Abstract
A robust marker to describe mass, hydrophobicity and polarizability distribution holds the key to deciphering structural and folding constraints within proteins. Since each of these distributions is inhomogeneous in nature, the construct should be sensitive in describing the patterns therein. We show, for the first time, that the hydrophobicity and polarizability distributions in protein interior follow fractal scaling. It is found that (barring ‘all-α’) all the major structural classes of proteins have an amount of unused hydrophobicity left in them. This amount of untapped hydrophobicity is observed to be greater in thermophilic proteins, than that in their (structurally aligned) mesophilic counterparts. ‘All-β’(thermophilic, mesophilic alike) proteins are found to have maximum amount of unused hydrophobicity, while ‘all-α’ proteins have been found to have minimum polarizability. A non-trivial dependency is observed between dielectric constant and hydrophobicity distributions within (α+β) and ‘all-α’ proteins, whereas absolutely no dependency is found between them in the ‘all-β’ class. This study proves that proteins are not as optimally packed as they are supposed to be. It is also proved that origin of α-helices are possibly not hydrophobic but electrostatic; whereas β-sheets are predominantly hydrophobic in nature. Significance of this study lies in protein engineering studies; because it quantifies the extent of packing that ensures protein functionality. It shows that myths regarding protein interior organization might obfuscate our knowledge of actual reality. However, if the later is studied with a robust marker of strong mathematical basis, unknown correlations can still be unearthed; which help us to understand the nature of hydrophobicity, causality behind protein folding, and the importance of anisotropic electrostatics in stabilizing a highly complex structure named ‘proteins’.
Highlights
A student of protein structure is constantly reminded of several myths prevalent in this paradigm
A maximum magnitude of MFD for a/b proteins explains the reason behind slowest folding rate in them, as reported recently [50]
The general trend of high magnitude of HFD (Table 2), can be attributed to the fact that hydrophobic residues are generally well conserved during evolution [51,52]
Summary
A student of protein structure is constantly reminded of several myths prevalent in this paradigm. He (she at any rate) studies that the globular proteins are so compactly packed that their interior mimics that of solids[1], but finds it a bit irreconcilable with reports of inhomogeneous packing[2] in protein interior and presence of cavities therein[3] He learns about ‘hydrophobic core’ and its immense importance in making the primary sequence fold the way it does[4], but a mapping between exact amount of hydrophobicity necessary to make a certain amount of mass fold in any of the SCOP(Structural Classification of Proteins) classes, remains elusive to him. We present a series of facts to prove the apt nature of fractal dimension based measures in describing protein structure and protein stability
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