The forces acting on an atom at a special position must have the same symmetry on average as the special position, so the atom will be in equilibrium, and there will at first sight be no net force (i.e. zero energy gradient) to push the atom away from the special position. However there are 2 solutions to this: metastable equilibrium where the energy is a maximum, and stable equilibrium where it's a minimum. In the metastable case it will be like a pencil balanced on its point where a small disturbance, such as from random thermal motion, will be sufficient to move it off the special position to an asymmetric position of lower energy thus breaking the symmetry, and of course the initial displacement will be completely random leading to the disorder you observe. In the case of stable equilibrium the atom will simply respond to the disturbance by executing random thermal motion centred on the special position. Which case you see in practice will obviously depend on the precise arrangement of forces acting on the atom.
Cheers -- Ian On Thu, Dec 9, 2010 at 4:12 PM, <herman.schreu...@sanofi-aventis.com> wrote: > Even with the famous waters on "true" Wyckoff positions, I usually > observe an elongated or even partly split density, suggesting that the > water is disordered, being sometimes closer to one monomer, sometimes > closer to the symmetry-related monomer. Since the position of proteins > in a crystal is in general not determined by a single water-mediated > hydrogen bond, the water will in general not be able to make perfect > hydrogen bonds to both symmetry-related monomers at the same time. I > think therefore that even waters should generally be considered to be > disordered and only in exceptional cases will occupy "true" Wyckoff > positions. > > Best, > Herman > > -----Original Message----- > From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of > Ian Tickle > Sent: Thursday, December 09, 2010 3:35 PM > To: CCP4BB@JISCMAIL.AC.UK > Subject: Re: [ccp4bb] Fwd: [ccp4bb] Wyckoff positions and protein atoms > >> cases out there (and so far I have heard of a disulfide bond on a >> 2-fold connecting two homodimers). > > I'm slightly puzzled by this example. If the S-S bond is on the special > position, then the rest of the molecule can't have 2-fold symmetry, so > would have to be rotationally disordered with occupancy = > 0.5 to avoid clashing with its symmetry mate: > > * > X -- C * > \ * > S > | > S > * \ > * C -- X > * > > where the *'s indicate the 2-fold axis (i.e. vertically in the plane of > the page). In this case, for the reasons I gave in my previous post > there's no reason for the disordered S atoms to be exactly on the > 2-fold; it would be pure coincidence if they were. If you mean instead > that the 2-fold is _perpendicular_ to the S-S bond (i.e. > coming straight out of the page in the diagram), the molecule does > indeed have 2-fold symmetry and can be ordered with occupancy = 1, but > then the S atoms are not on special positions, so this would not be an > example of protein atoms _on_ a special position. > > One could imagine an example, say where the same side-chain on each > monomer is cross-linked (e.g. LYS with glutaraldehyde), forming the > homodimer: > > X -- C -- N = C -- C -- C -- C -- C = N -- C -- X > > Here the central C atom could be on a 2-fold (i.e. axis perpendicular to > the page) special position without rotational disorder. I've no idea > whether such a structure actually exists! > > Cheers > > -- Ian >
