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.

Effects of red brick production on land use, household income, and greenhouse gas emissions in Khartoum, Sudan

In Khartoum (Sudan) a particular factor shaping urban land use is the rapid expansion of red brick making (BM) for the construction of houses which occurs on the most fertile agricultural Gerif soils along the Nile banks. The objectives of this study were to assess the profitability of BM, to explore the income distribution among farmers and kiln owners, to measure the dry matter (DM), nitrogen (N), phosphorus (P), potassium (K) and organic carbon (C_org) in cow dung used for BM, and to estimate the greenhouse gas (GHG) emissions from burned biomass fuel (cow dung and fuel wood). About 49 kiln owners were interviewed in 2009 using a semi-structured questionnaire that allowed to record socio-economic and variable cost data for budget calculations, and determination of Gini coefficients. Samples of cow dung were collected directly from the kilns and analyzed for their nutrients concentrations. To estimate GHG emissions a modified approach of the Intergovernmental Panel on Climate Change (IPCC) was used. The land rental value from red brick kilns was estimated at 5-fold the rental value from agriculture and the land rent to total cost ratio was 29% for urban farms compared to 6% for BM. The Gini coefficients indicated that income distribution among kiln owners was more equal than among urban farmers. Using IPCC default values the 475, 381, and 36 t DM of loose dung, compacted dung, and fuel wood used for BM emit annually 688, 548, and 60 t of GHGs, respectively.

Effects of changing water availability on land use in irrigated mountain oases of Al Jabal Al Akhdar, northern Oman

In Oman, during the last three decades, agricultural water use and groundwater extraction has dramatically increased to meet the needs of a rapidly growing population and major changes in lifestyle. This has triggered agricultural land-use changes which have been poorly investigated. In view of this our study aimed at analysing patterns of shortterm land-use changes (2007-2009) in the five irrigated mountain oases of Ash Sharayjah, Al’Ayn, Al’Aqr, Qasha’ and Masayrat ar Ruwajah situated in the northern Oman Hajar mountains of Al Jabal Al Akhdar where competitive uses of irrigation water are particularly apparent. Comprehensive GIS-based field surveys were conducted over three years to record changes in terrace use in these five oases where farmers have traditionally adapted to rain-derived variations of irrigation water supply, e.g. by leaving agricultural terraces of annual crops uncultivated in drought years. Results show that the area occupied with field crops decreased in the dry years of 2008 and 2009 for all oases. In Ash Sharayjah, terrace areas grown with field crops declined from 4.7 ha (32.4 % of total terrace area) in 2007 to 3.1 ha (21.6 %) in 2008 and 3.0 ha (20.5 %) in 2009. Similarly, the area proportion of field crops shrunk in Al’Ayn, Qasha’ and Masayrat from 35.2, 36.3 and 49.6 % in 2007 to 19.8, 8.5 and 41.3 % in 2009, respectively. In Al’Aqr, the area of field crops slightly increased from 0.3 ha (17.0 %) in 2007 to 0.7 (39.1 %) in 2008, and decreased to 0.5 ha (28.8 %) in 2009. During the same period annual dry matter yields of the cash crop garlic in Ash Sharayjah increased from 16.3 t ha-1 in 2007 to 19.8 t ha-1 in 2008 and 18.3 t ha-1 in 2009, while the same crop yielded only 0.4, 1.6 and 1.1 t ha-1 in Masayrat. In 2009, the total estimated agricultural area of the new town of Sayh Qatanah above the five oases was around 13.5 ha. Our results suggest that scarcity of irrigation water as a result of low precipitation and increased irrigation and home water consumption in the new urban settlements above the five oases have led to major shifts in the land-use pattern and increasingly threaten the centuries-long tradition and drought-resilience of agriculture in the oases of the studied watershed.