A continuum theory for the prediction of lateral and rotational positioning of alpha-helices in membrane proteins: bacteriorhodopsin.

We have developed a new method for the prediction of the lateral and the rotational positioning of transmembrane helices, based upon the present status of knowledge about the dominant interaction of the tertiary structure formation. The basic assumption about the interaction is that the interhelix binding is due to the polar interactions and that very short extramembrane loop segments restrict the relative position of the helices. Another assumption is made for the simplification of the prediction that a helix may be regarded as a continuum rod having polar interaction fields around it. The polar interaction field is calculated by a probe helix method, using a copolymer of serine and alanine as probe helices. The lateral position of helices is determined by the strength of the interhelix binding estimated from the polar interaction field together with the length of linking loop segments. The rotational positioning is determined by the polar interaction field, assuming the optimum lateral configuration. The structural change due to the binding of a prosthetic group is calculated, fixing the rotational freedom of a helix that is connected to the prosthetic group. Applying this method to bacteriorhodopsin, the optimum lateral and rotational positioning of transmembrane helices that are very similar to the experimental configuration was obtained. This method was implemented by a software system, which was developed for this work, and automatic calculation became possible for membrane proteins comprised of several transmembrane helices.