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P Systems Model Optimisation by Means of Evolutionary Based Search Algorithms
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.
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P Systems Model Optimisation by Means of Evolutionary Based Search Algorithms
- 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 asan 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 asan 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’sPreferred 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 ecorrect 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
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- 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 SystemsStructures 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
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- 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
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- 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 myteam 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
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