Editorial overview: Folding and binding: In silico, in vitro and in cellula

The essence of any biological processes relies on the conformational states of macromolecules and their interactions. It comes therefore with no surprises that the study of folding and binding has been centre stage since the birth of structural biology. In this context, the collaborative efforts of experimen- talists and theoreticians have tremendously increased our current knowl- edge on macromolecular structure and recognition. Nevertheless, several challenges and open questions are still present and a multidisciplinary approach would appear the most appropriate means to shed light onto the mechanisms of folding and binding to the highest level of detail. This thematic issue brings together a collection of reviews describing our current understanding of folding and binding, looking at these fundamental pro- blems from a wide perspective ranging from the single molecule to the complexity of the living cell, drawing on approaches that span from compu- tational (in silico), to the test tube (in vitro) and cell cultures (in cellula)

Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas

We consider the development of Monte Carlo schemes for molecules with Coulomb interactions. We generalize the classic algorithms of Bird and Nanbu-Babovsky for rarefied gas dynamics to the Coulomb case thanks to the approximation introduced by Bobylev and Nanbu (Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation, Physical Review E, Vol. 61, 2000). Thus, instead of considering the original Boltzmann collision operator, the schemes are constructed through the use of an approximated Boltzmann operator. With the above choice larger time steps are possible in simulations; moreover the expensive acceptance-rejection procedure for collisions is avoided and every particle collides. Error analysis and comparisons with the original Bobylev-Nanbu (BN) scheme are performed. The numerical results show agreement with the theoretical convergence rate of the approximated Boltzmann operator and the better performance of Bird-type schemes with respect to the original scheme

Global existence, singular solutions, and ill-posedness for the Muskat problem

The Muskat, or Muskat--Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher viscosity fluid expands into the lower viscosity fluid, we show global in time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher viscosity fluid contracts, we construct singular solutions that start off with smooth initial data, but develop a point of infinite curvature at finite time