Protein structure designability: The consequences of amino-acid alphabet and the underlying energy model.

Abstract

It has been noted by scientists that certain native, protein structures occur more frequently than others in the Protein Data Bank. A variety of models have been developed to explain this phenomenon by considering protein structure designability. A protein structure is more designable if a larger fraction of all possible sequences can <italic>fold</italic> into it. Such highly-designable structures are more likely to have been found and maintained through the process of evolution hence they are likely to be over-represented. Proteins are biopolymers and the key to designability lies with understanding the thermodynamic constraints of how a biologically relevant protein sequence folds into a native protein structure. We begin by discussing protein folding in the context of free energy landscapes and phase transitions. The role of protein evolution, critical transitions, such as freezing into the native state (<italic> T_f</italic>), collapse into molten globules (T_theta), and glassy phase transitions (<italic>T_g)</italic>, folding-funnels, and free energy landscape measures is a well studied subject of protein folding both computationally and theoretically. In particular, the relationship between folding funnels and relevant phase transition temperatures (<italic>T_f, T_g</italic>) can be related to free energy landscape measures, such as foldability F and energy gap Delta. Using the Random Energy Model, we analytically demonstrate the statistical relationship between F , Delta. Using simplified models of protein structure and interactions, we have explored the relationship between protein structure designability, foldability, interaction parameters, and amino-acid alphabet. We shed new light on which structures are expected to be highly designable, for which types of energy models (solvation or pair-contact), and why these structures are designable. Moreover, we can also understand why free energy landscape measures, such as foldability F and energy gap Delta, must be correlated to protein structure designability. We further demonstrate that pair-contact model results turn into solvation model results for special aminoacid alphabet cases and offer an explanation for this behavior. The last half of the thesis presents two separate, yet related topics: a novel algorithm for protein NMR sequence-specific resonance assignments and the stretching of biopolymers.