From sklenar@mdc-berlin.de Date: Sun, 08 Jun 2003 15:52:24 +0200 From: Heinz Sklenar To: David Beveridge , Zippi Shakked , Remo Rohs , Thomas Cheatham , Stephen Neidle , Victor Zhurkin , martin.egli , ponzy , Juan.A.Subirana , Karolin.Luger , schlick , loren.williams , sklenar , e.westhof , xiangjun , Krystyna.Zakrzewska , sponer , m.zacharias , agor , heinemann , olson , haim.rozenberg , Manju Bansal Cc: Richard Lavery , Richard E. Dickerson , Rama Sarma Subject: Olson-Zhurkin letter Dear colleagues, we should thank Drs. Olson and Zhurkin for their letter, because that gives us the possibility for starting the discussion already before the workshop. The intention of the workshop proposed by Dr. Sarma is to come up with agreed parameter definitions to make sure that all programs yield exactly the same values for the parameters designated by the Cambridge conventions. This is not a question of efficient calculation procedures, but only of mathematical definitions. I stay to my opinion that both order of rotations and mean frame definition are the central issue in this context. It is not true that we are discussing this point 'again and again'. On the contrary, I have the feeling that discussions have been avoided because of controversial points of view. In Tsukuba we have only discussed on reference frame definitions assigned to bases and, with the work done in Dr. Olson's group, this is now agreed by the community. In the moment, different definitions of order of rotations and mean frames are used in various programs and such definitions have also been changed from time to time. Thus, I see differences between the definitions described in the 3DNA manuscript on the one hand and those used in RNA on the other hand. If I understand Drs. Olson and Zhurkin right, we should now follow the definitions implemented in 3DNA without any discussion, but then we wouldn't need a workshop on parameter definitions. By the way, I had already adapted the CURVES definitions to those used in RNA before I came to the solution described in my draft, and don't see a convincing reason why I now should adapt to the revision used in 3DNA. It should be stressed that the definitions do not only concern local step and 'local' helical parameters, but also global parameters and curvature description are affected. It seems also not true that the mean frame dubbed 'reverse mean frame R' in my draft, is already used in 3DNA. As I understand Equation (1) in the manuscript, the 3DNA 'middle frame' is not symmetric with respect to the z-rotation by the phase angle and is therefore, strictly speaking, not a real 'middle frame'. I hope to have shown in my draft that there are only two symmetric mean frames, one (frame H) for traveling from the mean frame to frames A and B and another (frame R) for traveling from frames A and B to the mean frame. Looking to the manuscript on 3DNA, I see that the primarily calculated rotation parameters are now twist, phase, and a single rotation in the (x-y) plane, where (omega+phase), lambda, and (omega-phase) are the corresponding Euler angles (with a possible confusion because small letter omega is used for local twist, in contrast to Cambridge conventions where small letter omega has been designated for helical twist). This is completely valid since any three angles (e. g. also Euler angles) can be used for describing the orientation relationship of two frames. It does not mean, however, that the finally calculated parameters are Euler angles (although they are 'used for more than 200 years') and will also not remove the need for defining the order of rotations. Following the Cambridge conventions, inclination and tilt are related to rotation about x, and tip and roll to rotation around y. The problem is that the same single rotation in the (x-y) plane can be obtained for different x- and y-components, if the order of rotations about x and y is changed, and this has also consequences for the translation parameters. Following the Cambridge conventions, these should be related to translations along x and y, but the x- and y-axes of the helical frame are affected by the order of rotations about x and y. This means that the 3DNA implementations imply an additional (and not yet agreed) convention on the order of rotations too, by saying that sqrt(tilt**2+roll**2) should be the single rotation angle in the (x-y) plane. In this case, it is an implicit convention on the pathway of rotations. In the same way, we could say that sqrt(twist**2 +tilt**2+roll**2) should be the total single rotation angle, equal to the twist angle in the local helical frame, as it was the case in RNA, but yielding clearly different values for the parameters. So having now separated the z-rotation as the first rotation about a distinguished axis (and this is a good choice in the view of Cambridge conventions), why not defining the order of x- and y-rotations in a similar direct way? In my opinion, this would follow the Cambridge conventions in a better understandable way. As a matter of fact, we cannot simply make a decision by chance on the definitions introduced by the authors of programs, without considering the underlying concepts. If so, I could also say that the definitions used in the old CURVES program (with most visible deviations of rise, compared with other definitions, that have been recognized and extensively discussed) are mathematically 'rigorous' in the sense that they allow for unique reconstruction and are independent of reading direction, being the only demands of the Cambridge conventions. But in contrast with Drs. Olson's and Zhurkin's point of view, we are ready to change our definitions on the basis of an overall reasonable agreement to be discussed at the workshop. I am sorry for insisting on such discussion, that has not taken place until now. Without agreement on additional conventions, I really don't see a way to come to a point where exactly the same parameter values are calculated by different programs. And this is a very acceptable demand of the program users. We have to expect that that small differences of parameter values in the examples studied by Dr. Lu on the basis of different definitions, will increase in largely distorted DNA and in describing unusual base pairing occurring both in DNA and RNA. Thank you all for paying attention to this point and discussing it on a scientific level, without considering personal prestige. Wit best regards, Heinz Sklenar