Effect of hydrogen bond networks on the nucleation mechanism of protein folding

A novel approach to the theory of homogeneous and heterogeneous nucleation

A new approach to the theory of nucleation, formulated relatively recently by Ruckenstein, Narsimhan, and Nowakowski (see Refs. [7-16]) and developed further by Ruckenstein and other colleagues, is presented. In contrast to the classical nucleation theory, which is based on calculating the free energy of formation of a cluster of the new phase as a function of its size on the basis of macroscopic thermodynamics, the proposed theory uses the kinetic theory of fluids to calculate the condensation (W(+)) and dissociation (W(-)) rates on and from the surface of the cluster, respectively. The dissociation rate of a monomer from a cluster is evaluated from the average time spent by a surface monomer in the potential well as obtained from the solution of the Fokker-Planck equation in the phase space of position and momentum for liquid-to-solid transition and the phase space of energy for vapor-to-liquid transition. The condensation rates are calculated using traditional expressions. The knowledge of those two rates allows one to calculate the size of the critical cluster from the equality W(+)=W(-) as well as the rate of nucleation. The developed microscopic approach allows one to avoid the controversial application of classical thermodynamics to the description of nuclei which contain a few molecules. The new theory was applied to a number of cases, such as the liquid-to-solid and vapor-to-liquid phase transitions, binary nucleation, heterogeneous nucleation, nucleation on soluble particles and protein folding. The theory predicts higher nucleation rates at high saturation ratios (small critical clusters) than the classical nucleation theory for both solid-to-liquid as well as vapor-to-liquid transitions. As expected, at low saturation ratios for which the size of the critical cluster is large, the results of the new theory are consistent with those of the classical one. The present approach was combined with the density functional theory to account for the density profile in the cluster. This approach was also applied to protein folding, viewed as the evolution of a cluster of native residues of spherical shape within a protein molecule, which could explain protein folding/unfolding and their dependence on temperature.

Invited review: Caseins and the casein micelle: their biological functions, structures, and behavior in foods

A typical casein micelle contains thousands of casein molecules, most of which form thermodynamically stable complexes with nanoclusters of amorphous calcium phosphate. Like many other unfolded proteins, caseins have an actual or potential tendency to assemble into toxic amyloid fibrils, particularly at the high concentrations found in milk. Fibrils do not form in milk because an alternative aggregation pathway is followed that results in formation of the casein micelle. As a result of forming micelles, nutritious milk can be secreted and stored without causing either pathological calcification or amyloidosis of the mother's mammary tissue. The ability to sequester nanoclusters of amorphous calcium phosphate in a stable complex is not unique to caseins. It has been demonstrated using a number of noncasein secreted phosphoproteins and may be of general physiological importance in preventing calcification of other biofluids and soft tissues. Thus, competent noncasein phosphoproteins have similar patterns of phosphorylation and the same type of flexible, unfolded conformation as caseins. The ability to suppress amyloid fibril formation by forming an alternative amorphous aggregate is also not unique to caseins and underlies the action of molecular chaperones such as the small heat-shock proteins. The open structure of the protein matrix of casein micelles is fragile and easily perturbed by changes in its environment. Perturbations can cause the polypeptide chains to segregate into regions of greater and lesser density. As a result, the reliable determination of the native structure of casein micelles continues to be extremely challenging. The biological functions of caseins, such as their chaperone activity, are determined by their composition and flexible conformation and by how the casein polypeptide chains interact with each other. These same properties determine how caseins behave in the manufacture of many dairy products and how they can be used as functional ingredients in other foods.

A probabilistic approach to the effect of water hydrogen bonds on the kinetics of protein folding and protein denaturation

Previously, we presented a review of our kinetic models for the nucleation mechanism of protein folding and for the protein thermal denaturation in a barrierless way. A protein was treated as a random heteropolymer consisting of hydrophobic, hydrophilic, and neutral beads. As a crucial idea of the model, an overall potential around the cluster of native residues wherein a residue performs a chaotic motion was considered as the combination of the average dihedral, effective pairwise, and confining potentials. The overall potential as a function of the distance from the cluster has a double well shape. This allowed one to develop kinetic models for the nucleation mechanism of protein folding (NMPF) and barrierless protein denaturation (BPD) by using the mean first passage time analysis. In the original models, however, hydrogen bonding effects were taken into account only indirectly which affected the accuracy of the models because hydrogen bonding does play a crucial role in the folding, stability, and denaturation of proteins. To improve the NMPF and BPD models and explicitly take into account the hydrogen bonding "water-water" and "water-protein residue", we have developed a probabilistic hydrogen bond (PHB) model for the effect of hydrogen bond networks of water molecules around two solute particles (immersed in water) on their interaction, and have then combined the PHB model with the NMPF and BPD models. In this paper, that can be regarded as sequel of our previous review, we analyze the modified NMPF and BPD models that explicitly take into account the effect of water-water hydrogen bonding on these processes. As expected, the application of the modified models to the folding/unfolding of two model proteins (one short, consisting of 124 residues and the other large, consisting of 2500 residues) demonstrate that the hydrogen bond networks play a very important role in the protein folding/unfolding phenomena.