The effect of mathematics and coordinate system on comparability and "dependencies" of nucleic acid structure...

This paper critically examines the methodologies used to analyze nucleic acid three-dimensional structure based on guidelines set at a 1988 EMBO workshop. The implications of these analyses cannot be fully understood without a thorough knowledge of how the numbers are calculated. This paper addresses one aspect of the calculations, namely the observed correlations between various parameters. These correlations are addressed in the mathematics by explicitly incorporating the concept of a pivot point, which is the point about which a base rotates as it buckles, propeller twists and opens. Pivot points enable one to model the physical motion of bases more accurately. As a result, they greatly reduce and/or eliminate the statistical correlations between rotational and translational parameters found in other approaches. The correlations that are reduced or eliminated are actually artifacts of the mathematics employed and do not reflect true structural properties of nucleic acids. The mathematics we have developed, including the mathematics of pivot points, are presented in the companion paper. Here, we explain how some of the observed correlations occur as a by-product of the method of calculation, while others are truly structural, and we show how optimum pivot points can be determined to minimize artifactual correlations. The observation that experimental bases often rotate about the long axis in a "propeller" motion as well as rotate about the Z-axis of each base, "opening" into the major groove, is evident in the location of the optimum region for the pivot point as determined in this study. We consider locating a pivot point as a calibration step to increase the agreement between physical intuition and the mathematics of our program.