Self-consistent field approach to protein structure and stability

The organization of the thesis is as follows: after a short introduction (chapter 1), chapter 2 presents a review of the basic physical principle that govern protein structure and focuses on the thermodynamics as well as kinetics of protein folding and ufolding. Then chapter 3 starts with a discussion on the basic elementary interactions, which contribute, to protein structure and stability, with emphasis on the electrostatic interactions.

Electrostatic interactions are described on the basis of novel approach, which uses the idea of a self-consistent field adapted from statistical mechanics. Properties such as titration curves, protein stability and pKa shifts are discussed. The main conclusions are: firstly, the calculated results are in excellent agreement with the experimental data, when the solution of Poisson-Boltzmann equation (PB) is based on the assumption that the ionized residues are seen as part of the high dielectric medium (rather than the interior of the protein molecule); Secondly, the solution of PB equation outside the protein interior, depends on local characteristics, such as the packing of chain portions around ionized residues, rather than on the detailed shape of the protein molecule. Lastly, at "natural-like" conditions the contribution of electrostatic interactions to the free energy difference between the unfolded and folded states of protein molecules is closed to zero. This indicates that the main driving forces for folding of protein molecules under these conditions are hydrophobic and backbone-backbone hydrogen bonding interactions.

Chapter 4 concern the application of the theory of electrostatic interactions to the calculation of the pKa's of the 98 residue b-elicitin protein, cryptogein. Unusual in this protein is the existence of four ionized groups buried in the hydrophobic core. The NMR structure of the 98 residue b-elicitin, cryptogein was determined using and labelled protein samples. Calculation of theoretical pKa's show general agreement with experimentally determined values and is similar for both thecrystal and solution structures.

In chapter 5 the topological requirement for nucleus formation of a two-state folding reaction is considered. The self-consistent field approach is used to calculate the free energy of the folding nucleus and to approximate the description of the elementary long-range interactions such as hydrogen-bonding, electrostatic and hydrophobic interactions. The local interactions between residues, which are close in sequence - as in the a-, b- or loop regions- are accounted for in an explicit form based on experimental parameters. A theoretical model for the folding of two-state small monomeric proteins is proposed. The folding problem is reduced to the question of how the folding nucleus in the transition state (TS) is formed from the ensemble of rapidly interconverting, partly structured conformations in the denatured state.

It is proposed that in the denatured state the folding is energetically favored by certain highly fluctuating nucleation regions (aa b- hairpins). In experiments based on site directed mutagenesis these nucleation regions are revealed by their high F-values. In the TS folding is favored by the packing of these nucleation regions together with other portions of the polypeptide chain thus leading to a broad distribution of the F-values. As a result, the folding nucleus with native-like topology and approximately correctly formed secondary structures and loops is favored over other folding nuclei.

In chapter 6 a discussion of the problem of protein fold recognition of small monomeric proteins with less than 80 residues is presented. The fold recognition strategy is based on the fact that: firstly, at the transition state level all possible protein conformations can be split out into different ensembles of similar structures. The crude characteristics of these ensembles can be described by the limited set of thermodynamically most favorable protein folds; secondly, the folding nucleus with native-like overall fold is separated from all other folding alternatives by a high free energy barrier. As a result, at the lowest free energy minimum of the TS state the protein molecules propagates toward its native state approximately isoenergetically through an ensemble of conformations of its native fold. The main contributions, which stabilize the protein folds at the TS level, are the hydrophobic and long-range backbone hydrogen bonding interactions, as well as the free energy of chain bending, and free energies of secondary structures formation.

The selection of the protein architectures is mainly determined by the most general characteristics encoded in the protein sequence, such as distribution of hydrophobic and hydrophilic residues along the chain, the ability of amino acids to form different secondary structures in compact chain conformations by hydrogen bonding with their spatial or chain neighbours, and the general rules which govern the packing of the secondary structures. At the TS, the free energies of the native folds are separated by a 'gap' from the lowest free energies of the folds from structurally different packing patterns. However, the difference between the free energies of the native folds and the lowest free energies of the folds from the same packing pattern is rather small. The thesis is concluded with a summary in English, Dutch and Bulgarian.