How computation has changed research in chemistry and biology

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2 How computation has changed research in chemistry and biology Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA IWR - 25 Jahre-Jubiläum Heidelberg,

3 Web-Page for further information:

4 Some technological revolutions in 20 th century science: 1. molecular spectroscopy, 2. micro-technology, 3. electronic computation, 4. molecular revolution in biology, 5. computational quantum chemistry, and 6. holistic chemistry of biological entities.

5 Gordon E. Moore, Exponential increase in hardware power Electronics 38 (8), 4-7,1965

6 . Grötschel, an expert in optimization, observes that a benchmark production planning model solved using linear programming would have taken 82 years to solve in 1988, using the computers and the linear programming algorithms of the day. Fifteen years later in 2003 the same model could be solved in roughly 1 minute, an improvement by a factor of roughly 43 million. Of this, a factor of roughly 1000 was due to increased processor speed, whereas a factor of roughly was due to improvements in algortihms! Martin Grötschel, Grötschel also cites an algorithmic improvement of roughly for mixed integer programming between 1991 and PCIT Report to the President, Progress in Algorithms Beats Moore s Law. J.P. Holdren, E. Lander, H. Varmus. Designing a digital future: Federally funded research and development in networking and information technology. President s council on science and technology, Washington, DC, p.71, 2010

7 Four selected examples 1. Parameter determination in chemical kinetics 2. Design of ribonucleic acid (RNA) structures 3. Kinetic folding of RNA molecules 4. Modeling evolution

8 Four selected examples 1. Parameter determination in chemical kinetics 2. Design of ribonucleic acid (RNA) structures 3. Kinetic folding of RNA molecules 4. Modeling evolution

9 L. Michaelis, M. Menten. Die Kinetik der Invertin-Wirkung. Biochemische Zeitschrift 49, ,1913 d[p] dt = v([s]) = v K max M [S] + [S] basic assumptions: k r k d [E] 0 << [S] 0 v([s]) = k vv v r K M = [ES] k r + k k f and d, v max = k r [E] 0 Michaelis-Menten mechanism of enzyme reactions

10 Linearization of a hyperbola: v([s]) = K v max M [S] + [S] Lineweaver-Burk: Eadie-Hofstee: Scatchard: 1/v = f (1/[S]) v = f (1/[S]) 1/[S] = f (v) Hanes: [S] / v = f ([S]) Hill: log (v/(v max v)) = f (log [S])

11 The Lineweaver-Burke plot of Michaelis-Menten kinetics Source: Wikipedia, Enzymkinetik

12 Validity of the Michaelis-Menten approximation

13 The forward problem of chemical reaction kinetics

14 Parameter identification and determination is an ill-posed problem Inverse problem solution techniques The inverse problem of chemical reaction kinetics

15 Y y Q q y q y q F = and (noisy) data; parameter vector,, ) ( δ δ Q q Y q F y min ) ( 2 δ ill-conditioned problem ), ( with min ), ( ) ( Q Q q Y q q q q q q q F y = + R α R δ regularization term R - here Tikhonov regularization - with q 0 being an initial parameter guess and the regularization parameter Parameter identification and determination as an inverse problem

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17 Four selected examples 1. Parameter determination in chemical kinetics 2. Design of ribonucleic acid (RNA) structures 3. Kinetic folding of RNA molecules 4. Modeling evolution

18 O 5' - end CH 2 O N 1 5'-end GCGGAUUUAGCUCAGUUGGGAGAGCGCCAGACUGAAGAUCUGGAGGUCCUGUGUUCGAUCCACAGAAUUCGCACCA 3 -end O OH N k = A, U, G, C O P O CH 2 O N 2 Na O O OH O P O CH 2 O N 3 Na O RNA structure The molecular phenotype O Na O P O OH O CH 2 O N 4 O OH O P O 3' - end Na O

19 The notion of structure

20 S 5 (h) S 4 (h) S 3 (h) Free energy G 0 S 6 (h) S 7 (h) S 8 (h) (h) S (h) 1 S 2 (h) S 9 Suboptimal conformations S 0 (h) Minimum of free energy The minimum free energy structures on a discrete space of conformations

21 RNA sequence linear programming RNA folding: structural biology, spectroscopy of biomolecules, understanding molecular function biophysical chemistry: thermodynamics and kinetics empirical parameters RNA structure of minimal free energy From RNA sequence to structure

22 RNA sequence Linear programming RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function iterative determination of a sequence for the given secondary structure inverse Folding Algorithm inverse folding of RNA: biotechnology, design of biomolecules with predefined structures and functions RNA structure of minimal free energy From RNA structure to sequence

23 ViennaRNA Package: Ivo L. Hofacker, Walter Fontana, Peter F. Stadler, Sebastian Bonhoeffer, Manfred Tacker, and Peter Schuster. Fast folding and comparison of RNA secondary structures. Mh.Chem. 125: , 1994 Ronny Lorenz, Stephan H. Bernhart, Christian Höner zu Siederissen, Hakim Tafer, Christioh Flamm, Peter F. Stadler, and Ivo L. Hofacker. ViennaRNA Package 2.0. Algorithms Mol. Biol. 6:26, 2011

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25 Space of genotypes: I = { I, I, I, I,..., I } ; Hamming metric N Space of phenotypes: S = { S, S, S, S,..., S } ; metric (not required) M N M ( I) = j S k -1 G k = ( S ) U I ( I) = S k j j k A mapping and its inversion

26 many genotypes one phenotype

27 Four selected examples 1. Parameter determination in chemical kinetics 2. Design of ribonucleic acid (RNA) structures 3. Kinetic folding of RNA molecules 4. Modeling evolution

28 Extension of the notion of structure

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30 Free energy G 0 Saddle point T { k S { Free energy G 0 T { k S { S k S k "Reaction coordinate" "Barrier tree" Definition of a barrier tree

31 Interconversion of suboptimal structures

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33 Computation of kinetic folding

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35 1D R 2D GGGUGGAACCACGAGGUUCCACGAGGAACCACGAGGUUCCUCCC 3 13 G An experimental RNA switch J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and C.W.A. Pleij. 1D 2D CG CG A A A A C G C G C G C G A U A U A U A U G C G C G C G C U A/G A U 3 G C G C 44 GG R 23 CC 5' kcal mol kcal mol -1 JN1LH R 23 CG G/ A A C G C G U A U A G C G C A A 13 1D G C 2D C G 33 A A C G C G A U A U G G C C U U 3G C G C G C 44 5' kcal mol kcal mol -1 Structural parameters affecting the kinetic competition of RNA hairpin formation. Nucleic Acids Res. 34: (2006)

36 Free energy [kcal / mole] J1LH barrier tree

37 Four selected examples 1. Parameter determination in chemical kinetics 2. Design of ribonucleic acid (RNA) structures 3. Kinetic folding of RNA molecules 4. Modeling evolution

38 Sewall Wright The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: D.F.Jones, ed. Int. Proceedings of the Sixth International Congress on Genetics. Vol.1, Ithaca, NY. Sewall Wrights fitness landscape as metaphor for Darwinian evolution

39 Sewall Wright, wild type a... alternative allele on locus A : : : abcde alternative alleles on all five loci The multiplicity of gene replacements with two alleles on each locus Sewall Wright Surfaces of selective value revisited. American Naturalist 131:

40 Evolution is hill climbing of populations or subpopulations Sewall Wright Surfaces of selective value revisited. American Naturalist 131:

41 Accuracy of replication: Q = q 1 q 2 q 3 q 4 The logics of DNA (or RNA) replication

42 Sol Spiegelman, Evolution in the test tube: G.F. Joyce, Angew.Chem.Int.Ed. 46 (2007),

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45 Christof K. Biebricher, Kinetics of RNA replication C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22: , 1983

46 Manfred Eigen = = = = = = = n i i n i i i i ji ji j i n i ji j x x f Φ f Q W n j Φ x x W x 1 1 1,, 1,2, ; dt d Mutation and (correct) replication as parallel chemical reactions M. Eigen Naturwissenschaften 58:465, M. Eigen & P. Schuster Naturwissenschaften 64:541, 65:7 und 65:341

47 quasispecies The error threshold in replication and mutation

48 The paradigm of structural biology

49 The simplified model

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51 single peak landscape step linear landscape Model fitness landscapes I

52 Quasispecies Uniform distribution Stationary population or quasispecies as a function of the mutation or error rate p Error rate p = 1-q

53 Error threshold on the single peak landscape

54 Error threshold on the step linear landscape

55 single peak landscape realistic landscape Rugged fitness landscapes over individual binary sequences with n = 10

56 Random distribution of fitness values: d = 1.0 and s = 637

57 s = 541 s = 637 s = 919 Error threshold on realistic landscapes n = 10, f 0 = 1.1, f n = 1.0, d = 0.5

58 s = 541 s = 637 s = 919 Error threshold on realistic landscapes n = 10, f 0 = 1.1, f n = 1.0, d = 0.995

59 s = 541 s = 637 s = 919 Error threshold on realistic landscapes n = 10, f 0 = 1.1, f n = 1.0, d = 1.0

60 0, 0 largest eigenvalue and eigenvector diagonalization of matrix W complicated but not complex W = G F mutation matrix fitness landscape ( complex ) complex sequence structure complex mutation selection Complexity in molecular evolution

61 The new biology provides a hitherto unknown challenge for mathematicians, computer scientists, and theorical biologists for mainly two reasons enormous amount of data and complexity of structure and dynamics:

62 . I was taught in the pregenomic era to be a hunter. I learnt how to identify the wild beasts and how to go out, hunt them down and kill them. We are now urged to be gatherers, to collect everything lying around and put it into storehouses. Someday, it is assumed, someone will come and sort through the storehouses, discard all the junk, and keep the rare finds. The only difficulty is how to recognize them. Sydney Brenner, Sydney Brenner. Hunters and gatherers. The Scientist 16(4): 14, 2002 The big data problem in bioinformatics

63 Theory mathematics and computation cannot remove complexity, but it shows what kind of regular behavior can be expected and what experiments have to be done to get a grasp on the irregularities. Manfred Eigen, Preface to E. Domingo, C.R. Parrish, J.J.Holland, eds. Origin and Evolution of Viruses. Academic Press 2008 Theory, mathematics and complexity

64 Coworkers Peter Stadler, Bärbel M. Stadler, Universität Leipzig, GE Paul E. Phillipson, University of Colorado at Boulder, CO Heinz Engl, Philipp Kügler, James Lu, Stefan Müller, RICAM Linz, AT Universität Wien Jord Nagel, Kees Pleij, Universiteit Leiden, NL Walter Fontana, Harvard Medical School, MA Martin Nowak, Harvard University, MA Christian Reidys, University of Southern Denmark, Odense, DK Christian Forst, University of Texas, Southwestern Medical Center, TX Thomas Wiehe, Ulrike Göbel, Walter Grüner, Stefan Kopp, Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE Ivo L.Hofacker, Christoph Flamm, Andreas Svrček-Seiler, Universität Wien, AT Kurt Grünberger, Michael Kospach, Andreas Wernitznig, Stefanie Widder, Stefan Wuchty, Jan Cupal, Stefan Bernhart, Lukas Endler, Ulrike Langhammer, Rainer Machne, Ulrike Mückstein, Erich Bornberg-Bauer, Universität Wien, AT

65 Acknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No , 10578, 11065, , and Universität Wien Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No , (NEST) Austrian Genome Research Program GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute

66 Happy 25th birthday IWR and ad multos annos. Thank you for your attention!

67 Web-Page for further information:

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