AMBER Archive (2005)

Subject: AMBER: RE: is calculated B-factors always smaller than experimental ones?

From: Yong Duan (duan_at_ucdavis.edu)
Date: Mon Aug 08 2005 - 13:24:26 CDT

Dear Haixiao:

I noticed your questions on AMBER mail reflector.

First, B-factors are composite measures of disorder and dynamics, disorder
in crystalline environment and dynamics of molecular motion at the time when
X-ray data is taken. From an ensemble average perspective, the two are
closely related. Since X-ray data reflects an ensemble average, both
disorder and dynamics will show up as disorder. In a sense, B-factors
provide an ensemble averaged measure of dynamics and disorder. From this
perspective, indeed, experimental B-factors should always be larger than
calculated ones since a) simulation time is always, for the time being,
shorter than the experimental time scales by orders of magnitude and b) we
may never have as many molecules in the system as what is available in any
crystal and c) global translation and rotation are removed before B-factor
calculation. However, this is an overly simplified interpretation.

Second, B-factors are simplified measures of rather complex processes. Now,
you've done some simulation and perhaps realized already that large-scale
motion is typically anharmonic. Depending on your simulation time,
large-scale dynamics, which contributes to your large calculated B-factors,
most likely involved some degree of conformational change. The movement is
typically anharmonic. Yet, you calculated B-factors using a harmonic
assumption. This is part of the simplification.

Third, the experimental B-factors were measured in crystalline environment
and your simulations are most likely done in solution. The difference is
quite substantial. In the crystalline environment molecules are in close
contacts. In many cases (probably safe to say in most cases), the dynamic
parts (e.g. loops) which contributes to the large calculated B-factors
typically form crystal contacts with neighboring molecules. As a consequence
of the crystal contacts, their measured B-factors are much smaller because
they can no longer move much. In many cases, this is the most important
contributor to the difference between calculated and experimental B-factors.

Fourth, there are also cases where very-high resolution of crystals were
obtained. Because of the high resolution, the measured B-factors are
typically small. In these cases, B-factors calculated from simulation can be
notably higher than the experimental ones throughout the molecule (not
limited to the dynamic parts). This is again largely due to the environment.
The high-resolution crystals are typically very well packed. On the other
hand, your simulations are done in solution and the molecule is entirely
solvated in solution, alone. Serious comparison should be done in the
crystalline environment.

Fifth, we should always keep in mind the approximation associated with our
simulation parameters besides the limited time and number of molecules. This
inevitably contributes to the error and discrepency. However, at this level,
I seriously doubt that B-factors are sensitive enough to be good measures
for comparison. When simulations are done in the same crystaline environment
with the right amount of salt, water, ions, etc., agreement has been
exceptionally good. Of course, this does not mean that our simulations are
perfect. It just means that the measure is not sensitive enough to pick up
the difference.

In summary, differences between calculated and experimental B-factors are
expected largely because of the substantial differences between the
environments.

yong

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