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We present a simple yet accurate numerical approach to compute the free energy of binding of multivalent objects on a receptor-coated surface. The method correctly accounts for the fact that one ligand can bind to at most one receptor. The numerical approach is based on a saddle-point approximation to the computation of a complex residue. We compare our theory with the powerful Valence-Limited InteractionTheory (VLIT) [P. Varilly et al., J. Chem. Phys. 137, 094108 (2012); S. Angioletti-Uberti et al., ibid. 138, 021102 (2013)] and find excellent agreement in the regime where that theory is expected to work. However, the present approach even works for low receptor/ligand densities, where VLIT breaks down. [ABSTRACT FROM AUTHOR]

As a result of rapid developments in biotechnology, there has been an explosive growth in the number of proteins that can he isolated. However, the determination of the three-dimensional structures [...], Numerical simulations of homogeneous crystal nucleation with a model for globular proteins with short-range attractive interactions showed that the presence of a metastable fluid-fluid critical point drastically changes the pathway for the formation of a crystal nucleus. Close to this critical point, the free-energy barrier for crystal nucleation is strongly reduced and hence, the crystal nucleation rate increases by many orders of magnitude. Because the location of the metastable critical point can be controlled by changing the composition of the solvent, the present work suggests a systematic approach to promote protein crystallization.

We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations, we compute the structural properties of this model as a function of density. We compare the results of our simulations with the structural data obtained in the corresponding non-equilibrium model of Corté et al. [Nat. Phys. 4, 420 (2008)]. We find that the structural properties of the non-equilibrium model are very different from those of the equilibrium model, even though the two models have exactly the same set of accessible states. This observation shows that the dynamical protocol does not sample all quiescent states with equal probability. In particular, we find that, whilst quiescent states prepared in a non-equilibrium protocol can be hyperuniform [see D. Hexner and D. Levine, Phys. Rev. Lett. 114, 110602 (2015); E. Tjhung and L. Berthier, Phys. Rev. Lett. 114, 148301 (2015); and J. H. Weijs et al., Phys. Rev. Lett. 115, 108301 (2015)], ergodic sampling never leads to hyperuniformity. In addition, we observe ordering phase transitions and a percolation transition in the equilibrium model that do not show up in the non-equilibrium model. Conversely, the quiescent-to-diffusive transition in the dynamical model does not correspond to a phase transition, nor a percolation transition, in the equilibrium model. [ABSTRACT FROM AUTHOR]

We use a coarse-grained model for generic proteins to investigate the formation of structures with P212121 symmetry, the most prevalent space group of protein crystals. To account for the string directionality of protein-protein interactions that has been suggested by previous studies, we represent proteins as spherical particles that are covered by a large number of small, attractive "patches" that are randomly distributed on the protein surface. Attractive interactions between two proteins can then involve several pairs of patches interacting simultaneously. Our results suggest that the unit cell with the lowest energy is not necessarily the one that grows fastest. Rather, growth is favoured if 1) newparticles can attach with enough bonds to the growth front and 2) particles that attach in crystallographically in equivalent positions bind to the surface with similar strength. We subsequently study the impact of interactions that are not part of crystalline contacts and find that when these non-specific interactions are few and weaker than the crystal contacts, both nucleation and growth are successful. If the proportion of non-specific interactions is increased, crystal growth is still possible in a small range of model temperature. [ABSTRACT FROM AUTHOR]

A coarse-grained simulation method to predict nuclear magnetic resonance (NMR) spectra of ions diffusing in porous carbons is proposed. The coarse-grained model uses input from molecular dynamics simulations such as the free-energy profile for ionic adsorption, and density-functional theory calculations are used to predict the NMR chemical shift of the diffusing ions. The approach is used to compute NMR spectra of ions in slit pores with pore widths ranging from 2 to 10 nm. As diffusion inside pores is fast, the NMR spectrum of an ion trapped in a single mesopore will be a sharp peak with a pore size dependent chemical shift. To account for the experimentally observed NMR line shapes, our simulations must model the relatively slow exchange between different pores. We show that the computed NMR line shapes depend on both the pore size distribution and the spatial arrangement of the pores. The technique presented in this work provides a tool to extract information about the spatial distribution of pore sizes from NMR spectra. Such information is difficult to obtain from other characterisation techniques. [ABSTRACT FROM AUTHOR]