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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion Modelling protein-trafficking with Bio-PEPA Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling protein-trafficking with Bio-PEPA

Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh 29 April 2013

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Outline

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Process algebras

◮ history

◮ developed to model concurrent computing (mid 1980’s) ◮ focus on dynamic behaviour ◮ originally no notion of time or space, some extensions ◮ Hillston developed PEPA, stochastic process algebra (1996) ◮ Hillston developed ODE interpretation of PEPA (2005) Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Process algebras

◮ history

◮ developed to model concurrent computing (mid 1980’s) ◮ focus on dynamic behaviour ◮ originally no notion of time or space, some extensions ◮ Hillston developed PEPA, stochastic process algebra (1996) ◮ Hillston developed ODE interpretation of PEPA (2005)

◮ Bio-PEPA, a biological process algebra (2009)

◮ close match between modelling artificial and natural systems ◮ developed by Ciocchetta and Hillston ◮ extension of PEPA, functional rates and stoichiometry Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Process algebras (cont)

◮ what is a process algebra?

◮ compact and elegant formal language ◮ behaviour given by semantics defined mathematically ◮ classical process algebras: labelled transition systems ◮ stochastic process algebras: continuous time Markov chains Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Process algebras (cont)

◮ what is a process algebra?

◮ compact and elegant formal language ◮ behaviour given by semantics defined mathematically ◮ classical process algebras: labelled transition systems ◮ stochastic process algebras: continuous time Markov chains

◮ why use Bio-PEPA?

◮ formalism to describe species and their interactions ◮ unambiguous and precise description ◮ different analyses available from a single description

stochastic simulation (individual view), continuous time Markov chain with levels (abstract view) deterministic simulation (population view),

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA (in brief)

◮ species: reactions, stoichiometry, locations

S@L

def

= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L where opi ∈ {↓, ↑, ⊕, ⊖, ⊙}

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA (in brief)

◮ species: reactions, stoichiometry, locations

S@L

def

= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L where opi ∈ {↓, ↑, ⊕, ⊖, ⊙}

◮ model: quantities of species, interaction between species

P

def

= S1@L1(x1) ⊲

⊳

∗ . . . ⊲

⊳

∗ Sp@Lp(xp) Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA (in brief)

◮ species: reactions, stoichiometry, locations

S@L

def

= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L where opi ∈ {↓, ↑, ⊕, ⊖, ⊙}

◮ model: quantities of species, interaction between species

P

def

= S1@L1(x1) ⊲

⊳

∗ . . . ⊲

⊳

∗ Sp@Lp(xp)

◮ other information required for modelling

L compartments and locations, dimensionality, sizes N species quantities, minimums, maximums, step size K parameter definitions F functional rates for reactions, definition of fα

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA (in brief)

◮ species: reactions, stoichiometry, locations

S@L

def

= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L where opi ∈ {↓, ↑, ⊕, ⊖, ⊙}

◮ model: quantities of species, interaction between species

P

def

= S1@L1(x1) ⊲

⊳

∗ . . . ⊲

⊳

∗ Sp@Lp(xp)

◮ other information required for modelling

L compartments and locations, dimensionality, sizes N species quantities, minimums, maximums, step size K parameter definitions F functional rates for reactions, definition of fα

◮ definition of behavioural semantics

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA Eclipse Plug-in

◮ software tool for Bio-PEPA modelling

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA Eclipse Plug-in

◮ software tool for Bio-PEPA modelling ◮ Eclipse front-end and separate back-end library

editor for the Bio-PEPA language

  • utline view for the reaction-centric view

graphing support via common plugin problems view User Interface parser for the Bio-PEPA language export facility (SBML; PRISM) ISBJava time series analysis (ODE, SSA) static analysis Core Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA Eclipse Plug-in

◮ software tool for Bio-PEPA modelling ◮ Eclipse front-end and separate back-end library

editor for the Bio-PEPA language

  • utline view for the reaction-centric view

graphing support via common plugin problems view User Interface parser for the Bio-PEPA language export facility (SBML; PRISM) ISBJava time series analysis (ODE, SSA) static analysis Core

◮ available for download at www.biopepa.org ◮ case studies, publications, manuals

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA Eclipse Plug-in (cont)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family ◮ Src inactive at perinuclear region, active at membrane

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family ◮ Src inactive at perinuclear region, active at membrane ◮ Src is trafficked in endosomes

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family ◮ Src inactive at perinuclear region, active at membrane ◮ Src is trafficked in endosomes ◮ results of experimental research

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family ◮ Src inactive at perinuclear region, active at membrane ◮ Src is trafficked in endosomes ◮ results of experimental research

After stimulation with growth factor, Src is found in endosomes with more inactive Src closer to the nucleus than further away. Most Src at the membrane is active. Hence, there is a gradient of inactive Src to active Src, and activation takes place in endosomes. (Sandilands et al, 2004)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK ◮ focus on active form of oncoprotein Src, member of Src family ◮ Src inactive at perinuclear region, active at membrane ◮ Src is trafficked in endosomes ◮ results of experimental research

After stimulation with growth factor, Src is found in endosomes with more inactive Src closer to the nucleus than further away. Most Src at the membrane is active. Hence, there is a gradient of inactive Src to active Src, and activation takes place in endosomes. (Sandilands et al, 2004) The persistence of active Src at the membrane is inversely related to the quantity of FGF added. (Sandilands et al, 2007)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Src: gradient from inactive to active

(Sandilands et al, Dev. Cell 7, 2004)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Src: persistence of response to FGF

(Sandilands et al, EMBO Reports 8, 2007)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE ◮ identification of recycling loops: number and type

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE ◮ identification of recycling loops: number and type ◮ assume one long and one short

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE ◮ identification of recycling loops: number and type ◮ assume one long and one short ◮ data is very limited

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE ◮ identification of recycling loops: number and type ◮ assume one long and one short ◮ data is very limited ◮ qualitative

◮ gradient of inactive versus active, activation within endosomes ◮ endosome movement is directional along

microfilaments/microtubules

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE ◮ identification of recycling loops: number and type ◮ assume one long and one short ◮ data is very limited ◮ qualitative

◮ gradient of inactive versus active, activation within endosomes ◮ endosome movement is directional along

microfilaments/microtubules

◮ quantitative

◮ estimates of endosome speeds and length of recycling loops ◮ timing from FGF stimulation experiment Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

membrane perinuclear region active Src inactive Src short loop long loop FGF FGFR

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@memb = (bind,1) << aSrc@memb + ... + (endo form,50) << aSrc@memb + (endo rel,50) >> aSrc@memb;

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@memb = (bind,1) << aSrc@memb + ... + (endo form,50) << aSrc@memb + (endo rel,50) >> aSrc@memb;

◮ endsome in short recycling loop

Endo@cyto = (endo form,1) >> Endo@cyto + (endo rel,1) << Endo@cyto + ... ;

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@memb = (bind,1) << aSrc@memb + ... + (endo form,50) << aSrc@memb + (endo rel,50) >> aSrc@memb;

◮ endsome in short recycling loop

Endo@cyto = (endo form,1) >> Endo@cyto + (endo rel,1) << Endo@cyto + ... ;

◮ model:

aSrc@memb[initial aSrc] <*> Endo@cyto[initial Endo]

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@memb = (bind,1) << aSrc@memb + ... + (endo form,50) << aSrc@memb + (endo rel,50) >> aSrc@memb;

◮ endsome in short recycling loop

Endo@cyto = (endo form,1) >> Endo@cyto + (endo rel,1) << Endo@cyto + ... ;

◮ model:

aSrc@memb[initial aSrc] <*> Endo@cyto[initial Endo]

◮ reactions

endo form: 50 aSrc@memb

  • >

Endo@cyto endo rel: Endo@cyto

  • >

50 aSrc@memb

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Two loop trafficking model – results

50000 100000 150000 200000 250000 300000 30 60 90 120 150 180 Quantity Time (minutes) different concentrations of FGF addition active Src (high concentration) FGFR (high concentration) active Src (low concentration) FGFR (low concentration)

addition after 60 minutes of FGF (average of 20 simulations)

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Other Bio-PEPA case studies

◮ Goldbeter’s model of oscillation of cyclin in the cell cycle ◮ Edelstein’s model for the acethylcholine receptor ◮ gp130/JAK/STAT pathway ◮ circadian clock in Neurospora ◮ circadian clock in Ostreococcus Tauri ◮ various models from BioModels Database

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Other Bio-PEPA case studies

◮ Goldbeter’s model of oscillation of cyclin in the cell cycle ◮ Edelstein’s model for the acethylcholine receptor ◮ gp130/JAK/STAT pathway ◮ circadian clock in Neurospora ◮ circadian clock in Ostreococcus Tauri ◮ various models from BioModels Database ◮ And now for something completely different . . .

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Other Bio-PEPA case studies

◮ Goldbeter’s model of oscillation of cyclin in the cell cycle ◮ Edelstein’s model for the acethylcholine receptor ◮ gp130/JAK/STAT pathway ◮ circadian clock in Neurospora ◮ circadian clock in Ostreococcus Tauri ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Other Bio-PEPA case studies

◮ Goldbeter’s model of oscillation of cyclin in the cell cycle ◮ Edelstein’s model for the acethylcholine receptor ◮ gp130/JAK/STAT pathway ◮ circadian clock in Neurospora ◮ circadian clock in Ostreococcus Tauri ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling ◮ emergency egress modelling Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Other Bio-PEPA case studies

◮ Goldbeter’s model of oscillation of cyclin in the cell cycle ◮ Edelstein’s model for the acethylcholine receptor ◮ gp130/JAK/STAT pathway ◮ circadian clock in Neurospora ◮ circadian clock in Ostreococcus Tauri ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling ◮ emergency egress modelling

◮ see www.biopepa.org for more details

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Conclusion

◮ Bio-PEPA

◮ biological process algebra ◮ formal and unambiguous description of a system ◮ behaviour derived mathematically ◮ various analyses can be applied to a model ◮ abstraction is a key principle Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Conclusion

◮ Bio-PEPA

◮ biological process algebra ◮ formal and unambiguous description of a system ◮ behaviour derived mathematically ◮ various analyses can be applied to a model ◮ abstraction is a key principle

◮ example of Bio-PEPA applied to modelling of protein

trafficking

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Acknowledgements

PEPA Group Cancer Research UK School of Informatics Edinburgh University of Edinburgh Margaret Frame Jane Hillston Emma Sandilands Stephen Gilmore Allan Clark SynthSys/CSBE Maria Luisa Guerriero University of Edinburgh Federica Ciocchetta Andrew Millar Adam Duguid Charl Troein Ozgur Akman

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Thank you

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

◮ well-defined Bio-PEPA model

P

def

= C1(ℓ1) ⊲

⊳

L1 . . .

⊲ ⊳

Lm−1 Cm(ℓm) with all Ci’s distinct Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

◮ well-defined Bio-PEPA model

P

def

= C1(ℓ1) ⊲

⊳

L1 . . .

⊲ ⊳

Lm−1 Cm(ℓm) with all Ci’s distinct Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

◮ well-defined Bio-PEPA model

P

def

= C1(ℓ1) ⊲

⊳

L1 . . .

⊲ ⊳

Lm−1 Cm(ℓm) with all Ci’s distinct

◮ well-defined Bio-PEPA system

P = V, N, K, F, Comp, P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Well-defined Bio-PEPA systems

◮ well-defined Bio-PEPA species

C

def

= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi’s distinct

◮ well-defined Bio-PEPA model

P

def

= C1(ℓ1) ⊲

⊳

L1 . . .

⊲ ⊳

Lm−1 Cm(ℓm) with all Ci’s distinct

◮ well-defined Bio-PEPA system

P = V, N, K, F, Comp, P

◮ well-defined Bio-PEPA model component with levels

◮ minimum and maximum concentrations/number of molecules ◮ fix step size, convert to minimum and maximum levels ◮ species S: 0 to NS levels Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-70
SLIDE 70

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-71
SLIDE 71

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-72
SLIDE 72

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-73
SLIDE 73

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-74
SLIDE 74

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-75
SLIDE 75

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

◮ S E

− → P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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SLIDE 76

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

◮ S E

− → P

◮ S′(ℓS′) ⊲

⊳

∗

E ′(ℓE ′) ⊲

⊳

∗

P′(ℓP′) where

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-77
SLIDE 77

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

◮ S E

− → P

◮ S′(ℓS′) ⊲

⊳

∗

E ′(ℓE ′) ⊲

⊳

∗

P′(ℓP′) where S′ def = (γ, 1) ↓ S′ E ′ def = (γ, 1) ⊕ E ′ P′ def = (γ, 1) ↑ P′

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-78
SLIDE 78

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

◮ S E

− → P

◮ S′(ℓS′) ⊲

⊳

∗

E ′(ℓE ′) ⊲

⊳

∗

P′(ℓP′) where S′ def = (γ, 1) ↓ S′ E ′ def = (γ, 1) ⊕ E ′ P′ def = (γ, 1) ↑ P′

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-79
SLIDE 79

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

◮ S(ℓS) ⊲

⊳

∗

E(ℓE) ⊲

⊳

∗

SE(ℓSE) ⊲

⊳

∗

P(ℓP) where S

def

= (α, 1) ↓ S + (β, 1) ↑ S E

def

= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E SE

def

= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE P

def

= (γ, 1) ↑ P

◮ S E

− → P

◮ S′(ℓS′) ⊲

⊳

∗

E ′(ℓE ′) ⊲

⊳

∗

P′(ℓP′) where S′ def = (γ, 1) ↓ S′ E ′ def = (γ, 1) ⊕ E ′ P′ def = (γ, 1) ↑ P′

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-80
SLIDE 80

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-81
SLIDE 81

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Choice, Cooperation for α ∈ L, Constant as expected

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

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SLIDE 82

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Choice, Cooperation for α ∈ L, Constant as expected ◮ Prefix rules

((α, κ) ↓ S)(ℓ)

(α,[S:↓(ℓ,κ)])

− − − − − − − − →c S(ℓ − κ) κ ≤ ℓ ≤ NS ((α, κ) ↑ S)(ℓ)

(α,[S:↑(ℓ,κ)])

− − − − − − − − →c S(ℓ + κ) 0 ≤ ℓ ≤ NS − κ ((α, κ) ⊕ S)(ℓ)

(α,[S:⊕(ℓ,κ)])

− − − − − − − − →c S(ℓ) κ ≤ ℓ ≤ NS ((α, κ) ⊖ S)(ℓ)

(α,[S:⊖(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS ((α, κ) ⊙ S)(ℓ)

(α,[S:⊙(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-83
SLIDE 83

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Choice, Cooperation for α ∈ L, Constant as expected ◮ Prefix rules

((α, κ) ↓ S)(ℓ)

(α,[S:↓(ℓ,κ)])

− − − − − − − − →c S(ℓ − κ) κ ≤ ℓ ≤ NS ((α, κ) ↑ S)(ℓ)

(α,[S:↑(ℓ,κ)])

− − − − − − − − →c S(ℓ + κ) 0 ≤ ℓ ≤ NS − κ ((α, κ) ⊕ S)(ℓ)

(α,[S:⊕(ℓ,κ)])

− − − − − − − − →c S(ℓ) κ ≤ ℓ ≤ NS ((α, κ) ⊖ S)(ℓ)

(α,[S:⊖(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS ((α, κ) ⊙ S)(ℓ)

(α,[S:⊙(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-84
SLIDE 84

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Choice, Cooperation for α ∈ L, Constant as expected ◮ Prefix rules

((α, κ) ↓ S)(ℓ)

(α,[S:↓(ℓ,κ)])

− − − − − − − − →c S(ℓ − κ) κ ≤ ℓ ≤ NS ((α, κ) ↑ S)(ℓ)

(α,[S:↑(ℓ,κ)])

− − − − − − − − →c S(ℓ + κ) 0 ≤ ℓ ≤ NS − κ ((α, κ) ⊕ S)(ℓ)

(α,[S:⊕(ℓ,κ)])

− − − − − − − − →c S(ℓ) κ ≤ ℓ ≤ NS ((α, κ) ⊖ S)(ℓ)

(α,[S:⊖(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS ((α, κ) ⊙ S)(ℓ)

(α,[S:⊙(ℓ,κ)])

− − − − − − − − →c S(ℓ) 0 ≤ ℓ ≤ NS

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-85
SLIDE 85

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ L

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

L Q

(α,v::u)

− − − − →c P′ ⊲

⊳

L Q′

α ∈ L

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-86
SLIDE 86

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ L

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

L Q

(α,v::u)

− − − − →c P′ ⊲

⊳

L Q′

α ∈ L

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-87
SLIDE 87

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ L

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

L Q

(α,v::u)

− − − − →c P′ ⊲

⊳

L Q′

α ∈ L

◮ operational semantics for stochastic relation −

→s P

(α,v)

− − − →c P′ V, N, K, F, Comp, P

(α,fα(v,N,K)/h)

− − − − − − − − − − →s V, N, K, F, Comp, P′

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-88
SLIDE 88

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ L

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

L Q

(α,v::u)

− − − − →c P′ ⊲

⊳

L Q′

α ∈ L

◮ operational semantics for stochastic relation −

→s P

(α,v)

− − − →c P′ V, N, K, F, Comp, P

(α,fα(v,N,K)/h)

− − − − − − − − − − →s V, N, K, F, Comp, P′

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting

slide-89
SLIDE 89

Process algebras Bio-PEPA Protein trafficking Model Results Other examples Conclusion

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ L

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

L Q

(α,v::u)

− − − − →c P′ ⊲

⊳

L Q′

α ∈ L

◮ operational semantics for stochastic relation −

→s P

(α,v)

− − − →c P′ V, N, K, F, Comp, P

(α,fα(v,N,K)/h)

− − − − − − − − − − →s V, N, K, F, Comp, P′

◮ Bio-PEPA system: P = T , P

Vashti Galpin Modelling protein-trafficking with Bio-PEPA 1st Quarterly Edinburgh Bioinformatics Meeting