Re: [ccp4bb] How to make fft-map more physically meaningful?
Dear Hailiang, This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Yes, you are right when you are talking about the electron density. You are wrong when you are talking about a Fourier synthesis calculated always at a finite resolution (it is what you have, is it?), even when the term F000 is used as suggested. Such a synthesis MUST have NEGATIVE values due to Fourier series truncation. Allowing such negative values was an important point at the beginning of density modification procedures (beginning of 80th) and it was one of the key moments when developping electron density histograms (see for example Lunin, 1988, Acta Cryst A). Moreover, these points even contain some information and can be used for example to identify the macromolecular region (since the deepest minima are usually close to the highest maxima). With best regards, Sacha
Re: [ccp4bb] How to make fft-map more physically meaningful?
Hi Sacha is absolutely right here. This was made plain to me during a plenary session at the recent BCA meeting in Warwick, given by a powder (not protein) crystallographer - who was using histogram matching density modification, with negative densities; an expert in density modification in protein crystallography tells me that using a map with no truncation (and hence no negative densities) always gives rubbish results in my hands. On 9 Jul 2010, at 06:37, Alexandre Urzhumtsev wrote: Dear Hailiang, This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Yes, you are right when you are talking about the electron density. You are wrong when you are talking about a Fourier synthesis calculated always at a finite resolution (it is what you have, is it?), even when the term F000 is used as suggested. Such a synthesis MUST have NEGATIVE values due to Fourier series truncation. Allowing such negative values was an important point at the beginning of density modification procedures (beginning of 80th) and it was one of the key moments when developping electron density histograms (see for example Lunin, 1988, Acta Cryst A). Moreover, these points even contain some information and can be used for example to identify the macromolecular region (since the deepest minima are usually close to the highest maxima). With best regards, Sacha Harry -- Dr Harry Powell, MRC Laboratory of Molecular Biology, MRC Centre, Hills Road, Cambridge, CB2 0QH
Re: [ccp4bb] How to make fft-map more physically meaningful?
Dear Sacha: Yes, I think Fourier synthesis at a finite resolution range will generate some negative, or more generally imaginary values in real space (hope I am right again:). For the imaginary values, I think the map should take the amplitude of it (maybe I am wrong). Do they normally make the density negative when the real-space density phase angle is between 90-270 degree, and positive other wise, or something else? Thanks a lot! Best Regards, Hailiang Dear Hailiang, This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Yes, you are right when you are talking about the electron density. You are wrong when you are talking about a Fourier synthesis calculated always at a finite resolution (it is what you have, is it?), even when the term F000 is used as suggested. Such a synthesis MUST have NEGATIVE values due to Fourier series truncation. Allowing such negative values was an important point at the beginning of density modification procedures (beginning of 80th) and it was one of the key moments when developping electron density histograms (see for example Lunin, 1988, Acta Cryst A). Moreover, these points even contain some information and can be used for example to identify the macromolecular region (since the deepest minima are usually close to the highest maxima). With best regards, Sacha
Re: [ccp4bb] How to make fft-map more physically meaningful?
Uhh. No. You will only get imaginary electron density if your structure factors violate Friedel's law. I am not aware of map calculation codes that do this (on purpose). BTW, imaginary electrons are really just slow electrons that don't respond to the x-rays as fast as the average electron in the unit cell. They can also be faster than average. Because of this, if you have a unit cell full of nothing but selenium atoms, you will get all Bijvoet differences equal to zero. Even at the selenium edge! -James Holton MAD Scientist Hailiang Zhang wrote: Dear Sacha: Yes, I think Fourier synthesis at a finite resolution range will generate some negative, or more generally imaginary values in real space (hope I am right again:). For the imaginary values, I think the map should take the amplitude of it (maybe I am wrong). Do they normally make the density negative when the real-space density phase angle is between 90-270 degree, and positive other wise, or something else? Thanks a lot! Best Regards, Hailiang Dear Hailiang, This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Yes, you are right when you are talking about the electron density. You are wrong when you are talking about a Fourier synthesis calculated always at a finite resolution (it is what you have, is it?), even when the term F000 is used as suggested. Such a synthesis MUST have NEGATIVE values due to Fourier series truncation. Allowing such negative values was an important point at the beginning of density modification procedures (beginning of 80th) and it was one of the key moments when developping electron density histograms (see for example Lunin, 1988, Acta Cryst A). Moreover, these points even contain some information and can be used for example to identify the macromolecular region (since the deepest minima are usually close to the highest maxima). With best regards, Sacha
[ccp4bb] Re : Re: [ccp4bb] How to make fft-map more physically meaningful?
Dear Hailiang,As James said, the hermitian symmetry of Fourier coefficients, F(h)=F*(-h), that is known in diffraction theory as the Friedel's law, is an equivalent of the condition that the corresponding function (electron density) is a real function.I think if you need further information you can make a look into some basic textbook or write me (or to somebody on your choice :-) a direct personal mail; I am not sure if we need to bother the whole community by further details of this discussion. You can write and send to CCP4bb the resume afterall if you want.Best regards,SachaDe: James Holton jmhol...@lbl.gov Uhh. No. You will only get imaginary electron density if your structure factors violate Friedel's law. I am not aware of map calculation codes that do this (on purpose). Yes, I think Fourier synthesis at a finite resolution range will generate some negative, or more generally imaginary values in real space (hope I am right again:).
[ccp4bb] How to make fft-map more physically meaningful?
Hi there: I found that the grid values in the map file generated by CCP4-fft generally has a mean value of ~0, and of course there will be lots of negative values. This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Can somebody give me any hint how to convert the fft map file which has mean value of 0, to a more physically meaningful map which has positive densities everywhere? (I thought about offsetting the whole map by the minimum negative values to make everything positive, but I doubt it is right). Best Regards, Hailiang
Re: [ccp4bb] How to make fft-map more physically meaningful?
Hailiang Zhang wrote: Hi there: I found that the grid values in the map file generated by CCP4-fft generally has a mean value of ~0, and of course there will be lots of negative values. This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Can somebody give me any hint how to convert the fft map file which has mean value of 0, to a more physically meaningful map which has positive densities everywhere? (I thought about offsetting the whole map by the minimum negative values to make everything positive, but I doubt it is right). Best Regards, Hailiang Actually taking the minimum value as zero might be a good approximation, as long as the resolution is high enough so there are gaps in the protein too small to be solvent-filled but large enough to be resolved from surrounding density. Maps from FFT will always have average value zero unless you include the 0,0,0 reflection: the transform is a sum of sin and cos terms, all of which have zero value when integrated over the unit cell, except the cos(0.X) term. So any linear combination of these terms will average to zero if it doesn't include the zero order term. The 0,0,0 reflection is hard or impossible to measure because it gets mixed up with the undiffracted beam. But it is easy to calculate, because the integral of unity against the electron density is just the average electron density times the volume, or the total number of electrons. So if you know the total number of electrons in the unit cell, you can divide by the unit cell volume to get the average electron density (OK, I guess that is obvious) and add it to the zero-average FFT map. This assumes the map is on an absolute scale, which won't be quite true, so your idea of offsetting the minimum to zero may be more satisfactory. Ed
Re: [ccp4bb] How to make fft-map more physically meaningful?
Edward A. Berry wrote: Hailiang Zhang wrote: Hi there: I found that the grid values in the map file generated by CCP4-fft generally has a mean value of ~0, and of course there will be lots of negative values. This apparently is not the real physics, since the electron density has to be positive everywhere (hope I am right). Can somebody give me any hint how to convert the fft map file which has mean value of 0, to a more physically meaningful map which has positive densities everywhere? (I thought about offsetting the whole map by the minimum negative values to make everything positive, but I doubt it is right). Best Regards, Hailiang Actually taking the minimum value as zero might be a good approximation, as long as the resolution is high enough so there are gaps in the protein too small to be solvent-filled but large enough to be resolved from surrounding density. Maps from FFT will always have average value zero unless you include the 0,0,0 reflection: the transform is a sum of sin and cos terms, all of which have zero value when integrated over the unit cell, except the cos(0.X) term. So any linear combination of these terms will average to zero if it doesn't include the zero order term. The 0,0,0 reflection is hard or impossible to measure because it gets mixed up with the undiffracted beam. But it is easy to calculate, because the integral of unity against the electron density is just the average electron density times the volume, or the total number of electrons. So if you know the total number of electrons in the unit cell, you can divide by the unit cell volume to get the average electron density (OK, I guess that is obvious) and add it to the zero-average FFT map. This assumes the map is on an absolute scale, which won't be quite true, so your idea of offsetting the minimum to zero may be more satisfactory. Ed Ed is right, of course. Just remember to include ALL the electrons in the unit cell - both those of the protein and those of the solvent, ordered and disordered. Dale Tronrud
