A Formal and Integrated Framework to Simulate Evolution of Biological Pathways

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A Formal and Integrated Framework to
SimulateEvolution of Biological Pathways

• Lorenzo Dematte, Corrado Priami, Alessandro
  Romanel and Orkun SoyerCMSB 07
• Edinburgh, 20/09/2007

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Introduction

• Interest in using evolutionary approaches to
  study pathways
• Current approaches to evolution use ad-hoc tools
  and representations of pathway dynamics
• Current available tools to model and simulate
  pathway dynamics do not allow for evolutionary
  simulations.
• Outline
• BetaWB language
• Evolutionary framework
• A running example

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BetaWB language
Bio-process
P
Internal behaviour

• Stochastic each action enabled in the system has
  a stochastic rate.
• Three types of rules
• Monomolecular describe the evolution of single
  entities
• Bimolecular describe actions that involve two or
  more entities
• Events global rules of the environment.

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The BetaWB language
Operational semantics set of syntax-driven
rules that automatically infer the possible
future of the system.
A
A
intra
P
P
Monomolecular
A
B
B
A
inter
P
Q
P
Q
Bimolecular
B
Q
B
C
D
C
B
C
D
C
join
Q
R
P
R
Complexes
Events
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BetaWB extensions deterministic events
let Kinase bproc (x1,Alpha) _at_(2).nil
let A bproc (y1,Gamma) _at_(2).nil
when (A step1500) delete(500) when (A
step2500) new(500) when (Kinase time3.5)
new(2000) when (Alt10) new(2000) when
(A1000) delete(200)
Injection or wash out of substances Determinis
tic events
Fixed step
Cardinality
Time
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Evolution on Computers

• How biological systems function, and why they
  function the way they do? What happened?
• Understand how pathways emerged during evolution
  can help us to understand their basic properties
• Role of complexity,
• Importance of topology
• Importance of feedback loops.

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Evolutionary Framework

• In silico evolution
• A population of individuals
• The behaviour of each individual
• A measure of success
• Reproduction based on success

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Compositional Model For Signalling Pathways
Bio-process
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Evolutionary algorithm
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1) Simulation
Each individual in the population is simulated
separately using the BetaWB stochastic simulator
Mapk1
Mapk1
Mapk1
BetaWB Simulator
Mapk1
Mapk123

• Stochastic simulator variant of next reaction
  method
• Species based on structural congruence

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2) Fitness

• Fitness measures how good an individual was
• According to some criteria, it determines if an
  individual was successful in its life
• If its fitness value is higher, it has a higher
  probability to live and reproduce
• Measures can be
• Directly on pathway output (quantity of an
  entity)
• Indirect, as a result of the pathway activity
  (food eaten, ability to move..)

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3) Selection and replication
Based on fitness values (normalized sum)
Each individual take a slice in a 0-1 bar
Repeat until we have a full population
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4) Mutations
a) Initial configuration
b) Duplication of DNA strand
c) DNA point mutation (domain structure changes)
d) Domain duplication (changes internal behaviour)
Duplication of Bio-process
Changing affinity file
Addition of binders, changing internal pi-process
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Mutations (2)
Modification of internal process manipulation of
the Pi-process AST
Only fixed transformations (have to match know
structure)
Must have sense biologically (further constraints
on what is technically possible)
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An example MAPK
The mitogen-activated protein kinase cascade

• Basic structure well conserved
• Three kinases in the cascade
• Phosphorylation at two sites
• Relay signals from membrane
• Stimulus / response curve very steep

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MAPK known facts

• Other signalling pathways use just a kinase
• Why three?
• Cascade arrangement and pathway dynamics
• Ultrasensitivity
• Ultrasensitivity important for biological
  function
• Noise filtering switch-like circuit
• Depends upon dual-collision double phosphorylation

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How MPAK evolved?

• How we reached the three kinases configuration?
• Are other configuration possible?
• Which intermediate steps lead to the final
  configuration?
• It is known that the high degree of
  ultrasensitivity depends also upon dual-collision
  double phosphorylation
• How have this structure arisen?
• Through which steps was it combined with the
  cascade configuration? (future work)

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MAPK experiment setup
Signals, 2-level phosphatases,kinases
Fitness ratio(area1) ratio(area2)
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Our results
Fitness
First phospatase added to pathway
First kinase activation (signal turn on)
Generations
Fitness
Generations
Have we obtained MAPK? Not really, but we had
interesting variations
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Possible explanations

• Case C)
• We allowed self-phosphorilation
• Response is quick (as quick as having 2 kinases)
• But phosphatases can target only one protein
  (signal switch off is slower)
• Case B)
• Only one phosphatase was introduced
• Signal switch off slower also in this case

MAPK cascade model
Typical curves for c) and b)
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Cluster computation

• Parallelization of execution
• Execute independent, sequential simulations on
  different processors
• Prepare simulation input for thewhole population
  in a generation
• Launch them on different nodes
• Gather results on a central node
• Compute fitness, duplicate and mutate
• Return to 1.
• Thousand of individuals mapped onto hundreds of
  CPUs
• Most expensive part of algorithm is distributed

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Cluster computation
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Conclusions and future work

• Designed a framework for studying evolution, both
  formal and practical
• Mutations for bio-processes
• Tools to automate the whole process
• Applied the framework to a biological example
• A good test for our approach, we got interesting
  results
• Plans to extend it to add more mutations,
  constraints, control of the process
• Also easier ways to write fitness functions
• Use the extended framework to answer more
  questions on our MAPK example

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Thank you! Any question?