Re: [ccp4bb] Method to calculate the axis of an alpha helix
Yuan, On Mon, Sep 13, 2010 at 6:12 PM, 商元 shangyuan5...@gmail.com wrote: Thanks, lan. For quaternions, it needs w^2+x^2+y^2+z^2=1, thus reduces variables to 3. The number of degrees of freedom is of course reduced to 3 but the number of variables is still to all intents and purposes 4, since no useful simplification is achieved by eliminating one of the variables using the above constraint (normalisation) equation. If you wanted to do an optimisation using quaternions as variables you would almost certainly use constrained optimisation with 4 variables/quaternion. All the standard formulae that involve quaternions are in terms of the 4 variables (w,x,y,z). But fortunately,(x,y,z) here only represents a direction of the rotation angle, and the absolute value of them are not that important. I think a rotation vector and the rotation angle could be a very good representation of any rotation in 3D space, and that's more directviewing than the rotation Matrix which is a Matrix, or Euler Angles, which need three rotation angles. How appropriate a particular representation is obviously depends on the purpose for which you are using it. I accept that the quaternion representation may well be the most appropriate one for your particular problem. The article I sent discusses the pros and cons of each (and they all have both pros and cons!). The Exponential Map, it's too complicated, so many mathematics Complicated? I didn't think it could get any simpler! Here's a comparison: Quaternion (q) Exp. map (v) No of variables 4 3 Constraint w^2+x^2+y^2+z^2=1 - Angle of rotation (A) 2 cos^(-1)(w/|q|) |v| Axis vector (x,y,z)/(|q|sin(A/2)) v/A where q is the quaternion before normalisation. the definition of q = e^v, I think they are identical. and the direction of v is identical to (x,y,z) in the quaternion. Not exactly identical: the expressions for angle axis vector are quite different as can be seen from the above definitions. However for a given rotation they clearly must have the same value (by definition!) if that's what you mean. Cheers -- Ian Regards, Yuan SHANG On Tue, Sep 14, 2010 at 12:09 AM, Ian Tickle ianj...@gmail.com wrote: Hi Yuan You might want to look at the 'exponential map' as an alternative to quaternions. This article evaluates all the various representations of rotations, including Eulerian angles, polar angles, rotation matrices, quaternions etc: http://webhome.cs.uvic.ca/~blob/courses/485c/notes/pdf/expmap.pdf The advantage of the exponential map representation is that only 3 variables are used, which, as for the Eulerian polar angle representations, is exactly the number that are needed to represent an arbitrary rotation in 3-D so it's an optimally parsimonious representation. However it doesn't suffer from the well-known singularities as Eulerian polar angles (it suffers from different singularities but it's possible to sweep them under the carpet). Quaternions, as you say, require 4 variables but a constraint is needed (i.e. normalisation of the vector) to reduce it back to 3. Cheers -- Ian On Mon, Sep 13, 2010 at 4:21 PM, 商元 shangyuan5...@gmail.com wrote: Dear CCP4 members, I have finally used Eleanor's idea, and it works very well. After applying SSM, we can get a rotation matrix(M), and a displacement vector N: (Xnew,Ynew,Znew)'=M*(X,Y,Z)'+N Then, from the rotation matrix M, we can get its another representative format-quaternion number. The quaternion number has 4 elements, the first element(w) of which represents the cosine value of half of the rotation anger, and the next 3 elements(x0,y0,z0) represent the rotation vector. That means the molecule rotates an angle of acos(w)*2*180/pi degrees around the vector (x0,y0,z0). The attached file is the matlab program i wrote to translate M into a quaternion number. That should be very easy to be translated into other language formats. Best regards, Yuan SHANG On Thu, Aug 19, 2010 at 7:34 PM, Frances C. Bernstein f...@bernstein-plus-sons.com wrote: Pete Artymiuk wrote: --- I have an old badly-written Fortran program (I wrote it for a Vax, but it still compiles and runs in g95 - isn't Fortran wonderful?) that takes Arnott Dover's polar coordinates and converts them to a helix of any required length* in PDB (or Diamond!) format. --- Wow, that is an old program! For everyone under the ago of 60 reading this list, Diamond format was the very first PDB format, used for the first 100 or so entries that we had. It was based on the output format of the Diamond real-space refinement program and each line was 132 characters long. Long lines were awkward, in
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Dear CCP4 members, I have finally used Eleanor's idea, and it works very well. After applying SSM, we can get a rotation matrix(M), and a displacement vector N: (Xnew,Ynew,Znew)'=M*(X,Y,Z)'+N Then, from the rotation matrix M, we can get its another representative format-*quaternion number. *The quaternion number has 4 elements, the first element(w) of which represents the cosine value of half of the rotation anger, and the next 3 elements(x0,y0,z0) represent the rotation vector. That means the molecule rotates an angle of acos(w)*2*180/pi degrees around the vector (x0,y0,z0). The attached file is the matlab program i wrote to translate M into a quaternion number. That should be very easy to be translated into other language formats. Best regards, Yuan SHANG On Thu, Aug 19, 2010 at 7:34 PM, Frances C. Bernstein f...@bernstein-plus-sons.com wrote: Pete Artymiuk wrote: --- I have an old badly-written Fortran program (I wrote it for a Vax, but it still compiles and runs in g95 - isn't Fortran wonderful?) that takes Arnott Dover's polar coordinates and converts them to a helix of any required length* in PDB (or Diamond!) format. --- Wow, that is an old program! For everyone under the ago of 60 reading this list, Diamond format was the very first PDB format, used for the first 100 or so entries that we had. It was based on the output format of the Diamond real-space refinement program and each line was 132 characters long. Long lines were awkward, in some ways, to handle on computers of that time so we designed what is now known as PDB format. If you want to know more, you can look at page 9 of the September 1974 PDB Newsletter (available on the RCSB web site if you start at http://www.rcsb.org/pdb/static.do?p=general_information/news_publications/newsletters/newsletter.html#pre1999) for the format of coordinate records in the original format. The reason that I know that there were about 100 entries released in the original format is that I was the one who had to convert them all into the new PDB format in 1976. Frances Bernstein = Bernstein + Sons * * Information Systems Consultants 5 Brewster Lane, Bellport, NY 11713-2803 * * *** *Frances C. Bernstein * *** f...@bernstein-plus-sons.com *** * * *** 1-631-286-1339FAX: 1-631-286-1999 = function V=Matrix2Quat(M) tq(1)=1+M(1,1)+M(2,2)+M(3,3); tq(2)=1+M(1,1)-M(2,2)-M(3,3); tq(3)=1-M(1,1)+M(2,2)-M(3,3); tq(4)=1-M(1,1)-M(2,2)+M(3,3); j=1; QW=0; QX=0; QY=0; QZ=0; for i=1:4 if(tq(i)tq(j)) j=i; end end % check the diagonal if (j==1) %/* perform instant calculation */ QW = tq(j); QX = M(2,3)-M(3,2); QY = M(3,1)-M(1,3); QZ = M(1,2)-M(2,1); elseif (j==2) QW = M(2,3)-M(3,2); QX = tq(j); QY = M(1,2)+M(2,1); QZ = M(1,3)+M(1,3); elseif (j==3) QW = M(3,1)-M(1,3); QX = M(1,2)+M(2,1); QY = tq(j); QZ = M(2,3)+M(3,2); else QW = M(1,2)-M(2,1); QX = M(3,1)+M(1,3); QY = M(2,3)+M(3,2); QZ = tq(j); end s = sqrt(0.25/tq(j)); QW = QW*s; QX = QX*s; QY = QY*s; QZ = QZ*s; V(1,1)=QX; V(2,1)=QY; V(3,1)=QZ; V(4,1)=QW; V(5,1)=acos(QW)*2*180/pi;
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Hi Yuan You might want to look at the 'exponential map' as an alternative to quaternions. This article evaluates all the various representations of rotations, including Eulerian angles, polar angles, rotation matrices, quaternions etc: http://webhome.cs.uvic.ca/~blob/courses/485c/notes/pdf/expmap.pdf The advantage of the exponential map representation is that only 3 variables are used, which, as for the Eulerian polar angle representations, is exactly the number that are needed to represent an arbitrary rotation in 3-D so it's an optimally parsimonious representation. However it doesn't suffer from the well-known singularities as Eulerian polar angles (it suffers from different singularities but it's possible to sweep them under the carpet). Quaternions, as you say, require 4 variables but a constraint is needed (i.e. normalisation of the vector) to reduce it back to 3. Cheers -- Ian On Mon, Sep 13, 2010 at 4:21 PM, 商元 shangyuan5...@gmail.com wrote: Dear CCP4 members, I have finally used Eleanor's idea, and it works very well. After applying SSM, we can get a rotation matrix(M), and a displacement vector N: (Xnew,Ynew,Znew)'=M*(X,Y,Z)'+N Then, from the rotation matrix M, we can get its another representative format-quaternion number. The quaternion number has 4 elements, the first element(w) of which represents the cosine value of half of the rotation anger, and the next 3 elements(x0,y0,z0) represent the rotation vector. That means the molecule rotates an angle of acos(w)*2*180/pi degrees around the vector (x0,y0,z0). The attached file is the matlab program i wrote to translate M into a quaternion number. That should be very easy to be translated into other language formats. Best regards, Yuan SHANG On Thu, Aug 19, 2010 at 7:34 PM, Frances C. Bernstein f...@bernstein-plus-sons.com wrote: Pete Artymiuk wrote: --- I have an old badly-written Fortran program (I wrote it for a Vax, but it still compiles and runs in g95 - isn't Fortran wonderful?) that takes Arnott Dover's polar coordinates and converts them to a helix of any required length* in PDB (or Diamond!) format. --- Wow, that is an old program! For everyone under the ago of 60 reading this list, Diamond format was the very first PDB format, used for the first 100 or so entries that we had. It was based on the output format of the Diamond real-space refinement program and each line was 132 characters long. Long lines were awkward, in some ways, to handle on computers of that time so we designed what is now known as PDB format. If you want to know more, you can look at page 9 of the September 1974 PDB Newsletter (available on the RCSB web site if you start at http://www.rcsb.org/pdb/static.do?p=general_information/news_publications/newsletters/newsletter.html#pre1999) for the format of coordinate records in the original format. The reason that I know that there were about 100 entries released in the original format is that I was the one who had to convert them all into the new PDB format in 1976. Frances Bernstein = Bernstein + Sons * * Information Systems Consultants 5 Brewster Lane, Bellport, NY 11713-2803 * * *** * Frances C. Bernstein * *** ...@bernstein-plus-sons.com *** * * *** 1-631-286-1339 FAX: 1-631-286-1999 =
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Thanks, lan. For quaternions, it needs w^2+x^2+y^2+z^2=1, thus reduces variables to 3. But fortunately,(x,y,z) here only represents a direction of the rotation angle, and the absolute value of them are not that important. I think a rotation vector and the rotation angle could be a very good representation of any rotation in 3D space, and that's more directviewing than the rotation Matrix which is a Matrix, or Euler Angles, which need three rotation angles. The Exponential Map, it's too complicated, so many mathematicsBut, from the definition of q = e^v, I think they are identical. and the direction of v is identical to (x,y,z) in the quaternion. Regards, Yuan SHANG On Tue, Sep 14, 2010 at 12:09 AM, Ian Tickle ianj...@gmail.com wrote: Hi Yuan You might want to look at the 'exponential map' as an alternative to quaternions. This article evaluates all the various representations of rotations, including Eulerian angles, polar angles, rotation matrices, quaternions etc: http://webhome.cs.uvic.ca/~blob/courses/485c/notes/pdf/expmap.pdfhttp://webhome.cs.uvic.ca/%7Eblob/courses/485c/notes/pdf/expmap.pdf The advantage of the exponential map representation is that only 3 variables are used, which, as for the Eulerian polar angle representations, is exactly the number that are needed to represent an arbitrary rotation in 3-D so it's an optimally parsimonious representation. However it doesn't suffer from the well-known singularities as Eulerian polar angles (it suffers from different singularities but it's possible to sweep them under the carpet). Quaternions, as you say, require 4 variables but a constraint is needed (i.e. normalisation of the vector) to reduce it back to 3. Cheers -- Ian On Mon, Sep 13, 2010 at 4:21 PM, 商元 shangyuan5...@gmail.com wrote: Dear CCP4 members, I have finally used Eleanor's idea, and it works very well. After applying SSM, we can get a rotation matrix(M), and a displacement vector N: (Xnew,Ynew,Znew)'=M*(X,Y,Z)'+N Then, from the rotation matrix M, we can get its another representative format-quaternion number. The quaternion number has 4 elements, the first element(w) of which represents the cosine value of half of the rotation anger, and the next 3 elements(x0,y0,z0) represent the rotation vector. That means the molecule rotates an angle of acos(w)*2*180/pi degrees around the vector (x0,y0,z0). The attached file is the matlab program i wrote to translate M into a quaternion number. That should be very easy to be translated into other language formats. Best regards, Yuan SHANG On Thu, Aug 19, 2010 at 7:34 PM, Frances C. Bernstein f...@bernstein-plus-sons.com wrote: Pete Artymiuk wrote: --- I have an old badly-written Fortran program (I wrote it for a Vax, but it still compiles and runs in g95 - isn't Fortran wonderful?) that takes Arnott Dover's polar coordinates and converts them to a helix of any required length* in PDB (or Diamond!) format. --- Wow, that is an old program! For everyone under the ago of 60 reading this list, Diamond format was the very first PDB format, used for the first 100 or so entries that we had. It was based on the output format of the Diamond real-space refinement program and each line was 132 characters long. Long lines were awkward, in some ways, to handle on computers of that time so we designed what is now known as PDB format. If you want to know more, you can look at page 9 of the September 1974 PDB Newsletter (available on the RCSB web site if you start at http://www.rcsb.org/pdb/static.do?p=general_information/news_publications/newsletters/newsletter.html#pre1999 ) for the format of coordinate records in the original format. The reason that I know that there were about 100 entries released in the original format is that I was the one who had to convert them all into the new PDB format in 1976. Frances Bernstein = Bernstein + Sons * * Information Systems Consultants 5 Brewster Lane, Bellport, NY 11713-2803 * * *** *Frances C. Bernstein * *** f...@bernstein-plus-sons.com *** * * *** 1-631-286-1339FAX: 1-631-286-1999 =
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Pete Artymiuk wrote: --- I have an old badly-written Fortran program (I wrote it for a Vax, but it still compiles and runs in g95 - isn't Fortran wonderful?) that takes Arnott Dover's polar coordinates and converts them to a helix of any required length* in PDB (or Diamond!) format. --- Wow, that is an old program! For everyone under the ago of 60 reading this list, Diamond format was the very first PDB format, used for the first 100 or so entries that we had. It was based on the output format of the Diamond real-space refinement program and each line was 132 characters long. Long lines were awkward, in some ways, to handle on computers of that time so we designed what is now known as PDB format. If you want to know more, you can look at page 9 of the September 1974 PDB Newsletter (available on the RCSB web site if you start at http://www.rcsb.org/pdb/static.do?p=general_information/news_publications/newsletters/newsletter.html#pre1999) for the format of coordinate records in the original format. The reason that I know that there were about 100 entries released in the original format is that I was the one who had to convert them all into the new PDB format in 1976. Frances Bernstein = Bernstein + Sons * * Information Systems Consultants 5 Brewster Lane, Bellport, NY 11713-2803 * * *** *Frances C. Bernstein * *** f...@bernstein-plus-sons.com *** * * *** 1-631-286-1339FAX: 1-631-286-1999 =
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Yuan SHANG 1) DIY The way that has been used is to calculate the inertia tensor matrix for helix (or any other secondary structure element). You can chose backbone atoms or just the CA atoms. Then calculate the eigen vectors and values from this and the largest eigen vector will be the best fit vector to the helix - and its lambda will define its length. For a strand or sheet you can use this method too. This was the standard way from molecular simulation work to look at simplified dynamics of proteins. 2) The program Squid http://www.ebi.ac.uk/~oldfield/squid/ (1992, 1998) has lots of different analysis methods for proteins including calculating vectors for helices, the angles between helices (torsion/distance/opening) and other things. You only problem is that it is very old (1988) and written in Fortran and requires a little effort to install - sorry - I no longer support it. There is a pre compiled linux-32 bit version and I still do all my structure analysis with it. http://www.ebi.ac.uk/~oldfield/xsquid - though this requires installation data too. Tom Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
I've put a couple of example programs that do this sort of thing (using the clipper libraries) in ftp://ftp.mrc-lmb.cam.ac.uk/pub/pre/helixanglethings.tar.gz Phil 1) helixangle.cpp Calculate angle beween two helices Superimpose standard helix on two specified chains ranges, then calculate angle between them 2) kinky.cpp Analyse change of helix axis directions between 2 structures On 17 Aug 2010, at 09:49, Tom Oldfield wrote: Yuan SHANG 1) DIY The way that has been used is to calculate the inertia tensor matrix for helix (or any other secondary structure element). You can chose backbone atoms or just the CA atoms. Then calculate the eigen vectors and values from this and the largest eigen vector will be the best fit vector to the helix - and its lambda will define its length. For a strand or sheet you can use this method too. This was the standard way from molecular simulation work to look at simplified dynamics of proteins. 2) The program Squid http://www.ebi.ac.uk/~oldfield/squid/ (1992, 1998) has lots of different analysis methods for proteins including calculating vectors for helices, the angles between helices (torsion/distance/opening) and other things. You only problem is that it is very old (1988) and written in Fortran and requires a little effort to install - sorry - I no longer support it. There is a pre compiled linux-32 bit version and I still do all my structure analysis with it. http://www.ebi.ac.uk/~oldfield/xsquid - though this requires installation data too. Tom Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Hello, Is there some C or C++ code out there doing what you described in 1). If not, is there a very detailed explanation of this procedure somewhere, detailed enough in order to implement it (just getting the best fit vector and its length, no other parameters)? Thanks a lot, Francois. Tom Oldfield wrote: Yuan SHANG 1) DIY The way that has been used is to calculate the inertia tensor matrix for helix (or any other secondary structure element). You can chose backbone atoms or just the CA atoms. Then calculate the eigen vectors and values from this and the largest eigen vector will be the best fit vector to the helix - and its lambda will define its length. For a strand or sheet you can use this method too. This was the standard way from molecular simulation work to look at simplified dynamics of proteins. 2) The program Squid http://www.ebi.ac.uk/~oldfield/squid/ (1992, 1998) has lots of different analysis methods for proteins including calculating vectors for helices, the angles between helices (torsion/distance/opening) and other things. You only problem is that it is very old (1988) and written in Fortran and requires a little effort to install - sorry - I no longer support it. There is a pre compiled linux-32 bit version and I still do all my structure analysis with it. http://www.ebi.ac.uk/~oldfield/xsquid - though this requires installation data too. Tom Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
The problem with the inertial matrix approach is that it is very sensitive to end effects on the helix, ie a helix is not a perfect cylinder. So superimposing an ideal helix is more reliable Phil On 17 Aug 2010, at 10:17, Francois Berenger wrote: Hello, Is there some C or C++ code out there doing what you described in 1). If not, is there a very detailed explanation of this procedure somewhere, detailed enough in order to implement it (just getting the best fit vector and its length, no other parameters)? Thanks a lot, Francois. Tom Oldfield wrote: Yuan SHANG 1) DIY The way that has been used is to calculate the inertia tensor matrix for helix (or any other secondary structure element). You can chose backbone atoms or just the CA atoms. Then calculate the eigen vectors and values from this and the largest eigen vector will be the best fit vector to the helix - and its lambda will define its length. For a strand or sheet you can use this method too. This was the standard way from molecular simulation work to look at simplified dynamics of proteins. 2) The program Squid http://www.ebi.ac.uk/~oldfield/squid/ (1992, 1998) has lots of different analysis methods for proteins including calculating vectors for helices, the angles between helices (torsion/distance/opening) and other things. You only problem is that it is very old (1988) and written in Fortran and requires a little effort to install - sorry - I no longer support it. There is a pre compiled linux-32 bit version and I still do all my structure analysis with it. http://www.ebi.ac.uk/~oldfield/xsquid - though this requires installation data too. Tom Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
When I started doing various analyses of conformational changes in AP2 (bending of helical solenoids, see supp data fig S2 for Jackson et al, Cell 141, 1220-1229 (2010)) I was first going to do lots of scripting around this sort of thing, but Kevin Cowtan persuaded me that it was easier to program exactly what you want to do, and that his clipper libraries made it very easy (in C++). The couple of example programs I posted show a framework that I've used in a series of little programs to do such analyses, and I've found it easier just to hack the programs within such a framework rather than to try to write some entirely general and flexible system. Clipper lets you select coordinate range, superimpose them, extract vectors (or indeed inertial tensors if you want: I found that didn't work well) in a reasonably straightforward way. I'm sure there are other ways to do it, but this suits me Phil On 17 Aug 2010, at 10:53, Eleanor Dodson wrote: As someone said - this is quite hard unless you have a very long helix - any ragged end bits can dominate the fit of one feature to another. In your case I think I would use SSM to superpose the two similar structures , then LSQKAB to fit any feature to its related one using the original molecule, plus the second one after the SSM overlap. LSQKAB will give you the relative rotation of any feature to its partner - look the the polar angles to get a estimate of rotation, and the translation to find how far apart the 2 features are. This is different to getting the direction of the helix. Centre of mas is easy LSQKAB gives you that, but the vector is easisest found with a bit of arithmetic. Find COM of residues 1-3 say and COM of residues n to n-3, vector connects these two COMs - direction cosines are xv/(sqrt(xv*xv +yv*yv +zv*zv) yv/(sqrt(xv*xv +yv*yv +zv*zv .. length is a function of number of residues The $CLIBD/fraglib/theor-helix-70.pdb suggests ~ 14.8A per 10 residues.. Eleanor Phil Evans wrote: The problem with the inertial matrix approach is that it is very sensitive to end effects on the helix, ie a helix is not a perfect cylinder. So superimposing an ideal helix is more reliable Phil On 17 Aug 2010, at 10:17, Francois Berenger wrote: Hello, Is there some C or C++ code out there doing what you described in 1). If not, is there a very detailed explanation of this procedure somewhere, detailed enough in order to implement it (just getting the best fit vector and its length, no other parameters)? Thanks a lot, Francois. Tom Oldfield wrote: Yuan SHANG 1) DIY The way that has been used is to calculate the inertia tensor matrix for helix (or any other secondary structure element). You can chose backbone atoms or just the CA atoms. Then calculate the eigen vectors and values from this and the largest eigen vector will be the best fit vector to the helix - and its lambda will define its length. For a strand or sheet you can use this method too. This was the standard way from molecular simulation work to look at simplified dynamics of proteins. 2) The program Squid http://www.ebi.ac.uk/~oldfield/squid/ (1992, 1998) has lots of different analysis methods for proteins including calculating vectors for helices, the angles between helices (torsion/distance/opening) and other things. You only problem is that it is very old (1988) and written in Fortran and requires a little effort to install - sorry - I no longer support it. There is a pre compiled linux-32 bit version and I still do all my structure analysis with it. http://www.ebi.ac.uk/~oldfield/xsquid - though this requires installation data too. Tom Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Fitting a helix is not trivial. If you have access to windows and mathematica, then you might try helfit. (Otherwise, you could implement the algorithm yourself and then share your code with the rest of us ;-) http://dx.doi.org/10.1016/j.compbiolchem.2008.03.012 James On Aug 15, 2010, at 12:29 AM, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
I don't know of any standard programs that do this, but I have a couple of programs that do this sort of thing, using a standard helix as a reference and the clipper libraries. I could send you the code if you like, though you'd probably have to hack them to do exactly what you want (I found that easier than trying to write a completely general program for doing every sort of comparison. Phil On 15 Aug 2010, at 08:29, 商元 wrote: Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do this？ Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG
Re: [ccp4bb] Method to calculate the axis of an alpha helix
Interhlx may be what you are looking for http://nmr.uhnres.utoronto.ca/ikura/resources/data+sw/interhlx/ Dear all, I want to compare the conformational change of two similar structures, using one alpha helix as the reference. Then, how can I get a vector that can represent both the position and direction of the helix? Is there any well-known software can do thisï¼Yuml; Or, should I build a cylinder model, with parameters [radius,bottom center(x1,y1,z1),top center(x1,y2,z2)], using the coordinates of C,C(alpha) and N to fit these parameters? Thanks for any suggestions Regards, Yuan SHANG -- Edwin Pozharski, PhD University of Maryland, Baltimore
