A Formal and Integrated
Framework to Simulate
Evolution of Biological Pathways
Lorenzo Dematte’, Corrado Priami, Alessandro Romanel and Orkun Soyer
CMSB 07
Edinburgh, 20/09/2007
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
BetaWB language
Bio-process
P
Interface
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.
The BetaWB language
Operational semantics: set of syntax-driven rules that automatically infer the possible future
of the system.
A
A
P
A
intra
P’
B
P
Q
inter
Monomolecular
A
B
P’
Q’
Bimolecular
B
C
R
Q
B
Q
Complexes
C
D
R
C
B
join
Events
C
P
D
BetaWB extensions: deterministic events
let Kinase : bproc = #(x:1,Alpha)
[ @(2).nil ];
let A : bproc = #(y:1,Gamma)
[ @(2).nil ];
when (A: step=1500) delete(500);
when (A: step=2500) new(500);
when (Kinase: time=3.5) new(2000);
when (|A|<10) new(2000);
when (|A|=1000) delete(200);
Fixed step
Cardinality
Time
“Injection” or “wash out” of substances
Deterministic events
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.
Evolutionary Framework
• In silico evolution
– A population of individuals
– The behaviour of each
individual
– A measure of “success”
– Reproduction based on success
Replicate &
Mutate
7
A signalling or metabolic
pathway
Fitness function
Compositional Model For Signalling Pathways
A+ AA
O
O
+
A
Bio-process
Inact
Act
-
Internal pi-process
O
Evolutionary algorithm
1) Simulation
Each individual in the population is simulated separately using
the BetaWB stochastic simulator
Mapk1
Mapk1
Mapk1
Mapk1
Mapk
123
BetaWB
Simulator
• Stochastic simulator –
variant of next reaction
method
• Species based on
structural congruence
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..)
3) Selection and replication
Based on fitness values (normalized sum)
Each individual take a slice in a 0-1 bar
0.0
1.0
0.345
Generate Random Number
Take individual, replicate it
Repeat until we have a full population
Possibly, Mutate it
4) Mutations
a) Initial configuration
b) Duplication of DNA strand
c) DNA point mutation (domain structure changes)
d) Domain duplication (changes internal behaviour)
Changing affinity file
Duplication of
Bio-process
Addition of binders, changing
internal pi-process
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)
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
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
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)
MAPK experiment setup
Signals,
2-level phosphatases,
kinases
Area below the curve: how “quick” is response
Area above curve: “switch off” response
Switch off signal
Introduction of signal
Fitness: ratio(area1) – ratio(area2)
Our results
Fitness
First phospatase added to pathway
First kinase activation (signal turn on)
Fitness
Generations
Generations
Have we obtained MAPK?
Not really, but we had interesting “variations”
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)
Cluster computation
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
Thank you!
Any question?