The Protein Surface as a Thermodynamic Frontier: A Fractal Approach

The objects in Nature cannot be simply described in terms of the Euclidean geometry. It is difficult to find natural objects that can be represented as perfect spheres, planes and stright lines. Unfortunatelly, when researchers are intent on describing Nature in detail, they usually fall in mathematical descriptions that are extremately complex, many times with no solution. The fractal geometry is a fascinating conceptual framework (Mandelbrot, 1982) as it possibilitates to characterize Nature irregularities with a single number, a really tempting idea per se. Moreover, this idea push us to a change in our minds when describing Nature, as we are used to the limited vision given by the Euclidean geometry. The word “irregular” itself remind us the idea that these objects do not fit into the Euclidean description of Nature. Fractals act as compression algorithms, as they contain minimal information and a reduced complexity (Abel & Trevors, 2006). Most of the objects in Nature are irregular, and the most fascinating thing is that irregular objects are the norm in the fractal geometry. Unfortunately, the application of the “fractal” label has been too extended, mainly because the mathematical law that rules this concept (a potential law) is versatile enough to allow that virtually all experimental data set fits the equation (Bryant et al., 1989). The surface of a protein constitutes the spatial domain through which the proteins interact with the surroundings. A great number of processes depend on surface phenomena, which at the same time depend on a wide range of structures and geometrical patterns. The protein surface is determined by the packing achieved in the folding process. Hence, the study of the geometrical characteristics yields valuable information not only on the folding process itself, but also related to the proteins in their interactions with the surroundings. The folded structure of a protein determines two different but closely related characteristics: stability and functionality. The stability of a protein relates with the surrounding media, while its functionality relates with its capacity to interact with that media through the interfacial surface. There is a consensus in considering the aqueous media surrounding the protein as the interacting media. In this regard, the protein surface is determined as the surface contacting the water molecules. However, this definition left behind other types of interactions that may take place, like protein-protein, protein-ligand, protein-DNA, or even, out of the natural context, protein-metallic surface. The immediate conclusion that one can take out is that the exact nature of the protein surface is highly dependent on the size of the interacting