The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence