I think it is important to remember here that although 2Fo-Fc maps can
have "Fourier ripples" (AKA series termination errors) difference maps
are "resistant" to them. This is because "leaving out" data in a map
calculation is equivalent to setting the coefficient to zero, and for
a difference map this is not such a bad guess, especially for
high-angle data.

However, difference maps are not "immune" to other kinds of errors,
like Fc not quite capturing the "real" electron density. This can be
particularly apparent around heavy atoms, since they are "taller" in
electrons/A^3 than protein atoms, and so a ~10% percent error on a Zn
atom amounts to 3 electrons, or half a carbon atom! One example of
where such a "bump" could come from is if the distribution of Zn
positions is not a perfect Gaussian. There is no way to exactly
capture non-Gaussian shapes with a Gaussian atom model (B factor).
So, the refinement programs does the best it can to line up the
shapes, but then you see "ripples". However, these ripples have
nothing to do with series-termination artifacts.

Note that some call non-Gaussian atomic displacement distributions
"anharmonic", but that word assumes the displacements are thermal in
origin, and I don't think that's appropriate for cryo-cooled protein
crystals. "non-Gaussian" is more general.

-James Holton
MAD Scientist

On Wed, Jul 6, 2011 at 10:58 AM, Fischmann, Thierry
<[log in to unmask]> wrote:
> Dear Zbyszek
>
> Wouldn't ripples be the results of calculating maps with truncated
> Fourier summations (unavoidably), and, consequently, be more obvious
> around a sharp feature such as an heavy atom metal center?
>
> The mathematic basis can be found here:
> http://en.wikipedia.org/wiki/Gibbs_phenomenon
>
> With best regards,
>
> Thierry
>
> Note: sent a 2nd time as it seems that it did not reach the BB the first
> time. Apologies if the message reaches you twice.
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
> Zbyszek Otwinowski
> Sent: Wednesday, July 06, 2011 1:19 PM
> To: [log in to unmask]
> Subject: Re: [ccp4bb] How to evaluate Fourier transform ripples
>
> The question about Fourier transformation ripples has a straightforward
> answer in a fairly typical situation:
> A) data are collected to the resolution limit of diffraction,
> B) phases are uniform in quality across the resolution range, which is
> equivalent to R-free being uniform with respect to resolution within a
> factor of 2  or so,
> C) maps are not sharpened.
>
> The ripples originate from not including unobserved structure factors.
> The
> intensity of diffraction decreases rapidly past the measurability limit,
> so, in the above situation, the unobserved diffraction contributes very
> little. Consequently, the answer is that typically one should not see
> ripples.
> Ripples should not be confused with the effect of electron density maps
> being smoothed by vibrations and other forms of disorder.
>
> Zbyszek Otwinowski
>
>>
>> Dear All,         Hi. I was asked in a manuscript revision to discuss
>> about the possible effects of Fourier transformation ripples on the
>> crystallographic results. Specifically, the reviewers question whether
>> ripples may affect on the electron density around heavy metal center
> which
>> has a Mo-S-As connection. From which angle or in which way this
> problem
>> should be addressed most convincingly ?         Thank you for any
>> suggestion.Best,Conan
>
>
> Zbyszek Otwinowski
> UT Southwestern Medical Center at Dallas
> 5323 Harry Hines Blvd.
> Dallas, TX 75390-8816
> Tel. 214-645-6385
> Fax. 214-645-6353
> Notice:  This e-mail message, together with any attachments, contains
> information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,
> New Jersey, USA 08889), and/or its affiliates Direct contact information
> for affiliates is available at
> http://www.merck.com/contact/contacts.html) that may be confidential,
> proprietary copyrighted and/or legally privileged. It is intended solely
> for the use of the individual or entity named on this message. If you are
> not the intended recipient, and have received this message in error,
> please notify us immediately by reply e-mail and then delete it from
> your system.
>