Subunit motions

Helix-coil transitions, in particular, are of widespread occurrence in peptides and in proteins. One peptide hormone that has been studied experimentally is glucagon, which has a nearly random coil structure as a monomer in aqueous solution,287 is partially helical when it interacts with a membrane288 or trimerized in aqueous solution,289 and is fully helical in a crystal where each molecule is involved in the formation of two trimers.290 

In what follows we describe some of the larger-scale motions in proteins for which theoretical studies of the dynamics are available.  

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FIGURE 15.31 Subunit motion in hemoglobin when the molecule goes from the (a) deoxy to the (b) oxy form. (Irving G sj... 

Subunit motion between two positions is also critical to the assembly of tobacco mosaic virus. In the partially assembled disks, having two stacked layers of 17 subunits each, the layers are wedged apart toward their inner radius. During assembly of the viral helix, RNA binds between the layers, which then clamp tightly together with 164 subunits per turn (Bloomer et al., 1978 Butler and Klug, 1978). 

Fig. 2. Quaternary structural transition in hemoglobin. (A) Subunit motion of hemoglobin in going from the deoxy (or T conformation) to the oxy (or R conformation) state (B) side views of deoxy and oxy states of hemoglobin. In oxy-Hb, the oiiPi dimer is rotated 15° relative to the a2p2 dimer. [Adapted from Dickerson and Geis (1983) illustration copyright by I. Geis],...

In unimolecular ET, the rate can be controlled by large-scale cofactor motion, such as the quinone motion in the photosynthetic reaction centers, the Rieske subunit motion in the cytochrome bc complex (47), or the cytochrome fcs-domain in sulfite oxidase. Theoretical models for conformationally controlled ET reactions have been suggested by Hoffman and Rat-ner (48) and Bnmschwig and Sutin (49). Large-scale protein or domain motions are themselves linked to the movement of water molecules. 

Fig. 14. Rotation of the mobile [2Fe 2S] cluster in the Cyt be, complex upon binding of the inhibitor stigmatellin. Cytb[bH,orb(HP) and bi or b(LP)], Cyt c and ISP (the [2Fe 2S]) are as indicated. (A) Arrangement oftheCyt bo, complex subunits when stigmatellin is bound to the Qo site. (B) Arrangement of the Cyt be, complex subunits in the absence of the inhibitor. Figure source Izrailev, Crofts, Berry and Schulten (1999) Steered molecular dynamics simulation of the Rieske subunit motion in the cytochrome be, complex. Biophys J 77 1754.

S Izrailev, AR Crofts, EA Berry and K Schulten (1999) Steered molecular simulation of the Rieske subunit motion in the cytochrome bc complex. Biophys J 77 1753-1768... 

During subunit motions in the above processes, hydrophobic bonds between acyl chains at subunit interfaces (Fig. 22d,e,f) would help keep the membrane sealed with the two following consequences. 

We have previously calculated conformational free energy differences for a well-suited model system, the catalytic subunit of cAMP-dependent protein kinase (cAPK), which is the best characterized member of the protein kinase family. It has been crystallized in three different conformations and our main focus was on how ligand binding shifts the equilibrium among these ([Helms and McCammon 1997]). As an example using state-of-the-art computational techniques, we summarize the main conclusions of this study and discuss a variety of methods that may be used to extend this study into the dynamic regime of protein domain motion. 

FIGURE 10.37 Gap Juoctioos consist of hexameric arrays of cylindrical protein subunits in the plasma membrane. The subunit cylinders are tilted with respect to the axis running through the center of the gap Junction. A gap Junction between cells is formed when two hexameric arrays of subunits in separate cells contact each other and form a pore through which cellular contents may pass. Gap Junctions close by means of a twisting, sliding motion in which the subunits decrease their tilt with respect to the central axis. Closure of the gap Junction is Ca -dependent. 

Fig. 14 The experimental geometries of benzene- -HC1 and benzene- -ClF (to scale) and the n-electron model of benzene. See text for discussion of the motion of the C1F subunit, as inferred from an analysis of the rotational spectrum of benzene- -ClF. See Fig. 1 for key to the colour coding of atoms... 

We now allow nuclear motion and seek vibrational wave functions corresponding to states i i and tjfg. We assume throughout that the subunits have the same point group symmetry in both oxidation states (M and N), and then it is only necessary to consider explicitly totally symmetric normal coordinates of the two subunits (4, 5). Let us assume that there are two on each... 

At present, the Brownian motions of isolated rigid macromolecules are quite well understood. The challenge now is to understand the Brownian deformations of nonrigid macromolecules and to ascertain the time scales on which the coupled motions of their subunits relax various experimental signals. 

Very low-frequency vibrations have been observed in proteins (e.g., Brown et al., 1972 Genzel et al., 1976), which must involve concerted motion of rather large portions of the structure. By choosing a suitable set of proteins to measure (preferably in solution), it should be possible to decide approximately what structural modes are involved. Candidates include helix torsion, coupled changes of peptide orientation in /3 strands, and perhaps relative motions of entire domains or subunits. These hypotheses should be tested, because the low-frequency vibrations probably reflect large-scale structural properties that would be very useful to know. 

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