The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson-Boltzmann equation, which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments.PACS numbers: 61.20. Qg,82.65.Dp,82.60.Lf The interaction between charged objects (interfaces, colloidal particles, membranes, etc) in solution is strongly affected by the presence of an electrolyte (salt) and is of great importance in biological systems and industrial applications [1,2]. The main effect is screening of the Coulomb interaction characterized by the so-called Debye-Hückel screening length [3], which depends on the ionic strength of the solution. The Deryaguin-LandauVerwey-Overbeek theory, based on the competition between screened Coulomb and attractive van der Waals interactions, has been very successful in explaining the stabilization of charged colloidal particles [4].One of the most widely used analytical method to describe electrolyte solutions is the Poisson-Boltzmann (PB) approach [5]. For low electrostatic potentials (less than 25 mV), the PB equation can be linearized and yields the Debye-Hückel theory [3]. The PB is a continuum mean-field like approach assuming point-like ions in thermodynamic equilibrium and neglecting statistical correlations. This theory has been successful in predicting ionic profiles close to planar and curved surfaces and the resulting forces. However, it is known to strongly overestimate ionic concentrations close to charged surfaces. In particular, this shortcoming of the PB theory is pronounced for highly charged surfaces and multivalent ions.Since the PB equation does not take into account the finite size of the adsorbing ions, the ionic concentration close to the surface can easily exceed the maximal allowed coverage by orders of magnitude. Several attempts have been proposed to include the steric repulsion in order to improve upon the PB approach [6,7]. One of the first attempts to incorporate steric effects is the Stern layer modification [6,8] of the PB approach. Steric effects are introduced by excluding the ions from the first molecular layer close to the surface. However, it seems difficult to improve on this method in a systematic way. More recent modifications [6,7,[9][10][11] rely either on Monte Carlo computer simulations or on numerical solutions of integral equations (the "hypernetted chain" equation [9]). These approaches involve elaborate numerical calculations and lack the simplicity of the original PB approach.In this Letter, we propose a simple way to include steric effects in the original PB approach. This modified PB equation clearly shows how ionic saturation takes place close to a charged surface. The equation is derived for 1:z asymmetric and z:z symmetric...

BackgroundThe Critical Assessment of Functional Annotation (CAFA) is an ongoing, global, community-driven effort to evaluate and improve the computational annotation of protein function.ResultsHere, we report on the results of the third CAFA challenge, CAFA3, that featured an expanded analysis over the previous CAFA rounds, both in terms of volume of data analyzed and the types of analysis performed. In a novel and major new development, computational predictions and assessment goals drove some of the experimental assays, resulting in new functional annotations for more than 1000 genes. Specifically, we performed experimental whole-genome mutation screening in Candida albicans and Pseudomonas aureginosa genomes, which provided us with genome-wide experimental data for genes associated with biofilm formation and motility. We further performed targeted assays on selected genes in Drosophila melanogaster, which we suspected of being involved in long-term memory.ConclusionWe conclude that while predictions of the molecular function and biological process annotations have slightly improved over time, those of the cellular component have not. Term-centric prediction of experimental annotations remains equally challenging; although the performance of the top methods is significantly better than the expectations set by baseline methods in C. albicans and D. melanogaster, it leaves considerable room and need for improvement. Finally, we report that the CAFA community now involves a broad range of participants with expertise in bioinformatics, biological experimentation, biocuration, and bio-ontologies, working together to improve functional annotation, computational function prediction, and our ability to manage big data in the era of large experimental screens.

The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson-Boltzmann equation which takes into account the volume excluded by the ions in addition to the electrostatic interactions is presented. In a formal lattice gas formalism the modified Poisson-Boltzmann equation can be obtained from a mean-field approximation of the partition function. In an alternative phenomenological approach, the same equation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of the steric repulsion, a simple case of a single, highly charged, flat surface is discussed. This situation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is expressed in terms of the surface charge density and the size of the ions. It is shown that when these effects are important a saturated layer is formed near the surface. A modified Grahame equation relating the ion concentration at the surface to the surface charge density is obtained.

Adsorption of charged polymers (polyelectrolytes) from a semi-dilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer Γ adsorbed to the surface and (ii)

The interaction between spherical particles covered with end-grafted polymers (brushes) immersed in a polymer melt is studied theoretically. It has been known for some time that two densely grafted brushes may attract each other in the presence of a chemically identical polymer melt. In this study we show that this attraction can be eliminated by choosing the melt material to be such that the Flory interaction parameter of the melt chains with the grafted ones is negative (χ < 0). This effect is accompanied by a change in the structure of the brush from a dry brush, where the melt chains do not penetrate deeply into the brush, to a wet brush, where the melt chains penetrate the brush and force the grafted chains to extend into the melt. Scaling arguments are used to describe how the structure of a single brush depends on the Flory interaction parameter, the grafting density, and the indices of polymerization of the grafted and free chains. The density profiles and the interactions between the particles are calculated by solving numerically the self-consistent field equations of the system within the Derjaguin approximation. The effect of van der Waals interactions between brushes is studied by taking into account the particle-brush contrast as well as that of the brush-melt interfaces.