Interhelical angle and distance preferences in globular proteins

Orientational preferences between interacting helices within globular proteins have been studied extensively over the years. A number of classical structural models such as "knobs into holes" and "ridges into grooves" were developed decades ago to explain perceived preferences in interhelical angle distributions. In contrast, relatively recent works have examined statistical biases in angular distributions which result from spherical geometric effects. Those works have concluded that the predictions of classical models are due in large part to these biases. In this article we perform an analysis on the largest set of helix-helix interactions within high-resolution structures of nonhomologous proteins studied to date. We examine the interhelical angle distribution as a function of spatial distance between helix pairs. We show that previous efforts to normalize angle distribution data did not include two important effects: 1), helices can interact with each other in three distinct ways which we refer to as "line-on-line," "endpoint-to-line," and "endpoint-to-endpoint," and each of these interactions has its own geometric effects which must be included in the proper normalization of data; and 2), all normalizations that depend on geometric parameters such as interhelical angle must occur before the data is binned to avoid artifacts of bin size from biasing the conclusions. Taking these two points into account, we find that there are very pronounced preferences for helices to interact at angles of approximately +/-160 and +/-20 degrees in the line-on-line case. This pattern persists when the closest alpha-carbons in the helices vary from 4 to 12 A. The endpoint-to-line and endpoint-to-endpoint cases also exhibit distinct preferences when the data is normalized properly. Analysis of the local structural interactions which give rise to these preferences has not been studied here and is left for future work.