The prediction of protein native conformations is still a big challenge in science, although a strong research activity has been carried out on this topic in the last decades. In this paper we focus on ab-initio computational methods for protein fold predictions that do not rely heavily on comparisons with known protein structures and hence appear to be the most promising methods for determining conformations not yet been observed experimentally. To identify main trends in the research concerning protein fold predictions, we briefly review several ab-initio methods, including a recent topological approach that models the protein conformation as a tube having maximum thickness without any self-contacts. This representation leads to a constrained global optimization problem. We introduce a modification in the tube model to increase the compactness of the computed conformations, and present results of computational experiments devoted to simulating alpha-helices and all-alpha proteins. A Metropolis Monte Carlo Simulated Annealing algorithm is used to search the protein conformational space.