How computation has changed research in chemistry and biology Peter - PowerPoint PPT Presentation

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, 21. – 22.02.2013

Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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.

Gordon E. Moore, 1929 - Exponential increase in hardware power Electronics 38 (8), 4-7,1965

 . 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 43000 was Martin Grötschel, 1948 - due to improvements in algortihms ! Grötschel also cites an algorithmic improvement of roughly 30000 for mixed integer programming between 1991 and 2008 . PCIT Report to the President, 2010. 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

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

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

L. Michaelis, M. Menten. Die Kinetik der ⋅ [ P ] [ S ] d v Invertin-Wirkung. Biochemische Zeitschrift 49 , = = ([ S ]) max v + 333-369,1913 [ S ] dt K M + k k = , r d K M k basic assumptions: k r  k d f = ⋅ = ⋅ ([ S ]) [ ES ] and [ E ] v k v k [E] 0 << [S] 0 max 0 r r vv v Michaelis-Menten mechanism of enzyme reactions

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

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

Validity of the Michaelis-Menten approximation

The forward problem of chemical reaction kinetics

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

    δ δ = ( ) , parameter vector , (noisy) data ;   F q y q y   ∈ ∈ and q Q y Y   2 δ − → ( ) min ill-conditioned problem y F q  ∈ Y q Q         2 2 δ R R − + α → = − ( ) ( , ) min with ( , ) y F q q q q q q q 0  0 0 ∈ Q Y q Q 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

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

5' - end N 1 O CH 2 O GCGGAU UUA GCUC AGUUGGGA GAGC CCAGA G CUGAAGA UCUGG AGGUC CUGUG UUCGAUC CACAG A AUUCGC ACCA 5'-end 3’-end N A U G C k = , , , OH O N 2 O P O CH 2 O Na  O O OH N 3 O P O CH 2 O Na  O O OH RNA structure N 4 O P O CH 2 O The molecular phenotype Na  O O OH 3' - end O P O Na  O

The notion of structure

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

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

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

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 :167-188, 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

I Space of genotypes: = { , , , , ... , } ; Hamming metric I I I I I 1 2 3 4 N S Space of phenotypes: = { , , , , ... , } ; metric (not required) S S S S S 1 2 3 4 M  N M  ( ) = I S j k U   -1   G k = ( ) | ( ) = I S I S ≡ k j j k  A mapping and its inversion

many genotypes  one phenotype

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

Extension of the notion of structure

0 G  y T g { k r 0 e Free energy G n e  e e r F S { S { Saddle point T { k S k S k "Barrier tree" "Reaction coordinate" Definition of a ‚barrier tree‘

Interconversion of suboptimal structures

Computation of kinetic folding

R 1D 2D GGGUGGAAC CACGAG GUUC CACGAG GAAC CACGAG GUUCCUCCC G 3 13 23 33 44 R 1D 2D 23 13 33 C G C G C G A A A A G/ A A C G C C G G G C G C G C A U U A A U U A A U A U G C G C G C G C G C G C A A U A /G A U G C 13 3 G C G CCC 44 1D 2D C G 33 GG 23 R 5' 3’ A A C G C G -1 -28.6 kcal·mol A U A U -1 -28.2 kcal·mol G C G C U U G C 3 An experimental G C G C 44 RNA switch 5' 3’ JN1LH -1 -28.6 kcal·mol J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, -1 -31.8 kcal·mol M.H. de Smit, P. Schuster, and C.W.A. Pleij. Structural parameters affecting the kinetic competition of RNA hairpin formation . Nucleic Acids Res . 34 :3568-3576 (2006)

-26.0 2.89 -28.0 4.88 -30.0 6.8 6.13 3.04 3.04 2.97 -32.0 ] 1.47 1.49 e 2.14 4 4 1 1 1 l 5 . 1 5 2 o . . 50 . 2 2 2 9 47 46 m 48 -34.0 4 45 44 43 1.9 41 40 42 38 39 36 37 35 / 33 34 32 1 0 8 9 l 3 3 6 27 2 a 24 2 25 3 2 1 -36.0 22 2 20 19 2 c 8 1.66 1 k 7 6 1 1 [ 5 1 4 3 2 1.44 -38.0 1.46 1 1 1 y 11 g 2.44 r 10 2.09 e 2.36 -40.0 n 3.4 e 9 8 e 7 -42.0 e 2.44 r 5 6 F 2.44 4 -44.0 5.32 3 -46.0 -48.0 2 2.77 J1LH barrier tree -50.0 1

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

Sewall Wright. 1932. 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, 356-366. Ithaca, NY. Sewall Wrights fitness landscape as metaphor for Darwinian evolution

Sewall Wright, 1889 - 1988 + …….. 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. 1988. Surfaces of selective value revisited. American Naturalist 131:115-123

Evolution is hill climbing of populations or subpopulations Sewall Wright. 1988. Surfaces of selective value revisited. American Naturalist 131:115-123

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

Sol Spiegelman, 1914 - 1983 Evolution in the test tube: G.F. Joyce, Angew.Chem.Int.Ed. 46 (2007), 6420-6436

Christof K. Biebricher, 1941-2009 Kinetics of RNA replication C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22 :2544-2559, 1983