We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1=N! to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S = − Σ(i)p(i) ln pi − lnN!, where pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed.

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 by means of Monte Carlo simulations and analytical calculations that a counter-intuitive repulsion between the two oppositely charged macromolecules exists at a nanometer range. We also show that this repulsion is due to a local increase of the osmotic pressure exerted by the ions which are trapped at the interface. For the concave shape of DNA-BPs, and for realistic protein charge densities, we find that the repulsion pushes the protein in a free energy minimum at a distance from DNA. As a consequence, a favorable path exists along which proteins can slide without interacting with the DNA bases. When a protein encounters its target, the osmotic barrier is completely counter-balanced by the H-bond interaction, thus enabling the sequence recognition.DNA stores the genetic material of all living cells and viruses. This huge amount of information is effective only if DNA binding proteins (DNA-BPs) manipulates DNA in very specific locations. When the protein finds its DNA target, the shape complementarity of DNA Binding Proteins and their specific DNA sequence enables to maximize the number of hydrogen bonds, thus leading to a strong protein-DNA association [1,2,3,4,5,6]. The rate of protein-DNA association is however not controlled by the association step itself, but by the whole searching process. It is well established now that DNA-BPs diffuse along DNA before they reach their specific site [7]. During this search, the only interactions between protein and DNA which can play a role are non sequence-specific. Those non-specific interactions between protein and DNA remain poorly documented. Altough the predominance of electrostatics is unquestionable [1,2,3,4,5,6], it remains unclear how the protein structure comes into play [5,6,7]. Does the typical concavity of DNA-BPs which favors the specific association also influence the non-specific electrostatic interaction? In DNA-protein complexes, the mean charge of the protein residues located at the interface is positive [1,2]. Nevertheless, structural studies of non-specific complexes have shown that the protein atoms and the DNA atoms are weakly packed together at the interface [1,2,3,5,6], thus suggesting that a force counterbalances the electrostatic attraction. In this letter, our purpose is to establish the general mechanisms that control the mean force between protein and DNA and that are applicable to a wide variety of DNA-BPs. That goal in mind, we design coarse-grained D...

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We investigate the effective interaction mediated by salt ions between charged nanoparticles (NPs) and DNA. DNA is modeled as an infinite cylinder with a constant surface charge in an implicit solvent. Monte Carlo simulations are used to compute the free energy of the system described in the framework of the primitive model of electrolytes, which accounts for excluded volumes of salt ions. A mean-field Poisson-Boltzmann theory also allows us to compute the free energy and provides us with explicit formulae for its main characteristics (position and depth of the minimum). We intend here to identify the physical parameters that have a major impact on the NP-DNA interaction, in an attempt to evaluate physico-chemical properties which could play a role in genotoxicity or, which could be exploited for therapeutic use. Thus, we investigate the influence on the effective interaction of: the shape of the nanoparticle, the magnitude of the nanoparticle charge and its distribution, the value of the pH of the solution, the magnitude of Van der Waals interactions depending on the nature of the constitutive material of the NP (metal vs. dielectric). We show that for positively charged concave NPs the effective interaction is repulsive at short distance, so that it presents a minimum at distance from the DNA. This short-range repulsion is specific to indented particles and is a robust property that holds for a large range of materials and charge densities.