Daniel L. Pagan

Phase behavior of short-range square-well model

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that the fluid-fluid critical point is metastable for both cases, with the case lambda = 1.25 being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma(II)-crystallin.

Protein condensation : kinetic pathways to crystallization and disease

Preface 1. Introduction 2. Globular protein structure 3. Experimental methods 4. Thermodynamics and statistical mechanics 5. Protein-protein interactions 6. Theoretical studies of equilibrium 7. Nucleation theory 8. Experimental studies of nucleation 9. Lysozyme 10. Some other globular proteins 11. Membrane proteins 12. Crystallins and cataracts 13. Sickle hemoglobin and sickle cell anemia 14, Alzheimers disease Index.

Role of solvent for globular proteins in solution

The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square-well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In particular we find for appropriate choices of parameters upper critical points, lower critical points, and even closed loops with both upper and lower critical points similar to those found before [Macromolecules 36, 5843 (2003)]. In the general case of systems whose interactions are not attractive square wells, this mapping procedure can be a first approximation to understand the phase diagram in the presence of solvent. We also present simulation results for both the square-well model and a modified Lennard-Jones model.

A finite-size scaling study of a model of globular proteins.

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel [Science, 277, 1975 (1997)]. Using both mixed-field finite-size scaling and histogram-reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulations.

Simple model of membrane proteins including solvent.

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.

Phase diagram for a model of urate oxidase

Urate oxidase from Asperigillus flavus has been shown to be a model protein for studying the effects of polyethylene glycol (PEG) on the crystallization of large proteins. Extensive experimental studies based on small angle x-ray scattering [Vivares and Bonnete, J. Phys. Chem. B 108, 6498 (2004)] have determined the effects of salt, pH, temperature, and most importantly PEG on the crystallization of this protein. Recently, some aspects of the phase diagram have also been determined experimentally. In this paper, we use Monte Carlo techniques to predict the phase diagram for urate oxidase in solution with PEG, including the liquid-liquid and liquid-solid coexistence curves. The model used includes an electrostatic interaction, van der Waals attraction, and a polymer-induced depletion interaction [Vivares et al., Eur. Phys. J. E 9, 15 (2002)]. Results from the simulation are compared with experimental results.

Protein Condensation: Sickle hemoglobin and sickle cell anemia

Another important globular protein that has received significant experimental and theoretical investigation is sickle hemoglobin. The reason it has received so much attention is that it is related to sickle cell anemia. This disease results from the polymerization of sickle hemoglobin molecules via a complex two-step homogeneous/heterogeneous nucleation process to form fibers in solution. Although this non-equilibrium fiber state eventually will form a crystalline state, for all practical purposes it is a long-lived pseudo-equilibrium state. This polymerization of sickle hemoglobin molecules does not occur in globular proteins such as lysozyme or the γ-crystallins. Thus its crystal nucleation process differs from most known globular proteins. Sickle cell anemia is a genetic disorder that affects red blood cells, which become hard and pointed instead of soft and round. More than 70 000 residents of the USA have sickle cell anemia; about 250 000 babies are born with this disease each year worldwide. The genetic nature of the disease is that two genes for the sickle hemoglobin must be inherited in order to have the disease. If only one mutated gene is inherited and another gene is normal, the person has a so-called “sickle cell trait.” People who have this sickle cell trait will not develop the disease, but they can pass the sickle cell gene to their children.