From dok707@cvx12.inet.dkfz-heidelberg.de Wed Nov 17 10:27:36 1993 Received: from cvx12.inet.dkfz-heidelberg.de for dok707@cvx12.inet.dkfz-heidelberg.de by www.ccl.net (8.6.1/930601.1506) id JAA15253; Wed, 17 Nov 1993 09:36:34 -0500 Received: by cvx12.inet.dkfz-heidelberg.de id AA04274 (5.65c/IDA-1.4.4 for chemistry@ccl.net); Tue, 16 Nov 1993 20:16:36 +0100 Date: Tue, 16 Nov 1993 20:16:36 +0100 From: Frank Herrmann Message-Id: <199311161916.AA04274@cvx12.inet.dkfz-heidelberg.de> To: chemistry@ccl.net Subject: quasiparticle force fields QUASIPARTICLE FORCE FIELDS -------------------------- Here are two (non review) articles: @article{mean force, author={Manfred J. Sippl}, title={Calculation of Conformational Ensembles from Potentials of Mean Force}, journal={Journal of Molecular Biology 213, 1990}, pages={859-883}, year=1990} @article{entire residues, author={Paul R. Gerber}, title={Peptide Mechanics: A Force Field for Peptides and Proteins Working with Entire Residues as Smallest Units}, journal={Biopolymers, Vol. 32}, pages={1003-1017}, year=1992} -------------------------------------------------- Frank Herrmann, Dept. of Molecular Biophysics 0810 German Cancer Research Center Im Neuenheimer Feld 280, D-69120 Heidelberg Tel: (49) 6221-422336, FAX: (49) 6221-422333 email: F.Herrmann@dkfz-heidelberg.de From mikes@bioch.ox.ac.uk Wed Nov 17 12:27:27 1993 Received: from oxmail.ox.ac.uk for mikes@bioch.ox.ac.uk by www.ccl.net (8.6.1/930601.1506) id MAA17229; Wed, 17 Nov 1993 12:12:44 -0500 From: Received: from bioch.ox.ac.uk by oxmail.ox.ac.uk with SMTP (PP) id <19801-0@oxmail.ox.ac.uk>; Wed, 17 Nov 1993 16:20:11 +0000 Received: from bioch.ox.ac.uk (nmrpcd.ocms) by biochemistry.oxford.ac.uk; Wed, 17 Nov 93 16:19:06 GMT Received: by bioch.ox.ac.uk (920330.SGI/bioch3.0) id AA10871; Wed, 17 Nov 93 16:19:15 GMT Date: Wed, 17 Nov 93 16:19:15 GMT Message-Id: <9311171619.AA10871@nmrpcd.ocms.bioch.ox.ac.uk> To: chemistry@ccl.net Subject: Cluster Analysis A while ago I sent in a query about Cluster Analysis, and got lots of helpful replies - thank you for everyone who sent me something. Here are most of them: Mike ----------------------------------------------------------------------------- Arun Malhotra: Cluster analysis is a useful way to classify structures - we have been using it to sort thru several (10-20) models of the 16S RNA. You may want to look up "Modeling the 3-D structure of RNA using discrete nucleotide conformational sets" Daniel Gautheret, Francois Major and Robert Cedergren, J. Mol. Biol. (1993) 229, 1049-1064. Francois and other have been using cluster analysis for classifying nucleotide structures and discuss some of this in the methods section. Another recent application of cluster analysis appeared in "Protein structure comparison by alignment of distance matrices" Liisa Holm and Chris Sander, J. Mol. Biol. (1993) 233, 123-138. Usually any measure (single-valued) of difference between two structures can be used depending on what property you are trying to cluster around - rmsd or a difference distance matrix is good for structural comparisons. There is a Mac package for multivariate analysis/cluster analysis on sumex (in sci/mac-dendro, mac-mul, graph-mu etc.) that works fairly well. Commercial statistical analysis packages such as Splus also have cluster analysis. ------------------------------------------------------------------------------ Alain St-Amant: A very nice piece of work has recently come out of Charlie Brooks' group. It should be just what you want. The reference is: M. E. Karpen, D. J. Tobias, and C. L. Brooks, "Statistical Clustering Techniques for the Analysis of Long Molecular Dynamics Trajectories -- Analysis of 2.2 ns Trajectories of YPGDV," Biochemistry, Volume 32, pages 412-420. ------------------------------------------------------------------------------ Peter S. Shenkin: I'm glad you asked that question. :-) Quentin McDonald and I have written a program that does exactly what you describe: cluster analysis of molecular conformations. An article that covers the approach we used, as well as the implementation, has been submitted to J. Comput. Chem. The program is called XCluster. It begins by constructing the matrix of inter-conformational "distances" between all pairs of conformations read in. There are several choices of "distance" available, including RMS of interatomic distances following rigid-body superposition (which is what I assume you mean by "rmsd"). Molecular symmetry can be taken into account, and clustering can, if desired, be performed on only a subset of the atoms -- for example, the ring atoms of a cyclic system. ---------------------------------------------------------------------------- David States: There are several issues here. If you do not know how many clusters there should be, then you don't want to use an algorithm that imposes a particular answer. This can happen either explicitly (for example a binary classification halted at 3 divisions by definition will give 8 classes) or implicitly in a leader-mean classification of the sort you describe (the number of classes is inversely dependent on the cutoff radius). To avoid biasing the results of the classification by class number, you need a method that allows you to compare classifications with different numbers of classes. This leads to the general field of Bayesian classification where a classification is viewed as a model for the observed distribution and the optimal classification is that classification which optimally describes the data. Larry Hunter and I used this to derive a classification of protein secondary structure several years ago (Hunter and States (1991), "Bayesian classificaiotn of protein structural motifs.", in Proceedings of HICSS-24, IEEE Press, Los Alamitos CA, 595-604). Another issue is flat vs. hierarchical classification. Are these proteins derived by an evolutionary process from a common ancestor in which case a hierarchical model might be more appropriate, or are they random samples of conformation space in which case a flat classification would be better. Defining the optimal tree structure for a set can itself be a demanding problem. The computational complexity of the problem depends on your class definition. If you seek connected classes (two structures are in the same class if there is a path of similarity relationships connecting them, transitive closure) then this is algorithmically a minimal spanning tree problem for which linear time solutions exist. On the other hand, if you demand that all members of a class to fall within some cutoff of every other member (cliques), then you have a graph partition problem that is NP-complete. The sensitivity of the classification to errors or ambiguities in the data is also dependent on class definition. Transitive closure is robust to less than perfect sensitivity in defining similarity relationships but false positive similarity judgements lead directly to classification errors. On the otherhand, clique definitions are very sensitive to false negative similarity judgements and robust to false positives. ----------------------------------------------------------------------------- Frank Kolakowski: I am not sure exactly what it is that you are asking, but look at recent efforts by C. Sander and colleagues from EMBL. AU Ouzounis-C. Sander-C. Scharf-M. Schneider-R. TI Prediction of protein structure by evaluation of sequence-structure fitness. Aligning sequences to contact profiles derived from three-dimensional structures. SO J-Mol-Biol. 1993 Aug 5. 232(3). P 805-25. AU Sander-C. Schneider-R. TI The HSSP data base of protein structure-sequence alignments. SO Nucleic-Acids-Res. 1993 Jul 1. 21(13). P 3105-9. ---------------------------------------------------------------------------- John Kapenga: There are a number of ways to cluster things (and some texts on cluster analysis as well as codes). If you have a pairwise distance function rmsd say, as d(p1,p2), then one method is to to define the distance between to groups G1 and G2 as the average of the distances between all pairs (p1,p2) with p1 in G1 and p2 in G2 (there are other posible group distances) Start with 100 groups Gi , each with a single point pi repeat k times merge the closest two groups Then you are left with 100-k groups. Another method requires yo to be able to find the mean of a group, which must be able to be input to d(,). Start with a random choice of q1, q2, ... qk from the pi's repeat until "converged" for each pi put pi in Gi if pi is closest to qi amoung all the qis let qi = mean(Gi) Which results in k clusters - you do need to watch empty Gis These (and their variations) are perhaps the two most common methods. ----------------------------------------------------------------------------- Eric Martin: One way to do this is to make a similarity matrix based on RMSD of chosen corresponding atoms. You could do cluster analysis directly, which would be treating distance from each member as a variable in a 100 dimensional property space. In my opinion, a better way is to 1st perform multidimensional scaling on the similarity matrix (proc MDS in SAS). MDS finds cartesian coordinates in a low dimensional euclidian space such that the distances between the points best reproduce the similarities. You can then either perform cluster analysis on these latent variables, or else superimpose a grid on the space and pick points near the grid points, or any other grouping or experimental design scheme. ----------------------------------------------------------------------------- Ganesan Ravishanker: That is the simplest way to cluster them. And this procedure, called 2-D RMS Map by us, turns out to be a very useful tool to cluster and monitor structural grouping in an MD. We construct a symmetrix matrix RMS(i,j) where i and j are indices of the average structures over portions of trajectory. This matrix is laid out on a 2-D grid using a continuous spectrum of color to code the value of RMS at the grid (i,j). As is obvious, the diagonals are zero and 1A blocks are usually around the diagonal and various squares or rectangles develop around the diagonal showing the persistence of a given structural group. We can also block them using the same color for say rmsd of 0-1, another color for 1-2 etc. Off diagonal blocks indicate revisitation of structural groups along the trajectory. We have succesfully extended this to even compare trajectories of similar systems to capture the common structural groups visited in various trajectories. There is also facility to calculate the rmsd on only a subset of atoms (say only the sugar atoms in a DNA) which might give the "substate" picture relevent to only those that are selected. This and another 50 or so applications are collectively known as "MD Toolchest" developed here at Wesleyan. A small subset of the program set is already being distributed and the next considerably expanded version of it is getting ready for distribution in November. If any of you wish to know more about it, please let me know and I will personally correspond with you. Thank you. -------------------------------------------------------------------------- Heather Gordon I have been using fuzzy c-means clustering (a partitional rather than hierarchical method) to locate similar structures explored in molecular dynamics or monte carlo simulations. We published a paper last year: "Fuzzy cluster analysis of molecular dynamics trajectories", H. Gordon and R.L. Somorjai, Proteins: Structure, Function, and Genetics 14:249-264 (1992). I have since applied fuzzy c-means clustering to some MD trajectories of a simple carbohydrate with great success. The approach is, as you suggested, to find an RMS distance matrix by optimally superimposing structures and then clustering the distance matrix. The superposition algorithm is one developed by Somorjai and Zuker (a quaternion method) and the fuzzy clustering algorithm is due to Bezdek. The code is definitely not elegant(!), but if you are interested, I can send a copy to you. You might also be interested in a clustering paper: "Statistical clustering techniques for the analysis for long molecular dynamics trajectories: analysis of a 2.2ns trajectory of YPGDV", ME Karpen, DJ Tobias, CL Brooks III, Biochemistry 32, 412-420 (1993). ------------------------------------------------------------------------------ Jeff Blaney: Many methods have been described for clustering conformations into families during the last decade or so. The RMS matrix is an effective measure of the pairwise similarities between all conformers (see Cohen, F. E., Sternberg, M. J. E. "On the Use of Chemically Derived Distance Constraints in the Prediction of Protein Structure with Myoglobin as an Example", J. Mol. Biol. 1980, 137, 9-22 and Seno, Y., Go, N. "Deoxymyoglobin Studied by the Conformational Normal Mode Analysis I. Dynamics of Globin and the Heme-Globin Interaction", J. Mol. Biol. 1990, 216, 95-109.) Cluster analysis performed on the NxN matrix containing the RMS least squares rotation/translation fit deviations for N conformers works well and has been used since the mid-80's (see Perkins, T. D. J., Barlow, D. J. "RAMBLE: A conformational search program", J. Mol. Graphics 1990, 8, 156-162). This method is also available in the program COMPARE, which was distributed with DGEOM in 1990 (QCPE Program #590). COMPARE reads a series of PDB format files and generates the RMS matrix in a format appropriate for input into ARTHUR (an old chemometrics software package) or DATADESK (Mac stats software package), which both perform hierarchical clustering. COMPARE's output format can be modified easily for other stats packages (e.g. SAS). Single or complete-linkage hierarchical clustering can be used on small problems with less than about 500 conformers; beyond this the hierarchical algorithms consume very large amounts of computer time and become impractical. Jarvis-Patrick clustering (Jarvis, R. A., Patrick, E. A. "Clustering Using a Similarity Measure Based on Shared Near Neighbors", IEEE Trans. Comp. 1973, C22, 1025-1034) is much faster than hierarchical clustering and can be applied to huge datasets (several 100,000 members). Jarvis-Patrick clustering is routinely used for clustering large chemical databases into structurally related families based on two-dimensional similarity (see Willett, P. Similarity and Clustering in Chemical Information Systems, Research Studies Press: Letchworth, 1987). Clustering 1000 conformers takes only a few seconds and requires an insignificant amount of time compared to calculating the RMS matrix. Jarvis-Patrick performs well for conformational clustering, and gives results comparable or superior to hierarchical clustering on small datasets and can be run easily on datasets that are too large for hierarchical clustering. The new release of DGEOM to QCPE (imminent...) will have a new version of COMPARE which is self- contained and includes Jarvis-Patrick clustering. Conformational clustering has also been performed directly on cartesian coordinates (Murray-Rust, P., Raftery, J. "Computer analysis of molecular geometry, Part VI: Classification of differences in conformation", J. Mol. Graphics 1985, 3, 50-59). Torsion angles are a poor choice due to their 'leverage' effect: a small torsion angle change at the beginning of a chain leads to a difference of many angstroms at the end of the chain. Yvonne Martin recently described a fast, simple approach that compares distance matrices and eliminates duplicate conformers based on any single distance difference being greater than a user-specified threshhold (Y. Martin, Meeting on Binding Sites: Characterising and Satisfying Steric and Chemical Restraints, Molecular Graphics Society, University of York, England, March 28-30, 1993). ------------------------------------------------------------------------------ Konrad Koehler: Cluster analysis based on conformation can easily be done by creating a matrix all pairwise least squares RMS deviations. The cluster analysis could also be based on torsional angles, but the least squares method is simipler and generally works better. Many statistical packages such as SAS can then perform a hierarchial cluster analysis based on this matrix. Hierarchial cluster analysis is only pratical for ~1,000 conformations. If you have more, you will have to resort to some non-hierarchial method such as Jarvis-Patrick. There are several packages already available for doing cluster analysis based on conformation. The XCluster program which is included with MacroModel (Clark Still, Columbia University) version 4.0 contains a fairly sophisticated conformational clustering package. The XCluster manual contains an in depth discussion of the theory. Other packages such as Sybyl also contain facilities for cluster analysis of conformations based on either RMS deviations or torsional angles. ----------------------------------------------------------------------------- From mam@xenon.chem.ucla.edu Wed Nov 17 13:27:28 1993 Received: from argon.chem.ucla.edu for mam@xenon.chem.ucla.edu by www.ccl.net (8.6.1/930601.1506) id MAA18360; Wed, 17 Nov 1993 12:53:17 -0500 Received: from xenon.chem.ucla.edu by argon.chem.ucla.edu (Sendmail 4.1/1.08) id AA12635; Wed, 17 Nov 93 09:50:32 PST Received: by xenon.chem.ucla.edu (4.1/SMI-4.1) id AA15282; Wed, 17 Nov 93 09:54:55 PST Date: Wed, 17 Nov 93 09:54:55 PST From: mam@xenon.chem.ucla.edu (McAllister Michael) Message-Id: <9311171754.AA15282@xenon.chem.ucla.edu> To: chemistry@ccl.net Subject: molecular mechanics and Z-matrices Does anyone know of a standard molecular mechanics program/platform that will accept Z-matrices at inputs ???? From my experience all MM programs want you to create the molecule within the application (ie draw it manually or call it up from a previously created MM file) however we have hundreds of Z-matrices lying around which we would like to run mechanics on, but don't particularly wish to recreate their geomtries by drawing them! So, are there any MM programs out there that will read a standard GAUSSIAN or MOPAC type Z-matrix??? Thanks in advance, Mike McAllister You can reply directly to me or to the net, whichever you prefer. 'mam@xenon.chem.ucla.edu' From jle@world.std.com Wed Nov 17 22:27:33 1993 Received: from world.std.com for jle@world.std.com by www.ccl.net (8.6.1/930601.1506) id VAA23058; Wed, 17 Nov 1993 21:35:00 -0500 Received: by world.std.com (5.65c/Spike-2.0) id AA04796; Wed, 17 Nov 1993 21:34:47 -0500 Date: Wed, 17 Nov 1993 21:34:47 -0500 From: jle@world.std.com (Joe M Leonard) Message-Id: <199311180234.AA04796@world.std.com> To: chemistry@ccl.net Subject: DGEOM questions for conf anal... Folks, I'm trying to use DGEOM ('89-'90 vintage) for conformational analysis, but am interested in having phenyl/aromatic groups remain unaltered during the calculations. I've tried making them their own residues (while the rest of the molecule's the "other" residue") and using the RIGID global keyword for the aromatic residues, but the various rings distort during the calculation. Am I missing something here? Should I also insert PLANE local constraints for things to work (I'm uniquely naming atoms in each aromatic residue, but the names are shared between residues). I realize that the rings will flatten out when some form of energy function's applied to the resulting structures, but I'm interested in trying to keep the number of opt cycles to a minimum (and since the initial phenyl group geoms are ok...). Have there been changes to newer versions that make this an easier process (or have changes been made that I should be aware of)? I'd appreciate learning from others who have solved this problem... If any of the authors have comments, I'd REALLY appreciate hearing from them. Joe Leonard jle@world.std.com