Biology Meets Chemistry Molecular Evolution and Systems Biology at - - PowerPoint PPT Presentation

Biology Meets Chemistry

Molecular Evolution and Systems Biology at the Cross-Roads

Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

Mini-Symposium on Theoretical Biology ETH-Zürich, 04.07.2005

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

Genotype, Genome Phenotype

Unfolding of the genotype

Highly specific environmental conditions Developmental program

Collection of genes

Evolution

The macroscopic biologists‘ nightmare: The conquest of biology by chemists and physicists and, eventually, by mathematicians and computer scientists has become reality in the last fifty years.

The macroscopic biologists‘ revenche: Chemists and physicists don‘t know any biology, and this is true even more for mathematicians and computer scientists. So they all have to learn biology.

The victory of the live sciences, 2005.

Genotype, Genome

GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATCTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA

Phenotype

Unfolding of the genotype

Highly specific environmental conditions Biochemistry molecular biology structural biology molecular evolution molecular genetics systems biology bioinfomatics

Max Perutz Hemoglobin sequence Gerhard Braunitzer Molecular evolution Linus Pauling and Emile Zuckerkandl The exciting RNA story evolution of RNA molecules, ribozymes and splicing, the idea of an RNA world, selection of RNA molecules, RNA editing, the ribosome is a ribozyme, small RNAs and RNA switches.

Omi Omics

‘the new biology is the chemistry of living matter’ James D. Watson und Francis H.C. Crick

GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATCTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA

1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Enzyme Metabolite Regulatory gene Structural gene

A model genome with 12 genes

Genotype RNA secondary structure RNA spatial structure Genetic and metabolic network

Three different genotype-phenotype mappings

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

• 1. RNA phenotypes

2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

Complementary replication is the simplest copying mechanism of RNA. Complementarity is determined by Watson-Crick base pairs: GC and A=U

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

• Time

1 2 3 4 5 6 69 70 The serial transfer technique applied to RNA evolution in vitro

Reproduction of the original figure of the serial transfer experiment with Q RNA β D.R.Mills, R,L,Peterson, S.Spiegelman, . Proc.Natl.Acad.Sci.USA (1967), 217-224 An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule 58

Decrease in mean fitness due to quasispecies formation

The increase in RNA production rate during a serial transfer experiment

RNA structure determines fitness in RNA evolution experiments

Definition and physical relevance of RNA secondary structures

RNA secondary structures are listings of Watson-Crick and GU wobble base pairs, which are free of knots and

• pseudokots. This definition allows for rigorous

mathematical analysis by means of combinatorics. „Secondary structures are folding intermediates in the formation of full three-dimensional structures.“ Secondary structures have been and still are frequently used to predict and discuss RNA function. D.Thirumalai, N.Lee, S.A.Woodson, and D.K.Klimov. Annu.Rev.Phys.Chem. 52:751-762 (2001):

5'-End

5'-End 5'-End 3'-End 3'-End

3'-End

70 60 50 40 30 20 10 GCGGAUUUAGCUCAGDDGGGAGAGCMCCAGACUGAAYAUCUGGAGMUCCUGUGTPCGAUCCACAGAAUUCGCACCA

Sequence Secondary structure Symbolic notation

• A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

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

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

The Vienna RNA-Package: A library of routines for folding, inverse folding, sequence and structure alignment, kinetic folding, cofolding, …

1. RNA phenotypes

• 2. Genotype-phenotype mappings

3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

A mapping and its inversion

• Gk =

( ) | ( ) =

• 1

U

• S

I S

k j j k

I

( ) = I S

j k Space of genotypes: = { I

S I I I I I S S S S S

1 2 3 4 N 1 2 3 4 M

, , , , ... , } ; Hamming metric Space of phenotypes: , , , , ... , } ; metric (not required) N M = {

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Structure space Real numbers Mapping from sequence space into structure space and into function

Sk I. = ( ) ψ

fk f Sk = ( )

Sequence space Structure space Real numbers

Sk I. = ( ) ψ

Sequence space Structure space

The pre-image of the structure Sk in sequence space is the neutral network Gk

Degree of neutrality of neutral networks and the connectivity threshold

Giant Component

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

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

Reference for postulation and in silico verification of neutral networks

Properties of RNA sequence to secondary structure mapping

• 1. More sequences than structures

Properties of RNA sequence to secondary structure mapping

• 1. More sequences than structures

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures

n = 100, stem-loop structures n = 30

RNA secondary structures and Zipf’s law

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures 3. Shape space covering of common structures

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures 3. Shape space covering of common structures

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures 3. Shape space covering of common structures 4. Neutral networks of common structures are connected

Properties of RNA sequence to secondary structure mapping 1. More sequences than structures 2. Few common versus many rare structures 3. Shape space covering of common structures 4. Neutral networks of common structures are connected

RNA 9:1456-1463, 2003

Evidence for neutral networks and shape space covering

Evidence for neutral networks and intersection of apatamer functions

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

1. RNA phenotypes 2. Genotype-phenotype mappings

• 3. Evolution on neutral networks

4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

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

Evolutionary trajectory Spreading of the population

• n neutral networks

Drift of the population center in sequence space

Spreading and evolution of a population on a neutral network: t = 150

Spreading and evolution of a population on a neutral network : t = 170

Spreading and evolution of a population on a neutral network : t = 200

Spreading and evolution of a population on a neutral network : t = 350

Spreading and evolution of a population on a neutral network : t = 500

Spreading and evolution of a population on a neutral network : t = 650

Spreading and evolution of a population on a neutral network : t = 820

Spreading and evolution of a population on a neutral network : t = 825

Spreading and evolution of a population on a neutral network : t = 830

Spreading and evolution of a population on a neutral network : t = 835

Spreading and evolution of a population on a neutral network : t = 840

Spreading and evolution of a population on a neutral network : t = 845

Spreading and evolution of a population on a neutral network : t = 850

Spreading and evolution of a population on a neutral network : t = 855

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks

• 4. Genetic and metabolic networks

5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATCTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA

1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Enzyme Metabolite Regulatory gene Structural gene

A model genome with 12 genes

Genotype RNA secondary structure RNA spatial structure Genetic and metabolic network

Three different genotype-phenotype mappings

The search for more complex phenotypes inevitably leads from evolvable molecules to genetic regulation and metabolism. The simplest systems of this kind are artificial regulatory systems on plasmids that can be expressed and studied in Escherichia coli cells.

1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Enzyme Metabolite Regulatory gene Structural gene

A model genome with 12 genes

Sketch of a genetic and metabolic network

1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Enzyme Metabolite Regulatory gene Structural gene

A model genome with 12 genes

Genetic regulatory network Metabolic network

Proposal of a new name: Genetic and metabolic network

A B C D E F G H I J K L 1

Biochemical Pathways

2 3 4 5 6 7 8 9 10

The reaction network of cellular metabolism published by Boehringer-Ingelheim.

The citric acid

• r Krebs cycle

(enlarged from previous slide).

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks

• 5. A glimpse of chemical kinetics and dynamics

6. How do model metabolisms evolve?

Time t Concentration xi (t)

Sequences

Vienna RNA Package

Structures and kinetic parameters Stoichiometric equations

SBML – systems biology markup language

Kinetic differential equations

ODE Integration by means of CVODE

Solution curves

A + B X 2 X Y Y + X D

y x k d y x k x k y y x k x k b a k x b a k b a

3 3 2 2 3 2 2 1 1

t d d t d d t d d t d d t d d = − = − − = − = =

The elements of the simulation tool MiniCellSim

SBML: Bioinformatics 19:524-531, 2003; CVODE: Computers in Physics 10:138-143, 1996

ATGCCTTATACGGCAGTCAGGTGCACCATT...GGC TACGGAATATGCCGTCAGTCCACGTGGTAA...CCG DNA string genotype environment mRNA Protein RNA

Metabolism

RNA and protein structures enzymes and small molecules Recycling of molecules cell membrane nutrition waste genotype-p e h p mapping e y not genetic regulation network metabolic reaction network transport system

The regulatory logic of MiniCellSym

The model regulatory gene in MiniCellSim

The model structural gene in MiniCellSim

Cross-regulation of two genes

2 , 1 , ) ( : Repression ) ( : Activation

n n n

= + = + = j i p K K p F p K p p F

j j i j j j i

Gene regulatory binding functions

2 P 2 2 P 2 2 1 P 2 1 P 1 1 2 Q 2 1 2 Q 2 2 1 Q 1 2 1 Q 1 1

) ( ) ( p d q k dt dp p d q k dt dp q d p F k dt dq q d p F k dt dq − = − = − = − =

2 2 1 1 2 2 1 1 2 1

] P [ , ] P [ , ] Q [ , ] Q [ . const ] G [ ] G [ p p q q g = = = = = = = 2 , 1 , ) ( : Repression ) ( : Activation

n n n

= + = + = j i p K K p F p K p p F

j j i j j j i

P 2 Q 2 P 2 Q 2 2 P 1 Q 1 P 1 Q 1 1 1 2 2 2 1 2 2 1 1 1

, ) ( , )) ( ( : points Stationary d d k k d d k k p F p p F F p = = = = − ϑ ϑ ϑ ϑ ϑ

Qualitative analysis of cross-regulation of two genes

) , ( ) ε ( ) ε ( ) ε ( ) ε (

2 1 P 2 P 1 Q 2 Q 1 P 2 P 1 Q 2 Q 1

p p k k k k D D d d d d Γ − = = + + + + +

Eigenvalues of the Jacobian of the cross-regulatory two gene system

) , ( ) ε ( ) ε ( ) ε ( ) ε (

2 1 P 2 P 1 Q 2 Q 1 P 2 P 1 Q 2 Q 1

p p k k k k D D d d d d Γ − = = + + + + +

Eigenvalues of the Jacobian of the cross-regulatory two gene system

2 P 2 P 1 Q 2 Q 1 P 2 P 1 P 2 Q 2 P 1 Q 2 P 2 Q 1 P 1 Q 1 Q 2 Q 1 Hopf P 2 P 1 Q 2 Q 1 trans

) ( ) )( )( )( )( )( ( d d d d d d d d d d d d d d d d D d d d d D + + + + + + + + + = − =

Regulatory dynamics at D < DHopf , act.-repr., n=3

Regulatory dynamics at D > DHopf , act.-repr., n=3

Hill coefficient: n Act.-Act. Act.-Rep. Rep.-Rep. 1 S , E S S 2 E , B(E,P) S S , B(P1,P2) 3 E , B(E,P) S , O S , B(P1,P2) 4 E , B(E,P) S , O S , B(P1,P2)

An example analyzed and simulated by MiniCellSim

The repressilator: M.B. Ellowitz, S. Leibler. A synthetic oscillatory network of transcriptional

• regulators. Nature 403:335-338, 2002

Stable stationary state Limit cycle oscillations Fading oscillations caused by a stable heteroclinic orbit Hopf bifurcation Bifurcation to May-Leonhard system Increasing inhibitor strength

P1 P2 P3

start start

The repressilator limit cycle

P1 P2 P2 P2 P3

Stable heteroclinic orbit Unstable heteroclinic orbit

1 1 2 2 2<0 2>0 2=0

Bifurcation from limit cycle to stable heteroclinic orbit at

The repressilator heteroclinic orbit

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics

• 6. How do model metabolisms evolve?

Evolutionary time: 0000 Number of genes 12 : + 06 structural 06 regulatory Number of interactions 15 : + + 04 inhibitory + 10 activating 1 self-activating

A genabolic network formed from a genotype of n = 200 nucleotides

100 1000 10000 1e+05 5 10 15 20 TF00 TF01 TF02 TF03 SP04 TF05 SP06 SP07 SP08 SP09 TF10 SP11

Evolutionary time 0000 , initial network : Intracellular time Stationary state Intracellular time scale Evolutionary time scale [generations]: 0000 initial network

Evolution of a genabolic network:

Initial genome: random sequence of length n = 200, AUGC alphabet Gene length: n = 25 Simulation with mutation rate: p = 0.01 Evolutionary time unit >> intracellular time unit

Number of genes: total / structural genes regulatory genes

Evolution of a genabolic network:

Initial genome: random sequence of length n = 200, AUGC alphabet Gene length: n = 25 Simulation with mutation rate: p = 0.01 Evolutionary time unit >> intracellular time unit Recorded events: (i) Loss of a gene through corruption of the start signal “TA” (analogue of the “TATA Box”), (ii) creation of a gene, (iii) change in the edges through mutation-induced changes in the affinities of translation products to the binding sites, and (iv) change in the class of genes (tf sp).

Statistics of one thousand generations Total number of genes: 11.67 2.69 Regulatory genes: 5.97 2.22 Structural genes: 5.70 2.17

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 Siemens AG, Austria Universität Wien, Austrian Academy of Sciences, and the Santa Fe Institute

Universität Wien

Coworkers

Walter Fontana, Harvard Medical School, MA Christian Forst, Christian Reidys, Los Alamos National Laboratory, NM Peter Stadler, Bärbel Stadler, Universität Leipzig, GE Sebastian Bonhoeffer, ETH Zürich, Erich Bornberg-Bauer, Universität Münster, Martin Nowak, Harvard University, Thomas Wiehe, Universität Köln Jord Nagel, Kees Pleij, Universiteit Leiden, NL Heinz Engl, Stefan Müller, Josef Schiko, Johann Radon-Institut für Angewandte und Computergestützte Mathematik der Österreichischen Akademie der Wissenschaften, Linz, AT Christoph Flamm, Ivo L.Hofacker, Andreas Svrček-Seiler, Universität Wien, AT Kurt Grünberger, Michael Kospach, Andreas Wernitznig, Stefanie Widder, Michael Wolfinger, Stefan Wuchty,Universität Wien, AT Stefan Bernhart, Jan Cupal, Lukas Endler, Ulrike Langhammer, Rainer Machne, Ulrike Mückstein, Hakim Tafer, Universität Wien, AT Ulrike Göbel, Walter Grüner, Stefan Kopp, Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE

Universität Wien

Afterthought in occasion of Sebastian Bonhoeffer’s promotion to full professor at the ETH

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