Complex behavior from simple molecular systems Peter Schuster - - PowerPoint PPT Presentation

Complex behavior from simple molecular systems

Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Franqui Symposium 2008 in honor of Pierre Gaspard Complex Systems: A fundamental Science Perspective Brussels, 03.– 06.09.2008

Web-Page for further information: http://www.tbi.univie.ac.at/~pks Review article: Peter Schuster. Prediction of RNA molecules: From theory to models and real molecules. Rep.Prog.Phys. 69:1419-1477, 2006.

RNA

RNA as scaffold for supramolecular complexes

ribosome ? ? ? ? ?

RNA – The magic molecule

The world as a precursor of the current + biology RNA DNA protein

RNA as catalyst Ribozyme

RNA as carrier of genetic information

RNA viruses and retroviruses RNA evolution in vitro

ENCODE Project Consortium. Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project. Nature 447:799-816, 2007

ENCODE stands for ENCyclopedia Of DNA Elements.

411 Autoren aus 80 Institutionen

1. Minimum free energy structures of RNA 2. Suboptimal structures of RNA 3. Kinetic folding and RNA switches 4. Chemistry of Darwinian evolution 5. Consequences of neutrality 6. Evolutionary optimization of RNA structure

• 1. Minimum free energy structures of RNA

2. Suboptimal structures of RNA 3. Kinetic folding and RNA switches 4. Chemistry of Darwinian evolution 5. Consequences of neutrality 6. Evolutionary optimization of RNA structure

O CH2 OH O O P O O O

N1

O CH2 OH O P O O O

N2

O CH2 OH O P O O O

N3

O CH2 OH O P O O O

N4

N A U G C

k =

, , ,

3' - end 5' - end Na Na Na Na

5'-end 3’-end

GCGGAU AUUCGC UUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCA GCUC GAGC CCAGA UCUGG CUGUG CACAG

Definition of RNA structure

N = 4n NS < 3n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ {AU,CG,GC,GU,UA,UG} A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

The paradigm of structural biology

What is neutrality ?

Selective neutrality = = several genotypes having the same fitness. Structural neutrality = = several sequences forming molecules with the same structure.

RNA sequence RNA structure

• f minimal free

energy

RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Empirical parameters Biophysical chemistry: thermodynamics and kinetics

Sequence, structure, and design

G G G G G G G G G G G G G G G G U U U U U U U U U U U A A A A A A A A A A A A U C C C C C C C C C C C C 5’-end 3’-end

S1

(h)

S9

(h)

F r e e e n e r g y G

• Minimum of free energy

Suboptimal conformations

S0

(h) S2

(h)

S3

(h)

S4

(h)

S7

(h)

S6

(h)

S5

(h)

S8

(h)

The minimum free energy structures on a discrete space of conformations

Extension of the notion of structure

RNA sequence RNA structure

• f minimal free

energy

RNA folding: Structural biology, spectroscopy of biomolecules, understanding molecular function Inverse Folding Algorithm Iterative determination

• f a sequence for the

given secondary structure

Sequence, structure, and design

Inverse folding of RNA: Biotechnology, design of biomolecules with predefined structures and functions

many sequences

• ne structure

Degree of neutrality of neutral networks and the connectivity threshold

A multi-component neutral network formed by a rare structure: < cr

A connected neutral network formed by a common structure: > cr

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

GGCUAUCGUAUGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUAGACG GGCUAUCGUACGUUUACUCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGCUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCCAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUGUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAACGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCUGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCACUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGUCCCAGGCAUUGGACG GGCUAGCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCGAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGCCUACGUUGGACCCAGGCAUUGGACG

G G C U A U C G U A C G U U U A C C C AA AAG UC UACG U UGGA CC C A GG C A U U G G A C G

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

Number Mean Value Variance Std.Dev. Total Hamming Distance: 150000 11.647973 23.140715 4.810480 Nonzero Hamming Distance: 99875 16.949991 30.757651 5.545958 Degree of Neutrality: 50125 0.334167 0.006961 0.083434 Number of Structures: 1000 52.31 85.30 9.24 1 (((((.((((..(((......)))..)))).))).))............. 50125 0.334167 2 ..(((.((((..(((......)))..)))).)))................ 2856 0.019040 3 ((((((((((..(((......)))..)))))))).))............. 2799 0.018660 4 (((((.((((..((((....))))..)))).))).))............. 2417 0.016113 5 (((((.((((.((((......)))).)))).))).))............. 2265 0.015100 6 (((((.(((((.(((......))).))))).))).))............. 2233 0.014887 7 (((((..(((..(((......)))..)))..))).))............. 1442 0.009613 8 (((((.((((..((........))..)))).))).))............. 1081 0.007207 9 ((((..((((..(((......)))..))))..)).))............. 1025 0.006833 10 (((((.((((..(((......)))..)))).))))).............. 1003 0.006687 11 .((((.((((..(((......)))..)))).))))............... 963 0.006420 12 (((((.(((...(((......)))...))).))).))............. 860 0.005733 13 (((((.((((..(((......)))..)))).)).)))............. 800 0.005333 14 (((((.((((...((......))...)))).))).))............. 548 0.003653 15 (((((.((((................)))).))).))............. 362 0.002413 16 ((.((.((((..(((......)))..)))).))..))............. 337 0.002247 17 (.(((.((((..(((......)))..)))).))).).............. 241 0.001607 18 (((((.(((((((((......))))))))).))).))............. 231 0.001540 19 ((((..((((..(((......)))..))))...))))............. 225 0.001500 20 ((....((((..(((......)))..)))).....))............. 202 0.001347 G G C U A U C G U A C G U U U A C C C AA AAG UC UACG U UGGA CC C A GG C A U U G G A C G

Shadow – Surrounding of an RNA structure in shape space: AUGC alphabet, chain length n=50

Results from RNA minimun free energy structures:

• RNA minimum free energy structures show neutrality: Many

sequences fold into the same (secondary) structure.

• The single base mutation neighborhood contains structures

from neutral sequences and a great variety of other structures: Biopolymer landscapes are rugged.

1. Minimum free energy structures of RNA

• 2. Suboptimal structures of RNA

3. Kinetic folding and RNA switches 4. Chemistry of Darwinian evolution 5. Consequences of neutrality 6. Evolutionary optimization of RNA structure

Extension of the notion of structure

Extension of the notion of structure

GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 ..........((((((.((....((((.....))))...))...)))))) -6.70 ..........((((((.((....(((((...)))))...))...)))))) -6.60 ..(((.((((..(((......)))..)))).)))..((((...))))... -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((.((..((((..((......))..))))..))....)))........ -6.00 GGCUAUCGUACGUUUACACAAAAGUCUACGUUGGACCCAGGCAUUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 .(((.((..((((..((......))..))))..))....)))........ -6.50 .(((.....((((..((......))..))))((....)))))........ -6.30 ..(((.((((..(((......)))..)))).)))..((((...))))... -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((...((((((..((......))..))))...))...)))........ -6.00 GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAAUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 ..(((.((((..(((......)))..)))).)))..(((.....)))... -7.20 ..........((((((.((....((((.....))))...))...)))))) -6.70 ..........((((((.((....(((((...)))))...))...)))))) -6.60 (((((.((((..(((......)))..)))).))).))((.....)).... -6.50 (.(((.((((..(((......)))..)))).))).)(((.....)))... -6.30 .((((.((((..(((......)))..)))).))).)(((.....)))... -6.30 .....(((.((((..((......))..)))))))..(((.....)))... -6.30 (.(((.((((..(((......)))..)))).)))..(((.....))).). -6.10 .....((..((((..((......))..))))..)).(((.....)))... -6.10 ......(((.((((...((....((((.....))))...)).)))).))) -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((.((..((((..((......))..))))..))....)))........ -6.00 ......(((.((((...((....(((((...)))))...)).)))).))) -6.00

sequence y probabilit pairing base ) , ( structure

• f

matrix adjacency ) ( K K K X T X p S S A

ij k k

Usage of the partition function to anayze the spectrum of suboptimal states

mfe-weight: 0.46336

CGUCCCGUCUCUUCCGAGCGCCAGGA ..(((((.(((....)))))...))) -4.50 ..(((.(((((....))).))..))) -3.70 ...((((.(((....)))))...)). -3.60 .....((.(((....)))))...... -3.00 ...((.(((((....))).))..)). -2.80 ..(((.(.(((....)))...).))) -2.60 (.(..((.(((....)))))..).). -2.50

Suboptimal structures and partition function

• f a small RNA molecule: n = 26

mfe-weight: 0.13642

CGGCCGGAGCGGAUAUGCCUAAAGGU ..(((((.(((....)))))...))) -3.70 ..(((...(((....))).....))) -3.60 ..(((.(.(((....))).)...))) -3.50 ..(((..((((....))).)...))) -3.30 ..(((..((((....)).))...))) -3.30 ..(((.(.(((....))))....))) -3.10 (.((....)).)....(((....))) -2.90 ..(((.....((.....))....))) -2.90 ...(((...)))....(((....))) -2.90 ..(((((.((......))))...))) -2.70 ..(((...((......)).....))) -2.60 ...((.....))....(((....))) -2.60 ..(((.(.((......)).)...))) -2.50 ..(((..((.(......)))...))) -2.50 .(((............)))....... -2.30 ..(((..(((......)).)...))) -2.30 ..(((..(((......).))...))) -2.30 .....((.(((....)))))...... -2.20

Suboptimal structures and partition function

• f a small RNA molecule: n = 26

mfe-weight: 0.09514

UUUGGUGCUCAUAUCUGACAGAUCCA ..(((((.(((....)))))...))) -1.10 ..(((...(((....))).....))) -1.00 ...((((.(((....)))))...)). -1.00 ...((...(((....))).....)). -0.90 ..(((((.((......))))...))) -0.70 ..(((...((......)).....))) -0.60 ...((((.((......))))...)). -0.60 ...((...((......)).....)). -0.50 .....((.(((....)))))...... -0.20 ..(((.(.(((....))))....))) -0.10 ..(((..((((....)))..)..))) -0.10 ((((...(........).)))).... 0.00 ...((.(.(((....))))....)). 0.00 ...((..((((....)))..)..)). 0.00 .......................... 0.00

Suboptimal structures and partition function

• f a small RNA molecule: n = 26

Structure S Structure S

1

The intersection of two compatible sets is always non empty: C0 C1

Reference for the definition of the intersection and the proof of the intersection theorem

Results from RNA suboptimal structures:

• Neutral RNA sequences differ with respect to their spectra of

suboptimal structures.

• Suboptimal RNA structures with low free energies contribute

substantially to the partition function.

• Nature selects for stable structures in the sense that the

contribution of the mfe structure to the partition function is large.

• For every pair of structures it is possible to find a sequence that

can form both. This is not (always) true for three structures.

1. Minimum free energy structures of RNA 2. Suboptimal structures of RNA

• 3. Kinetic folding and RNA switches

4. Chemistry of Darwinian evolution 5. Consequences of neutrality 6. Evolutionary optimization of RNA structure

Extension of the notion of structure

Extension of the notion of structure

The Folding Algorithm

A sequence I specifies an energy ordered set of compatible structures S(I):

S(I) = {S0 , S1 , … , Sm , O}

A trajectory Tk(I) is a time ordered series of structures in S(I). A folding trajectory is defined by starting with the open chain O and ending with the global minimum free energy structure S0 or a metastable structure Sk which represents a local energy minimum:

T0(I) = {O , S (1) , … , S (t-1) , S (t) , S (t+1) , … , S0} Tk(I) = {O , S (1) , … , S (t-1) , S (t) , S (t+1) , … , Sk}

Master equation

( )

1 , , 1 , ) ( ) (

1 1 1

+ = − = − =

∑ ∑ ∑

+ = + = + =

m k k P P k t P t P dt dP

m i ki k i m i ik m i ki ik k

K

Transition probabilities Pij(t) = Prob{Si→Sj} are defined by

Pij(t) = Pi(t) kij = Pi(t) exp(-∆Gij/2RT) / Σi Pji(t) = Pj(t) kji = Pj(t) exp(-∆Gji/2RT) / Σj exp(-∆Gki/2RT)

The symmetric rule for transition rate parameters is due to Kawasaki (K. Kawasaki, Diffusion constants near the critical point for time dependent Ising models. Phys.Rev. 145:224-230, 1966).

∑

+ ≠ =

= Σ

2 , 1 m i k k k

Formulation of kinetic RNA folding as a stochastic process

F r e e e n e r g y G

• "Reaction coordinate"

Sk S{ Saddle point T

{ k

F r e e e n e r g y G

• Sk

S{ T

{ k

"Barrier tree"

Definition of a ‚barrier tree‘

JN1LH

1D 1D 1D 2D 2D 2D R R R

G GGGUGGAAC GUUC GAAC GUUCCUCCC CACGAG CACGAG CACGAG

• 28.6 kcal·mol
• 1

G/

• 31.8 kcal·mol
• 1

G G G G G G C C C C C C A A U U U U G G C C U U A A G G G C C C A A A A G C G C A A G C /G

• 28.2 kcal·mol
• 1

G G G G G G GG CCC C C C C C U G G G G C C C C A A A A A A A A U U U U U G G C C A A

• 28.6 kcal·mol
• 1

3 3 3 13 13 13 23 23 23 33 33 33 44 44 44

5' 5' 3’ 3’

J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, 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)

An experimental RNA switch

4 5 8 9 11

1 9 2 2 4 2 5 2 7 3 3 3 4

36

38 39 41 46 47

3

49

1

2 6 7 10

1 2 1 3 1 4 1 5 1 6 1 7 1 8 2 1 22 2 3 2 6 2 8 2 9 3 3 1 32 3 5 3 7

40

4 2 4 3 44 45 48 50

• 26.0
• 28.0
• 30.0
• 32.0
• 34.0
• 36.0
• 38.0
• 40.0
• 42.0
• 44.0
• 46.0
• 48.0
• 50.0

2.77 5.32 2 . 9 3.4 2.36 2 . 4 4 2.44 2.44 1.46 1.44 1.66

1.9

2.14

2.51 2.14 2.51

2 . 1 4 1 . 4 7

1.49

3.04 2.97 3.04 4.88 6.13 6 . 8 2.89

Free energy [kcal / mole]

J1LH barrier tree

A ribozyme switch

E.A.Schultes, D.B.Bartel, Science 289 (2000), 448-452

Two ribozymes of chain lengths n = 88 nucleotides: An artificial ligase (A) and a natural cleavage ribozyme of hepatitis--virus (B)

The sequence at the intersection: An RNA molecules which is 88 nucleotides long and can form both structures

Two neutral walks through sequence space with conservation of structure and catalytic activity

The purine riboswitch

A natural metabolic riboswitch

• M. Mandal, B. Boese, J.E. Barrick, W.C. Winkler, and R.R. Breaker. 2003.

Molecular Cell. 11:1419-1420, Cell 113:577-586.

AAAAAUAAAAAAUGAAUUACUCAUAUAAUCUCGGGAAUAUGGCCCGGGAGUUUCUAGCAGGCAACCGUAAAUGCCUGACUAUGAGUAAUUUUGAAAAAUA .............((((((((((((...(((((((.......)))))))........((((((........))))))..))))))))))))......... -32.10 .............((((((((((((...(((((((.......))))))).......(((((((........)))))).)))))))))))))......... -31.80 .............(((((((((((....(((((((.......)))))))......((((((((........)))))).)))))))))))))......... -31.80 .............((((((((((.....(((((((.......))))))).....(((((((((........)))))).)))))))))))))......... -31.80 .............(((((((((((....(((((((.......)))))))........((((((........))))))...)))))))))))......... -31.00 .............(((((((((......(((((((.......))))))).....(((((((((........)))))).))).)))))))))......... -31.00 ..............(((((((((((...(((((((.......)))))))........((((((........))))))..))))))))))).......... -31.00 .............(((((((((((....(((((((.......))))))).......(((((((........)))))).).)))))))))))......... -30.70 .................((((((((...(((((((.......)))))))........((((((........))))))..))))))))............. -28.60 .....(((......(((((((((((((.(((((((.......))))))).....))(((((((........)))))).)))))))))))))))....... -24.80 ......((((......((((((((.....((((((.......)))))).......((((((((........)))))).))))))))))))))........ -24.60 ......((((......(((((((......((((((.......))))))......(((((((((........)))))).))))))))))))))........ -24.60 ........(((((.....(((((((...((((((.........))))))........((((((........))))))..))))))).)))))........ -24.60 ...............(((((((((....(((((((.......))))))).......(((((((........)))))).).)))))))))(((...))).. -24.50 ................(((((((((....((((((.......)))))).........((((((........))))))..)))))))))(((....))).. -24.50 .................((((((((...((((((.........))))))........((((((........))))))..))))))))((((....)))). -24.50

The purine riboswitch: Molecular Cell. 2003. 11:1419-1420.

mfe-weight: 0.1459

The thiamine-pyrophosphate riboswitch

• S. Thore, M. Leibundgut, N. Ban.

Science 312:1208-1211, 2006.

Results from RNA folding kinetics:

• In addition to the minimum free energy structure RNA

molecules can exist in one, two or more long-lived metastable structures.

• RNA switches are molecules with two or more long-lived

conformations that allow for metabolic control.

1. Minimum free energy structures of RNA 2. Suboptimal structures of RNA 3. Kinetic folding and RNA switches

• 4. Chemistry of Darwinian evolution

5. Consequences of neutrality 6. Evolutionary optimization of RNA structure

Complementary replication is the simplest copying mechanism

• f RNA.

Complementarity is determined by Watson-Crick base pairs: GC and A=U

1 1 2 2 2 1

and x f dt dx x f dt dx = =

2 1 2 1 2 1 2 1 2 1 2 1

, , , , f f f f x f x = − = + = = = ξ ξ η ξ ξ ζ ξ ξ

ft ft

e t e t ) ( ) ( ) ( ) ( ζ ζ η η = =

−

Complementary replication as the simplest molecular mechanism of reproduction

Chemical kinetics of replication and mutation as parallel reactions

Quasispecies

Driving virus populations through threshold

The error threshold in replication

A fitness landscape showing an error threshold

Error rate p = 1-q

0.00 0.05 0.10

Quasispecies Uniform distribution

Stationary population or quasispecies as a function of the mutation or error rate p

Fitness landscapes showing error thresholds

Error threshold: Individual sequences n = 10, = 2 and d = 0, 1.0, 1.85

Evolution of RNA molecules based on Qβ phage

D.R.Mills, R.L.Peterson, S.Spiegelman, An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc.Natl.Acad.Sci.USA 58 (1967), 217-224 S.Spiegelman, An approach to the experimental analysis of precellular evolution. Quart.Rev.Biophys. 4 (1971), 213-253 C.K.Biebricher, Darwinian selection of self-replicating RNA molecules. Evolutionary Biology 16 (1983), 1-52 G.Bauer, H.Otten, J.S.McCaskill, Travelling waves of in vitro evolving RNA. Proc.Natl.Acad.Sci.USA 86 (1989), 7937-7941 C.K.Biebricher, W.C.Gardiner, Molecular evolution of RNA in vitro. Biophysical Chemistry 66 (1997), 179-192 G.Strunk, T.Ederhof, Machines for automated evolution experiments in vitro based on the serial transfer concept. Biophysical Chemistry 66 (1997), 193-202 F.Öhlenschlager, M.Eigen, 30 years later – A new approach to Sol Spiegelman‘s and Leslie Orgel‘s in vitro evolutionary studies. Orig.Life Evol.Biosph. 27 (1997), 437-457

RNA sample Stock solution: Q RNA-replicase, ATP, CTP, GTP and UTP, buffer

• Time

1 2 3 4 5 6 69 70 Anwendung der seriellen Überimpfungstechnik auf RNA-Evolution in Reagenzglas

Evolutionary design of RNA molecules

A.D. Ellington, J.W. Szostak, In vitro selection of RNA molecules that bind specific ligands. Nature 346 (1990), 818-822

• C. Tuerk, L. Gold, SELEX - Systematic evolution of ligands by exponential enrichment: RNA

ligands to bacteriophage T4 DNA polymerase. Science 249 (1990), 505-510 D.P. Bartel, J.W. Szostak, Isolation of new ribozymes from a large pool of random sequences. Science 261 (1993), 1411-1418 R.D. Jenison, S.C. Gill, A. Pardi, B. Poliski, High-resolution molecular discrimination by RNA. Science 263 (1994), 1425-1429

• Y. Wang, R.R. Rando, Specific binding of aminoglycoside antibiotics to RNA. Chemistry &

Biology 2 (1995), 281-290

• L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside

antibiotic-RNA aptamer complex. Chemistry & Biology 4 (1997), 35-50

An example of ‘artificial selection’ with RNA molecules or ‘breeding’ of biomolecules

tobramycin

A A A A A C C C C C C C C G G G G G G G G U U U U U U

5’- 3’-

A A A A A U U U U U U C C C C C C C C G G G G G G G G

5’-

• 3’

RNA aptamer

Formation of secondary structure of the tobramycin binding RNA aptamer with KD = 9 nM

• L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside antibiotic-

RNA aptamer complex. Chemistry & Biology 4:35-50 (1997)

The three-dimensional structure of the tobramycin aptamer complex

• L. Jiang, A. K. Suri, R. Fiala, D. J. Patel,

Chemistry & Biology 4:35-50 (1997)

Christian Jäckel, Peter Kast, and Donald Hilvert. Protein design by directed evolution. Annu.Rev.Biophys. 37:153-173, 2008

Application of molecular evolution to problems in biotechnology

Artificial evolution in biotechnology and pharmcology G.F. Joyce. 2004. Directed evolution of nucleic acid enzymes. Annu.Rev.Biochem. 73:791-836.

• C. Jäckel, P. Kast, and D. Hilvert. 2008. Protein design by

directed evolution. Annu.Rev.Biophys. 37:153-173. S.J. Wrenn and P.B. Harbury. 2007. Chemical evolution as a tool for molrcular discovery. Annu.Rev.Biochem. 76:331-349.

Results from replication kinetics and molecular evolution in laboratory experiments:

• Evolutionary optimization does not require cells and occurs in

molecular systems too.

• In vitro evolution allows for production of molecules for

predefined purposes and gave rise to a branch of biotechnology.

• Novel antiviral strategies were developed from known molecular

mechanisms of virus evolution.

1. Minimum free energy structures of RNA 2. Suboptimal structures of RNA 3. Kinetic folding and RNA switches 4. Chemistry of Darwinian evolution

• 5. Consequences of neutrality

6. Evolutionary optimization of RNA structure

Motoo Kimura

Is the Kimura scenario correct for frequent mutations?

dH = 1

5 . ) ( ) ( lim

2 1

= =

→

p x p x

p

dH = 2

a p x a p x

p p

− = =

→ →

1 ) ( lim ) ( lim

2 1

dH ≥3

random fixation in the sense of Motoo Kimura Pairs of genotypes in neutral replication networks

Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

N = 7 Neutral networks with increasing : = 0.10, s = 229

N = 7 Neutral networks with increasing : = 0.10, s = 229

N = 24 Neutral networks with increasing : = 0.15, s = 229

N = 70 Neutral networks with increasing : = 0.20, s = 229

Results from replication kinetics and RNA neutral networks:

• RNA sequences with Hamming distance d = 1 and d = 2 form

strongly coupled replication ensembles. For d > 2 random drift in the sense of Kimura‘s theory occurs.

• Direct evidence that neutrality is increasing the repertoire of

structures and properties in populations.

• Implication for virus replication in infected hosts.

Neutrality in evolution

Charles Darwin: „ ... neutrality might exist ...“ Motoo Kimura: „ ... neutrality is unaviodable and represents the main reason for changes in genotypes and leads to molecular phylogeny ...“ Current view: „ ... neutrality is essential for successful

• ptimization on rugged landscapes ...“

Proposed view: „ ... neutrality provides the genetic reservoir in the rare and frequent mutation scenario ...“

1. Minimum free energy structures of RNA 2. Suboptimal structures of RNA 3. Kinetic folding and RNA switches 4. Chemistry of Darwinian evolution 5. Consequences of neutrality

• 6. Evolutionary optimization of RNA structure

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

Phenylalanyl-tRNA as target structure Structure of randomly chosen initial sequence

Replication rate constant (Fitness): fk = / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Selection pressure: The population size, N = # RNA moleucles, is determined by the flux: Mutation rate: p = 0.001 / Nucleotide Replication N N t N ± ≈ ) ( The flow reactor as a device for studying the evolution of molecules in vitro and in silico.

In silico optimization in the flow reactor: Evolutionary Trajectory

28 neutral point mutations during a long quasi-stationary epoch Transition inducing point mutations change the molecular structure Neutral point mutations leave the molecular structure unchanged

Neutral genotype evolution during phenotypic stasis

Randomly chosen initial structure Phenylalanyl-tRNA as target structure

A sketch of optimization on neutral networks

Results from in silico simulation of RNA evolution:

• Evolutionary optimization occurs on two time scales: Fast

adaptive phases and random walk on neutral networks.

• Neutral networks are essential for searching sequence space.

Acknowledgement of support

Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute

Universität Wien

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 Jord Nagel, Kees Pleij, Universiteit Leiden, NL Walter Fontana, Harvard Medical School, MA Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM 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, Universität Wien, AT Jan Cupal, Stefan Bernhart, Lukas Endler, Ulrike Langhammer, Rainer Machne, Ulrike Mückstein, Hakim Tafer, Thomas Taylor, Universität Wien, AT

Universität Wien

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