A variational approach to assess reaction coordinates for two-step crystallization.

Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavor, determining nucleation mechanisms and rates for phase separation requires an appropriately defined reaction coordinate to describe the transformation of an out-of-equilibrium parent phase for which myriad options are available to the simulator. In this article, we describe the application of the variational approach to Markov processes to quantify the suitability of reaction coordinates to study crystallization from supersaturated colloid suspensions. Our analysis indicates that collective variables (CVs) that correlate with the number of particles in the condensed phase, the system potential energy, and approximate configurational entropy often feature as the most appropriate order parameters to quantitatively describe the crystallization process. We apply time-lagged independent component analysis to reduce high-dimensional reaction coordinates constructed from these CVs to build Markov State Models (MSMs), which indicate that two barriers separate a supersaturated fluid phase from crystals in the simulated environment. The MSMs provide consistent estimates for crystal nucleation rates, regardless of the dimensionality of the order parameter space adopted; however, the two-step mechanism is only consistently evident from spectral clustering of the MSMs in higher dimensions. As the method is general and easily transferable, the variational approach we adopt could provide a useful framework to study controls for crystal nucleation.

Molecular dynamics simulations of solutions at constant chemical potential.

Molecular dynamics studies of chemical processes in solution are of great value in a wide spectrum of applications, which range from nano-technology to pharmaceutical chemistry. However, these calculations are affected by severe finite-size effects, such as the solution being depleted as the chemical process proceeds, which influence the outcome of the simulations. To overcome these limitations, one must allow the system to exchange molecules with a macroscopic reservoir, thus sampling a grand-canonical ensemble. Despite the fact that different remedies have been proposed, this still represents a key challenge in molecular simulations. In the present work, we propose the Constant Chemical Potential Molecular Dynamics (CµMD) method, which introduces an external force that controls the environment of the chemical process of interest. This external force, drawing molecules from a finite reservoir, maintains the chemical potential constant in the region where the process takes place. We have applied the CµMD method to the paradigmatic case of urea crystallization in aqueous solution. As a result, we have been able to study crystal growth dynamics under constant supersaturation conditions and to extract growth rates and free-energy barriers.

Structural characterization of a Protein A mimetic peptide dendrimer bound to human IgG.

Understanding the chemical physical properties of protein binding sites is at the basis of the rational design of protein ligands. The hinge region of the Fc fragment of immunoglobulin G is an important and well characterized protein binding site, known to interact with several natural proteins and synthetic ligands. Here, we report structural evidence that a Staphylococcus aureus Protein A mimetic peptide dendrimer, deduced by a combinatorial approach, binds close to the Cgamma2/Cgamma3 interface of the constant fragment of a human IgG1 molecule, partially hindering the Protein A binding site. The X-ray analysis evidenced a primary binding site located between a terminal Arg residue of the ligand peptidic arm and a hydrophobic protein site consisting of Val308, Leu309, and His310. A molecular dynamic analysis of the model derived from the X-ray structure showed that in water at room temperature the complex is further stabilized by the formation of at least one more contact between a terminal Arg residue of the second arm of the peptide and the carboxylic group of a protein amino acid, such as Glu318, Asp312, or Asp280. It appears thus that stability of the Fc-dendrimer complex is determined by the synergetic formation of multiple bonds of different nature between the dendrimer arms and the protein accessible sites. The electrostatic and van der Waals energies of the complex were monitored during the MD simulations and confirmed the energetic stability of the two interactions.