P Systems Model Optimisation by Means of Evolutionary Based Search Algorithms

PSystemModelOp/misa/onbyMeansofEvolu/onaryBasedSearch

Algorithms

C.García‐Mar+nez,C.Lima,

J.Twycross,M.Lozano,N.Krasnogor

1

Outline

• Mo+va+on:Systems&Synthe+cBiology,PSystemsbasedmodeling

• Methods&ExperimentalSetup

• ResultsandDiscussion

• Conclusions

2

/136

•The Cell senses the environment and its own internal states•Makes Plans, Takes Decisions and Act•Evolution is the master programmer

3

The Cell as an Intelligent (Evolved) Machine

Cell

Internal States

Environmental Inputs

Actions

Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.

3

/136

•The Cell senses the environment and its own internal states•Makes Plans, Takes Decisions and Act•Evolution is the master programmer

3

The Cell as an Intelligent (Evolved) Machine

Cell

Internal States

Environmental Inputs

Actions

Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.

Wikimedia Commons

3

/136

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

•Moreover, these patterns are organised in non-trivial/non-random hierarchies

•Each network motif carries out a specific information-processing function

4

“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)

Radu Dobrin et al., Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network. BMC Bioinformatics. 2004; 5: 10.

4

/1365

Y positively regulates X

Negative autoregulation

Positive autoregulation

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

Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)

5

/1366

Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)

•The correct abstract ions facilitates understanding in complex systems.

•Provide a route to engineering , programming and evolving cells and their models

6

7

7

• Cells(andmostbiologists)don’tdodifferen/alcalculus!

• Psystemsareaexecutablespecifica/onsthatcloselymimicbiologicalreality.

• Theseareprogramsthatexplicitlymimictheinternalbehaviorofcellsystems.

• Theseprogramsareexecutedinavirtualmachinethatcapturestheintrinsicstochas5cityinherentinbiology

7

FundamentalECChallenge

• Learningaprogramwithstochas/cbehaviorvs.learningaPsystem.

•A cell is a living example of distributed stochastic computing.

function f1(p1,p2,p3,p4){if (p1<p2) and (rand<0.5) print p3else print p4}

function f1(p1,p2,p3,p4){if (p1<p2) RND print p3 RNDelse RND print p4 RND}

8

ModularAssemblyofPSystems

• Modules:setofrulesrepresen/ngmolecularinterac/onsthatoccuroNen.

• Elementalmodules:Degrada/on,complexa/on,unregulatedgeneexpression,nega/vegeneexpression,etc.

• Combinatorics:Combina/onofbasicmodules(building‐blocks)originatesmorecomplexmodules,allowingmodularandhierarchicalmodellingwithPsystems.

• Challenge:Explorethelargecombinatorialspaceofmodulesandcorrespondingparameters.

9

/136

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.

1010

/136

Parameter Optimisation in Metabolic Models

11

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

Evolving P Systems Structures

12

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

Outline

• Mo/va/on:Systems&Synthe/cBiology,PSystemsbasedmodeling

• Methods&ExperimentalSetup

• ResultsandDiscussion

• Conclusions

13

Methods&ExperimentalSetup

• Comparedifferentevolu/onaryalgorithmstoop/miseparameters(kine/cconstants)inPsystems.

• Fourtestcasesofincreasingdifficultyanddimension:1.TC1:Pulsegeneratorfordifferentini/alcondi/ons(13parameters).

2.TC2:SameproblemasTC1butwithalargerparameters’domain.

3.TC3:Moregeneralpulsegenerator:feed‐forwardloopmo/f(18parameters).

4.TC4:Bandwidthdetector(34parameters).

• Experimentalbudgetwasrestrictedto1000func/onevalua/ons.

14

TargetModels

15

TargetModels

•HighlyDimensional•Noisy&Uncertainoutcomes•Non‐lineari+es•ExpensiveFunc+onevalua+ons

15

TargetModels

•HighlyDimensional•Noisy&Uncertainoutcomes•Non‐lineari+es•ExpensiveFunc+onevalua+ons

Op+misa+onHell!

15

Evolu/onaryAlgorithms

• CovarianceMatrixAdapta/onAlgorithm(CMA‐ES)

• Differen/alEvolu/on(DE)

• Opposi/on‐BasedDifferen/alEvolu/on(ODE)

• Real‐CodedGene/cAlgorithm(GA)

• VariableNeighbourhoodSearchwithEvolu/onaryComponents(VNS‐ECsv1andv2)

16

ExperimentalDetails

• Fitnessofagivencandidatesolu/onisgivenby:1. RunthecorrespondingPsystemwiththe

mul/compartmentGillespiestochas/csimula/onalgorithm(20runs).

2. Averagetheoutput/meseriesofallrunsandcalculatethedifferencetothetargetseries,usingtherandomlyweightedsummethod.

• Be\er(forguidingthesearch)thansimpleconsideringtheRMSE,par/cularlywhen/meseriesrangeroverdifferentscales.

• Op/misa/onresultsareaveragedover50runs.

17

Outline

• Mo/va/on:Systems&Synthe/cBiology,PSystemsbasedmodeling

• ExperimentalSetup

• ResultsandDiscussion

• Conclusions

18

Results

19

Discussion

• AlgorithmsrankedaccordingtoRMSE.• Mann‐WhitneyUtestwithp‐value=0.05todeterminewhichalgorithmsperformsignificantlybe\erthanothers.

• ForTC1,mostalgorithmsperformequallywell,withexcep/ontoCMA‐ESandVNS‐EC1.

• ForTC2,wecanfindsignificantdifferencesbetweenalgorithms,whereGAisthebe\er.

• Reducingbiologicalknowledge(fromTC1toTC2)clearlyaffectstheperformanceofthealgorithms.

20

Discussion

• ForTC3,manyalgorithmsperformsimilar,butDE,ODE,andGAseemtoperformslightlybe\er.SimilartoTC1butnowVNS‐EC2performsconsiderablyworse.

• ForTC4,wherethereisalargernumberofparameters,resultsaresignificantlydifferentfromotherproblems.

• VNS‐ECsnowperformsignificantlybe\erthanremainingapproaches.

• CMA‐ES,ODE,andDEperformsimilarly,whileGAistheleastcompe//ve.

21

Discussion

• Ingeneral,GA,ODE,andDEperformbe\erforproblemswithfewparameters(13and18).GAperformsbe\erwhenbiologicalknowledgeisreduced.

• Ontheotherhand,VNS‐ECsperformbe\erforthelargerproblem(38parameters).

• Whyisthis?Thenumberofevalua/onsallowedissmall(1000).Let’shavealook…

22

BestFitness

23

BestFitness

• Twoimportantobserva/ons:1. ForTC4(largernumberofparameters),GA,DE,and

ODEreducetheirconvergencespeedsbecauseevolvingpopula/onsofindividualsconsumesmanyresources.However,VNS‐ECswhichfocusthesearchononesolu/onmakeabe\erusageofthereducedbudget.

2. Whentheprobleminvolvesfewerparameters,theallowedbudgetisenoughtoproperlyconvergeapopula/onofsolu/ons.Inthiscase,VNS‐ECsarenotcompe//veanymore.

24

AverageModelFit

• TestCase1

• TestCase2

25

AverageModelFit

• TestCase3

Forprotein1,allalgorithmshavesimilaroutputtothetarget.

26

AverageModelFit

• TestCase4

27

Outline

• Mo/va/on:Systems&Synthe/cBiology,PSystemsbasedmodeling

• Methods&ExperimentalSetup

• ResultsandDiscussion

• Conclusions

28

Conclusions• Considered4testcasesofincreasingdifficulty.• Limitedcomputa/onalresources(1000evalua/ons)havebeenimposedgiventheincreased/metoevaluatecandidatesolu/ons.

• Forthisexperimentalsetup,ithasbeenfoundthat:1. Whennumberofkine/cconstantsissmall,GA,DE,andODEare

robustop/misers.2. Whennumberofparametersincreases,theVNS‐Ecsobtain

be\erresults.

• DE(and,notreported,PSO)giveagoodcompromiseofquality/speedandconfigura/oneffortforsmalltomediumsizeproblems.

• Forlargerproblems,VNS‐Ecs(withouttoomanyparameters)seemthewaytogo.

• Fitnesscriterionmustberevisited!!!

29

/136

Acknowledgements

•Jonathan Blake

•Claudio Lima

•Francisco Romero-Campero

•Karima Righetti

•Jamie Twycross

Integrated Environment

Machine Learning & Optimisation

Modeling & Model Checking

Molecular Micro-Biology

Stochastic Simulations

Members of my team working on SB2

EP/E017215/1

EP/H024905/1

BB/F01855X/1

BB/D019613/1

University of NottinghamProf. M. Camara, Dr. S. Heeb, Dr. G. Rampioni, Prof. P. WilliamsWeizmann Institute of ScienceProf. D. Lancet, Prof. I. Pilpel

3030

31

31

31

31