A simplified mechanical model of proteins tested on the globin fold

It has been shown that the distribution of presently known protein loop lengths is consistent with even the simplest available theory of rubber-like elasticity, and with the idea that such loops generate an entropically derived end-to-end tension. It has also been asserted that the molten globule phase, just like the native form, must be mechanically stable, and that a simple demonstration of the potential for mechanical stability would be a powerful test in predictions of new protein folds. This paper amplifies this suggestion by explicit calculation of a familiar but non-trivial test case: sperm-whale myoglobin. The method used is to describe the protein molecule in terms of a highly simplified mechanical model bearing some resemblance to a pre-stressed mechanism. The alpha-helices are treated as rigid rods and the loops are treated as elastic strings. The entropic tensions exerted by the loops are imposed on the mechanism using an approximation proposed earlier. The helices are then held to generate frictionless reaction forces at their mutual points of contact. These contact forces are calculated to null out maximally the effects of the loop tensions, and hence stabilize the molecule. It is shown that the crystallographically determined structure of myoglobin has a significantly higher mechanical stability on this model than does any of a previously published set of combinatorially generated predictions. Amongst the predictions alone, the best is also the one with the highest stability. It is anticipated that this result could be of general importance in sorting or filtering out bad predictions. A further exciting feature of the model is that it offers a natural explanation for the strong conservation of the C2 proline and the invariably long unconserved sequence from the end of the C helix to the start of the E helix in the globins and phycocyanins.