Fractal nature of protein surface roughness: a note on quantification of change of surface roughness in active sites, before and after binding.

Year 2010 marked the 25th year since we came to know that roughness of a protein surface has fractal symmetry. Ever since the publication of Lewis and Rees' paper, hundreds of works from a spectrum of perspectives have established that fractal dimension (FD) can be considered as a reliable marker that describes roughness of protein surface objectively. In this article, we introduce readers to the fundamentals of fractals and present categorical biophysical and geometrical reasons as to why FD-based constructs can describe protein surface roughness more accurately. We then review the commonality (and the lack of it) between numerous approaches that have attempted to investigate protein surface with fractal measures, before exploring the patterns in the results that they have produced. Apart from presenting the genealogy of approaches and results, we present an analysis that quantifies the difference in surface roughness in stretches of protein surface containing the active site, before and after binding to ligands, to underline the utility of FD-based measures further. It has been found that surface stretches containing the active site, in general, undergo a significant increment in its roughness after binding. After presenting the entire repertoire of FD-based surface roughness studies, we talk about two yet-unexplored problems where application of FD-based techniques can help in deciphering underlying patterns of surface interactions. Finally, we list the limitations of FD-based constructs and put down several precautions that one must take while working with them.