Matteo Salvalaglio

Uncovering molecular details of urea crystal growth in the presence of additives

Controlling the shape of crystals is of great practical relevance in fields like pharmacology and fine chemistry. Here we examine the paradigmatic case of urea which is known to crystallize from water with a needle-like morphology. To prevent this undesired effect, inhibitors that selectively favor or discourage the growth of specific crystal faces can be used. In urea the most relevant faces are the {001} and the {110} which are known to grow fast and slow, respectively. The relevant growth speed difference between these two crystal faces is responsible for the needle-like structure of crystals grown in water solution. To prevent this effect, additives are used to slow down the growth of one face relative to another, thus controlling the shape of the crystal. We study the growth of fast {001} and slow {110} faces in water solution and the effect of shape controlling inhibitors like biuret. Extensive sampling through molecular dynamics simulations provides a microscopic picture of the growth mechanism and of the role of the additives. We find a continuous growth mechanism on the {001} face, while the slow growing {110} face evolves through a birth and spread process, in which the rate-determining step is the formation on the surface of a two-dimensional crystalline nucleus. On the {001} face, growth inhibitors like biuret compete with urea for the adsorption on surface lattice sites; on the {110} face instead additives cannot interact specifically with surface sites and play a marginal sterical hindrance of the crystal growth. The free energies of adsorption of additives and urea are evaluated with advanced simulation methods (well-tempered metadynamics) allowing a microscopic understanding of the selective effect of additives. Based on this case study, general principles for the understanding of the anisotropic growth of molecular crystals from solutions are laid out. Our work is a step toward a rational development of novel shape-affecting additives.

Assessing the reliability of the dynamics reconstructed from metadynamics

Sampling a molecular process characterized by an activation free energy significantly larger than kBT is a well-known challenge in molecular dynamics simulations. In a recent work [Tiwary and Parrinello, Phys. Rev. Lett. 2013, 111, 230602], we have demonstrated that the transition times of activated molecular transformations can be computed from well-tempered metadynamics provided that no bias is deposited in the transition state region and that the set of collective variables chosen to enhance sampling does not display hysteresis. Ensuring though that these two criteria are met may not always be simple. Here we build on the fact that the times of escape from a long-lived metastable state obey Poisson statistics. This allows us to identify quantitative measures of trustworthiness of our calculation. We test our method on a few paradigmatic examples.

Determination of Energies and Sites of Binding of PFOA and PFOS to Human Serum Albumin

Structure and energies of the binding sites of perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) to human serum albumin (HSA) were determined through molecular modeling. The calculations consisted of a compound approach based on docking, followed by molecular dynamics simulations and by the estimation of the free binding energies adopting WHAM-umbrella sampling and semiempirical methodologies. The binding sites so determined are common either to known HSA fatty acids sites or to other HSA sites known to bind to pharmaceutical compounds such as warfarin, thyroxine, indole, and benzodiazepin. Among the PFOA binding sites, five have interaction energies in excess of -6 kcal/mol, which become nine for PFOS. The calculated binding free energy of PFOA to the Trp 214 binding site is the highest among the PFOA complexes, -8.0 kcal/mol, in good agreement with literature experimental data. The PFOS binding site with the highest energy, -8.8 kcal/mol, is located near the Trp 214 binding site, thus partially affecting its activity. The maximum number of ligands that can be bound to HSA is 9 for PFOA and 11 for PFOS. The calculated data were adopted to predict the level of complexation of HSA as a function of the concentration of PFOA and PFOS found in human blood for different levels of exposition. The analysis of the factors contributing to the complex binding energy permitted to outline a set of guidelines for the rational design of alternative fluorinated surfactants with a lower bioaccumulation potential.

Molecular-dynamics simulations of urea nucleation from aqueous solution

Significance Nucleation from solution is a ubiquitous process that plays important roles in physics, chemistry, engineering, and material science. Despite its importance, nucleation is far from being completely understood. In this work, we combine advanced molecular-dynamics simulation techniques and theory to provide a description of urea nucleation from aqueous solution. In particular, our analysis shows that a two-step nucleation mechanism is favorable and that two polymorphs are seen to compete in the early stages of the nucleation process. In our analysis, we have derived and validated a theoretical correction to finite-size effects to compute free-energy profiles in the limit of a macroscopic system at constant supersaturation. Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

Controlling and Predicting Crystal Shapes: The Case of Urea

Understanding crystal growth from solution is crucial to control the evolution of crystal morphologies. Experiments, molecular simulations, and theory were combined to examine the morphology of urea crystals grown in different solutions. To get a rational representation of all the possible habits a shape diagram (see picture) is introduced in which the habit dependence on the relative growth rates is illustrated.

Diffusion and Aggregation of Sodium Fluorescein in Aqueous Solutions

The diffusion and aggregation of sodium fluorescein in aqueous solutions was investigated adopting density functional theory (DFT) and molecular dynamics (MD) simulations. First, DFT calculations in implicit water were used to determine minimum energy structure and atomic charges of the solute, which were then used as input for explicit water MD simulations. The self-diffusion coefficient of sodium fluorescein was calculated using the Einstein equation, computing the mean square displacement from 24 ns trajectories. The calculated diffusion coefficient, 0.42 · 10(-5) cm(2) s(-1), is in good agreement with literature experimental data. The simulations confirmed the tendency of fluorescein to form dimers. In order to achieve a deeper understanding of aggregation phenomena, the dimer geometry was investigated through DFT calculations both in vacuo and in implicit water using different functionals and solvation theories. The results showed that dimerization does not occur in vacuo, as charge repulsion dominates, and that the minimum energy dimer structure is symmetric and stabilized by edge-to-face π-π interactions. The interaction energy was computed both at the DFT level and through MD simulations using Umbrella Sampling. The free interaction energy calculated with the WHAM and Umbrella Integration protocol, -1.3 kcal/mol, is in good agreement with experimental data, while the value determined using DFT calculations is significantly smaller and depends largely from the chosen functional and the computational methodology used to determine the solute-solvent boundary surface.

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.

Metadynamics studies of crystal nucleation

Crystallization processes are characterized by activated events, thus the application of enhanced sampling techniques such as metadynamics in order to study phenomena occurring at the molecular scale through molecular modelling. This paper provides an introduction to metadynamics and an overview of its applications in the context of crystal nucleation.

Experimental and Theoretical Investigation of Effect of Spacer Arm and Support Matrix of Synthetic Affinity Chromatographic Materials for the Purification of Monoclonal Antibodies

The aim of this study was to elucidate the influence of each material component-the support, the spacer, and the surface chemistry-on the overall material performance of an affinity type purification media for the capture of immunoglobulin G (IgG). Material properties were investigated in terms of an experimental evaluation using affinity chromatography as well as computer modeling. The biomimetic triazine-based A2P affinity ligand was chosen as a fixed point, while spacer and support were varied. The investigated spacers were 1-2-diaminoethane (2LP), 1,3-propanedithiol (SS3), 3,6-dioxo-1,8-octanedithiol (DES), and a 1,4-substituted [1,2,3]-triazole spacer (TRZ). The support media considered were the agarose (AG) resins, PuraBead, the polyvinylether, Fractoprep, the polymethacrylate, Fractogel, and the porous silica, Fractosil. All materials were tested with pure IgG standard solution, with a mock feed solution as well as real cell culture supernatant. The interaction between IgG and A2P linked through the investigated spacers to AG was studied using molecular dynamics. The effect of a modification of the support chemical structure or of the protein-ligand binding site on the material performances was studied through target oriented simulations. Dynamic binding experiments (DBC) revealed that the performances of materials containing 2LP spacers were significantly decreased in the presence of Pluronic F68. The simulations indicated that this is probably determined by the establishment of intermolecular interactions between the 2LP charged amino group and the ether oxygen of Pluronic F68. The spacer giving the highest IgG dynamic binding capacity when Pluronic F68 was present in the feed was TRZ. The simulations showed that, among the investigated spacers, TRZ is the only one that prevents the adsorption of A2P on the support surface, thus suggesting that the mobility and lack of interaction of the ligand with the support is an important property for an affinity material. Both experiments and calculations agree that the chemistry of the support surface can have a significant impact on IgG binding, either affecting the IgG DBC, as found experimentally for materials having similar ligand densities and spacer arms but different supports, or competing with the affinity ligand when hydrophobic groups are added to the model surface, as was computationally predicted.

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.