Pathways Have Evolved Using Evolutionary Approaches To Study Biological Pathways Orkun S. Soyer The Microsoft Research - University of Trento Centre for Computational and Systems Biology
Protein-protein interactions map from yeast. Jeong H. et. al., Nature 411, 2001 Proteins do interact...
... constituting biological pathways. Generic representation of pathways involving camp
Studying Biological Pathways: Common Approaches Experimental techniques Which proteins are involved? How do specific proteins interact? What are the interaction kinetics? Conventional Modeling What are the response dynamics? How do they change with different conditions (e.g. under drug treatment)? Pathway Discovery Can we detect new pathways from low level data like protein sequences? Large Scale Data Analysis Are there any general network properties? Connectivity distribution, re-occuring interaction motifs, etc. Design Principles???
Studying Biological Pathways: Limitations Experimental techniques Time, techniques, and money System specific results Conventional Modeling Sparse data System specific results Large Scale Data Analysis Broad conclusions (too broad?) Pathway Discovery Usual suspects; reliability of data, algorithms, etc.
Bacterial Chemotaxis: The Behavior Chemotaxis is a biased random walk: Constant Tumbling Frequency Decreasing Tumbling Frequency
Bacterial Chemotaxis: The Pathway Tumbling: - CheY-P bound - Motor rotates CW Smooth Swimming: - CheY-P unbound - Motor rotates CCW
Bacterial Chemotaxis Solved Adaptive response Receptor and protein localization 6.0 5.0 4.0 3.0 h c ar 2.0 1.0 0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 time e s e r f o s r a 3 e y 0 Biased random walk
Bacterial Chemotaxis Solved Or Not??? Halobacterium salinarum Escherichia Coli Bacillus subtilis Rhodobacter sphaeroides Helicobacter pylori???? 6.0? 5.0 4.0 3.0 2.0 1.0 0.0 0 200 400 600 800 1000 time 1200 1400 1600 1800 2000
Evolutionary Approaches for Studying Biological Pathways?...?... Escherichia Coli Bacillus subtilis Rhodobacter sphaeroides Helicobacter pylori?? 6.0 5.0 4.0 3.0 2.0 1.0?? 0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 time?
Abstract Models for Studying Biological Pathways Ligand P1 P1* P2 P2* P4* response P4 P3 P3* d½p i Š dt ¼ " # ½P i Š X l ij ½P j Š j " ½P i Š d i1 ½LŠ þ X!# k ij ½P j Š, j Ligand P1* P2* P3* P4* P1 P1* 0.5 0.0 0.0 0.0 0.0 P2 P2* 0.0 0.9 0.0 0.0-0.5 P3 P3* 0.0 0.0 0.7 0.0 0.0 P4 P4* 0.0 0.0 0.0-0.7 0.0 A Generic Pathway Model
Putting The Two Together: In Silico Evolution Ligand P1* P2* P3* P4* P1 P1* 0.5 0.0 0.0 0.0 0.0 P2 P2* 0.0 0.9 0.0 0.0-0.5 P3 P3* 0.0 0.0 0.7 0.0 0.0 P4 P4* 0.0 0.0 0.0-0.7 0.0 Evaluate Response Iterate until no improvement Introduce Mutations Ligand P1* P2* P3* P4* P1 P1* 0.5 0.0 0.0 0.3 0.0 P2 P2* 0.0 0.9 0.0 0.0-0.5 P3 P3* 0.0 0.0 0.2 0.0 0.0 P4 P4* 0.0 0.0 0.0-0.1 0.0 Analysis of pathway evolution using generic, extendable pathway models
walk towards higher food concentrations. The base f Fitness: tumbling Capturing frequency Bacterial of bacteria Chemotaxis not zero, enabling them r both to explore the space efficiently and to overcome the l Chemotaxis issues related is achieved withvia living a derivative-like in an environment response: with a low f Reynolds number (Berg, 1983). Hence, we assume that the 6.0 d main selective pressures on chemotactic behavior are the 5.0 s ability to explore the environment while making maximal Ropt. 4.0 gain out of available food sources. Here, we therefore assume that there is an optimal 3.0 tumbling frequency R opt.. A good responder should decrease (increase) its tumbling 2.0 frequency below (above) R opt. in increasing (decreasing) 1.0 food gradients and should tumble with a frequency close to F 0.0 Þ R opt. in absence of any food change. These two selective time pressures on the motility of bacteria are captured in the following fitness function: e Fitness ¼ X C DF ðr t opt: R avg: Þ ðropt: R avg: Þ 2 Chemotactic. Ability t s Reward food intake over a Penalize deviation from a time interval base (optimum) response (5) n CheY-P Ravg. conc. Ligand conc. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Rao CV et. al., PLOS Biology, 2(2), 2004
Evolving Chemotaxis Pathways Introduce Mutations Iterate Until No Improvement Evaluate Response C DF ðr opt: R avg: Þ ðropt: R avg: Þ 2. Chemotactic Fitness ¼ X Ability t ~-50 Ligand conc. Effector conc.
Evolved Pathways Are able to give a derivative-like response: 3-protein Pathway Response Ligand conc. Effector conc. 4-protein Pathway Response 5-protein Pathway Response
Evolved Pathways Are able to mediate chemotaxislike behavior:
Evolved Pathways
Distilling Key Features: Topology Analysis Important Interactions Important Dynamical Features Receptor fast Effector Parameters For 3-protein Network slow Intermediary Protein(s)
Distilling Key Features: Response Analysis Imbalance in response to increasing and decreasing signals Adaptation
Evolutionary Systems Biology: Chemotaxis Pathway => Dynamics => Behavior Shall I tumble or swim?? Active Effector Concentration E R
Evolutionary Systems Biology: Chemotaxis Behavior => Fitness => Evolution Do I survive? Can pathways evolve that allow bacteria to find the food? How would the structure/dynamics of these pathways change with environment/pathway constraints? Do all bacteria evolve the same strategy (i.e. pathway structure)? Do we find population wide variances?
A more realistic evolutionary setup.... ' Initial Population Time Selection Fitness = Food Encountered Final (evolved) Population ()&'*40.(!$"'$*'54$(&!"'i'()0('!2'0.(!#0(&3F'$7&A2' ij ' 3! P J" i 3( * - ( k ) ii +. j/ i '! P J" + 0 k! A" % K,! P J" # $ * ' 45%.%' H(x)' /"' (5%' ''''''''''''''''''''''''''''''''''''+ C%!7/"/&%' "(%0'( lii +. <#+2(/)+8' lij! Pj J" + 0 iklka! A%D#!1' "%! Pi J" () dynamics k ij j ( ) ik j/ i KA % & i % & '''''''''''' )(5%.4/"%,'95%'0.)*!*/1/(3'p ' 9#$*1% ')<'!'0.)(%/+'(#$*1/+6'! ' ' behavior 8)&4&'k ij 'Gl ij H'!2'()&'40(&'0('8)!.)'0.(!#0(&3'54$(&!"'j'0.(!#0(&2'G3&0.(!#0(&2H'54$!2'54$(&!"'iL2'40(&'$*'2&%*+0.(!#0(!$"'G3&0.(!#0(!$"HF'k 1A ''Gl 1A 'H'4&54&2&"(2'()&'4 ()&'0((40.(0"('0.(!#0(&2'G3&0.(!#0(&2H'()&'4&.&5($4'54$(&!"'KF'! "! H! " l % # A$ # A '!2'()&'%$.0%'. m N $*' 0((40.(0"(F' 0"3'!'!2' 0' M4$"&.6&4' 3&%(09' <)&' ($(0%'.$".&"(40(!$"' & p p $*' ' &0. 9#$*1% % '''' A( # m PN F 45%.%'! m '/"'(5%'!<</+/(3')<'0.)(%/+'N p '<).'(5%'$)().,'' ' evolution ij # & P F p ij '
Evolution Of Chemotaxis
Evolution Of Chemotaxis Pathways adaptive dynamics biased random walk couch potato non - adaptive dynamics
Non - Adaptive Chemotaxis is not due to Initial Population Initial Population with adaptive dynamics Final (evolved) Population Final population with non-adaptive dynamics
Non - Adaptive chemotaxis under fluctuating environments
Minimal Non-Adaptive Chemotaxis Mechanisms
Reality or Modeling Curiosity? Chemotaxis in absence of adaptation has already been observed in nature in Rhodobacter sphaeroides and in mutant strains of Escherichia coli. Poole PS and Armitage JP, J. Bacteriology, 170, 1988 Barak R and Eisenbach M, Mol. Microbiology, 31, 1999 Pathways with non-adaptive dynamics - possible existence in many bacterial species - a simple mechanism to couple metabolic and/ or other signals to conventional chemotaxis - evolutionary origins of chemotaxis
Insights from Evolutionary Systems Biology Natural Evolution... How Evolutionary do evolutionary Systems processes Biology approaches affect pathway allow... properties? - Detecting key system properties - Exploring alternative and minimal solutions for achieving a behavior - Allows hypothesis development Transfer of Knowledge Transfer of Knowledge In Silico Evolution Soyer OS, Pfeiffer T, Bonhoeffer S, JTB, 2006, 241(2) Goldstein RA, Soyer OS, submitted
Pathway Modularity How does modularity arise in biological systems and how is it maintained? Adaptation to alternating environments... Kashtan, N. & Alon, U. (2005) PNAS 102, 13773-8. Selection for evolvability... Kirschner, M. & Gerhart, J. (1998) PNAS 95, 8420-7.
Evolution of Modularity Selection Fitness = Ability to mediate separate responses Through simple evolutionary processes...
Two responses mediated by different structures modular cross-talk complex
The Model Initial Homogenous Population F = 1 4! #$ (E1A + E B 2 ) + (E A 1 + E B 2 " E B 1 " E A 2 )% & " n! c.... Time Fitness 0 200 400 600 800 1000 Generation Final Population
The Model replication with mutations MUTATION PER PROTEIN P = 0.05 - Delete Interaction (P = 0.4) - Delete Protein (P = 0.2) - Change Interaction (P = 0.2) - Duplicate Protein (P = 0.1) - Add Interaction (P = 0.1)? with new protein (i.e. Protein Recruitment) between existing proteins
Modularity maintenance depends on mutational mechanisms complex cross-talk modular
Modularity evolution depends on initial pathway topology simulation 1 Random simulation Initial Population Of Pathways 2 With Size 6 simulation 3 random initial pathways of size 6 Frequency Frequency Frequency 0 200 400 600 800 1000 Generation 0 200 400 600 800 1000 Generation 0 200 400 600 800 1000 Generation Random Initial Population Of Pathways With Size 7 of size 7 Frequency Frequency Frequency 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 Generation Generation Generation Random Initial Population Of Pathways With Size 9 of size 9 P(rcrtmnt) = 1.0 Frequency 0 200 400 600 800 1000 Generation Frequency 0 200 400 600 800 1000 Generation Frequency 0 200 400 600 800 1000 Generation
Duplications and pathway growth Interaction Loss Protein Recruitment Protein duplications drive pathway evolution... N Mutations 0 200 500 0 200 500 0.0 0.2 0.5 0.0 0.2 0.5 Fitness Effect 0.6 0.2 0.1 0 200 400 600 800 1000 Generation N Mutations 0 200 500 Interaction Formation 0.0 0.2 0.5 0 200 500 Protein Loss 0.0 0.2 0.5 Pathway Size 0 4 8 12 0 200 400 600 800 1000 Generation N Mutations 0 200 500 Coefficient Change 0.0 0.2 0.5 Fitness Effect 0 200 500 Protein Duplication 0.0 0.2 0.5 Fitness Effect
New Answers To Old Questions Through Study of Evolution Natural Evolution Modularity emerges readily under simple evolutionary processes without any specific selective pressure. In Silico Evolution Determinants of modularity are the relevant rates of different mutational events and the initial location of a pathway in topology space Approach extendable to study Transfer of Knowledge - Complexity - Modularity - Robustness - Evolvability Soyer OS, Bonhoeffer S, PNAS, 2006, 103(44) Soyer OS, BMC Evolutionary Biology, in print
Modularity evolution depends on pathway topology simulation 1 Random simulation Initial Population Of Pathways 2 With Size 6 simulation 3 random initial pathways of size 6 Frequency Frequency Frequency 0 200 400 600 800 1000 Generation 0 200 400 600 800 1000 Generation 0 200 400 600 800 1000 Generation Random Initial Population Of Pathways With Size 7 of size 7 Frequency Frequency Frequency 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 Generation Generation Generation Random Initial Population Of Pathways With Size 9 of size 9 P(rcrtmnt) = 1.0 Frequency 0 200 400 600 800 1000 Generation Frequency 0 200 400 600 800 1000 Generation Frequency 0 200 400 600 800 1000 Generation
Pathway Evolution: A random walk in topology space Larger, Non-Functional Pathways Larger, Functional Pathways Smaller, Non-Functional Pathways Functional Minimum-Size Pathways, Initial Population How does the topology space look like?
Topology space is big Ligand P1* P2* P3* P4* P1 P1* 0.5 0.0 0.0 0.0 0.0 P2 P2* 0.0 0.9 0.0 0.0-0.5 P3 P3* 0.0 0.0 0.7 0.0 0.0 P4 P4* 0.0 0.0 0.0-0.7 0.0 which topologies matter? 2 N params = N prots N prots N N ntwrks = N params values = 729 for N = 3 and values = {-1,0,1} = 531.444 for N = 4 > 3x10 9 for N = 5
Topology space is heterogeneous Constant Switch (step - like) Transient (Gauss - like) Adaptive (derivative - like) Oscillatory how do we classify topologies?
Topology space and pathway nature d½p i Š dt ¼ " # ½P i Š X l ij ½P j Š j " ½P i Š d i1 ½LŠ þ X!# k ij ½P j Š, j Ligand P1* P2* P3* P4* P1 P1* 0.5 0.0 0.0 0.0 0.0 P2 P2* 0.0 0.9 0.0 0.0-0.5 P3 P3* 0.0 0.0 0.7 0.0 0.0 P4 P4* 0.0 0.0 0.0-0.7 0.0 3! P J" i 3( * - ( k ) ii +. j/ i * ''''''''''''''''''''''''''''''''''''+ ( l ) k ij '! P J" + 0 k! A" % K,! P J" j ii + ik. j/ i KA l ij % & # $ '! P J" + 0 l! A" %! P J" j i ik KA % & i ''''''''' d[p i ] dt = [P * i ] (l ij [P * j ] + sd + δ i1 dd) [P i ] (k ij [P * j ] + sa + δ i1 ([L] + da) j how do we model topologies?
Topologies and Models: Biochemistry Topology space for all 3-protein pathways Autophosphorylation Interaction Only Inhibitory Dimerization
Topologies and Models: Kinetics Topology space for all 3-protein pathways Binary Strength Kinetics {0 or 1} Random Strength Kinetics [0, 1] Kinetics do not seem to affect overall distribution
What Determines Pathway Dynamics? Topology or Kinetics Answer depends on topology and biochemistry
Specific Topologies Steady state concentration Histogram of finalvalues[, of active Protein 3] 3 Solution of ODEs indicate neutral stability with respect to protein 3 P i sa+ k ij [P * j ] j * P sd + l ij [P * i j ] j Pi + Pi* = const. Frequency 0 20 40 60 80 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 In numerical simulations, finalvalues[, protein 3] 3 has specific SS value with changing active fraction of proteins at start of simulation.
Histogram of finalvaluesa[, 3] Specific Topologies Histogram of finalvaluespre[, 3] Steady state concentration of active Protein 3 0 20 40 60 80 100 120 Frequency 0 5 10 15 20 changing coefficients. finalvaluesa[, 3] changing finalvaluespre[, total protein 3] concentrations.
Topologies, Biochemistry, and Evolution d½p i Š dt ¼ " # ½P i Š X l ij ½P j Š j " ½P i Š d i1 ½LŠ þ X!# k ij ½P j Š, j Topology dynamics relation is complex Biochemical processes, even those treated as negligable, can have important effects on pathway dynamics Dimerization, auto phosphorylation might be important as determinants of dynamic behavior and robustness Soyer OS, Salathe M, Bonhoeffer S, JTB, 2006, 238
Big Picture System Specific Understanding?? realistic models ( ) theory ( ) toy models experiments?? Nothing in biology makes sense except in light of evolution Theodosius Dobzhansky EVOLUTIONARY SYSTEMS BIOLOGY - From Systems to Behavior - Global Properties - Design Principles??
The Microsoft Research - University of Trento Centre for Computational and Systems Biology Theoretical Biology Group at ETH, Zürich Richard Goldstein MRC, UK