Andrey Shiryayev

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.

Crystal nucleation for a model of globular proteins

A continuum model of globular proteins proposed by Talanquer and Oxtoby [J. Chem. Phys. 109, 223 (1998)] is investigated numerically, with particular emphasis on the region near the metastable fluid-fluid coexistence curve. Classical nucleation theory is shown to be invalid not only in the vicinity of the metastable critical point but also close to the liquidus line. An approximate analytic solution is also presented for the shape and properties of the nucleating crystal droplet.

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.

Simple model of sickle hemogloblin

A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A solution of this model, however, requires accurate estimates of the interaction parameters which are currently unavailable. Therefore, as a first step toward a molecular understanding of the nucleation mechanisms in sickle hemoglobin, a Monte Carlo simulation of a simplified two patch model is carried out. A gradual transition from monomers to one dimensional chains is observed as one varies the density of molecules at fixed temperature, somewhat similar to the transition from monomers to polymer fibers in sickle hemoglobin molecules in solution. An observed competition between chain formation and crystallization for the model is also discussed. The results of the simulation of the equation of state are shown to be in excellent agreement with a theory for a model of globular proteins, for the case of two interacting sites.

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.

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.