Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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C"N s *" Gl(g@L.88.L.  .  .xLx.HH..L.WW8Num1@FFPGTimes New Roman5Symbol3&ArialmNimbus Roman No9 LTimes New RomanKTahomaLucidasansBhiEiE'0DyK yK lhttp://kinemage.biochem.duke.edu/databases/top500.phpDyK yK nhttp://kinemage.biochem.duke.edu/databases/rotamer.phpDyK yK @http://dunbrack.fccc.edu/bbdep/DyK yK |http://kinemage.biochem.duke.edu/suppinfo/StructureDavis2006/=DyK yK http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16472746&dopt=AbstractDyK yK dhttp://kinemage.biochem.duke.edu/research/aac.phpDyK yK rhttp://kinemage.biochem.duke.edu/research/rnarotamer.phpDyK yK Hhttp://www.cs.unc.edu/~xwang/RNABC/DyK yK http://graphics.stanford.edu/courses/cs468-01-winter/papers/wr-ghao-97.pdfOh+'0( p x  4@V@0:@x'@ΰ Snoeyink Normal.dotProblems refined:M 08Caolan70EJFl&4Zn$4 p   "83:, Problems refined: Here are some suggestions to make more specific problems from the general problem areas (in roman numerals) that we listed on the board last week, along with places to begin to look for directions or resources. These are just suggestions; there can certainly be others. Each of the lettered subproblems would be enough for a project, although sometimes you want solutions to two or more subproblems to demonstrate your results  for some, Yves and I can cobble together solutions that will enable fou to extend the application of your specific part. If two people want to work together, consider working on different subproblems to complement each other. Idealizing protein structure Replace the lengths/bond angles of a pdb structure with standard parameters and adjust phi/psi to reduce RMSD to original Engh R A & Huber R (1991). Accurate bond and angle parameters for X-ray protein structure refinement. Acta Cryst., A47, 392-400. Clustering fragments of pdb structures: Mine the pdb (or an subset of accurate structures, such as HYPERLINK "http://kinemage.biochem.duke.edu/databases/top500.php"http://kinemage.biochem.duke.edu/databases/top500.php) for backbones of, say, 3 to 5 amino acids and find representative structures and their probability of occurrence. From a set of fragments, construct the closest structure to a native PDB structure. Replace side chains with rotamers from a rotamer library  how fine do the angles need to be sampled to avoid introducing collisions? (Rotamer libraries: HYPERLINK "http://kinemage.biochem.duke.edu/databases/rotamer.php"http://kinemage.biochem.duke.edu/databases/rotamer.php HYPERLINK "http://dunbrack.fccc.edu/bbdep/"http://dunbrack.fccc.edu/bbdep/ ) Improving Rosetta hydrogen bonds: we can dump out all the hydrogen bonds recognized by Rosetta Evaluate statistics of distances and angles for hydrogen bonds in the PDB. The hard part is deciding what is a hydrogen bond. Recognize beta sheets and alpha helixes from hydrogen bonding patterns. See whether the geometry of energy of these hydrogen bonds have different statistics than other hydrogen bonds. Hydrogen bonds for charged amino acids are too long in Rosetta; adjust the polynomial that assigns energy as a function of distance to improve statistics of structures generated by Rosetta. Energy for hydrogen bonds in Rosetta is computed by summing three univariate polynomials for distance and two angles q, and y. This means that a bond with bad distances but good angles can still get a large fraction of the available energy. Should there be a function of all three that couples the variables more? The torsion angle c is not used because no-one has worked out the derivatives for the change between two coordinate frames when c is rotated. Energy for hydrogen bonds depend on distance Right now, hydrogen bond energy is computed by summing three univariate polynomials. Protein backbone adjustment Using a database of alternate conformations seen in high resolution X-ray structures HYPERLINK "http://kinemage.biochem.duke.edu/suppinfo/StructureDavis2006/"http://kinemage.biochem.duke.edu/suppinfo/StructureDavis2006/ (where the side chain can have two positions) determine how much the backbone moves. I m particularly interested in cases where two adjacent residues have alternate conformations, which are not covered in this paper: HYPERLINK "http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16472746&dopt=Abstract"http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16472746&dopt=Abstract For places where dots scores like in Molprobity show clashes with a side chain, see if a small backbone tweak will allow a better fitting sidechain. Loop motion Extend your CCD implementation to avoid collisions and match the target coordinate frame, instead of just the atom position. Dot scores are the easiest way to test collisions. HYPERLINK "http://kinemage.biochem.duke.edu/research/aac.php"http://kinemage.biochem.duke.edu/research/aac.php Incorporate electron density into the evaluation of fitting. Ramachandran plots for RNA backbone: RNA has six or seven degrees of freedom along its backbone. From RNA structures in the PDB, how do we derive something like the Ramachandran plots for protein to help specify The Richardson and Berman labs have been classifying RNA backbone angles: HYPERLINK "http://kinemage.biochem.duke.edu/research/rnarotamer.php"http://kinemage.biochem.duke.edu/research/rnarotamer.php Given a fragment of RNA, determine which class it falls into. Adjust RNA backbones to improve their MolProbity scores? One of my students has code that samples angles and evaluates collisions for pairs of nucleotides; are there examples where applying it to overlapping pairs gives improvement? HYPERLINK "http://www.cs.unc.edu/~xwang/RNABC/"http://www.cs.unc.edu/~xwang/RNABC/ Pebble game to analyze rigidity of graphs from molecules: see class notes & paper on webpages. Implementing the pebble game to count degrees of freedom in a graph, and to determine rigid components Obtaining graphs from molecular structures: for scoring hydrogen bonds, see II.a or use dot scores from probe (from molprobity). Looking for proteins with allosteric behavior explained by degree of freedom counting: where binding at one position changes the rigid structure to remove degrees of freedom at another position in the protein. Docking is like solving a 3d jigsaw puzzle: I can get conformations of docked proteins that can be separated and rigidly re-docked. (The real problem is flexibility and  induced fit but that is larger than a course project. Geometric hashing (survey here: HYPERLINK "http://graphics.stanford.edu/courses/cs468-01-winter/papers/wr-ghao-97.pdf"http://graphics.stanford.edu/courses/cs468-01-winter/papers/wr-ghao-97.pdf) tries to match triples of atoms on the surface of a protein and can be the basis of an algorithm for docking. Algorithmic and data resources: Given two structures, find the translation and rotation that minimizes RMSD. Apply cyclic coordinate descent to establish loop closure. PDB structures: protein and a few RNA Rotamer libraries: list of allowed chi angles for side chains Given a pdb file, find all hydrogen bonds and their strengths -using rosetta -using probe (kinemage dot scores) Given a backbone loop with six chosen torsional degrees of freedom (usually phi/psi angles), find all angles that satisfy loop closure constraints (matching coordinate frames at the start and end). 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