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Abstract

As the most abundant type of protein secondary structure helices play an essential role within a protein and in various protein-protein interactions. Thus it is especially important to understand what criteria influences the geometry of helices and helps successfully perform their functions. There are many computational tools used by protein biophysicists. However, it is rare for them to use computer algebra systems. Thus we explored the use of such systems to show how they could be used to study structural properties of proteins. As an example, we chose the geometry of helical structure.,We begin by considering two types of protein helices, $\alpha$- and $3_{10}$-helices stabilized by 1-5 and 1-4 hydrogen bonding pattern respectively and study the relationship between hydrogen bond geometrical requirements and stability of protein helices via mathematical optimization. In particular, we take two major hydrogen bond requirements: linearity and length constraints and ask whether the most common $\alpha$- and $3_{10}$-helix motifs in protein folds result from optimization with respect to a linear combination of these two criteria. We show that these criteria are not sufficient to explain the observed angles. Instead, we suggest that maximizing the solvation of the protein backbone has a significant effect on the observed $(\varphi,\psi)$ angles. ,The above work suggested that a completely unexpected ``solvation signature" should be observable in protein structure. There are many tools that can be used to study this suggestion. Since ``data science" is a theme of significant current interest, we explored this approach to see what issues arise with these techniques. So, as a next step, we investigated the effects of solvation by collecting and analyzing a high quality protein dataset. We found that helical backbone actively interacts with water irrespective of whether it is located at the surface or buried inside protein. This interaction, as expected, highly correlates with larger $\varphi$ angles and larger distances between neighboring main-chain carbonyl oxygens. Moreover, we observe a distinct periodic backbone solvation pattern in $\alpha$-helices, suggesting that most helices have a very specific orientation and position specific residue preferences. ,We have seen that new tools can enhance the study of protein biophysics. The success of data mining depends strongly on the quality of the questions being addressed as well as the quality and quantity of the data. This suggests that data science (1) needs to have a firm foundation in basic science and (2) needs to have appropriate analytic tools to examine the data faithfully.,Other tools, such as molecular dynamics and density functional theory have also been used to study protein-water interactions. Given the right questions to ask, these too can be potentially useful and would be interesting to consider in the future.

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