Entropic benefit of a cross-link in protein association. Proteins

ABSTRACT We introduce a method to estimate the loss of configurational entropy upon insertion of a cross-link to a dimeric system. First, a clear distinc-tion is established between the loss of entropy upon tethering and binding, two quantities that are often considered to be equivalent. By comparing the prob-ability distribution of the center-to-center distances for untethered and cross-linked versions, we are able to calculate the loss of translational entropy upon cross-linking. The distribution function for the untethered helices is calculated from the prob-ability that a given helix is closer to its partner than to all other helices, the “Nearest Neighbor ” method. This method requires no assumptions about the nature of the solvent, and hence resolves difficulties normally associated with calculations for systems in liquids. Analysis of the restriction of angular free-dom upon tethering indicates that the loss of rota-tional entropy is negligible. The method is applied in the context of the folding of a ten turn helical coiled coil with the tether modeled as a Gaussian chain or a flexible amino acid chain. After correct-ing for loop closure entropy in the docked state, we estimate the introduction of a six-residue tether in the coiled coil results in an effective concentration of the chain to be about 4 or 100 mM, depending upon whether the helices are denatured or pre-folded prior to their association. Thus, tethering results in significant stabilization for systems with millimolar or stronger dissociation constants. Proteins 2002;48:341–351. © 2002 Wiley-Liss, Inc. Key words: translational entropy; rotational en-tropy; probability distribution func-tion; coiled coil; Gaussian random coil; tether; bindin