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Spatio-temporal Biological Process Modelling Vashti Galpin - - PowerPoint PPT Presentation

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion Spatio-temporal Biological Process Modelling Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Spatio-temporal Biological Process Modelling

Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh 16 May 2012

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Outline

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Process algebras

◮ history

◮ developed to model concurrent computing (mid 1980’s) ◮ 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Process algebras

◮ history

◮ developed to model concurrent computing (mid 1980’s) ◮ 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

◮ close match between modelling artificial and natural systems ◮ developed by Ciocchetta and Hillston (2009) ◮ extension of PEPA, functional rates and stoichiometry Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Process algebras (cont)

◮ what is a process algebra?

◮ compact and elegant formal language ◮ behavior given by semantics defined mathematically ◮ classical process algebras: labelled transition systems ◮ stochastic process algebras: continuous time Markov chains Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Process algebras (cont)

◮ what is a process algebra?

◮ compact and elegant formal language ◮ behavior 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 interactions ◮ unambiguous, precise ◮ different analyses available from a single description

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

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA Eclipse Plug-in

◮ software tool for Bio-PEPA modelling

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA Eclipse Plug-in (cont)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Protein trafficking in the cell

◮ research from the Frame laboratory at Cancer Research UK

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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

There is more inactive Src in endosomes closer to the nucleus than those further away. Furthermore, almost all Src at the membrane is active. Hence, there is a gradient of inactive Src to active Src. (Sandilands et al, 2004)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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

There is more inactive Src in endosomes closer to the nucleus than those further away. Furthermore, almost all Src at the membrane is active. Hence, there is a gradient of inactive Src to active Src. (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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Src: gradient from inactive to active

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

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Src: persistence of response to FGF

(Sandilands et al, EMBO Reports 8, 2007)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Modelling

◮ work in progress: Bio-PEPA, HYPE

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Modelling

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

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Src trafficking

membrane perinuclear region 10 seconds 20 seconds

aSrc FGF FGFR aFGFR aSrc aFGFR aFGFR aSrc Src Src Src

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@mb = (bind,1) << aSrc@mb + (out sh,150) << aSrc@mb + (in sh,75) >> aSrc@mb + (in long,100) >> aSrc@mb;

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@mb = (bind,1) << aSrc@mb + (out sh,150) << aSrc@mb + (in sh,75) >> aSrc@mb + (in long,100) >> aSrc@mb;

◮ endsome in short recycling loop

Endo short@cyto = (out sh,1) >> Endo short@cyto + (in sh,1) << Endo short@cyto + ... ;

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@mb = (bind,1) << aSrc@mb + (out sh,150) << aSrc@mb + (in sh,75) >> aSrc@mb + (in long,100) >> aSrc@mb;

◮ endsome in short recycling loop

Endo short@cyto = (out sh,1) >> Endo short@cyto + (in sh,1) << Endo short@cyto + ... ;

◮ model:

aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Simplified Bio-PEPA model

◮ active Src at membrane

aSrc@mb = (bind,1) << aSrc@mb + (out sh,150) << aSrc@mb + (in sh,75) >> aSrc@mb + (in long,100) >> aSrc@mb;

◮ endsome in short recycling loop

Endo short@cyto = (out sh,1) >> Endo short@cyto + (in sh,1) << Endo short@cyto + ... ;

◮ model:

aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]

◮ reactions

  • ut sh:

150 aSrc

  • >

Endo short in sh: Endo short

  • >

75 aSrc

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Two loop trafficking model – results

5000 10000 15000 20000 25000 30000 35000 40000 20000 40000 60000 80000 100000 Time aSrc at membrane aFGFR at membrane

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Circadian clock

◮ Ostreococcus tauri, tiny green alga

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Circadian clock

◮ Ostreococcus tauri, tiny green alga ◮ two genes involved in circadian rhythm

(Akman et al, FBTC 10, EPTCS 19, 2010)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Circadian clock in Bio-PEPA: alternating light dark

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(d) LD 12:12 – ODE

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(e) LD 12:12 – average 10000 SSA runs

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(f) LD 12:12 – single SSA run

(Akman et al, FBTC 10, EPTCS 19, 2010)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Circadian clock in Bio-PEPA: light only

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(d) LL – ODE

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(e) LL – average 10000 SSA runs

50 100 150 200 250 100 200 300 400 500 Time (hours)

Level

LHY mRNA TOC1 mRNA Total LHY Total TOC1

(f) LL – single SSA run

(Akman et al, FBTC 10, EPTCS 19, 2010)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 ◮ various models from BioModels Database

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 ◮ various models from BioModels Database ◮ And now for something completely different . . .

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling ◮ emergency egress modelling Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 ◮ various models from BioModels Database ◮ And now for something completely different . . .

◮ epidemiological modelling ◮ emergency egress modelling

◮ see www.biopepa.org for more details

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Emergency egress modelling in Bio-PEPA

1 2 3 4 5

Time [min]

5 10 15 20 25 30 35

Population

Room At (g) Room At (f) Room Bt (g) Room Ct (f) Room Ag (g) Room Ag (f) Room As (f) Room As (g) Room Bs (f) Room Bs (g)

(Massink et al, SEFM 2010)

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock 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

◮ how can Bio-PEPA contribute towards atlases?

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Thank you

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters

◮ initial parameters for species representing basal behaviour

◮ no decision species, no added FGF, no active FGFR ◮ long recycling loop inactive so no species from it ◮ hence only 3 species present initially Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters

◮ initial parameters for species representing basal behaviour

◮ no decision species, no added FGF, no active FGFR ◮ long recycling loop inactive so no species from it ◮ hence only 3 species present initially

◮ rate of entry and probability of recycling in each loop

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters

◮ initial parameters for species representing basal behaviour

◮ no decision species, no added FGF, no active FGFR ◮ long recycling loop inactive so no species from it ◮ hence only 3 species present initially

◮ rate of entry and probability of recycling in each loop ◮ input and output stoichiometry for each loop

◮ short loop: input and output the same ◮ long loop: output much larger than input Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters

◮ initial parameters for species representing basal behaviour

◮ no decision species, no added FGF, no active FGFR ◮ long recycling loop inactive so no species from it ◮ hence only 3 species present initially

◮ rate of entry and probability of recycling in each loop ◮ input and output stoichiometry for each loop

◮ short loop: input and output the same ◮ long loop: output much larger than input

◮ creation rate of active Src during basal behaviour ◮ binding rate for active Src and active FGFR ◮ time to pick up inactive Src in perinuclear region ◮ assume time taken in each loop fixed using calculations

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters (continued)

◮ at least 13 unknown parameters – not so simple

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters (continued)

◮ at least 13 unknown parameters – not so simple ◮ enable short recycling loop only ◮ find parameters to balance short loop

◮ 50% of active Src at membrane ◮ 50% of active Src in the short recycling loop

◮ 6 parameters not yet specified

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Parameters (continued)

◮ at least 13 unknown parameters – not so simple ◮ enable short recycling loop only ◮ find parameters to balance short loop

◮ 50% of active Src at membrane ◮ 50% of active Src in the short recycling loop

◮ 6 parameters not yet specified ◮ enable the long recycling loop ◮ guess some parameters ◮ enable the doser and see what happens

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier

◮ model component, system

P ::= S(ℓ) | P ⊲

⊳

L P Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

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Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier

◮ model component, system

P ::= S(ℓ) | P ⊲

⊳

L P Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-61
SLIDE 61

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier

◮ model component, system

P ::= S(ℓ) | P ⊲

⊳

L P Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-62
SLIDE 62

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

◮ α action, reaction name, κ stoichiometric coefficient ◮ ↑ product, ↓ reactant ◮ ⊕ activator, ⊖ inhibitor, ⊙ generic modifier

◮ model component, system

P ::= S(ℓ) | P ⊲

⊳

L P

◮ need a more constrained form

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-63
SLIDE 63

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-64
SLIDE 64

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-65
SLIDE 65

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-66
SLIDE 66

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-67
SLIDE 67

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-68
SLIDE 68

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-69
SLIDE 69

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-70
SLIDE 70

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-71
SLIDE 71

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-72
SLIDE 72

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-73
SLIDE 73

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-74
SLIDE 74

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-75
SLIDE 75

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-76
SLIDE 76

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-77
SLIDE 77

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-78
SLIDE 78

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-79
SLIDE 79

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-80
SLIDE 80

Process algebras Bio-PEPA Protein trafficking Circadian clock Other examples Conclusion

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

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

Vashti Galpin Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-81
SLIDE 81

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-82
SLIDE 82

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-83
SLIDE 83

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-84
SLIDE 84

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-85
SLIDE 85

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-86
SLIDE 86

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-87
SLIDE 87

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics

slide-88
SLIDE 88

Process algebras Bio-PEPA Protein trafficking Circadian clock 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 Spatio-temporal Biological Process Modelling Joint MRC/INCF/SICSA Workshop on Atlas Informatics