Re: [ccp4bb] odd request: add phase error linearly with resolution
Hi Francis, Check out the CALC command in sftools. It allows you to apply quite a number of mathematical operations on MTZ column data, including phases. It also has built-in funtions to return the resolution of reflections which you can use in your calculation. CALC HELP should explain how to use it. Bart Francis E Reyes wrote: Hi all I'd like to add a phase error to my PHIB's and FOM's (experimental phases) that increases linearly with higher resolution.. it's akin to taking good phases and making them bad. Any approaches on how this can be done? Thanks FR - Francis Reyes M.Sc. 215 UCB University of Colorado at Boulder gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D -- Bart Hazes (Associate Professor) Dept. of Medical Microbiology & Immunology University of Alberta 1-15 Medical Sciences Building Edmonton, Alberta Canada, T6G 2H7 phone: 1-780-492-0042 fax:1-780-492-7521
Re: [ccp4bb] inexpensive source of DDM
Hi Tony, maybe Glycon in Germany might be useful for you (www.glycon.de). They sell bDDM for around 900 Euro/25 g and also can make bulk pricing on request. We have been very happy with their quality in the past (especially the content of alpha was lower than in products from other companies). Hope that helps, Jan Tony Wu wrote: Hello, I am looking for an inexpensive US source for large quantities of dodecylmaltoside. Can anyone help me? Thank you!
Re: [ccp4bb] Why Do Phases Dominate?
Dear Marius, Thank you for pointing this out - I was about to argue in the same direction, i.e. that the Fourier transform is at the heart of diffraction and is not just a convenient, but perhaps renegotiable, procedure for analysing diffraction data. Another instance of such natural "hardwiring" of the Fourier transform into a physical phenomenon is Free Induction Decay in NMR. There, however, one can measure the phases, as it is the Larmor precession of the population of spins that is measured along two orthogonal directions and gives the real and imaginary parts of the FID signal. Equal opportunity for real and imaginary part: doesn't that make a crystallographer dream ... ? With best wishes, Gerard. -- On Fri, Mar 19, 2010 at 08:15:05PM +0100, Marius Schmidt wrote: > The great thing with diffraction, from crystals and > from objects in microscopy is THAT this is > A NATURALLY OCCURRING FORM of Fourier transform once > one accepts that light is a wave (could be something > else). > If Fourier transform would not have been invented with > another problem from engineering, then it would > have emerged NATURALLY from diffraction. > Diffraction is an analog (not a digital) Fourier transform. > A crystal is a low-noise, analog, natural > Fourier amplifier!!! > If you want to build the fastest Fourier transform > of the world, you could represent your function, which > you want to Fourier transform, as > density fluctuation and scatter from it, or, you > could amplify scattering into certain direction > by putting this, your, function in a unit cell of a > 1-D, 2-D or even 3-D lattice. > The Patterson function is also a special Fourier-transform, > the convolution of one Fourier with itself. > > Yes there are other functions that are also conceivable. > They also map real space (E-density) to reciprocal > space (structure factor). For example, manifold embedding > techniques might never ever even refer to a Fourier transform and > other highly flexible functions are used for this mapping. But > the physics behind it is scattering of waves (as long > as you believe that there are waves, of course). > > Marius > > > >> Perhaps this was really my question: > >> > >> Do phases *necessarily* dominate a reconstruction of an entity from phases > >> and amplitudes, or are we stuck in a Fourier-based world-view? (Lijun > >> pointed out that the Patterson function is an example of a reconstruction > >> which ignores phases, although obviously it has its problems for > >> reconstructing the electron density when one has too many atoms.) But > >> perhaps there are other phase-ignoring functions besides the Patterson > >> that > >> could be used, instead of the Fourier synthesis? > >> > >> Simply: are phases *inherently* more important than amplitudes, or is this > >> merely a Fourier-thinking bias? > >> > >> Also, > >> > >> Are diffraction phenomena inherently or essentially Fourier-related, just > >> as, e.g., projectile trajectories are inherently and essentially > >> parabola-related? Is the Fourier synthesis really the mathematical essence > >> of the phenomenon, or is it just a nice tool? > > > > In far-field diffraction from a periodic object, yes, diffraction is > > inherently Fourier-related. The scattered amplitudes correspond > > mathematically to the Fourier coefficients of the periodic electron > > density function. You can find this in a solid state physics textbook, > > like Kittel, for example. > > > >> > >> Jacob > >> > >> *** > >> Jacob Pearson Keller > >> Northwestern University > >> Medical Scientist Training Program > >> Dallos Laboratory > >> F. Searle 1-240 > >> 2240 Campus Drive > >> Evanston IL 60208 > >> lab: 847.491.2438 > >> cel: 773.608.9185 > >> email: j-kell...@northwestern.edu > >> *** > >> > >> - Original Message - > >> From: "Marius Schmidt" > >> To: > >> Sent: Friday, March 19, 2010 11:10 AM > >> Subject: Re: [ccp4bb] Why Do Phases Dominate? > >> > >> > >>> You want to have an intuitive picture without > >>> any mathematics and theorems, here it is: > >>> > >>> each black spot you measure on the detector is > >>> the square of an amplitude of a wavelet. The amplitude > >>> says simply how much the wavelet goes up and down > >>> in space. > >>> Now, you can imagine that when you have many > >>> wavelets that go up and down, in the average, they > >>> all cancel and you have a flat surface on a > >>> body of water in 2D, or, in 3-D, a constant > >>> density. However, if the wavelet have a certain > >>> relationship to each other, hence, the mountains > >>> and valleys of the waves are related, you are able > >>> to build even higher mountains and even deeper valleys. > >>> This, however, requires that the wavelets have > >>> a relationship. They must start from a certain > >>> point with a certain PHASE so that they are able > >>> to overlap at another cert
Re: [ccp4bb] Why Do Phases Dominate?
The great thing with diffraction, from crystals and from objects in microscopy is THAT this is A NATURALLY OCCURRING FORM of Fourier transform once one accepts that light is a wave (could be something else). If Fourier transform would not have been invented with another problem from engineering, then it would have emerged NATURALLY from diffraction. Diffraction is an analog (not a digital) Fourier transform. A crystal is a low-noise, analog, natural Fourier amplifier!!! If you want to build the fastest Fourier transform of the world, you could represent your function, which you want to Fourier transform, as density fluctuation and scatter from it, or, you could amplify scattering into certain direction by putting this, your, function in a unit cell of a 1-D, 2-D or even 3-D lattice. The Patterson function is also a special Fourier-transform, the convolution of one Fourier with itself. Yes there are other functions that are also conceivable. They also map real space (E-density) to reciprocal space (structure factor). For example, manifold embedding techniques might never ever even refer to a Fourier transform and other highly flexible functions are used for this mapping. But the physics behind it is scattering of waves (as long as you believe that there are waves, of course). Marius >> Perhaps this was really my question: >> >> Do phases *necessarily* dominate a reconstruction of an entity from phases >> and amplitudes, or are we stuck in a Fourier-based world-view? (Lijun >> pointed out that the Patterson function is an example of a reconstruction >> which ignores phases, although obviously it has its problems for >> reconstructing the electron density when one has too many atoms.) But >> perhaps there are other phase-ignoring functions besides the Patterson >> that >> could be used, instead of the Fourier synthesis? >> >> Simply: are phases *inherently* more important than amplitudes, or is this >> merely a Fourier-thinking bias? >> >> Also, >> >> Are diffraction phenomena inherently or essentially Fourier-related, just >> as, e.g., projectile trajectories are inherently and essentially >> parabola-related? Is the Fourier synthesis really the mathematical essence >> of the phenomenon, or is it just a nice tool? > > In far-field diffraction from a periodic object, yes, diffraction is > inherently Fourier-related. The scattered amplitudes correspond > mathematically to the Fourier coefficients of the periodic electron > density function. You can find this in a solid state physics textbook, > like Kittel, for example. > >> >> Jacob >> >> *** >> Jacob Pearson Keller >> Northwestern University >> Medical Scientist Training Program >> Dallos Laboratory >> F. Searle 1-240 >> 2240 Campus Drive >> Evanston IL 60208 >> lab: 847.491.2438 >> cel: 773.608.9185 >> email: j-kell...@northwestern.edu >> *** >> >> - Original Message - >> From: "Marius Schmidt" >> To: >> Sent: Friday, March 19, 2010 11:10 AM >> Subject: Re: [ccp4bb] Why Do Phases Dominate? >> >> >>> You want to have an intuitive picture without >>> any mathematics and theorems, here it is: >>> >>> each black spot you measure on the detector is >>> the square of an amplitude of a wavelet. The amplitude >>> says simply how much the wavelet goes up and down >>> in space. >>> Now, you can imagine that when you have many >>> wavelets that go up and down, in the average, they >>> all cancel and you have a flat surface on a >>> body of water in 2D, or, in 3-D, a constant >>> density. However, if the wavelet have a certain >>> relationship to each other, hence, the mountains >>> and valleys of the waves are related, you are able >>> to build even higher mountains and even deeper valleys. >>> This, however, requires that the wavelets have >>> a relationship. They must start from a certain >>> point with a certain PHASE so that they are able >>> to overlap at another certain point in space to form, >>> say, a mountain. Mountains are atomic positions, >>> valleys represent free space. >>> So, if you know the phase, the condition that >>> certain waves overlap in a certain way is sufficient >>> to build mountains (and valleys). So, in theory, it >>> would not even be necessary to collect the amplitudes >>> IF YOU WOULD KNOW the phases. However, to determine the >>> phases you need to measure amplitudes to derive the phases >>> from them in the well known ways. Having the phase >>> you could set the amplitudes all to 1.0 and you >>> would still obtain a density of the molecule, that >>> is extremely close to the true E-density. >>> >>> Although I cannot prove it, I have the feeling >>> that phases fulfill the Nyquist-Shannon theorem, since they >>> carry a sign (+/- 180 deg). Without additional assumptions >>> you must do a MULTIPLE isomorphous replacement or >>> a MAD experiment to determine a unique phase (to resolve >>> the phase ambiguity, and the word multiple is stres
Re: [ccp4bb] Why Do Phases Dominate?
> Perhaps this was really my question: > > Do phases *necessarily* dominate a reconstruction of an entity from phases > and amplitudes, or are we stuck in a Fourier-based world-view? (Lijun > pointed out that the Patterson function is an example of a reconstruction > which ignores phases, although obviously it has its problems for > reconstructing the electron density when one has too many atoms.) But > perhaps there are other phase-ignoring functions besides the Patterson > that > could be used, instead of the Fourier synthesis? > > Simply: are phases *inherently* more important than amplitudes, or is this > merely a Fourier-thinking bias? > > Also, > > Are diffraction phenomena inherently or essentially Fourier-related, just > as, e.g., projectile trajectories are inherently and essentially > parabola-related? Is the Fourier synthesis really the mathematical essence > of the phenomenon, or is it just a nice tool? In far-field diffraction from a periodic object, yes, diffraction is inherently Fourier-related. The scattered amplitudes correspond mathematically to the Fourier coefficients of the periodic electron density function. You can find this in a solid state physics textbook, like Kittel, for example. > > Jacob > > *** > Jacob Pearson Keller > Northwestern University > Medical Scientist Training Program > Dallos Laboratory > F. Searle 1-240 > 2240 Campus Drive > Evanston IL 60208 > lab: 847.491.2438 > cel: 773.608.9185 > email: j-kell...@northwestern.edu > *** > > - Original Message - > From: "Marius Schmidt" > To: > Sent: Friday, March 19, 2010 11:10 AM > Subject: Re: [ccp4bb] Why Do Phases Dominate? > > >> You want to have an intuitive picture without >> any mathematics and theorems, here it is: >> >> each black spot you measure on the detector is >> the square of an amplitude of a wavelet. The amplitude >> says simply how much the wavelet goes up and down >> in space. >> Now, you can imagine that when you have many >> wavelets that go up and down, in the average, they >> all cancel and you have a flat surface on a >> body of water in 2D, or, in 3-D, a constant >> density. However, if the wavelet have a certain >> relationship to each other, hence, the mountains >> and valleys of the waves are related, you are able >> to build even higher mountains and even deeper valleys. >> This, however, requires that the wavelets have >> a relationship. They must start from a certain >> point with a certain PHASE so that they are able >> to overlap at another certain point in space to form, >> say, a mountain. Mountains are atomic positions, >> valleys represent free space. >> So, if you know the phase, the condition that >> certain waves overlap in a certain way is sufficient >> to build mountains (and valleys). So, in theory, it >> would not even be necessary to collect the amplitudes >> IF YOU WOULD KNOW the phases. However, to determine the >> phases you need to measure amplitudes to derive the phases >> from them in the well known ways. Having the phase >> you could set the amplitudes all to 1.0 and you >> would still obtain a density of the molecule, that >> is extremely close to the true E-density. >> >> Although I cannot prove it, I have the feeling >> that phases fulfill the Nyquist-Shannon theorem, since they >> carry a sign (+/- 180 deg). Without additional assumptions >> you must do a MULTIPLE isomorphous replacement or >> a MAD experiment to determine a unique phase (to resolve >> the phase ambiguity, and the word multiple is stressed here). >> You need at least 2 heavy atom derivatives. >> This is equivalent to a sampling >> of space with double the frequency as required by >> Nyquist-Shannon's theorem. >> >> Modern approaches use exclusively amplitudes to determine >> phase. You either have to go to very high resolution >> or OVERSAMPLE. Oversampling is not possible with >> crystals, but oversampled data exist at very low >> resolution (in the nm-microm-range). But >> these data clearly show, that also amplitudes carry >> phase information once the Nyquist-Shannon theorem >> is fulfilled (hence when the amplitudes are oversampled). >> >> Best >> Marius >> >> >> >> >> >> >> >> Dr.habil. Marius Schmidt >> Asst. Professor >> University of Wisconsin-Milwaukee >> Department of Physics Room 454 >> 1900 E. Kenwood Blvd. >> Milwaukee, WI 53211 >> >> phone: +1-414-229-4338 >> email: m-schm...@uwm.edu >> http://users.physik.tu-muenchen.de/marius/ >
Re: [ccp4bb] Why Do Phases Dominate?
Perhaps this was really my question: Do phases *necessarily* dominate a reconstruction of an entity from phases and amplitudes, or are we stuck in a Fourier-based world-view? (Lijun pointed out that the Patterson function is an example of a reconstruction which ignores phases, although obviously it has its problems for reconstructing the electron density when one has too many atoms.) But perhaps there are other phase-ignoring functions besides the Patterson that could be used, instead of the Fourier synthesis? Simply: are phases *inherently* more important than amplitudes, or is this merely a Fourier-thinking bias? Also, Are diffraction phenomena inherently or essentially Fourier-related, just as, e.g., projectile trajectories are inherently and essentially parabola-related? Is the Fourier synthesis really the mathematical essence of the phenomenon, or is it just a nice tool? Jacob *** Jacob Pearson Keller Northwestern University Medical Scientist Training Program Dallos Laboratory F. Searle 1-240 2240 Campus Drive Evanston IL 60208 lab: 847.491.2438 cel: 773.608.9185 email: j-kell...@northwestern.edu *** - Original Message - From: "Marius Schmidt" To: Sent: Friday, March 19, 2010 11:10 AM Subject: Re: [ccp4bb] Why Do Phases Dominate? You want to have an intuitive picture without any mathematics and theorems, here it is: each black spot you measure on the detector is the square of an amplitude of a wavelet. The amplitude says simply how much the wavelet goes up and down in space. Now, you can imagine that when you have many wavelets that go up and down, in the average, they all cancel and you have a flat surface on a body of water in 2D, or, in 3-D, a constant density. However, if the wavelet have a certain relationship to each other, hence, the mountains and valleys of the waves are related, you are able to build even higher mountains and even deeper valleys. This, however, requires that the wavelets have a relationship. They must start from a certain point with a certain PHASE so that they are able to overlap at another certain point in space to form, say, a mountain. Mountains are atomic positions, valleys represent free space. So, if you know the phase, the condition that certain waves overlap in a certain way is sufficient to build mountains (and valleys). So, in theory, it would not even be necessary to collect the amplitudes IF YOU WOULD KNOW the phases. However, to determine the phases you need to measure amplitudes to derive the phases from them in the well known ways. Having the phase you could set the amplitudes all to 1.0 and you would still obtain a density of the molecule, that is extremely close to the true E-density. Although I cannot prove it, I have the feeling that phases fulfill the Nyquist-Shannon theorem, since they carry a sign (+/- 180 deg). Without additional assumptions you must do a MULTIPLE isomorphous replacement or a MAD experiment to determine a unique phase (to resolve the phase ambiguity, and the word multiple is stressed here). You need at least 2 heavy atom derivatives. This is equivalent to a sampling of space with double the frequency as required by Nyquist-Shannon's theorem. Modern approaches use exclusively amplitudes to determine phase. You either have to go to very high resolution or OVERSAMPLE. Oversampling is not possible with crystals, but oversampled data exist at very low resolution (in the nm-microm-range). But these data clearly show, that also amplitudes carry phase information once the Nyquist-Shannon theorem is fulfilled (hence when the amplitudes are oversampled). Best Marius Dr.habil. Marius Schmidt Asst. Professor University of Wisconsin-Milwaukee Department of Physics Room 454 1900 E. Kenwood Blvd. Milwaukee, WI 53211 phone: +1-414-229-4338 email: m-schm...@uwm.edu http://users.physik.tu-muenchen.de/marius/
Re: [ccp4bb] self rotation education
Hi Francis, On Thu, Mar 18, 2010 at 09:03:13AM -0600, Francis E Reyes wrote: > Hi all > > I have a solved structure that crystallizes as a trimer I guess you mean that you have 3 mol/asu? And not just "a trimer in solution that then forms crystals", right? > to a reasonable R/Rfree, but I'm trying to rationalize the peaks in > my self rotation. That has very often fooled me: selfrotation functions can be very misleading - at least in my hands (even using different programs, resoluton limits, E vs F etc etc). Often peaks that should be there aren't and vice versa. > The space group is P212121, calculating my self > rotations from 50-3A, integration radius of 22 (the radius of my > molecule is about 44). I can see the three fold NCS from my > structure on the 120 slice Which one is it: the one at (90,90) or the one at (45,45)? Or both? > but I'm trying to rationalize apparent two folds in my kappa=180. A > picture of both slices is enclosed. The non crystallographic peaks > for kappa=180, P222 begin to appear at kappa=150 and are strongest > on the 180 slice. If you had a D_3 multimer (3-fold with three 2-folds perpendicular to it) I could interpret those as (a) 3-fold at (90,90) ==> 2-fold at ( 90,0) [direction cosines = 1.0 0.0 0.0] 2-fold at (210,0) [direction cosines = -0.5 -0.0 -0.86603] 2-fold at (330,0) [direction cosines = -0.5 -0.0 0.86603] (b) 3-fold at (45,45) ==> 2-fold at ( 90,315) [direction cosines = 0.70711 -0.70711 0.0] 2-fold at ( 45,180) [direction cosines = -0.70711 0.0 0.70711] 2-fold at (135, 90) [direction cosines = 0.0 0.70711 -0.70711] All those 2-folds axes have a 120-degree angle between them (obviously). I might have the exact angles wrong (there could be slight offsets from thoise ideal values and the self-rotation plot just piles the peaks exactly onto crystallographic symmetry operators because of the multiplicity of those symmetry elements) ... or maybe even more? But for both 3-fold axes in the kappa=120 section I can convince myself that there are the corresponding 2-folds to make up a D_3 multimer. Since you probably only have space for 3 mol/asu, I would guess case (a) to be the correct 3-fold NCS with the 2-folds in (a) resulting from the 21 parallel to your 3-fold and the peaks in (b) resulting from the remaining symmetry. Does that fit? Cheers Clemens > > My molecule looks close to a bagel (44A wide and 28A tall). The > three fold NCS is down the axis of looking down on the bagel > hole. I'm trying to find the two fold. I imagine it could be slicing > the bagel in half (like to eat it for yourself) or slicing it > vertically (like to share amongst kids) but I'm not exactly sure > what's the best way to visualize this. Is there something easier > than correlation maps with getax (since I have the rotation > (polarrfn) and translation?). If you have an eye for spotting > symmetry, Ill send the pdb in confidence. > Thanks! > > FR > > > > - > Francis Reyes M.Sc. > 215 UCB > University of Colorado at Boulder > > gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D > > 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D > > > -- *** * Clemens Vonrhein, Ph.D. vonrhein AT GlobalPhasing DOT com * * Global Phasing Ltd. * Sheraton House, Castle Park * Cambridge CB3 0AX, UK *-- * BUSTER Development Group (http://www.globalphasing.com) ***
Re: [ccp4bb] Why Do Phases Dominate?
You want to have an intuitive picture without any mathematics and theorems, here it is: each black spot you measure on the detector is the square of an amplitude of a wavelet. The amplitude says simply how much the wavelet goes up and down in space. Now, you can imagine that when you have many wavelets that go up and down, in the average, they all cancel and you have a flat surface on a body of water in 2D, or, in 3-D, a constant density. However, if the wavelet have a certain relationship to each other, hence, the mountains and valleys of the waves are related, you are able to build even higher mountains and even deeper valleys. This, however, requires that the wavelets have a relationship. They must start from a certain point with a certain PHASE so that they are able to overlap at another certain point in space to form, say, a mountain. Mountains are atomic positions, valleys represent free space. So, if you know the phase, the condition that certain waves overlap in a certain way is sufficient to build mountains (and valleys). So, in theory, it would not even be necessary to collect the amplitudes IF YOU WOULD KNOW the phases. However, to determine the phases you need to measure amplitudes to derive the phases from them in the well known ways. Having the phase you could set the amplitudes all to 1.0 and you would still obtain a density of the molecule, that is extremely close to the true E-density. Although I cannot prove it, I have the feeling that phases fulfill the Nyquist-Shannon theorem, since they carry a sign (+/- 180 deg). Without additional assumptions you must do a MULTIPLE isomorphous replacement or a MAD experiment to determine a unique phase (to resolve the phase ambiguity, and the word multiple is stressed here). You need at least 2 heavy atom derivatives. This is equivalent to a sampling of space with double the frequency as required by Nyquist-Shannon's theorem. Modern approaches use exclusively amplitudes to determine phase. You either have to go to very high resolution or OVERSAMPLE. Oversampling is not possible with crystals, but oversampled data exist at very low resolution (in the nm-microm-range). But these data clearly show, that also amplitudes carry phase information once the Nyquist-Shannon theorem is fulfilled (hence when the amplitudes are oversampled). Best Marius Dr.habil. Marius Schmidt Asst. Professor University of Wisconsin-Milwaukee Department of Physics Room 454 1900 E. Kenwood Blvd. Milwaukee, WI 53211 phone: +1-414-229-4338 email: m-schm...@uwm.edu http://users.physik.tu-muenchen.de/marius/
Re: [ccp4bb] self rotation education
Francis, I would at least compute all the maps to the same resolution, and as I suggested earlier use all the Fobs data you have, and finally try using E's. The differences could be due to the solvent model (or lack of it) in the Fcalc's, though I concede that doesn't explain the difference between Molrep & Polarrfn for the Fobs data. Using E's down-weights the low-res solvent contribution, so it might help here. Sorry can't help with Molrep, I've never tried doing comparisons with Polarrfn. It could be that Molrep is applying some default sharpening factor. Cheers -- Ian On Fri, Mar 19, 2010 at 2:41 PM, Francis E Reyes wrote: > All, > > I recalculated in molrep_srfn, using F and SIGF of the original data > (foo_30_rf.pdf) and FCalc/SIGF on the refined model (foo_29_rf.pdf). Note > that foo_29_rf.pdf ( calculated phases using 50A to ~2.5A ) is extremely > different than the original self rf functions I sent (which was the > calculated phases from 50A-3A calculated in polarrfn). In both cases, > molrep_srfn greatly diminishes the psuedo peaks on the 180 slice independent > of whether I use the original F's or calculated Fs. > > This is a little disconcerning as the purpose of this exercise is to > determine whether I can properly interpret the self rotation peaks with a > known model so that I can extend what I learned to a much more difficult > present case where I have NCS but quite poor phases. Now I don't know which > program to use. > > Does molrep_srfn do some fancy scaling to the data that polarrfn does not? > > F > > > > - > Francis Reyes M.Sc. > 215 UCB > University of Colorado at Boulder > > gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D > > 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D > > > > On Mar 19, 2010, at 8:12 AM, Ian Tickle wrote: > >> Dirk, I'm not sure this is right, the NCS 2-folds clearly occur at phi >> = 45, 135 ..., not at phi = 30, 150 ... as required by your >> explanation. Also you haven't explained the very clear peaks near >> theta = 45, phi = 0. 90 ... . I won't be convinced until I see the >> results from RFCORR! >> >> Cheers >> >> -- Ian >> >> On Fri, Mar 19, 2010 at 9:47 AM, Dirk Kostrewa >> wrote: >>> ... and here a slightly clearer version where I numbered the NCS-related >>> positions 1,2,3 and their crystallographic equivalent positions 1',2',3', >>> which makes the NCS dyads a bit easier to understand ... >>> >>> Sorry for sending two pictures. >>> >>> Best regards, >>> >>> Dirk. >>> >>> Am 19.03.10 10:31, schrieb Dirk Kostrewa: >>> >>> Dear Francis Reyes, >>> >>> from the self-rotation function at kappa=120 degrees, you can see that one >>> threefold NCS axis is perpendicular to a crystallographic twofold axis. I >>> haven't worked this out for your particular case, but the combination of a >>> threefold (n-fold) NCS axis perpendicular to a crystallographic twofold axis >>> creates three (n) NCS twofold axes (that can be viewed from both directions >>> and in case of an uneven NCS axis appear "twice"). I've appended a schematic >>> stereographic projection to make this a bit clearer (full dyad symbol >>> crystallographic, open dyad and triangle symbols NCS, green circles >>> positions above plane, red circles positions below plane created by >>> crystallographic dyad, dashed lines help to visualize the NCS threefold, >>> thick solid line crystallographic twofold, thin solid lines NCS twofolds). >>> >>> Good luck, >>> >>> Dirk. >>> >>> Am 18.03.10 16:03, schrieb Francis E Reyes: >>> >>> Hi all >>> >>> I have a solved structure that crystallizes as a trimer to a reasonable >>> R/Rfree, but I'm trying to rationalize the peaks in my self rotation. The >>> space group is P212121, calculating my self rotations from 50-3A, >>> integration radius of 22 (the radius of my molecule is about 44). I can see >>> the three fold NCS from my structure on the 120 slice, but I'm trying to >>> rationalize apparent two folds in my kappa=180. A picture of both slices is >>> enclosed. The non crystallographic peaks for kappa=180, P222 begin to appear >>> at kappa=150 and are strongest on the 180 slice. >>> >>> My molecule looks close to a bagel (44A wide and 28A tall). The three fold >>> NCS is down the axis of looking down on the bagel hole. I'm trying to find >>> the two fold. I imagine it could be slicing the bagel in half (like to eat >>> it for yourself) or slicing it vertically (like to share amongst kids) but >>> I'm not exactly sure what's the best way to visualize this. Is there >>> something easier than correlation maps with getax (since I have the rotation >>> (polarrfn) and translation?). If you have an eye for spotting symmetry, Ill >>> send the pdb in confidence. >>> Thanks! >>> >>> FR >>> >>> >>> >>> >>> - >>> Francis Reyes M.Sc. >>> 215 UCB >>> University of Colorado at Boulder >>> >>> gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D >>> >>> 8AE2 F2F4 90F7 9
Re: [ccp4bb] imosflm plot question?
Just sending along the answers to my question about the imosflm crystal missets and mosaicity plot from Ethan Meritt and Harry Powell. >Value of the parameter as a function of diffraction image number. If the parameter didn't vary, it would show as a horizontal line. phi(x), etc are the crystal orientation angles. mosaicity is self-named. Ethan Hi Hari phi(x) phi(y) and phi(z) are the crystal missetting angles - how much the apparent orientation differs from the calculated one from indexing. Historically, with crystals mounted in capillaries, the crystal would often really slide about, but these days (with cryocooled crystals held rigidly in loops) they account for things like the rotation axis not ebing perpendicular to the X-ray beam. "Mosaic" should be self explanatory... - Show quoted text - > - Show quoted text - > > Harry -- Dr Harry Powell, MRC Laboratory of Molecular Biology, MRC Centre, Hills Road, Cambridge, CB2 0QH -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742 On Wed, Mar 17, 2010 at 5:17 PM, hari jayaram wrote: > Hello , > > I had a question about the imosflm plots during data integration. > > I am attaching the plot for one of my datasets ...Just curious what the > middle plot is plotting > > > Thanks a lot for your help > > Hari > > > >
Re: [ccp4bb] Soaking to Remove Bound Ligands from Crystals
Dear Critton We have done a case, which was to remove the ligand A from the crystal in complex with ligand B and metal ions. Please see the link of this case below (Methods). http://www.ncbi.nlm.nih.gov/pubmed/20139160 Cheers, Tao-Hsin
Re: [ccp4bb] Why Do Phases Dominate?
On Thu, 2010-03-18 at 12:51 -0500, Jacob Keller wrote: > Does anybody have a good way to understand this? Sure, it just depends on what would one consider a "good" way to understand. For a pure empiricist, it's good enough to see one of those two-dimensional phase swap pictures. For a "mathematically inclined" there is nothing better than the song that Fourier transform sings to them. Based on the fact that you find the simple statement that "Fourier synthesis emphasizes phases" "pretty unsatisfying" I would allow myself to guess that you are a person trying to grasp concepts in physics without learning its language, which is math. This is not meant in a bad sense - it is beyond doubt that true understanding of physics comes from explaining things with words and analogies, not by writing down a bunch of equations. Let's try a couple of things. 1. Why are some reflections stronger than others? This is easy to understand by invoking the Richard Feynman's picture of every scatterer contributing a little arrow to the final result. All arrows are the same length, but are rotated depending on how long does it take for a photon to fly to the detector. (Helps if you draw them as we go along). Every reflection is produced by an imaginary set of Bragg planes. When atoms are randomly distributed in the direction perpendicular to the planes, their corresponding arrows assume all possible orientations and the resulting "big arrow" is likely close to zero. Now if atoms tend to cluster near the Bragg planes, majority of the arrows will all be pointing the same way and the resulting arrow gets longer. Other words, the amplitude of the reflection increases when atoms are arranged in space with periodicity matching the distance between Bragg planes. This is how Patterson map gives you the set of interatomic distances. Unfortunately, there are so many atoms in proteins that their motions combined with experimental uncertainties turn it into incomprehensible mess. So what is the phase? It is the orientation of the big arrow, and we have so far only addressed its length. If you prevent Bragg planes from sliding (i.e. one of the planes must pass through the fixed origin), then the arrow orientation will tell you where exactly in space the "clustering" of atoms is located - halfway between the planes, or three quarters away from the origin, etc. Hopefully you see how this information is crucial in determining the structure. Actual structure determination is done by combining information from different reflections, and without phase information the corresponding "atom clusters" or "density packs" can slide all around the place, producing great deal of uncertainty. 2. Sports analogies are always popular. Let's remember that intensities/amplitudes tell you how many photons have arrived, while phases tell you when they did. I'll stick to B-sports. Baseball. A blind and deaf catcher only knows how many balls he received (amplitude). This can tell him how many pitches were made, but not how far in the field they landed. A catcher who is only blind hears when bat hits the ball and can time how long it took for the field players to return the ball to him (phase). He can then delineate how far balls usually fly, thus determining a 1D structure. If field players record when they received the ball (multiple reflections), the exact place where ball landed can be figured out (actually,you need to split every ball and send a copy to every field player for triangulation to work, but sports analogies do not have to be perfect :) Basketball. A team always plays a primitive game, where ball is thrown in and followed by jumpshot. They are so great, however, that they never miss. If you only count the score (amplitude), you will only know how many possessions they had. But if you record the time between the whistle and scoring (phases), and take into account that pass is horizontal and shot has a significant vertical component thus its horizontal speed is lower, you can figure out from what distance they shoot more often. Again, to pinpoint exact location of all four players (who never move), you'll need to allow two/three/four/etc passes (multiple reflections). But sports analogies do not have to be perfect :) Biathlon. If you only count the shots at all targets of shooting range (amplitude), you only know how many are running the race. If you record the time when shots are made (phases), you know who is running first, second, etc. Structure here is inherently 1D, but sports analogies do not have to be perfect :) HTH, Ed. -- Edwin Pozharski, PhD, Assistant Professor University of Maryland, Baltimore -- When the Way is forgotten duty and justice appear; Then knowledge and wisdom are born along with hypocrisy. When harmonious relationships dissolve then respect and devotion arise; When a nation falls to chaos then loyalty and patriotism are born. --
Re: [ccp4bb] self rotation education
Hi Ian, o yes, I didn't work out the particular case that Francis Reyes was asking for, but intended to give a more general idea where additional twofold NCS axes could come from, by a combination of a NCS axis perpendicular to a crystallographic twofold axis. The image should just support this. I hope, that with this pointer, Francis Reyes will be able to work out how the self-rotation function peaks are related. Cheers, Dirk. Am 19.03.10 15:12, schrieb Ian Tickle: Dirk, I'm not sure this is right, the NCS 2-folds clearly occur at phi = 45, 135 ..., not at phi = 30, 150 ... as required by your explanation. Also you haven't explained the very clear peaks near theta = 45, phi = 0. 90 ... . I won't be convinced until I see the results from RFCORR! Cheers -- Ian On Fri, Mar 19, 2010 at 9:47 AM, Dirk Kostrewa wrote: ... and here a slightly clearer version where I numbered the NCS-related positions 1,2,3 and their crystallographic equivalent positions 1',2',3', which makes the NCS dyads a bit easier to understand ... Sorry for sending two pictures. Best regards, Dirk. Am 19.03.10 10:31, schrieb Dirk Kostrewa: Dear Francis Reyes, from the self-rotation function at kappa=120 degrees, you can see that one threefold NCS axis is perpendicular to a crystallographic twofold axis. I haven't worked this out for your particular case, but the combination of a threefold (n-fold) NCS axis perpendicular to a crystallographic twofold axis creates three (n) NCS twofold axes (that can be viewed from both directions and in case of an uneven NCS axis appear "twice"). I've appended a schematic stereographic projection to make this a bit clearer (full dyad symbol crystallographic, open dyad and triangle symbols NCS, green circles positions above plane, red circles positions below plane created by crystallographic dyad, dashed lines help to visualize the NCS threefold, thick solid line crystallographic twofold, thin solid lines NCS twofolds). Good luck, Dirk. Am 18.03.10 16:03, schrieb Francis E Reyes: Hi all I have a solved structure that crystallizes as a trimer to a reasonable R/Rfree, but I'm trying to rationalize the peaks in my self rotation. The space group is P212121, calculating my self rotations from 50-3A, integration radius of 22 (the radius of my molecule is about 44). I can see the three fold NCS from my structure on the 120 slice, but I'm trying to rationalize apparent two folds in my kappa=180. A picture of both slices is enclosed. The non crystallographic peaks for kappa=180, P222 begin to appear at kappa=150 and are strongest on the 180 slice. My molecule looks close to a bagel (44A wide and 28A tall). The three fold NCS is down the axis of looking down on the bagel hole. I'm trying to find the two fold. I imagine it could be slicing the bagel in half (like to eat it for yourself) or slicing it vertically (like to share amongst kids) but I'm not exactly sure what's the best way to visualize this. Is there something easier than correlation maps with getax (since I have the rotation (polarrfn) and translation?). If you have an eye for spotting symmetry, Ill send the pdb in confidence. Thanks! FR - Francis Reyes M.Sc. 215 UCB University of Colorado at Boulder gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de *** -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de *** -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de ***
Re: [ccp4bb] self rotation education
Dirk, I'm not sure this is right, the NCS 2-folds clearly occur at phi = 45, 135 ..., not at phi = 30, 150 ... as required by your explanation. Also you haven't explained the very clear peaks near theta = 45, phi = 0. 90 ... . I won't be convinced until I see the results from RFCORR! Cheers -- Ian On Fri, Mar 19, 2010 at 9:47 AM, Dirk Kostrewa wrote: > ... and here a slightly clearer version where I numbered the NCS-related > positions 1,2,3 and their crystallographic equivalent positions 1',2',3', > which makes the NCS dyads a bit easier to understand ... > > Sorry for sending two pictures. > > Best regards, > > Dirk. > > Am 19.03.10 10:31, schrieb Dirk Kostrewa: > > Dear Francis Reyes, > > from the self-rotation function at kappa=120 degrees, you can see that one > threefold NCS axis is perpendicular to a crystallographic twofold axis. I > haven't worked this out for your particular case, but the combination of a > threefold (n-fold) NCS axis perpendicular to a crystallographic twofold axis > creates three (n) NCS twofold axes (that can be viewed from both directions > and in case of an uneven NCS axis appear "twice"). I've appended a schematic > stereographic projection to make this a bit clearer (full dyad symbol > crystallographic, open dyad and triangle symbols NCS, green circles > positions above plane, red circles positions below plane created by > crystallographic dyad, dashed lines help to visualize the NCS threefold, > thick solid line crystallographic twofold, thin solid lines NCS twofolds). > > Good luck, > > Dirk. > > Am 18.03.10 16:03, schrieb Francis E Reyes: > > Hi all > > I have a solved structure that crystallizes as a trimer to a reasonable > R/Rfree, but I'm trying to rationalize the peaks in my self rotation. The > space group is P212121, calculating my self rotations from 50-3A, > integration radius of 22 (the radius of my molecule is about 44). I can see > the three fold NCS from my structure on the 120 slice, but I'm trying to > rationalize apparent two folds in my kappa=180. A picture of both slices is > enclosed. The non crystallographic peaks for kappa=180, P222 begin to appear > at kappa=150 and are strongest on the 180 slice. > > My molecule looks close to a bagel (44A wide and 28A tall). The three fold > NCS is down the axis of looking down on the bagel hole. I'm trying to find > the two fold. I imagine it could be slicing the bagel in half (like to eat > it for yourself) or slicing it vertically (like to share amongst kids) but > I'm not exactly sure what's the best way to visualize this. Is there > something easier than correlation maps with getax (since I have the rotation > (polarrfn) and translation?). If you have an eye for spotting symmetry, Ill > send the pdb in confidence. > Thanks! > > FR > > > > > - > Francis Reyes M.Sc. > 215 UCB > University of Colorado at Boulder > > gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D > > 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D > > > > > > -- > > *** > Dirk Kostrewa > Gene Center, A 5.07 > Ludwig-Maximilians-University > Feodor-Lynen-Str. 25 > 81377 Munich > Germany > Phone:+49-89-2180-76845 > Fax: +49-89-2180-76999 > E-mail: kostr...@genzentrum.lmu.de > WWW: www.genzentrum.lmu.de > *** > > > -- > > *** > Dirk Kostrewa > Gene Center, A 5.07 > Ludwig-Maximilians-University > Feodor-Lynen-Str. 25 > 81377 Munich > Germany > Phone:+49-89-2180-76845 > Fax: +49-89-2180-76999 > E-mail: kostr...@genzentrum.lmu.de > WWW: www.genzentrum.lmu.de > *** >
[ccp4bb] odd request: add phase error linearly with resolution
Hi all I'd like to add a phase error to my PHIB's and FOM's (experimental phases) that increases linearly with higher resolution.. it's akin to taking good phases and making them bad. Any approaches on how this can be done? Thanks FR - Francis Reyes M.Sc. 215 UCB University of Colorado at Boulder gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D
Re: [ccp4bb] Why Do Phases Dominate?
On Thu, Mar 18, 2010 at 10:36 PM, Edward A. Berry wrote: > I have been politely reminded offline that by definition amplitudes > cannot be negative. We could call them coefficients, but: Hi Edward This obviously depends on whether you're talking about the physical entity 'amplitude' or the quantity you are calling an 'amplitude' purely for mathematical convenience. As you say, if what is meant by the former is the usual meaning 'peak amplitude' then by definition it cannot be negative, but of course there's no problem for the practical purposes of doing the calculations if the peak amplitude is a negative number: the mathematics of amplitudes and phases works equally well if negative numbers are substituted for amplitudes (multiplying the amplitude by -1 obviously produces the same result as adding Pi to the phase). Look at the MTZ file produced by the SIGMAA program & you'll see negative amplitudes (it's been that way for ~ 25 years and no-one has ever objected!). The amplitude is defined as the maximum excursion of the field variable in either the positive *or negative* direction. We are used to dealing with sinusoidal waves which are symmetric about the time or distance axis, so we don't need to consider the wave troughs independently of the wave peaks, but clearly the trough amplitude is a negative number equal to minus the peak amplitude for symmetric waves, and not equal to minus the peak amplitude for asymmetric waves At least I'm assuming from what you say that the objection was purely a semantic one, and not that the calculation would produce an incorrect result if you used a negative number as the amplitude. Unbelievably, European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century (according to Wikipedia!), and in AD 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". In the 18th century it was common practice to ignore any negative results derived from equations, on the assumption that they were meaningless. The objection to the use of the word 'amplitude' (implying 'peak amplitude') is therefore really not that it's negative, but that you're using the wrong word to describe your quantity, and maybe 'trough amplitude' would have been more accurate. But there are plenty of examples where apparently nonsensical values are used purely for mathematical convenience, take negative intensities or negative B factors as cases in point. Since an intensity is a physical entity it cannot by definition be negative. Nevertheless everyone understands what is meant by 'negative intensity'. Are we instead obliged to use the term 'negative squared amplitude' henceforth? Yours somewhat tongue in cheek, -- Ian
Re: [ccp4bb] self rotation education
... and here a slightly clearer version where I numbered the NCS-related positions 1,2,3 and their crystallographic equivalent positions 1',2',3', which makes the NCS dyads a bit easier to understand ... Sorry for sending two pictures. Best regards, Dirk. Am 19.03.10 10:31, schrieb Dirk Kostrewa: Dear Francis Reyes, from the self-rotation function at kappa=120 degrees, you can see that one threefold NCS axis is perpendicular to a crystallographic twofold axis. I haven't worked this out for your particular case, but the combination of a threefold (n-fold) NCS axis perpendicular to a crystallographic twofold axis creates three (n) NCS twofold axes (that can be viewed from both directions and in case of an uneven NCS axis appear "twice"). I've appended a schematic stereographic projection to make this a bit clearer (full dyad symbol crystallographic, open dyad and triangle symbols NCS, green circles positions above plane, red circles positions below plane created by crystallographic dyad, dashed lines help to visualize the NCS threefold, thick solid line crystallographic twofold, thin solid lines NCS twofolds). Good luck, Dirk. Am 18.03.10 16:03, schrieb Francis E Reyes: Hi all I have a solved structure that crystallizes as a trimer to a reasonable R/Rfree, but I'm trying to rationalize the peaks in my self rotation. The space group is P212121, calculating my self rotations from 50-3A, integration radius of 22 (the radius of my molecule is about 44). I can see the three fold NCS from my structure on the 120 slice, but I'm trying to rationalize apparent two folds in my kappa=180. A picture of both slices is enclosed. The non crystallographic peaks for kappa=180, P222 begin to appear at kappa=150 and are strongest on the 180 slice. My molecule looks close to a bagel (44A wide and 28A tall). The three fold NCS is down the axis of looking down on the bagel hole. I'm trying to find the two fold. I imagine it could be slicing the bagel in half (like to eat it for yourself) or slicing it vertically (like to share amongst kids) but I'm not exactly sure what's the best way to visualize this. Is there something easier than correlation maps with getax (since I have the rotation (polarrfn) and translation?). If you have an eye for spotting symmetry, Ill send the pdb in confidence. Thanks! FR - Francis Reyes M.Sc. 215 UCB University of Colorado at Boulder gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de *** -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de *** Combination-Crystallographic-NCS.pdf Description: Adobe PDF document
Re: [ccp4bb] self rotation education
Dear Francis Reyes, from the self-rotation function at kappa=120 degrees, you can see that one threefold NCS axis is perpendicular to a crystallographic twofold axis. I haven't worked this out for your particular case, but the combination of a threefold (n-fold) NCS axis perpendicular to a crystallographic twofold axis creates three (n) NCS twofold axes (that can be viewed from both directions and in case of an uneven NCS axis appear "twice"). I've appended a schematic stereographic projection to make this a bit clearer (full dyad symbol crystallographic, open dyad and triangle symbols NCS, green circles positions above plane, red circles positions below plane created by crystallographic dyad, dashed lines help to visualize the NCS threefold, thick solid line crystallographic twofold, thin solid lines NCS twofolds). Good luck, Dirk. Am 18.03.10 16:03, schrieb Francis E Reyes: Hi all I have a solved structure that crystallizes as a trimer to a reasonable R/Rfree, but I'm trying to rationalize the peaks in my self rotation. The space group is P212121, calculating my self rotations from 50-3A, integration radius of 22 (the radius of my molecule is about 44). I can see the three fold NCS from my structure on the 120 slice, but I'm trying to rationalize apparent two folds in my kappa=180. A picture of both slices is enclosed. The non crystallographic peaks for kappa=180, P222 begin to appear at kappa=150 and are strongest on the 180 slice. My molecule looks close to a bagel (44A wide and 28A tall). The three fold NCS is down the axis of looking down on the bagel hole. I'm trying to find the two fold. I imagine it could be slicing the bagel in half (like to eat it for yourself) or slicing it vertically (like to share amongst kids) but I'm not exactly sure what's the best way to visualize this. Is there something easier than correlation maps with getax (since I have the rotation (polarrfn) and translation?). If you have an eye for spotting symmetry, Ill send the pdb in confidence. Thanks! FR - Francis Reyes M.Sc. 215 UCB University of Colorado at Boulder gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D -- *** Dirk Kostrewa Gene Center, A 5.07 Ludwig-Maximilians-University Feodor-Lynen-Str. 25 81377 Munich Germany Phone: +49-89-2180-76845 Fax:+49-89-2180-76999 E-mail: kostr...@genzentrum.lmu.de WWW:www.genzentrum.lmu.de *** Combination-Crystallographic-NCS.pdf Description: Adobe PDF document
Re: [ccp4bb] Why Do Phases Dominate?
Dear Jacob, That's a good question, as you can see from the amount of debate you've inspired. There have been a lot of good answers already. Depending on how your intuition works, you might prefer Gerard's explanation in terms of convolutions, or Bart's in terms of the size of errors in the electron density. The argument Bart uses is the same as one I used for a chapter in Methods in Enzymology, which was then revised for volume F of the International Tables. And it actually turns out that the mathematical analysis isn't that difficult. Basically, from Parseval's theorem, we know that the rms error of an electron density map is proportional to the rms error of the structure factors (including both amplitude and phase). It's not that difficult to work out the rms error that is introduced in a structure factor either by taking the phase randomly from a uniform distribution of phases or by taking the amplitude randomly from a Wilson distribution of amplitudes. The random choice of phases will introduce structure factor errors proportional to the square root of 2 (approximately 1.41) times the rms structure factor amplitude, whereas the random choice of amplitudes will introduce structure factor errors proportional to the square root of [(4-Pi)/2] (approximately 0.66) times the rms structure factor amplitude. In comparison, if you just set all the amplitudes to zero (in which case you could use anything for the phases), the rms error in the structure factors would simply be equal to the rms value of the structure factors. To summarise this, the random phase map looks *less* like the real structure than a completely flap map (Fourier transform of all zeros), but the random amplitude map looks *more* like the real structure than the flat map. There's a schematic illustration of this on our web page (http://www-structmed.cimr.cam.ac.uk/Course/Fourier/Fourier.html#Parseval), but I see I could add a bit about the simple integrals that give the results above. Regards, Randy Read On 18 Mar 2010, at 20:57, Bart Hazes wrote: > Hi Jacob here is another stab at it. Not as forme > > When you create an electron density map you can think of each amplitude F and > phase P as forming a vector Vmap that consists of two sub-vectors: one that > represents the true vector Vtrue and the other representing the vector, > Vdiff, that connects Vtrue to Vmap. Just try to picture this. > > You can now think of calculating three maps based on Vtrue, Vdiff, and Vmap. > Since FFTs are additive you can consider the map you would normally > calculate, Vmap, as being the sum of the two others; Vtrue being reality and > Vmap being noise. > > If you have a phase error of 60 degrees Vdiff will actually already be of the > same magnitude as Vtrue. If you have random phases you will, on average, be > 90 degrees off, and Vdiff will be 1.41 times as large as Vtrue (sqrt(2)). > Even relatively small phase errors give significant Vdiff/Vtrue ratios > (2*sin(half-the-phase-error) if I'm right) > > You mentioned "Amplitudes as numbers presumably carry at least as much > information as phases, or perhaps even more, as phases are limited to 360deg, > whereas amplitudes can be anything." > > But in reality amplitudes cannot be anything since they follow a Wilson's > distribution which has the bulk of the amplitudes cluster near the peak of > the distribution. The real mathematicians can probably tell you the expected > amplitude error in such a scenario but that would certainly go beyond an > intuitive explanation and my own math skills. If you look at experimental > errors in the amplitudes it is even much less. Rmerge tends to be in the > 3-10% range and that is on intensities, it will be considerable less on > amplitudes. > > Bart > > > Jacob Keller wrote: >> Dear Crystallographers, >> >> I have seen many demonstrations of the primacy of phase information for >> determining the outcome of fourier syntheses, but have not been able to >> understand intuitively why this is so. Amplitudes as numbers presumably >> carry at least as much information as phases, or perhaps even more, as >> phases are limited to 360deg, whereas amplitudes can be anything. Does >> anybody have a good way to understand this? >> >> One possible answer is "it is the nature of the Fourier Synthesis to >> emphasize phases." (Which is a pretty unsatisfying answer). But, could there >> be an alternative summation which emphasizes amplitudes? If so, that might >> be handy in our field, where we measure amplitudes... >> >> Regards, >> >> Jacob Keller >> >> *** >> Jacob Pearson Keller >> Northwestern University >> Medical Scientist Training Program >> Dallos Laboratory >> F. Searle 1-240 >> 2240 Campus Drive >> Evanston IL 60208 >> lab: 847.491.2438 >> cel: 773.608.9185 >> email: j-kell...@northwestern.edu >> *** >> > > -- > > ===
