From xiangjun@rutchem.rutgers.edu Date: Mon, 9 Jun 2003 19:53:55 -0400 From: Xiangjun LU To: Heinz Sklenar Cc: David Beveridge , Zippi Shakked , Remo Rohs , Thomas Cheatham , Stephen Neidle , Victor Zhurkin , martin.egli , ponzy , Juan.A.Subirana , Karolin.Luger , schlick , loren.williams , e.westhof , Krystyna.Zakrzewska , sponer , m.zacharias , agor , heinemann , olson , haim.rozenberg , Manju Bansal , Richard Lavery , Richard E. Dickerson , Rama Sarma Subject: Re: Olson-Zhurkin letter Dear colleagues, It is nice to see further discussion from Dr. Sklenar on the importance of the order of rotation and definition of "mean-frame" on getting *exactly* the same numerical values from all nucleic acid analyzing programs. While I have restrained myself to get into too much technical details, experience tells me that not "only of mathematical definitions", but also computer implementations would also make a difference, unless a clearly defined procedure is followed exactly. Think, for example, the different implementations of (the same) force field in MM/MD. In nucleic acid world, fitting vs. non-fitting a standard base to the experimental ones in Curves would make a much larger difference in base-pair parameters (e.g. propeller twist) than the subtle difference in "mean-frame" definitions. Thus, to ensure that all programs (essentially only one, at least for this part) would give exactly the same numbers, every technical details need to be specified: (1) fitting (or not fitting, or how to fit?) standard base with em-bedded reference frame; (2) order of rotation (z-x-y or z-y-x or other options); (3) definition of "mean-frame", including how to ensure orthogonality of the axes; (4) how to project to get the translational parameters. If we think of analysis/rebuilding as two sides of the same coin, whatever procedure specified above for calculating structural parameters should be reversible to allow for *exact* construction of the base pair geometry. Take each base-pair as a rigid block, only 6 parameters are required to relate one bp to the other. Two sets are commonly used: one set is "shift, slide, rise, tilt, roll and twist", and the other set is "x-displacement, y-displacement, helical rise, inclination, tip, and helical twist". Obviously, these two sets of parameters should be directly convertible, as demonstrated by Calladine and Drew in their 1984 JMB B-to-A transition paper, and illustrated in 3DNA manuscript. If we try to set up a new convention on the *exact definition* of the parameters, the above two issues are clearly relevant to make sure the mathematical is sound. The way to calculate the local helical axis and helical parameters in 3DNA is *essentially the same* as in RNA, but expressed in a much simpler way. First, the local helical axis is calculated as dx-times-dy, following Bansal, which gives the *same* result as the "single rotation axis" detailed in the RNA paper. I still could not figure out WHY, but verified this numerically. The location where the helix passes through is based directly on the RNA paper (i.e., following Chasles's theorem). The procedure to calculate helical parameters, i.e., tip/inclination/x-disp/y-disp/etc, following the SCHNAaP paper (i.e, with tip-inclination combination, which is consisent with the roll-tilt, propeller-buckle combinations in 3DNA). What amazed us is that this much simpler tip-inclination implementation in 3DNA gives *exactly* the same numerical values as the original RNA algorithm. For those who are interested, I could provide MATLAB code with working examples. As far as the "possible confusion because small letter omega is used for local twist [in 3DNA], in contrast to Cambridge conventions". This follows the revision after the Cambridge convention by an international committee, and was first reported by Dr. Dickerson. This point was mentioned in the Tsukuba report, if I remembered it correctly. Apart from getting all-agreed-upon parameters, another issue is what does these numbers mean. In the Tsukuba report, 4 set of intrinsic correlations between base-pair and step parameters were reported. The dShear vs. Twist correlation is the key to solve the discrepancy in Twist angles among G-U wobble pair involved steps, as seen between FreeHelix and Curves (see also discussion in 3DNA manuscript). In *RNA* (not to be confused with RNA program mentioned above) structures, there are many non-Watson-Crick base-pairs, which sometimes could give crazy Shift/Slide etc values. Looking back, 3DNA has never been intended to set up a new standard for the exact definition of various parameters. We selected what made best sense to us from what were already available. This was made possible by knowing the exact technical details of how other programs work. In the meantime, 3DNA also provide a program called "cehs" which gives the original CEHS/SCHNAaP parameters, to which Freehelix parameters would be similar. Believe it or not, "cehs -r" would give the authentic RNA parameters. We also see Curves unique in defining global parameters, bending analysis and groove dimensions. Of course, we are willing to make changes to accommodate any new convention the community might agree upon. Best regards and see you at Albany. Xiang-Jun On Sun, 8 Jun 2003, Heinz Sklenar wrote: > 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 >