BioSimWare: A P Systems-based Simulation Environment for Biological - PowerPoint PPT Presentation

BioSimWare: A P Systems-based Simulation Environment for Biological Systems Daniela Besozzi 1 , Paolo Cazzaniga 2 , Giancarlo Mauri 2 , Dario Pescini 2 Universit` a degli Studi di Milano Dipartimento di Informatica e Comunicazione Via Comelico 39, 20135 Milano, Italy besozzi@dico.unimi.it Universit` a degli Studi di Milano-Bicocca Dipartimento di Informatica, Sistemistica e Comunicazione Viale Sarca 336, 20126 Milano, Italy cazzaniga/mauri/pescini@disco.unimib.it

Outline 1 BioSimWare 2 Stochastic Simulations Algorithms for Single and Multi-Volume Systems 3 Tools for The Analysis of Stochastic Simulations Parameter Estimation (PE) Parameter sweep applications (PSA) 4 Applications The Schl¨ ogl System The Brussellator Stiff Systems Bacterial Chemotaxis Simulation of Fredkin Circuits by Chemical Reaction Systems 5 Conclusion

Outline 1 BioSimWare 2 Stochastic Simulations Algorithms for Single and Multi-Volume Systems 3 Tools for The Analysis of Stochastic Simulations Parameter Estimation (PE) Parameter sweep applications (PSA) 4 Applications The Schl¨ ogl System The Brussellator Stiff Systems Bacterial Chemotaxis Simulation of Fredkin Circuits by Chemical Reaction Systems 5 Conclusion

Introduction BioSimWare is a simulation environment based on P systems, that provides a user-friendly framework for the modeling of biological systems ranging from cellular processes to population phenomena. substances (objects) reactions (evolution rules) b+c→(a, here) b a a→(a, out) a c b c c b c a a a 3 c a a+b→(c, here) a b c c→(c', out) b c a 2 a+c→(b, out) c'→(c, in 2 ) 1 membrane organelles (regions)

User Interface: rules specification

User Interface: system conditions specification

User Interface: plot of the dynamics

Outline 1 BioSimWare 2 Stochastic Simulations Algorithms for Single and Multi-Volume Systems 3 Tools for The Analysis of Stochastic Simulations Parameter Estimation (PE) Parameter sweep applications (PSA) 4 Applications The Schl¨ ogl System The Brussellator Stiff Systems Bacterial Chemotaxis Simulation of Fredkin Circuits by Chemical Reaction Systems 5 Conclusion

Available simualtion algorithm Single Volume SSA tau leaping adaptive tau leaping average tau leaping dynamics ODE integrator Multi Volume DPP tau-DPP Stau-DPP

Outline 1 BioSimWare 2 Stochastic Simulations Algorithms for Single and Multi-Volume Systems 3 Tools for The Analysis of Stochastic Simulations Parameter Estimation (PE) Parameter sweep applications (PSA) 4 Applications The Schl¨ ogl System The Brussellator Stiff Systems Bacterial Chemotaxis Simulation of Fredkin Circuits by Chemical Reaction Systems 5 Conclusion

PE: the goal We would like to reproduce the target dynamics via stochastic simulations: 760 740 720 700 680 molecules 660 640 620 600 580 target generated 560 0 0.5 1 1.5 2 2.5 3 3.5 time [a.u.] not necessarily using the same set of constants.

PE: the problem Quantify the “distance” among the dynamics and find the closest one 760 740 720 700 680 molecules 660 640 620 600 target 0.00245015 0.0015 580 0.001 0.0005 0.0001 560 0 0.5 1 1.5 2 2.5 3 3.5 time[a.u.]

The fitness: Standard Distance

The fitness: tricks Facts related to intrinsic noise that should not be neglected: each outcome j is quantitatively different { X ( τ i ) } j not evenly sampled { τ i } j not same number of points {� = X ( τ i ) } j in the thermodynamic limit { X ( τ i ) } → [ X ]( t i ) exploit ensemble behavior (may flatten oscillations, not in phase outcome) ? � F ( X ( τ i )) � = F ( � X ( τ i ) � ) same parameters, possibly (almost always), generate different values of the fitness function (“weak convergence”)

The fitness: “Area” distance

Reconstructed dynamics 1500 HC PSO Target 1450 1400 1350 CheYp Molecules 1300 1250 1200 1150 1100 0 0.05 0.1 0.15 0.2 Time [a.u.]

Parameter sweep applications (PSA) A PSA consists in a repeated execution of an application (usually performed a large number of times), where each execution is achieved using a different parametrisation. In the context of biochemical stochastic models a PSA could be viewed as PSA = ( P ; D ; M ) , where P = ( p 1 ; . . . ; p n ) is the set of parametrisations with p i = ( x i 0 ; c i ) D = ( d 1 ; . . . ; d n ) d i = ( x i ( 0 ); . . . ; x i ( t )) where t is the halting time of the simulation i M is the biochemical model that provides the map p i → d i

PSA: EGEE Grid EGEE project infrastructure, a wide area grid platform for scientific applications, com- posed of thousands of CPUs, which im- plements the Virtual Organisation (VO) paradigm. More than 90 partners in 32 countries, organised in 13 Federations A Grid infrastructure spanning almost 240 sites across 45 countries An infrastructure of 41,000 CPU available to users 24 hours a day, 7 days a week More than 5 Petabytes (5 million Gigabytes) of storage Sustained and regular workloads of 30K jobs/day, reaching up to 98K jobs/day

Perturbed parameters fitness 20000 18000 16000 14000 fitness fitness 12000 10000 8000 100 6000 90 4000 80 2000 70 60 0 0 50 10 40 c i perturbation 20 30 30 20 40 10 c i 50 60 0 6500 6000 5500 5000 fitness fitness 4500 4000 3500 3000 0.0005 2500 0.00045 0.0004 0.00035 2000 0.0003 0 0.00025 5e-05 0.0002 0.0001 0.00015 0.0002 0.00025 0.0003 0.00015 0.0001 5e-05 0

Outline 1 BioSimWare 2 Stochastic Simulations Algorithms for Single and Multi-Volume Systems 3 Tools for The Analysis of Stochastic Simulations Parameter Estimation (PE) Parameter sweep applications (PSA) 4 Applications The Schl¨ ogl System The Brussellator Stiff Systems Bacterial Chemotaxis Simulation of Fredkin Circuits by Chemical Reaction Systems 5 Conclusion

The Schl¨ ogl System 700 3 · 10 − 7 r 1 : A + 2 X − → 3 X 600 10 − 4 500 r 2 : 3 X − → A + 2 X X Molecules 400 10 − 3 300 r 3 : B − → 3 X 200 3 . 5 r 4 : X − → B 100 0 0 5 10 15 20 Time [a.u.] A = 1 · 10 5 B = 2 · 10 5 X = 250 800 1e+06 900000 700 800000 600 700000 500 600000 X Molecules Frequency 400 500000 400000 300 300000 200 200000 100 100000 0 0 0 50000 100000 150000 200000 250000 300000 350000 400000 0 100 200 300 400 500 600 700 800 Time [a.u.] X Molecules

The Brusselator 1 r 1 : A − → X 5 · 10 − 3 r 2 : B + X − → Y 2 . 5 · 10 − 5 r 3 : 2 X + Y − → 3 X 1 . 5 r 4 : X − → λ A = X = 200 B = 600 Y = 300

Comparison GA & PSO: Oscillating Brusselator 2500 PSO1 X 20000 PSO2 Y GA X target Average Best Fitness 2000 Y target 15000 Molecules 1500 10000 1000 500 5000 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 5 10 15 20 25 Fitness Evaluations Time [a.u.] 1 PSO1 PSO2 GA 0.8 Successful Runs 0.6 PSO1/2 best performers 0.4 GA worst average fitnesses 0.2 dynamics faithfully 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 reconstructed Fitness Evaluations

Comparison GA & PSO: Damped Brusselator 1800 400 PSO1 X PSO2 Y 1600 350 GA X target Average Best Fitness Y target 1400 300 Molecules 1200 250 1000 200 800 150 600 100 400 50 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 5 10 15 20 25 Fitness Evaluations Time [a.u.] 50 PSO1 PSO2 GA 40 Successful Runs 30 PSO1/2 best performers 20 GA worst average fitnesses 10 dynamics unfaithfully 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 reconstructed Fitness Evaluations

Stiff systems: an example A system is said to be stiff if is characterized by well-separeted fast and slow dynamical modes, the fastest of which is stable. The decaying dimerization model: 1 r 1 : S 1 − → λ 10 r 2 : S 1 + S 1 − → S 2 103 r 3 : S 2 − → S 1 + S 1 0 . 1 r 4 : S 2 − → S 3 S 1 = 10 4 S 2 = S 3 = 0 SSA tau leaping adaptive tau leaping 2 . 46 · 10 7 1 · 10 6 average number of steps 945 total execution time 175h 1m 11h 47m 1m 51s

Decaying dimerization: algorithms comparison 5000 5000 4000 4000 S2 S2 3000 3000 Molecules Molecules 2000 2000 S3 S3 1000 S1 1000 S1 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [a.u.] Time [a.u.] 5000 5000 SSA tau-leaping adaptive tau-leaping 4000 4000 S2 S2 3000 3000 Molecules Molecules 2000 2000 S3 S3 1000 S1 1000 S1 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [a.u.] Time [a.u.]

Bacterial chemotaxis Chemotaxis allows bacteria to respond to ligand concentration gradients in their surroundings: random walk through an homogeneous environment → high switching frequency of flagellar rotation directional swimming in presence of ligand concentration gradient → reduced switching frequency of flagellar rotation adaptation: if ligand concentration remains constant → switching frequency is reset to random walk level