ABSTRACT: Protein secondary structure elements (PSSEs) such as ?-helices, ?-strands, and turns are the primary building blocks of the tertiary protein structure. Our primary interest here is to reveal the characteristics of the nanoenvironment formed by both PSSEs and their surrounding amino acid residues (AARs), which might contribute to the general understanding of how proteins fold. The characteristics of such nanoenvironments must be specific to each secondary structure element, and we have set our goal here to gather the fullest possible description of the ?-helical nanoenvironment. In general, this postulate (the existence of specific nanoenvironments for specific protein substructures/neighbourhoods/regions with distinct functionality) was already successfully explored and confirmed for some protein regions, such as protein-protein interfaces and enzyme catalytic sites. Consequently, PSSEs were the obvious next choice for additional work for further evidence showing that specific nanoenvironments (having characteristics fully describable by means of structural and physical chemical descriptors) do exist for the corresponding and determined intraprotein regions. The nanoenvironment of ?-helices (nEo?H) is defined as any region of the protein where this secondary structure element type is detected. The nEo?H, therefore, includes not only the ?-helix amino acid residues but also the residues immediately around the ?-helix. The hypothesis that motivated this work is that it might in fact be possible to detect a postulated "signal" or "signature" that distinguishes the specific location of ?-helices. This "signal" must be discernible by tracking differences in the values of physical, chemical, physicochemical, structural and geometric descriptors immediately before (or after) the PSSE from those in the region along the ?-helices. The search for this specific nanoenvironment "signal" was made possible by aligning previously selected ?-helices of equal length. Afterward, we calculated the average value, standard deviation and mean square error at each aligned residue position for each selected descriptor. We applied Student's t-test, the Kolmogorov-Smirnov test and MANOVA statistical tests to the dataset constructed as described above, and the results confirmed that the hypothesized "signal"/"signature" is both existing/identifiable and capable of distinguishing the presence of an ?-helix inside the specific nanoenvironment, contextualized as a specific region within the whole protein. However, such conclusion might rarely be reached if only one descriptor is considered at a time. A more accurate signal with broader coverage is achieved only if one applies multivariate analysis, which means that several descriptors (usually approximately 10 descriptors) should be considered at the same time. To a limited extent (up to a maximum of 15% of cases), such conclusion is also possible with only a single descriptor, and the conclusion is also possible in general for up to 50-80% of cases when no less than 5 nonlinear descriptors are selected and considered. Using all the descriptors considered in this work, provided all assumptions about data characteristics for this analysis are met, multivariate analysis regularly reached a coverage and accuracy above 90%. Understanding how secondary structure elements are formed and maintained within a protein structure could enable a more detailed understanding of how proteins reach their final 3D structure and consequently, their function. Likewise, this knowledge may also improve the tools used to determine how good a structure is by means of comparing the "signal" around a selected PSSE with the one obtained from the best (resolution and quality wise) protein structures available.
