Re: [ccp4bb] Summary: Phasing statistics
Since it is suggested to run SHARP in order to obtain the phasing statistics, I take the liberty to provide a link where the expressions for relevant quantities are specified : http://www.globalphasing.com/pipermail/sharp-discuss/2003-March/001490.html As a general problem, all these statistical indicators were defined in the early days of protein crystallography, in the context of the Blow Crick (1959) framework (i.e. assuming error-free native measurements) using MIR data (i.e. essentially yielding unimodal phase probability distributions). The R-Cullis was initially defined for centric reflections only. Modern maximum-likelihood phasing methods have abandoned the Blow Crick concept of error-free native measurements and use a full 2-dimensional probability distribution for acentric structure factors on the complex plane. The methods are therefore capable of adequately dealing with highly bimodal probability distributions (e.g. SIR, SAD) and with data where there is no native (or otherwise special) data set (e.g. MAD). It is not entirely evident how the Blow Crick Phasing-Power, R-Cullis and FOM can be extended and generalized. The approach adopted in SHARP is described in the page whose link is given above. Concerning the FOM, it is not strictly true that the FOM, evaluated on a 2-dimensional probability distribution is equal to the cosine of the phase error., This is only the case if one assumes the native amplitude to be error-free. However, the cases discussed by Ian (bimodal distributions in SIR or SAD) will be correctly dealt with by SHARP. Things become also more tricky when computing and using Hendrickson-Lattman (1970) coefficients since, in the general case, these can not be calculated in a meaningful way for the native phase probability distribution (see the discussion in section 8 of Bricogne et al. (2003) [Acta Cryst D.59, 2023-2030]. This is a very important issue in connection with the subsequent use of density-modification techniques, but it is often overlooked. Marc Harmer, Nicholas wrote: Dear Colleagues, I am very grateful to everyone who contributed to the discussion regarding phasing statistics that I initiated. I certainly found it very informative. Below is a summary of the technical responses that I regarding this problem. 1) Use some of the statistics that SHELXD and SHELXE do provide (e.g. CC/CCfree for SHELXD, CCfree and connectivity for SHELXE). These could be compared to statistics produced for well determined structures (e.g. see Debreczeni et al. 2003 Acta Cryst. D., D59, 688-696). 2) Take the results from SHELX and put them into SHARP to generate the statistics. 3) Take the results from SHELX and put them into phaser_er, CRANK, or MLPHARE (perhaps with more difficulty) to generate the statistics. Thanks to Rick Lewis, Boaz Shaanan, Ed Lowe and Eleanor Dodson for suggestions. Cheers, Nic Harmer [For anyone interested, I took approaches 1 and 2. I got a good figures for phasing power from SHARP (somehow I failed to find the Rcullis, never mind), quoted the FOM at the end of SHELX, and the values for CC/CCfree from SHELXD, and the map contrast in the original and inverted hands from SHELXE. These all looked quite convincing, so hopefully my referees will be happy.] -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] units of f0, f', f''
Quoting Dale Tronrud det...@uoxray.uoregon.edu: P.S. to respond out-of-band to Dr. Schiltz: On the US flag I see 7 red stripes, 6 white stripes, and 50 stars. If I state I see 7 I have conveyed no useful information. Yes, but cast in a mathematical equations one would write : Number of red stripes = 7 Number of white stripes = 6 Number of stars = 50 i.e. without units one would not write : Number = 7 red stripes Number = 6 white stripes Number = 50 stars Marc
Re: [ccp4bb] units of f0, f', f''
James Holton wrote: Anyway, the structure factor is a ratio, and therefore is technically a dimensionless quantity, but even a dimensionless quantity has a unit Like the index of refraction, which is also a ratio and therefore a dimensionless quantity whose unit is...what again ? -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] units of f0, f', f''
I fully agree with Ian and would again point to the authoritative documentation : http://www.bipm.org/en/si/derived_units/2-2-3.html The quantities f^0, f' and f are unitless, i.e. simply numbers (or rather: their unit is the number one, which is usually omitted). The unit of the electron density is really just 1/Å^3. To see this, consider that the electron density is defined to be \rho = (Number of electrons)/volume The numerator is simply a count, and thus unitless (or rather: its unit is the number one). In practice, we like to a remind ourselves that these values refer to electrons and therefore like to think of e/Å^3 as the unit of electron density, but this is somewhat incoherent, if not incorrect. The fact that we are dealing with electrons (as opposed to apples) is contained in the definition of the quantity electron density. It does not need to be explicitly specified in the unit. Marc Quoting Bernhard Rupp b...@ruppweb.org: NOTATION Notation f0: atomic scattering factor for normal scattering, defined as the ratio of scattered amplitude to that for a free electron. /NOTATION -- Hmmm...where does the 'electron' in electron density then come from after integration/summation over the structure factors? -- BR
Re: [ccp4bb] units of the B factor
This is absolutely correct. Radian is in fact just another symbol for 1. Thus : 1 rad = 1 From the official SI documentation (http://www.bipm.org/en/si/si_brochure)(section 2.2 - table 3) : The radian and steradian are special names for the number one that may be used to convey information about the quantity concerned. In practice the symbols rad and sr are used where appropriate, but the symbol for the derived unit one is generally omitted in specifying the values of dimensionless quantities. Marc Quoting Ian Tickle i.tic...@astex-therapeutics.com: Back to the original problem: what are the units of B and u_x^2? I haven't been able to work that out. The first wack is to say the B occurs in the term Exp( -B (Sin(theta)/lambda)^2) and we've learned that the unit of Sin(theta)/lamda is 1/Angstrom and the argument of Exp, like Sin, must be radian. This means that the units of B must be A^2 radian. Since B = 8 Pi^2 u_x^2 the units of 8 Pi^2 u_x^2 must also be A^2 radian, but the units of u_x^2 are determined by the units of 8 Pi^2. I can't figure out the units of that without understanding the defining equation, which is in the OPDXr somewhere. I suspect there are additional, hidden, units in that definition. The basic definition would start with the deviation of scattering points from the Miller planes and those deviations are probably defined in cycle or radian and later converted to Angstrom so there are conversion factors present from the beginning. I'm sure that if the MS sits down with the OPDXr and follows all these units through he will uncover the units of B, 8 Pi^2, and u_x^2 and the mystery will be solved. If he doesn't do it, I'll have to sit down with the book myself, and that will make my head hurt. Hi Dale A nice entertaining read for a Sunday afternoon, but I think you can only get so far with this argument and then it breaks down, as evidenced by the fact that eventually you got stuck! I think the problem arises in your assertion that the argument of 'exp' must be in units of radians. IMO it can also be in units of radians^2 (or radians^n where n is any unitless number, integer or real, including zero for that matter!) - and this seems to be precisely what happens here. Having a function whose argument can apparently have any one of an infinite number of units is somewhat of an embarrassment! - of course that must mean that the argument actually has no units. So in essence I'm saying that quantities in radians have to be treated as unitless, contrary to your earlier assertions. So the 'units' (accepting for the moment that the radian is a valid unit) of B are actually A^2 radian^2, and so the 'units' of 8pi^2 (it comes from 2(2pi)^2) are radian^2 as expected. However since I think I've demonstrated that the radian is not a valid unit, then the units of B are indeed A^2! Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing i.tic...@astex-therapeutics.com and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] units of the B factor
steradians pop up in the Fourier domain (spatial frequencies). In the case of B it is (4*pi)^2/2 because the second coefficient of a Taylor series is 1/2. Along these lines, quoting B in A^2 is almost precisely analogous to quoting an angular frequency in Hz. Yes, the dimensions are the same (s^-1), but how does one interpret the statement: the angular frequency was 1 Hz. Is that cycles per second or radians per second? The dimension of an angular frequency can not be cycles per second, because that contradicts the definition of this quantity, which is defined to be an angle per time. Again, there is no need to specifically pack this information into the unit (although it can be done by specifying rad/s as unit - but this is not strictly necessary). Marc That's all I'm saying... -James Holton MAD Scientist Marc SCHILTZ wrote: Frank von Delft wrote: Hi Marc Not at all, one uses units that are convenient. By your reasoning we should get rid of Å, atmospheres, AU, light years... They exist not to be obnoxious, but because they're handy for a large number of people in their specific situations. Hi Frank, I think that you misunderstood me. Å and atmospheres are units which really refer to physical quantities of different dimensions. So, of course, there must be different units for them (by the way: atmosphere is not an accepted unit in the SI system - not even a tolerated non SI unit, so a conscientious editor of an IUCr journal would not let it go through. On the other hand, the Å is a tolerated non SI unit). But in the case of B and U, the situation is different. These two quantities have the same dimension (square of a length). They are related by the dimensionless factor 8*pi^2. Why would one want to incorporate this factor into the unit ? What advantage would it have ? The physics literature is full of quantities that are related by multiples of pi. The frequency f of an oscillation (e.g. a sound wave) can be expressed in s^-1 (or Hz). The same oscillation can also be charcterized by its angular frequency \omega, which is related to the former by a factor 2*pi. Yet, no one has ever come up to suggest that this quantity should be given a new unit. Planck's constant h can be expressed in J*s. The related (and often more useful) constant h-bar = h/(2*pi) is also expressed in J*s. No one has ever suggested that this should be given a different unit. The SI system (and other systems as well) has been specially crafted to avoid the proliferation of units. So I don't think that we can (should) invent new units whenever it appears convenient. It would bring us back to times anterior to the French revolution. Please note: I am not saying that the SI system is the definite choice for every purpose. The nautical system of units (nautical mile, knot, etc.) is used for navigation on sea and in the air and it works fine for this purpose. However, within a system of units (whichever is adopted), the number of different units should be kept reasonably small. Cheers Marc Sounds familiar... phx Marc SCHILTZ wrote: Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference
Re: [ccp4bb] units of the B factor
is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674 -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] units of the B factor
James, I don't think that you are re-phrasing me correctly. At least I can not understand how your statement relates to mine. You simply have to tell us whether a value of 27.34 read from the last column of a PDB file means : (1) B = 27.34 Å^2 , as I (and hopefully some others) think, or (2) B = 27.34 A^2/(8*pi^2) = 0.346 Å^2 , as you seem to suggest Once you have settled for one of the two options, you can convert your B to U and you will get for either choice : (1) U = 0.346 Å^2 (2) U = 0.00438 Å^2 Even small-molecule crystallographers (who almost always compute and refine U's) rarely see values as low as U = 0.00438 Å^2. Cheers Marc Quoting James Holton jmhol...@lbl.gov: Marc SCHILTZ wrote: Hi James I must confess that I do not understand your point. If you read a value from the last column of a PDB file, say 27.34, then this really means : B = 27.34 Å^2 for this atom. And, since B=8*pi^2*U, it also means that this atom's mean square atomic displacement is U = 0.346 Å^2. It does NOT mean : B = 27.34 Born = 27.34 A^2/(8*pi^2) = 27.34/(8*pi^2) A^2 = 0.346 Å^2 as you seem to suggest. Marc, Allow me to re-phrase your argument in a slightly different way: If we replace the definition B=8*pi^2*U, with the easier-to-write C = 100*M, then your above statement becomes: It does NOT mean : C = 27.34 millimeters^2 = 27.34 centimeter^2/100 = 27.34/100 centimeter^2 = 0.2734 centimeter^2 Why is this not true? If it was like this, the mean square atomic displacement of this atom would be U = 0.00438 Å^2 (which would enable one to do ultra-high resolution studies). I feel I should also point out that B = 0 is not all that different from B = 2 (U = 0.03 A^2) if you are trying to do ultra-high resolution studies. This is because the form factor of carbon and other light atoms are essentially Gaussians with full-width at half-max (FWHM) ~0.8 A (you can plot the form factors listed in ITC Vol C to verify this), and blurring atoms with a B factor of 2 Borns increases this width to only ~0.9 A. This is because the real-space blurring kernel of a B factor is a Gaussian function with FWHM = sqrt(B*log(2))/pi Angstrom. The root-mean-square RMS width of this real-space blurring function is sqrt(B/8*pi^2) Angstrom, or sqrt(U) Angstrom. This is the real-space size of a B factor Gaussian, and I, for one, find this a much more intuitive way to think about B factors. I note, however, that the real-space manifestation of the B factor is an object that can be measured in units of Angstrom with no funny scale factors. It is only in reciprocal space (which is really angle space) that we see all these factors of pi popping up. More on that when I find my copy of James... -James Holton MAD Scientist
Re: [ccp4bb] units of the B factor
Not at all ! If I want to compute the sinus of 15 degrees, using the series expansion, I write X = 15 degrees = 15 * pi/180 = 0.2618 because, 1 degree is just a symbol for the unitless, dimensionless number pi/180. I plug this X into the series expansion and get the right result. Marc Quoting Clemens Grimm clemens.gr...@biozentrum.uni-wuerzburg.de: Zitat von marc.schi...@epfl.ch: Dale Tronrud wrote: While it is true that angles are defined by ratios which result in their values being independent of the units those lengths were measured, common sense says that a number is an insufficient description of an angle. If I tell you I measured an angle and its value is 1.5 you cannot perform any useful calculation with that knowledge. I disagree: you can, for instance, put this number x = 1.5 (without units) into the series expansion for sin X : x - x^3/(3!) + x^5/(5!) - x^7/(7!) + ... and compute the value of sin(1.5) to any desired degree of accuracy (four terms will be enough to get an accuracy of 0.0001). Note that the x in the series expansion is just a real number (no dimension, no unit). ... However you get this Taylor expansion under the assumption that sin'(0)=1 sin''(0)=0, sin'''(0)=-1, ... this only holds true under the assumption that the sin function has a period of 2pi and this 'angle' is treated as unitless. Taking e. g. the sine function with a 'degree' argument treated properly as 'unit' will result in a Taylor expansion showing terms with this unit sticking to them.
Re: [ccp4bb] units of the B factor
I would believe that the official SI documentation has precedence over Wikipedia. In the SI brochure it is made quite clear that Radian is just another symbol for the number one and that it may or may no be used, as is convenient. Therefore, stating alpha = 15 (without anything else) is perfectly valid for an angle. Marc Quoting Douglas Theobald dtheob...@brandeis.edu: Argument from authority, from the omniscient Wikipedia: http://en.wikipedia.org/wiki/Radian Although the radian is a unit of measure, it is a dimensionless quantity. The radian is a unit of plane angle, equal to 180/pi (or 360/(2 pi)) degrees, or about 57.2958 degrees, It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level. … the radian is now considered an SI derived unit. On Nov 23, 2009, at 1:31 PM, Ian Tickle wrote: James, I think you misunderstood, no-one is suggesting that we can do without the degree (minute, second, grad, ...), since these conversion units have considerable practical value. Only the radian (and steradian) are technically redundant, and as Marc suggested we would probably be better off without them! Cheers -- Ian -Original Message- From: owner-ccp...@jiscmail.ac.uk [mailto:owner-ccp...@jiscmail.ac.uk] On Behalf Of James Holton Sent: 23 November 2009 16:35 To: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] units of the B factor Just because something is dimensionless does not mean it is unit-less. The radian and the degree are very good examples of this. Remember, the word unit means one, and it is the quantity of something that we give the value 1.0. Things can only be measured relative to something else, and so without defining for the relevant unit, be it a long-hand description or a convenient abbreviation, a number by itself is not useful. It may have meaning in the metaphysical sense, but its not going to help me solve my structure. A world without units is all well and good for theoreticians who never have to measure anything, but for those of us who do need to know if the angle is 1 degree or 1 radian, units are absolutely required. -James Holton MAD Scientist Artem Evdokimov wrote: The angle value and the associated basic trigonometric functions (sin, cos, tan) are derived from a ratio of two lengths* and therefore are dimensionless. It's trivial but important to mention that there is no absolute requirement of units of any kind whatsoever with respect to angles or to the three basic trigonometric functions. All the commonly used units come from (arbitrary) scaling constants that in turn are derived purely from convenience - specific calculations are conveniently carried out using specific units (be they radians, points, seconds, grads, brads, or papaya seeds) however the units themselves are there only for our convenience (unlike the absolutely required units of mass, length, time etc.). Artem * angle - the ratio of the arc length to radius of the arc necessary to bring the two rays forming the angle together; trig functions - the ratio of the appropriate sides of a right triangle -Original Message- From: CCP4 bulletin board [mailto:ccp...@jiscmail.ac.uk] On Behalf Of Ian Tickle Sent: Sunday, November 22, 2009 10:57 AM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] units of the B factor Back to the original problem: what are the units of B and u_x^2? I haven't been able to work that out. The first wack is to say the B occurs in the term Exp( -B (Sin(theta)/lambda)^2) and we've learned that the unit of Sin(theta)/lamda is 1/Angstrom and the argument of Exp, like Sin, must be radian. This means that the units of B must be A^2 radian. Since B = 8 Pi^2 u_x^2 the units of 8 Pi^2 u_x^2 must also be A^2 radian, but the units of u_x^2 are determined by the units of 8 Pi^2. I can't figure out the units of that without understanding the defining equation, which is in the OPDXr somewhere. I suspect there are additional, hidden, units in that definition. The basic definition would start with the deviation of scattering points from the Miller planes and those deviations are probably defined in cycle or radian and later converted to Angstrom so there are conversion factors present from the beginning. I'm sure that if the MS sits down with the OPDXr and follows all these units through he will uncover the units of B, 8 Pi^2, and u_x^2 and the mystery will be solved. If he doesn't do it, I'll have to sit down with the book myself, and that will make my head hurt. Hi Dale A nice entertaining read for a Sunday afternoon, but I think you can only get so far with this argument and then it breaks down, as evidenced by the fact that eventually you got stuck! I think the problem arises in your assertion that the argument of 'exp' must be in units of radians. IMO it can also be in units of radians^2 (or radians^n where n is any unitless number, integer or real,
Re: [ccp4bb] units of the B factor
Quoting James Holton jmhol...@lbl.gov: Now the coefficients of a Taylor polynomial are themselves values of the derivatives of the function being approximated. Each time you take a derivative of f(x), you divide by the units (and therefore dimensions) of x. So, Pete's coefficients below: 1, -1/6, and 1/120 have dimension of [X]^-1, [X]^-2, [X]^-3, respectively. James, The the factors 1, 1/6, 1/120, etc. in the Taylor series of a funcion f(x) do not come from the derivatives of that function. They simply come from the coefficients 1/(n!) that pre-multiply each term (each derivative) in the series. They are, of course, dimensionless (note that n is just an integer number). Marc
Re: [ccp4bb] units of the B factor
Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference have the dimension of a length, and therefore have the same unit. Both B and u^2 have the dimension of the square of a length and therefoire have the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and does not change the unit. The B units, which are ~1/80th of a A^2, do not have a name. So, I think we have a new unit? It is A^2/(8pi^2) and it is the units of the B factor that we all know and love. What should we call it? I nominate the Born after Max Born who did so much fundamental and far-reaching work on the nature of disorder in crystal lattices. The unit then has the symbol B, which will make it easy to say that the B factor was 80 B. This might be very handy indeed if, say, you had an editor who insists that all reported values have units? Anyone disagree or have a better name? Good luck in submitting your proposal to the General Conference on Weights and Measures. -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
Frank von Delft wrote: Hi Marc Not at all, one uses units that are convenient. By your reasoning we should get rid of Å, atmospheres, AU, light years... They exist not to be obnoxious, but because they're handy for a large number of people in their specific situations. Hi Frank, I think that you misunderstood me. Å and atmospheres are units which really refer to physical quantities of different dimensions. So, of course, there must be different units for them (by the way: atmosphere is not an accepted unit in the SI system - not even a tolerated non SI unit, so a conscientious editor of an IUCr journal would not let it go through. On the other hand, the Å is a tolerated non SI unit). But in the case of B and U, the situation is different. These two quantities have the same dimension (square of a length). They are related by the dimensionless factor 8*pi^2. Why would one want to incorporate this factor into the unit ? What advantage would it have ? The physics literature is full of quantities that are related by multiples of pi. The frequency f of an oscillation (e.g. a sound wave) can be expressed in s^-1 (or Hz). The same oscillation can also be charcterized by its angular frequency \omega, which is related to the former by a factor 2*pi. Yet, no one has ever come up to suggest that this quantity should be given a new unit. Planck's constant h can be expressed in J*s. The related (and often more useful) constant h-bar = h/(2*pi) is also expressed in J*s. No one has ever suggested that this should be given a different unit. The SI system (and other systems as well) has been specially crafted to avoid the proliferation of units. So I don't think that we can (should) invent new units whenever it appears convenient. It would bring us back to times anterior to the French revolution. Please note: I am not saying that the SI system is the definite choice for every purpose. The nautical system of units (nautical mile, knot, etc.) is used for navigation on sea and in the air and it works fine for this purpose. However, within a system of units (whichever is adopted), the number of different units should be kept reasonably small. Cheers Marc Sounds familiar... phx Marc SCHILTZ wrote: Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference have the dimension of a length, and therefore have the same unit. Both B and u^2 have the dimension of the square of a length and therefoire have the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and does not change the unit. The B units, which are ~1/80th of a A^2, do not have a name. So, I think we have a new unit? It is A^2/(8pi^2) and it is the units of the B factor that we all know and love. What should we call it? I nominate the Born after Max Born who did so much fundamental and far-reaching work on the nature of disorder in crystal lattices. The unit then has the symbol B, which will make it easy to say that the B factor was 80 B. This might be very handy indeed if, say, you had an editor who insists that all reported values have
Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] {Spam?} Re: {Spam?} Re: [ccp4bb] units of the B factor
Yes, but Å is really only just tolerated. It has evaded the Guillotine - for the time being ;-) Frank von Delft wrote: Eh? m and Å are related by the dimensionless quantity 10,000,000,000. Vive la révolution! Marc SCHILTZ wrote: Frank von Delft wrote: Hi Marc Not at all, one uses units that are convenient. By your reasoning we should get rid of Å, atmospheres, AU, light years... They exist not to be obnoxious, but because they're handy for a large number of people in their specific situations. Hi Frank, I think that you misunderstood me. Å and atmospheres are units which really refer to physical quantities of different dimensions. So, of course, there must be different units for them (by the way: atmosphere is not an accepted unit in the SI system - not even a tolerated non SI unit, so a conscientious editor of an IUCr journal would not let it go through. On the other hand, the Å is a tolerated non SI unit). But in the case of B and U, the situation is different. These two quantities have the same dimension (square of a length). They are related by the dimensionless factor 8*pi^2. Why would one want to incorporate this factor into the unit ? What advantage would it have ? The physics literature is full of quantities that are related by multiples of pi. The frequency f of an oscillation (e.g. a sound wave) can be expressed in s^-1 (or Hz). The same oscillation can also be charcterized by its angular frequency \omega, which is related to the former by a factor 2*pi. Yet, no one has ever come up to suggest that this quantity should be given a new unit. Planck's constant h can be expressed in J*s. The related (and often more useful) constant h-bar = h/(2*pi) is also expressed in J*s. No one has ever suggested that this should be given a different unit. The SI system (and other systems as well) has been specially crafted to avoid the proliferation of units. So I don't think that we can (should) invent new units whenever it appears convenient. It would bring us back to times anterior to the French revolution. Please note: I am not saying that the SI system is the definite choice for every purpose. The nautical system of units (nautical mile, knot, etc.) is used for navigation on sea and in the air and it works fine for this purpose. However, within a system of units (whichever is adopted), the number of different units should be kept reasonably small. Cheers Marc Sounds familiar... phx Marc SCHILTZ wrote: Hi James, James Holton wrote: Many textbooks describe the B factor as having units of square Angstrom (A^2), but then again, so does the mean square atomic displacement u^2, and B = 8*pi^2*u^2. This can become confusing if one starts to look at derived units that have started to come out of the radiation damage field like A^2/MGy, which relates how much the B factor of a crystal changes after absorbing a given dose. Or is it the atomic displacement after a given dose? Depends on which paper you are looking at. There is nothing wrong with this. In the case of derived units, there is almost never a univocal relation between the unit and the physical quantity that it refers to. As an example: from the unit kg/m^3, you can not tell what the physical quantity is that it refers to: it could be the density of a material, but it could also be the mass concentration of a compound in a solution. Therefore, one always has to specify exactly what physical quantity one is talking about, i.e. B/dose or u^2/dose, but this is not something that should be packed into the unit (otherwise, we will need hundreds of different units) It simply has to be made clear by the author of a paper whether the quantity he is referring to is B or u^2. It seems to me that the units of B and u^2 cannot both be A^2 any more than 1 radian can be equated to 1 degree. You need a scale factor. Kind of like trying to express something in terms of 1/100 cm^2 without the benefit of mm^2. Yes, mm^2 have the dimensions of cm^2, but you can't just say 1 cm^2 when you really mean 1 mm^2! That would be silly. However, we often say B = 80 A^2, when we really mean is 1 A^2 of square atomic displacements. This is like claiming that the radius and the circumference of a circle would need different units because they are related by the scale factor 2*pi. What matters is the dimension. Both radius and circumference have the dimension of a length, and therefore have the same unit. Both B and u^2 have the dimension of the square of a length and therefoire have the same unit. The scalefactor 8*pi^2 is a dimensionless quantity and does not change the unit. The B units, which are ~1/80th of a A^2, do not have a name. So, I think we have a new unit? It is A^2/(8pi^2) and it is the units of the B factor that we all know and love. What should we call it? I nominate the Born after Max Born who did so much fundamental and far-reaching work on the nature
Re: [ccp4bb] phasing with se-met at low resolution
Kevin Cowtan wrote:
This is absolutely correct - in the analysis you present, the
non-anomalous scattering drops with resolution, but the anomalous part
does not. And since counting noise varies with intensity, we should
actually be better off at high resolution, since there is less
non-anomalous scattering to contribute to the noise! (This is somewhat
masked by the background, however).
So why don't we see this in practice?
The reason is that you've missed out one important term: the atomic
displacement parameters (B-factors), which describe a combination of
thermal motion and positional disorder between unit cells. This motion
and disorder applies equally to the core and outer electrons, and so
causes a drop-off in both the anomalous and non-anomalous scattering,
over and above that caused by the atomic scattering factors.
I agree with everything but would like to add the following: if we
assume an overall atomic displacement parameter, the drop-off in both
the anomalous and non-anomalous scattering is the same. Therefore, the
ratio of anomalous differences over mean intensity (which is what comes
closest to R_{ano} - in whichever way this is defined) is essentially
unaffected by atomic displacements and should still go up at high
resolution, irrespective of the values of the atomic displacement
parameter !
Things are more complicated if individual isotropic atomic displacements
are considered, because the anomalously scattering atoms (e.g. the Se
atoms) may have significantly larger or smaller displacement parameters
than the average.
All this is discussed in section 4.4. of Flack Shmueli (2007) Acta
Cryst. A63, 257--265.
Marc
But your reasoning was sound as far as it went, and it is a point which
many people haven't recognised!
Kevin
Raja Dey wrote:
Dear James,
I don't understand why measuring anomalous differences has nothing to do
with resolution.
Heavy atoms
scatter anomalously because the inner shell electrons
of the heavy atom cannot be considered to be free anymore
as was assumed for normal Thomson scattering. As a result
the atomic scattering factor of the heavy atom becomes
complex and this compex contribution to the structure
factor leads to non-equality of Friedel pairs in non-centro
symmetric systems(excluding centric zone). This feature is taken
advantage in
phase determination. Since the inner shell electrons
being relatively more strongly bound in heavy atoms
contribute to anomalous scattering and its effect
is more discernable for high angle reflections . Here
the anomalous component of the scattering do not
decrease much because of the effectively small atomic
radii (only inner shell being effective). FOR HIGH
ANGLE REFLECTIONS ANOMALOUS DATA
BECOMES IMPORTANT.
Raja
--
Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] phasing with se-met at low resolution
Kevin Cowtan wrote:
Marc SCHILTZ wrote:
I agree with everything but would like to add the following: if we
assume an overall atomic displacement parameter, the drop-off in both
the anomalous and non-anomalous scattering is the same. Therefore, the
ratio of anomalous differences over mean intensity (which is what comes
closest to R_{ano} - in whichever way this is defined) is essentially
unaffected by atomic displacements and should still go up at high
resolution, irrespective of the values of the atomic displacement
parameter !
OK, that's new to me. My understanding was that f does not drop off
with resolution in the stationary atom case, since the anomalous
scattering arises from the core atoms. Can you elaborate?
Yes, this is correct. And if there are atomic displacements, we would
have to multiply f by an overall Debye-Waller factor (t) to get an
effective f which then would drop off with resolution. But the
Debye-Waller factor also affects the normal scattering factors in the
same way. So the ratio of rms Friedel differences over mean intensities
remains essentially unaffected by an overall atomic displacement parameter.
Interpreting the Flack Shmueli (2007) paper :
D = F^2(+) - F^2(-) is the Friedel difference of a reflection and A =
0.5 * [F^2(+) + F^2(-)] is its Friedel average
Then D^2 = t^4 D^2(static) and A = t ^2 A(static)
So the ratio SQRT(D^2) / A is independent of t (i.e. the same as for
the static case).
Marc
--
Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
Quoting Jacob Keller j-kell...@md.northwestern.edu: Aha, so I have re-invented the wheel! But I never made sense of why f' is negative--this is beautiful! Just to make sure: you are saying that the real part of the anomalous scattering goes negative because those photons are sneaking out of the diffraction pattern through absorption--fluorescence? I doubt that this is a correct interpretation. It is f which is related to absorption (and therefore to fluorescence) not f' ! In fact f' can be positive, even if there is absorption (and fluorescence). Examples: the f' factors of C, O, S, Cl and most other lighter elements are positive at the Cu K-alpha wavelength, but they are still absorbing. The optical theorem relates \mu, the macroscopic absorption coefficient, to f, NOT to f' ! The amount that any material absorbs is in no way related to the f' factors of the atoms of which it is build up. But it is directly related to their f factors. When you collect a fluorescence scan, you get a quantity which is directly related to f and NOT to f' (the raw scan resembles already very much the spectral curve of f). To get f', you have to perform a Kramers-Kronig transform. The macroscopic counterpart of f' is dispersion, i.e. a change of phase velocity. Marc
Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
Quoting Jacob Keller j-kell...@md.northwestern.edu: Also, in your selenium crystal example, I think there would still be an anomalous signal, because there would always be regular scattering as well as the anomalous effect. Isn't that true? It is certainly not correct to state that there is no anomalous scattering in elemental Se. There is anomalous scattering: the atomic form factors f' and f have the specific wavelength-dependence, which can be measured from the diffraction data (by collecting data at different wavelengths); you can collect a fluorescence scan over the absorption edge etc. However, because there is only one type of scatterer (the f' + if for all atoms are the same), Friedel's law remains valid, i.e. I(+h) and I(-h) remain the same. And even this is only true as long as we consider that the atoms are spherical and neglect anisotropy of anomalous scattering etc. Marc
Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
James Holton wrote:
marc.schi...@epfl.ch wrote:
The elastically scattered photons (which make up the Bragg peaks) also
do not not retain the momentum of the incident photon.
Although technically true to say that photons traveling in different
directions have different momenta, all elastically scattered photons
have the same wavelength (momentum) as the incident photon. Otherwise,
I would definitely avoid to amalgamate wavelength and momentum, as is
more-or-less suggested in the final part of this statement. Momentum is
a vector quantity, although it is true that the NORM of the momentum
vector of a particle is related to its energy (by the De Broglie
wavelength relation). In X-ray diffraction, the momentum of the
elastically scattered photon does change, while its energy does not. In
X-ray physics, the change in momentum is actually called the momentum
transfer : \vec{Q} = \vec{k'} - \vec{k}. The word says it all.
they would not interfere constructively to form Bragg peaks and they
would be called Compton-scattered photons. The small change in energy
required to preserve wavelength upon a change in direction during
elastic scattering is contributed by the entire crystal as a recoil
phonon. Arthur Compton wrote a paper about this:
http://www.pnas.org/cgi/reprint/9/11/359.pdf
Very interesting paper, but I see no mention of a recoil phonon and I
would be surprised if that is what Compton really meant. No mention
about lattice dynamics (phonons) can be found in this paper. The crystal
is implicitly assumed to be a rigid body. In fact, what the paper nicely
demonstrates is that the conservation of wavelength (i.e. photon energy)
between incident and diffracted rays is achieved in the limiting case
when the total mass of the crystal is very large with respect to the
mass of one photon - a condition which, I presume, is always satisfied
in X-ray crystallography, even when going towards microcrystals.
This is really the same situation as a tennis ball that bounces
(elastically) off the surface of the earth. In principle, we must assume
that some of its energy is transferred to the earth during the
collision. But because the mass of the earth is so vastly superior to
the mass of the tennis ball, the transfer of energy is vanishingly
small. It certainly can not be measured. The change of momentum of the
tennis ball, however, is not negligible and can be measured.
Back to X-ray diffraction, the reciprocal lattice is just a
representation of momentum transfer vectors \vec{Q} = 2\pi \vec{h}. You
may never have thought of it like this, but when we index an X-ray
pattern, we are really measuring the change in momentum of the photons
which were scattered into the various Bragg peaks. But we can not
measure their change in energy, as it is practically zero.
The situation becomes somewhat different if we take into account lattice
dynamics (phonons) as it is now possible to measure the energy transfer
of a scattered X-ray photon upon phonon creation in the crystal. But
these are very difficult measurements (much easier with neutrons) and
are certainly of no relevance for macromolecular X-ray crystallography.
It is anyway called inelastic scattering.
which probably contributed to his Nobel four years later. This is a
classic example of the confusion that can arise from the particle-wave
duality.
It seems to me that the confusion here is between energy and momentum.
--
Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
For those who are still following this discussion...
Following a comment by James, I clarify my previous statement about
the limiting case when the total mass of the crystal is very large
with respect to the mass of one photon
I meant of course the relativistic mass of one photon [which is given
by h/(\lambda c)]. The rest mass of a photon is of course zero.
A photon of \lambda = 1 Angstroem has a relativistic mass of the order
of 10^{-32} kg. Certainly much smaller than the mass of even a
nano-crystal...
I was really just re-phrasing what Arthur Compton wrote in the quoted
paper [read the sentence just after his equation (9)].
--
Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
Quoting Ethan Merritt merr...@u.washington.edu: On Wednesday 22 April 2009 09:23:19 Jacob Keller wrote: Hello All, What is the reason that x-ray fluorescence is neglected in our experiments? Obviously it is measureable, as in EXAFS experiments to determine anomalous edges, but should it not play a role in the intensities as well? What am I missing? Fluorescence is directly proportional to f, so in one sense we do account for it in any calculation that includes the anomalous scattering terms. If you were thinking of direct contribution of the fluorescent X-rays to the measured Bragg peak - that is negligible. Those photons do not retain the momentum vector of the original incident photon, and are emitted in all I am not sure whether this is a good explanation. The elastically scattered photons (which make up the Bragg peaks) also do not not retain the momentum of the incident photon. directions. I.e., they contribute even less to the diffraction image than air-scatter from the direct beam or from the diffracted beam. Well, this clearly depends on the sample content and on the X-ray wavelength. There are many examples of data collected at an absorption edge, where fluorescence is the dominating contributor to the background, i.e. it is much larger than air-scatter from the direct beam or from the diffracted beams. For an extreme case, see fig. 4 in Shepard et al.(2000). Acta Cryst. D56, 1288-1303. Marc Ethan 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: rui To: CCP4BB@JISCMAIL.AC.UK Sent: Wednesday, April 22, 2009 11:06 AM Subject: [ccp4bb] microbatch vs hanging drop Hi, I have a question about the method for crystallization. With traditional hanging drop(24 wells), one slide can also hold for multiple drops but it requires the buffer quite a lot, 600uL? Microbatch can save buffers,only 100uL is required, and also can hold up to three samples in the sitting well. Other than saving the buffer, what's the advantage of microbatch? Which method will be easier to get crystals or no big difference? Thanks for sharing. R -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742
Re: [ccp4bb] Crick-Magdoff and anomalous
Ethan Merritt wrote: Please also have a look at A Olczak, M Cianci, Q Hao, PJ Rizkallah, J Raferty, JR Helliwell (2003). S-SWAT (softer single-wavelength anomalous technique) Acta Cryst. A59, 327-334. in which the authors show several derivations for the estimated anomalous signal, based on slightly different assumptions. And the generalization of their formulae is given in : Flack, H. D. Shmueli, U. (2007). Acta Cryst. A63, 257-265. In a follow-up paper, their derivations were extended to all spacegroups, also taking account of special reflections. -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] structure (factor) amplitude
Ian Tickle wrote: I think there's a confusion here between the name of an object (what you call it) and its description (i.e. its properties). The name of the object is structure amplitude and it's description is amplitude of the structure factor, or if you prefer the shortened form structure factor amplitude. But one does not name the modulus of a complex number a complex modulus; one does not name the amplitude of a molecular vibration a molecular amplitude; and one does not name the trace of a rotation matrix a rotation trace. Mal nommer les choses, c'est ajouter au malheur des hommes. A.Camus. -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] structure (factor) amplitude
Ian Tickle wrote: OK, limiting the vote to people whom I think we can assume know what vaguely they're talking about, i.e. Acta Cryst. / J. Appl. Cryst. authors, and using the IUCr search engine we get 553 hits for structure amplitude and 256 for structure factor amplitude But be warned that not all Acta Cryst. authors give the term structure amplitude the meaning that you think they do, i.e. a shortcut version for structure factor amplitude ! In particular, P.P. Ewald (no less an authority than the ones you quote), uses the term structure amplitude for the complex number F(hkl). See e.g. Acta Cryst. A35 (1979), page 8. To my surprise, M. von Laue in his treatise Rontgenstrahlinterferenzen also uses the term structure amplitude (Strukturamplitude) for the complex quantity F. He defines the structure factor (Strukturfaktor) as the square-modulus of F. This seems to go back to early papers by P.P. Ewald. Both of these quantities are also defined in exactly the same way by Hosemann Bagchi in their 1962 textbook on X-ray diffraction. In optics it makes perfect sense to speak about complex amplitudes. We thus have the historic definitions : structure amplitude = complex F structure factor = square-modulus of F This comes from the fact that the intensity formulae which these authors derive, and which remain valid for finite crystals and for paracrystals, there is a neat factorization into a lattice-factor (Gitterfaktor) on one hand and a structure factor (Strukturfaktor) on the other hand. The lattice factor only depends on the number and spatial arrangement of unit cells within the crystal, whereas the structure factor only depends on the atomic structure of one unit cell. The latter is of course equal to the square-modulus of F. To add to the confusion: Current-day small-angle scattering (SAXS) specialists call structure factor the quantity which von Laue would have called lattice factor (and they call formfactor the quantity which von Laue called structure factor) . Seems that there will be little agreement -- Marc SCHILTZ http://lcr.epfl.ch Ian Tickle wrote: OK, limiting the vote to people whom I think we can assume know what vaguely they're talking about, i.e. Acta Cryst. / J. Appl. Cryst. authors, and using the IUCr search engine we get 553 hits for structure amplitude and 256 for structure factor amplitude But be warned that not all Acta Cryst. authors give the term structure amplitude the meaning that you think they do, i.e. a shortcut version for structure factor amplitude ! In particular, P.P. Ewald (no less an authority than the ones you quote), uses the term structure amplitude for the complex number F(hkl). See e.g. Acta Cryst. A35 (1979), page 8. To my surprise, M. von Laue in his treatise Rontgenstrahlinterferenzen also uses the term structure amplitude (Strukturamplitude) for the complex quantity F. He defines the structure factor (Strukturfaktor) as the square-modulus of F. This seems to go back to early papers by P.P. Ewald. Both of these quantities are also defined in exactly the same way by Hosemann Bagchi in their 1962 textbook on X-ray diffraction. In optics it makes perfect sense to speak about complex amplitudes. We thus have the historic definitions : structure amplitude = complex F structure factor = square-modulus of F This comes from the fact that the intensity formulae which these authors derive, and which remain valid for finite crystals and for paracrystals, there is a neat factorization into a lattice-factor (Gitterfaktor) on one hand and a structure factor (Strukturfaktor) on the other hand. The lattice factor only depends on the number and spatial arrangement of unit cells within the crystal, whereas the structure factor only depends on the atomic structure of one unit cell. The latter is of course equal to the square-modulus of F. To add to the confusion: Current-day small-angle scattering (SAXS) specialists call structure factor the quantity which von Laue would have called lattice factor (and they call formfactor the quantity which von Laue called structure factor) . Seems that there will be little agreement -- Marc SCHILTZ http://lcr.epfl.ch Ian Tickle wrote: OK, limiting the vote to people whom I think we can assume know what vaguely they're talking about, i.e. Acta Cryst. / J. Appl. Cryst. authors, and using the IUCr search engine we get 553 hits for structure amplitude and 256 for structure factor amplitude Well, then you may be warned that not all Acta Cryst. authors give the term structure amplitude the meaning that you think they do, i.e. a shortcut version of structure factor amplitude ! In particular, P.P. Ewald (no less an authority than the ones you quote), uses the term structure amplitude for the complex number F(hkl). See Acta Cryst. A35 (1979), page 8. To my surprise, M. von Laue in his (german) treatise
Re: [ccp4bb] Reading the old literature / truncate / refinement programs
this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674 -- Marc SCHILTZ http://lcr.epfl.ch[13] Links: -- [1] mailto:[EMAIL PROTECTED] [2] mailto:[EMAIL PROTECTED] [3] mailto:[EMAIL PROTECTED] [4] mailto:[EMAIL PROTECTED] [5] mailto:[EMAIL PROTECTED] [6] mailto:[EMAIL PROTECTED] [7] mailto:CCP4BB@JISCMAIL.AC.UK [8] mailto:[EMAIL PROTECTED] [9] mailto:[EMAIL PROTECTED] [10] mailto:[EMAIL PROTECTED] [11] mailto:CCP4BB@JISCMAIL.AC.UK [12] mailto:[EMAIL PROTECTED] [13] http://lcr.epfl.ch Hi Ian, I did not follow up our recent discussion about the respective merits of various truncate procedures, in particular the comparison of the French Wilson (1978) and Sivia David (1994) methods. Following your mail to the BB yesterday, which extends the previous simulations, I feel that I should relaunch the debate. My main objection is that I can still not understand why you are so focused on the shell averages (i.e. intensity averages over many reflections in resolution shells). This is apparently the criterion that you use to claim that the FW method is superior to all others. The truncate method (whichever prior is used) is a procedure to estimate amplitudes for individual reflections. This is the goal of the whole procedure. So we have an estimator E(Im,Sm) for the true intensity J (or amplitude sqrt(J)) of one reflection, given its measured intensity Im and sigma Sm. According to the usual statistical definition of bias, this estimator is unbiased if its expectation value (NOT its average aver many different reflections) is equal to the true value J (or sqrt(J)), for all values of J. We seem to agree that neither the estimator proposed by FW, nor the one proposed by SD are unbiased, and I gave a simple example in an earlier mail : for J=0, both estimators will return an estimate greater than 0, whatever the measured data are. They are thus biased. Now, you seem to be be highly preoccupied by the reflection averages in resolution shells. Why ? The quantities that are used in all subsequent computations are individual reflection intensities/amplitudes. The shell averages are not used in any important crystallographic computation (apart maybe the Wilson plot). So what matters really is to get good estimates for individual reflection intensities/amplitudes. Of course, both the FW and the SD methods also return an estimate for the shell averages, and your simulations seem to show that the FW estimates for these shell averages are unbiased. But again, shell averages are not used in any crystallographic refinement: we refine against individual reflections ! They are not used in phasing: we phase individual reflections. So what matters is the bias on individual reflections, not on shell averages. I think that you can not simply claim that, because the FW method returns unbiased shell averages, it is necessarily superior to the SD method. In that sense, your previous statement that the average bias of J is the same as the bias of the average J may be formally correct, but is completely irrelevant. Because even if the average bias is zero, this does not mean that the estimator is unbiased. Otherwise, I would suggest a truncate procedure where the intensities of all reflections are simply set equal to their shell averages. Clearly, this would yield unbiased estimates for the shell averages, but the estimates for individual reflection intensities would be highly biased. Also, your simulations are flawed by the fact that you assume you exactly know S. However, this is not the case in reality. In the FW procedure, S is estimated in shells of resolution from the measured intensities. This turns S into a random variable and you will never have S=0 exactly. If you now imagine the case of data collected and integrated when there is no diffraction at all, you would get some random number for S
Re: [ccp4bb] truncate ignorance
Well, I was pointing to the Sivia David (1994) paper because I thought it might be helpful in the discussion about how to convert intensities to amplitudes. The paper is probably not so well known in the PX community, so I decided that I would advertise it on this BB. However, since I am not one of the authors, I feel that it is inappropriate for me to go into a detailed defense of every sentence and equation which is written in it. The paper is clear and speaks for itself. I can only recommend a careful reading of it. I will nevertheless make some general comments in response to the criticism that was raised: Quoting Ian Tickle [EMAIL PROTECTED]: But there's a fundamental difference in approach, the authors here assume the apparently simpler prior distribution P(I) = 0 for I 0 P(I) = const for I = 0. As users of Bayesian priors well know this is an improper prior since it integrates to infinity instead of unity. Despite of their disparaging name, improper priors can be used in Bayesian analysis without major difficulties (at least for estimation problems), provided that the posterior integrates to a finite value. If you object to the use of an improper prior in the Sivia David paper, I suggest to use a prior where P(I) = 0 for I 0 as well as for I 10^30 and P(I) = constant in between these two boundaries. Technically speaking this would then be a proper prior, but for all intents and purposes it would not make any difference at all. This means that, unlike the case I described for the French Wilson formula based on the Wilson distribution which gives unbiased estimates of the true I's and their average, the effect on the corrected intensities of using this prior really will be to increase all intensities (since the mean I for this prior PDF is also infinite!), hence the intensities and their average must be biased ( I'm sure the same goes for the corresponding F's). Two different bias concepts in this statement : ... unbiased estimates of the true I's and their average... (1) Regarding unbiased estimates of the true I's: The use of a Wilson prior does by no means guarantee that the posterior expectation values will be unbiased estimates of the true I's. Whether one uses the Wilson prior or the naive prior of Sivia David, the posterior probability distribution on I will be a truncated normal distribution (see French Wilson, appendix A). There is nothing which allows us to claim that the expectation value (which is what we use as estimate of the true intensity) over such a posterior will be unbiased (whichever prior was used !). Simple example: take a reflection which has true F=0. The posterior probability distribution p_J(J|I) (here I am using the French Wilson notation) will be a truncated normal (see French Wilson, appendix A) and its expectation value E_J(J|I) will thus always be greater than 0, even if the Wilson prior is used ! Both the the French Wilson and the Sivia David procedures will yield a biased estimate of the true intensity: the estimate will always be greater than 0 (the true value), whatever the measured I is. (2) Regarding intensity averages: Here, your argument about bias seems to be about averages of intensities computed in resolution shells, i.e. you are concerned that the corrected I's, averaged over all reflections in a given resolution bin, should equal the average of the uncorrected intensities in the same resolution bin. I would like to see a proof that the French Wilson procedure actually achieves this goal (none is given in the French Wilson paper - they are actually not addressing this issue). But apart from this, I wonder whether this is of any relevance at all. Why would this be so important ? Why are you so concerned that the intensity averages over many different reflections in a resolution bin is a quantity which should at all price be conserved ? In any event, I think that the discussions about bias on corrected intensities is a somewhat academic side-issue. The real reason why we use the truncate procedure is not so much do get corrected I's, but rather to get estimates of the amplitudes. In that sense, I think that the important message conveyed in the Sivia David paper is the following: the awkward truncated Gaussian pdf's in intensity space (whichever prior was used...) are transformed to well-behaved Gaussian-like pdf's in amplitude-space. This is an argument in favouring F's rather than I's (even corrected I's) for subsequent crystallographic computations. In that regime (i.e. in the regime where we accept that the posterior probability distribution on F's is close to a Gaussian), the estimator given by equation (11) in Sivia David is actually unbiased ! Side argument: to use the French Wilson procedure, it is necessary to know the crystal spacegroup (in order to apply the correct statistical weights for the various classes of reflections). To use the Sivia David procedure, you don't need to know the
Re: [ccp4bb] truncate ignorance
I would also recommend reading of the following paper: D.S. Sivia W.I.F. David (1994), Acta Cryst. A50, 703-714. A Bayesian Approach to Extracting Structure-Factor Amplitudes from Powder Diffraction Data. Despite of the title, most of the analysis presented in this paper applies equally well to single-crystal data (see especially sections 3 and 5). If you are not interested in the specific powder-diffraction problems (i.e. overlapping peaks), you can simply skip sections 4 and 6. A few interesting points from this paper : (1) The conversion from I's to F's can be done (in a Bayesian way) by applying two simple formula (equations 11 and 12 in the paper), which, for all practical purposes, are as valid as the more complicated French Wilson procedure (see discussion in section 5). (2) Re. the use of I's rather than F's : this is discussed on page 710 (final part of section 5). The authors seem to be more in favor of using F's. Marc Schiltz Quoting Jacob Keller [EMAIL PROTECTED]: Does somebody have a .pdf of that French and Wilson paper? Thanks in advance, 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: [EMAIL PROTECTED] *** - Original Message - From: Ethan Merritt [EMAIL PROTECTED] To: CCP4BB@JISCMAIL.AC.UK Sent: Monday, September 08, 2008 3:03 PM Subject: Re: [ccp4bb] truncate ignorance On Monday 08 September 2008 12:30:29 Phoebe Rice wrote: Dear Experts, At the risk of exposing excess ignorance, truncate makes me very nervous because I don't quite get exactly what it is doing with my data and what its assumptions are. From the documentation: ... the truncate procedure (keyword TRUNCATE YES, the default) calculates a best estimate of F from I, sd(I), and the distribution of intensities in resolution shells (see below). This has the effect of forcing all negative observations to be positive, and inflating the weakest reflections (less than about 3 sd), because an observation significantly smaller than the average intensity is likely to be underestimated. = But is it really true, with data from nice modern detectors, that the weaklings are underestimated? It isn't really an issue of the detector per se, although in principle you could worry about non-linear response to the input rate of arriving photons. In practice the issue, now as it was in 1977 (FrenchWilson), arises from the background estimation, profile fitting, and rescaling that are applied to the individual pixel contents before they are bundled up into a nice Iobs. I will try to restate the original French Wilson argument, avoiding the terminology of maximum likelihood and Bayesian statistics. 1) We know the true intensity cannot be negative. 2) The existence of Iobs0 reflections in the data set means that whatever we are doing is producing some values of Iobs that are too low. 3) Assuming that all weak-ish reflections are being processed equivalently, then whatever we doing wrong for reflections with Iobs near zero on the negative side surely is also going wrong for their neighbors that happen to be near Iobs=0 on the positive side. 4) So if we correct the values of Iobs that went negative, for consistency we should also correct the values that are nearly the same but didn't quite tip over into the negative range. Do I really want to inflate them? Yes. Exactly what assumptions is it making about the expected distributions? Primarily that 1) The histogram of true Iobs is smooth 2) No true Iobs are negative How compatible are those assumptions with serious anisotropy and the wierd Wilson plots that nucleic acids give? Not relevant Note the original 1978 French and Wilson paper says: It is nevertheless important to validate this agreement for each set of data independently, as the presence of atoms in special positions or the existence of noncrystallographic elements of symmetry (or pseudosymmetry) may abrogate the application of these prior beliefs for some crystal structures. It is true that such things matter when you get down to the nitty-gritty details of what to use as the expected distribution. But *all* plausible expected distributions will be non-negative and smooth. Please help truncate my ignorance ... Phoebe == Phoebe A. Rice Assoc. Prof., Dept. of Biochemistry Molecular Biology The University of Chicago phone 773 834 1723 http://bmb.bsd.uchicago.edu/Faculty_and_Research/01_Faculty/01_Faculty_Alphabetically.php?faculty_id=123 RNA is really nifty DNA is over fifty We have put them both in one book Please do take a really good look
Re: [ccp4bb] Is anomalous signal a different wavelength?
Ethan A Merritt wrote: And please note that resonant scattering is not a standard term. Resonant Scattering is now the standard term accepted and used anywhere in the X-ray physics and crystallography literature, except in protein crystallography. It is the more adequate term since the X-ray phenomena under discussion involve resonant interactions of photons with matter and are actually not at all 'anomalous'. -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] Is anomalous signal a different wavelength?
Quoting Jacob Keller [EMAIL PROTECTED]: The reason I called the phenomenon resonant scattering is because that is the term used by Elements of Modern X-ray Physics by Jens Als-Nielsen, Des McMorrow. I prefer the term also because this scattering is, as somebody has said, no longer really anomalous-- it fits well into x-ray physical theory. Let the heroes speak: In 1994 D. H. Templeton wrote: The index of refraction of transparent materials for visible light generally increases as the wavelength decreases and this dispersion is said to be 'normal'. Near absorption bands there are intervals of wavelength where the slope of n versus \lambda is positive, and the dispersion is 'anomalous'. According to this convention and the relation between n and f', x-ray dispersion is anomalous only in those intervals where df'/d\lambda is negative. Yet 'anomalous dispersion' and 'anomalous scattering' have come to be used for the effects of absorption on x-ray optical properties at all wavelengths, or sometimes perhaps only for those related to the imaginary term f. These effects are significant for nearly all atoms at all wavelengths commonly used for diffraction experiments, and therefore 'anomalous' is somewhat inappropriate. I prefer 'dispersion' or 'resonant scattering'. (in 'Resonant Anomalous X-ray Scattering: Theory and Applications', G.Materlik, C.J.Sparks K.Fischer (eds.), Elsevier Science, Amsterdam: 1994) The editors (G.Materlik, C.J.Sparks K.Fischer) of that same book wrote in the preface: Since resonant interactions are characteristic of the interaction of photons with matter, we suggest that 'resonant' better describes the field than 'anomalous' scattering. But note that they used the pleonasm Resonant Anomalous X-ray Scattering as a title for their book ;-) More recent review articles use the term resonant scattering or resonant diffraction, e.g. Hodeau JL, Favre-Nicolin V, Bos S, Renevier H, Lorenzo E, Berar JF (2002). Resonant diffraction. Chem Rev. 101, 1843--1867. which includes a section on MAD phasing. Thus, resonant scattering and anomalous scattering are synonyms and it is almost a matter of taste which term one prefers. Both are perfectly acceptable. The x-ray physics and crystallography communities (except protein crystallography) have shifted from the usage of anomalous scattering to resonant scattering. But then, as you write, if we want to keep the MAD SAD SIRAS etc acronyms we are tied to anomalous. Marc Schiltz
