This document discusses using evolutionary algorithms to optimize parameters in P systems, which are computational models of biological cells. Four test cases of increasing difficulty are used to compare different algorithms. The results show that genetic algorithms, differential evolution, and opposition-based differential evolution perform better for problems with fewer parameters, while variable neighbourhood search algorithms perform better for the largest problem with 38 parameters. This is because the evolutionary algorithms are less efficient at optimizing large populations within the limited evaluation budget, whereas variable neighbourhood search focuses on a single solution.

1. P System Model Op/misa/on by
Means of Evolu/onary Based Search
Algorithms
C. García‐Mar+nez, C. Lima,
J. Twycross, M. Lozano, N. Krasnogor
1

2. Outline
• Mo+va+on: Systems & Synthe+c Biology, P
Systems based modeling
• Methods & Experimental Setup
• Results and Discussion
• Conclusions
2

3. The Cell as an Intelligent (Evolved)
Machine
•The Cell senses the environment and its own
internal states
•Makes Plans, Takes Decisions and Act
•Evolution is the master programmer
Environmental Inputs
Internal States
Cell
Actions
Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.
3 /136
3

4. The Cell as an Intelligent (Evolved)
Machine
•The Cell senses the environment and its own
internal states
•Makes Plans, Takes Decisions and Act
•Evolution is the master programmer
Environmental Inputs
Internal States
Cell
Actions
Wikimedia Commons
Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.
3 /136
3

5. Network Motifs: Evolution’s Preferred Circuits
•Biological networks are complex and vast
•To understand their functionality in a scalable way one must
choose the correct abstraction
“Patterns that occur in the real network significantly
more often than in randomized networks are called
network motifs” Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation
network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)
•Moreover, these patterns are organised in non-trivial/non-
random hierarchies Radu Dobrin et al., Aggregation of topological motifs in the Escherichia
coli transcriptional regulatory network. BMC Bioinformatics. 2004; 5: 10.
•Each network motif carries out a specific information-
processing function
4 /136
4

6. Y positively Negative Positive
regulates X autoregulation autoregulation
Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation
network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)
The C1-FFL is a ‘sign-sensitive delay’ element and a persistence detector.
The I1-FFL is a pulse generator and response accelerator
U. Alon. Network motifs: theory and experimental approaches. Nature Reviews Genetics (2007) vol. 8 (6) pp. 450-461
5 /136
5

7. •T h e correct abstractions
facilitates understanding in
complex systems.
•Provide a route to engineering ,
programming and evolving Shai S. Shen-Orr et al., Network motifs in the
transcriptional regulation network of Escherichia
cells and their models coli. Nature Genetics 31, 64 - 68 (2002)
6 /136
6

8. 7

9. 7

10. • Cells (and most biologists)
don’t do differen/al
calculus!
• P systems are a executable
specifica/ons that closely
mimic biological reality.
• These are programs that
explicitly mimic the internal
behavior of cell systems.
• These programs are
executed in a virtual
machine that captures the
intrinsic stochas5city
inherent in biology
7

11. Fundamental EC Challenge
• Learning a program with stochas/c behavior
vs. learning a P system.
function f1(p1,p2,p3,p4) function f1(p1,p2,p3,p4)
{ {
if (p1<p2) and (rand<0.5) if (p1<p2) RND
print p3 print p3 RND
else else RND
print p4 print p4 RND
} }
•A cell is a living example of distributed
stochastic computing.
8

12. Modular Assembly of P Systems
• Modules: set of rules represen/ng molecular interac/ons
that occur oNen.
• Elemental modules: Degrada/on, complexa/on,
unregulated gene expression, nega/ve gene expression, etc.
• Combinatorics: Combina/on of basic modules (building‐
blocks) originates more complex modules, allowing modular
and hierarchical modelling with P systems.
• Challenge: Explore the large combinatorial space of modules
and corresponding parameters.
9

13. Multi-Objective Optimisation in
Morphogenesis
Rui Dilão, Daniele Muraro, Miguel
Nicolau, Marc Schoenauer.
Validation of a morphogenesis
model of Drosophila early
development by a multi-objective
evolutionary optimization algorithm.
Proc. 7th European Conference on
Evolutionary Computation, ML and
Data Mining in BioInformatics
(EvoBIO'09), April 2009.
10 /136
10

14. Parameter Optimisation in
Metabolic Models
A. Drager et al. (2009).
Modeling metabolic networks
in C. glutamicum: a
comparison of rate laws in
combination with various
parameter optimization
strategies. BMC Systems Biol
ogy 2009, 3:5
11 /136
11

15. Evolving P Systems Structures
F. Romero-Campero,
H.Cao, M. Camara, and N.
Krasnogor. Structure and
parameter estimation for
cell systems biology
models. Proceedings of the
Genetic and Evolutionary
Computation Conference
(GECCO-2008), pages
331-338. ACM Publisher,
2008.
H. Cao, F.J. Romero-
Campero, S. Heeb, M.
Camara, and N. Krasnogor.
Evolving cell models for
systems and synthetic
biology. Systems and
Synthetic Biology , 2009
12 /136
12

16. Outline
• Mo/va/on: Systems & Synthe/c Biology, P
Systems based modeling
• Methods & Experimental Setup
• Results and Discussion
• Conclusions
13

17. Methods & Experimental Setup
• Compare different evolu/onary algorithms to op/mise
parameters (kine/c constants) in P systems.
• Four test cases of increasing difficulty and dimension:
1. TC1: Pulse generator for different ini/al condi/ons (13
parameters).
2. TC2: Same problem as TC1 but with a larger parameters’
domain.
3. TC3: More general pulse generator: feed‐forward loop mo/f
(18 parameters).
4. TC4: Bandwidth detector (34 parameters).
• Experimental budget was restricted to 1000 func/on
evalua/ons.
14

18. Target Models
15

19. Target Models
• Highly Dimensional
• Noisy & Uncertain outcomes
• Non‐lineari+es
• Expensive Func+on evalua+ons
15

20. Target Models
• Highly Dimensional
• Noisy & Uncertain outcomes Op+misa+on Hell!
• Non‐lineari+es
• Expensive Func+on evalua+ons
15

21. Evolu/onary Algorithms
• Covariance Matrix Adapta/on Algorithm (CMA‐
ES)
• Differen/al Evolu/on (DE)
• Opposi/on‐Based Differen/al Evolu/on (ODE)
• Real‐Coded Gene/c Algorithm (GA)
• Variable Neighbourhood Search with
Evolu/onary Components (VNS‐ECs v1 and v2)
16

22. Experimental Details
• Fitness of a given candidate solu/on is given by:
1. Run the corresponding P system with the
mul/compartment Gillespie stochas/c simula/on
algorithm (20 runs).
2. Average the output /me series of all runs and
calculate the difference to the target series, using the
randomly weighted sum method.
• Beer (for guiding the search) than simple
considering the RMSE, par/cularly when /me
series ranger over different scales.
• Op/misa/on results are averaged over 50 runs.
17

23. Outline
• Mo/va/on: Systems & Synthe/c Biology, P
Systems based modeling
• Experimental Setup
• Results and Discussion
• Conclusions
18

24. Results
19

25. Discussion
• Algorithms ranked according to RMSE.
• Mann‐Whitney U test with p‐value=0.05 to
determine which algorithms perform significantly
beer than others.
• For TC1, most algorithms perform equally well,
with excep/on to CMA‐ES and VNS‐EC1.
• For TC2, we can find significant differences
between algorithms, where GA is the beer.
• Reducing biological knowledge (from TC1 to TC2)
clearly affects the performance of the algorithms.
20

26. Discussion
• For TC3, many algorithms perform similar, but DE,
ODE, and GA seem to perform slightly beer.
Similar to TC1 but now VNS‐EC2 performs
considerably worse.
• For TC4, where there is a larger number of
parameters, results are significantly different from
other problems.
• VNS‐ECs now perform significantly beer than
remaining approaches.
• CMA‐ES, ODE, and DE perform similarly, while GA
is the least compe//ve.
21

27. Discussion
• In general, GA, ODE, and DE perform beer for
problems with few parameters (13 and 18). GA
performs beer when biological knowledge is
reduced.
• On the other hand, VNS‐ECs perform beer for
the larger problem (38 parameters).
• Why is this? The number of evalua/ons
allowed is small (1000). Let’s have a look…
22

28. Best Fitness
23

29. Best Fitness
• Two important observa/ons:
1. For TC4 (larger number of parameters), GA, DE, and
ODE reduce their convergence speeds because
evolving popula/ons of individuals consumes many
resources. However, VNS‐ECs which focus the search
on one solu/on make a beer usage of the reduced
budget.
2. When the problem involves fewer parameters, the
allowed budget is enough to properly converge a
popula/on of solu/ons. In this case, VNS‐ECs are not
compe//ve anymore.
24

30. Average Model Fit
• Test Case 1
• Test Case 2
25

31. Average Model Fit
• Test Case 3
For protein1, all
algorithms have similar
output to the target.
26

32. Average Model Fit
• Test Case 4
27

33. Outline
• Mo/va/on: Systems & Synthe/c Biology, P
Systems based modeling
• Methods & Experimental Setup
• Results and Discussion
• Conclusions
28

34. Conclusions
• Considered 4 test cases of increasing difficulty.
• Limited computa/onal resources (1000 evalua/ons) have
been imposed given the increased /me to evaluate
candidate solu/ons.
• For this experimental setup, it has been found that:
1. When number of kine/c constants is small, GA, DE, and ODE are
robust op/misers.
2. When number of parameters increases, the VNS‐Ecs obtain
beer results.
• DE (and, not reported, PSO) give a good compromise of quality/speed
and configura/on effort for small to medium size problems.
• For larger problems, VNS‐Ecs (without too many parameters) seem
the way to go.
• Fitness criterion must be revisited!!!
29

35. Acknowledgements
Members of my team working on SB2 University of Nottingham
Prof. M. Camara, Dr. S. Heeb, Dr. G.
•Jonathan Blake Integrated Environment
Rampioni, Prof. P. Williams
•Claudio Lima Weizmann Institute of Science
Machine Learning & Optimisation
Prof. D. Lancet, Prof. I. Pilpel
•Francisco Romero-Campero Modeling & Model Checking
•Karima Righetti Molecular Micro-Biology
•Jamie Twycross Stochastic Simulations
BB/F01855X/1
BB/D019613/1
EP/E017215/1
EP/H024905/1
30 /136
30

36. 31
31

37. 31
31