Optimal bundling of transmembrane helices using sparse distance constraints.

We present a two-step approach to modeling the transmembrane spanning helical bundles of integral membrane proteins using only sparse distance constraints, such as those derived from chemical cross-linking, dipolar EPR and FRET experiments. In Step 1, using an algorithm, we developed, the conformational space of membrane protein folds matching a set of distance constraints is explored to provide initial structures for local conformational searches. In Step 2, these structures refined against a custom penalty function that incorporates both measures derived from statistical analysis of solved membrane protein structures and distance constraints obtained from experiments. We begin by describing the statistical analysis of the solved membrane protein structures from which the theoretical portion of the penalty function was derived. We then describe the penalty function, and, using a set of six test cases, demonstrate that it is capable of distinguishing helical bundles that are close to the native bundle from those that are far from the native bundle. Finally, using a set of only 27 distance constraints extracted from the literature, we show that our method successfully recovers the structure of dark-adapted rhodopsin to within 3.2 A of the crystal structure.