proteins convert chemical energy into mechanical work. Here we present a mathematical model for the chemistry and three dimensional mechanics of the Kinesin motor protein which captures many of the force dependent features of the motor. For the elasticity of the tether tha…
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 …
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 …
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 …
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…
Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP alpha-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent smFRET experiments. We find that alpha-synuclein is disordered with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of cali…
We present a hybrid Brownian dynamics / Monte Carlo algorithm for simulating solutions of highly entangled semiflexible polymers or filaments. The algorithm combines a Brownian dynamics time-stepping approach with an efficient scheme for rejecting moves that cause chains to cross or that lead to excluded volume overlaps. The algorithm allows simulation of the limit of infinitely thin but uncrossable threads, and is suitable for simulating the conditions obtained in experiments on solutions of long actin protein filaments.
In the approach of biomolecules to a nanopore, it is essential to capture the effects of hydrodynamic anisotropy of the molecules and the near-wall hydrodynamic interactions which hinder their diffusion. We present a detailed theoretical analysis of the behaviour of a rod-like molecule attracted electrostatically by a charged nanopore. We first estimate the time scales corresponding to Brownian and electrostatic translations and reorientation. We find that Brownian motion becomes negligible at distances within the pore capture radius, and numerically determine the trajectories of the nano-rod …
Microtubules and motor proteins self organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by ATP-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield such larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-m…
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 …
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））
Absorption of radiation by solution is described by the solution dielectric constant and can be viewed as a specific application of the dielectric theory of solutions. For ideal solutions, the dielectric boundary value problem separates the polar response into the polarization of the void in the liquid created by the solute and the response of the solute dipole. In the case of a protein as a solute, its nuclear dynamics do not project on significant fluctuations of the dipole moment in the terahertz domain of frequencies and the protein dipole can be viewed as dynamically frozen. Absorption of…
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…
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 …
An increasing number of proteins with intrinsically disordered domains have been shown to phase separate in buffer to form liquid-like phases. These protein condensates serve as simple models for the investigation of the more complex membrane-less organelles in cells. To understand the function of such proteins in cells, the material properties of the condensates they form are important. However, these material properties are not well understood. Here, we develop a novel method based on optical traps to study the frequency-dependent rheology and the surface tension of PGL-3 condensates as a fu…
The dynamics of contact pair formation between various hydrophobic residues during folding of a model protein Hp-36 is investigated by Brownian dynamics simulation. Hydropathy scale and non-local helix propensity of amino acids are used to model the complex interaction potential. The resulting structure of the model protein mimics the native state of the real protein with a $RMSD$ of 4.5 Å. A contact pair distance time correlation function (CPCF), $C_{P}^{ij}(t)$, is introduced which shows multistage decay, including a {\it slow late stage dynamics} for a few specific pairs. {\it These pairs d…
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…
Control and transport of nanoscale objects in fluids is challenging because of the unfavorable scaling of most interaction mechanisms to small length scales. We design energy landscapes for nanoparticles by accurately shaping the geometry of a nanofluidic slit and exploiting the electrostatic interaction between like charged particles and walls. Directed transport is performed by combining asymmetric potentials with an oscillating electric field to achieve a rocking Brownian motor. Using 60\,nm diameter gold spheres, we investigate the physics of the motors with high spatio-temporal resolution…
