Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

The periplasmic domain of the barrel assembly machinery protein A (BamA) from Escherichia coli assists folding of outer membrane protein A

The assembly of outer membranes of the cell wall of Gram-negative bacteria and of various organelles of eukaryotic cells requires the evolutionarily conserved β-barrel-assembly machinery (BAM) complex. This thesis describes the biochemical and biophysical properties of the periplasmic domain of the β-barrel assembly machinery protein A (PD-BamA) of the E. coli BAM complex, its effect on insertion and folding of the Outer membrane protein A (OmpA) into lipid bilayers and the identification of regions of PD-BamA that may be involved in protein-protein interactions. The secondary structure of PD-BamA in mixed lipid bilayers, analyzed by Circular dichroism (CD) spectroscopy, contained less β-sheet at an increased content of phosphatidylglycerol (PG) in the lipid membrane. This result showed membrane binding, albeit only in the presence of negatively charged lipids. Fluorescence spectroscopy demonstrated that PD-BamA only binds to lipid bilayers containing the negatively charged DOPG, confirming the results of CD spectroscopy. PD-BamA did not bind to zwitterionic but overall neutral lipid bilayers. PD-BamA bound to OmpA at a stoichiometry of 1:1. PD-BamA strongly facilitated insertion and folding of OmpA into lipid membranes. Kinetics of PD-BamA mediated folding of OmpA was well described by two parallel folding processes, a fast folding process and a slow folding process, differing by 2-3 orders of magnitude in their rate constants. The folding yields of OmpA depended on the concentration of lipid membranes and also on the lipid head groups. The presence of PD-BamA resulted in increased folding yields of OmpA in negatively charged DOPG, but PD-BamA did not affect the folding kinetics of OmpA into bilayers of zwitterionic but overall neutral lipids. The efficiency of folding and insertion of OmpA into lipid bilayers strongly depended on the ratio PD-BamA/OmpA and was optimal at equimolar concentrations of PD-BamA and OmpA. To examine complexes of unfolded OmpA with PD-BamA in more detail, site-directed spectroscopy was used to explore contact regions in both, PD-BamA and OmpA. Similarly, contact regions were also investigated for another protein complex formed by PD-BamA and the lipoprotein BamD. The obtained data suggest, that the site of interaction on PD-BamA for OmpA might be oriented towards the exterior environment away from the preceding POTRA domains, but that PD-BamA is oriented with its short α-helix α1 of POTRA domain 5 towards the C-terminal end of BamD.