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Modelling protein trafficking: progress and challenges Vashti - - PowerPoint PPT Presentation

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions Modelling protein trafficking: progress and challenges Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling protein trafficking: progress and challenges

Vashti Galpin Laboratory for Foundations of Computer Science School of Informatics University of Edinburgh 21 May 2012

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Outline

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein: inactive and active

(Martin, Nature Rev. Mol. Cell Biol. 2, 2001) Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 6

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration ◮ active Src at membrane linked to cell motility and adhesion

hence important for understanding and treatment of cancer

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration ◮ active Src at membrane linked to cell motility and adhesion

hence important for understanding and treatment of cancer

◮ location in normal cell without growth factor (FGF) addition

◮ lots of inactive Src in perinuclear region ◮ much less active Src on membrane Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration ◮ active Src at membrane linked to cell motility and adhesion

hence important for understanding and treatment of cancer

◮ location in normal cell without growth factor (FGF) addition

◮ lots of inactive Src in perinuclear region ◮ much less active Src on membrane

◮ added FGF binds with FGF receptor (FGFR) which becomes

active and binds with active Src

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration ◮ active Src at membrane linked to cell motility and adhesion

hence important for understanding and treatment of cancer

◮ location in normal cell without growth factor (FGF) addition

◮ lots of inactive Src in perinuclear region ◮ much less active Src on membrane

◮ added FGF binds with FGF receptor (FGFR) which becomes

active and binds with active Src

◮ location in normal cell after FGF addition

◮ lots of inactive Src in perinuclear region ◮ increase in amount of active Src on membrane Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src protein

◮ non-receptor protein tyrosine kinase, member of Src family ◮ in either inactive or active configuration ◮ active Src at membrane linked to cell motility and adhesion

hence important for understanding and treatment of cancer

◮ location in normal cell without growth factor (FGF) addition

◮ lots of inactive Src in perinuclear region ◮ much less active Src on membrane

◮ added FGF binds with FGF receptor (FGFR) which becomes

active and binds with active Src

◮ location in normal cell after FGF addition

◮ lots of inactive Src in perinuclear region ◮ increase in amount of active Src on membrane

◮ how does this happen?

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Endosomes

◮ endosomes: membrane-bound compartments within cells ◮ endocytosis: engulfing of molecules by vesicles on the inner

side of the membrane, which then merge with endosomes

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Endosomes

◮ endosomes: membrane-bound compartments within cells ◮ endocytosis: engulfing of molecules by vesicles on the inner

side of the membrane, which then merge with endosomes

◮ different types: early, late, recycling, lysosomes ◮ role is to sort molecules either for recycling or degradation ◮ identify type by Rab family protein and Rho family protein

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Endosomes

◮ endosomes: membrane-bound compartments within cells ◮ endocytosis: engulfing of molecules by vesicles on the inner

side of the membrane, which then merge with endosomes

◮ different types: early, late, recycling, lysosomes ◮ role is to sort molecules either for recycling or degradation ◮ identify type by Rab family protein and Rho family protein ◮ move along microfilaments or microtubules ◮ movement is in one direction mostly

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Endosomes

◮ endosomes: membrane-bound compartments within cells ◮ endocytosis: engulfing of molecules by vesicles on the inner

side of the membrane, which then merge with endosomes

◮ different types: early, late, recycling, lysosomes ◮ role is to sort molecules either for recycling or degradation ◮ identify type by Rab family protein and Rho family protein ◮ move along microfilaments or microtubules ◮ movement is in one direction mostly ◮ vary in contents rather than number or speed

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in

  • endosomes. (Sandilands et al, 2004)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms: gradient from inactive to active

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src activation takes place in

  • endosomes. (Sandilands et al, 2004)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src 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: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms: persistence of response to FGF

(Sandilands et al, EMBO Reports 8, 2007)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src 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: progress and challenges Biology + Computing = ??

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SLIDE 23

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms

◮ experimental research from the Frame laboratory has shown

After stimulation with FGF, Src is found in endosomes throughout the cytoplasm. There is a gradient of inactive Src to active Src from perinuclear region to membrane. Src 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) In cancerous cells, Src is sequestered in autophagosomes when FAK is absent, to avoid cell death as a result of excess Src not bound to FAK. (Sandilands et al, 2012)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Mechanisms: sequestration in autophagosomes

FAK pTyr-416-Src Merge FAK +/+ FAK–/–

b

(Sandilands et al, Nature Cell Biology 14, 2012)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling protein trafficking

◮ modelling aspects

dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling protein trafficking

◮ modelling aspects

dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities

◮ choice of formalism: process algebras

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling protein trafficking

◮ modelling aspects

dynamic: behaviour, change over time change on addition of FGF spatial: reactions happen in different parts of the cell molecules move within the cell populations: molecular species exist in reasonable numbers each species has a small number of possibilities

◮ choice of formalism: process algebras ◮ modelling challenges

concrete: generate hypotheses for further experiment abstract: modelling must be computationally feasible data: very limited

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Experimental data

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Experimental data

◮ very limited at this stage

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Experimental data

◮ very limited at this stage ◮ qualitative: gradient of activity ◮ quantitative: persistence of response

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Experimental data

◮ very limited at this stage ◮ qualitative: gradient of activity ◮ quantitative: persistence of response ◮ data from general literature

◮ endosomes move along microfilaments and microtubules ◮ they move in one direction (mostly) ◮ they can move at 1µm/s ◮ cells have diameters of between 10µm and 100µm Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Experimental data

◮ very limited at this stage ◮ qualitative: gradient of activity ◮ quantitative: persistence of response ◮ data from general literature

◮ endosomes move along microfilaments and microtubules ◮ they move in one direction (mostly) ◮ they can move at 1µm/s ◮ cells have diameters of between 10µm and 100µm

◮ both long and short recycling loops

◮ time taken for half of short loop: assuming a distance of 10µm

then 10 seconds

◮ time take for half of long loop: assuming a distance of 20µm

then 20 seconds

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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

◮ developed by Ciocchetta and Hillston ◮ close match between modelling artificial and natural systems ◮ extension of PEPA, functional rates and stoichiometry Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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

◮ developed by Ciocchetta and Hillston ◮ close match between modelling artificial and natural systems ◮ extension of PEPA, functional rates and stoichiometry

◮ Stochastic HYPE, a stochastic hybrid process algebra

◮ developed by Bortolussi, Galpin and Hillston from HYPE ◮ existing hybrid process algebras treated ODEs monolithically Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Process algebras (continued)

◮ what is a process algebra?

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

Markov processes

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Process algebras (continued)

◮ what is a process algebra?

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

Markov processes

◮ why use a process algebra?

◮ formalism to describe concurrent behaviour ◮ provide an unambiguous and precise description ◮ different analyses available from a single description

simulation, model checking, CTMC analysis

◮ they are mathematically beautiful Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ species: reactions, stoichiometry, locations

S@L

def

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ species: reactions, stoichiometry, locations

S@L

def

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 40

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ species: reactions, stoichiometry, locations

S@L

def

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 41

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ species: reactions, stoichiometry, locations

S@L

def

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-42
SLIDE 42

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ 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: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ 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: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ 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)

◮ system: includes 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: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ 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)

◮ system: includes 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

◮ process-as-species rather than process-as-molecules

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Prefix rules

((α, κ) ↓ S@L)(ℓ)

(α,[S@L:↓(ℓ,κ)])

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

(α,[S@L:↑(ℓ,κ)])

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

(α,[S@L:⊕(ℓ,κ)])

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

(α,[S@L:⊖(ℓ,κ)])

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

(α,[S@L:⊙(ℓ,κ)])

− − − − − − − − − − →c S@L(ℓ) 0 ≤ ℓ ≤ NS@L

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-48
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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Prefix rules

((α, κ) ↓ S@L)(ℓ)

(α,[S@L:↓(ℓ,κ)])

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

(α,[S@L:↑(ℓ,κ)])

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

(α,[S@L:⊕(ℓ,κ)])

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

(α,[S@L:⊖(ℓ,κ)])

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

(α,[S@L:⊙(ℓ,κ)])

− − − − − − − − − − →c S@L(ℓ) 0 ≤ ℓ ≤ NS@L

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-49
SLIDE 49

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics

◮ operational semantics for capability relation −

→c

◮ Prefix rules

((α, κ) ↓ S@L)(ℓ)

(α,[S@L:↓(ℓ,κ)])

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

(α,[S@L:↑(ℓ,κ)])

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

(α,[S@L:⊕(ℓ,κ)])

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

(α,[S@L:⊖(ℓ,κ)])

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

(α,[S@L:⊙(ℓ,κ)])

− − − − − − − − − − →c S@L(ℓ) 0 ≤ ℓ ≤ NS@L

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ M

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

M Q

(α,v::u)

− − − − →c P′ ⊲

⊳

M Q′

α ∈ M

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-51
SLIDE 51

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ M

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

M Q

(α,v::u)

− − − − →c P′ ⊲

⊳

M Q′

α ∈ M

◮ operational semantics for stochastic relation −

→s P

(α,v)

− − − →c P′ V, N, K, F, Comp, P

(α,fα(v,V,N,K)/h)

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

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-52
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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA semantics (continued)

◮ Cooperation for α ∈ M

P

(α,v)

− − − →c P′ Q

(α,u)

− − − →c Q′ P ⊲

⊳

M Q

(α,v::u)

− − − − →c P′ ⊲

⊳

M Q′

α ∈ M

◮ operational semantics for stochastic relation −

→s P

(α,v)

− − − →c P′ V, N, K, F, Comp, P

(α,fα(v,V,N,K)/h)

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

◮ rate function fα uses information about the species and

locations in the string v, together with the species and location information and rate parameters in calculating the actual rate of the reaction

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-53
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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling with Bio-PEPA

◮ modelled gradient successfully without cycle

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-54
SLIDE 54

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component seemed to make model insensitive to

changes

◮ very difficult to work with, too many parameters Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-55
SLIDE 55

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component seemed to make model insensitive to

changes

◮ very difficult to work with, too many parameters

◮ next: combined loop model with abstract gradient

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-56
SLIDE 56

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src trafficking: combined loop model

membrane perinuclear region 20 seconds

aSrc FGF FGFR aFGFR aSrc aFGFR aSrc Src Src Src

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-57
SLIDE 57

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling progess with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component made model insenstive to changes ◮ very difficult to work with, too many parameters

◮ next: combined loop model with abstract gradient

◮ no match with experimental results but useful for discussions Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-58
SLIDE 58

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Combined loop trafficking model – results

200 400 600 800 1000 1200 1400 1000 2000 3000 4000 5000 Time aSrc at membrane aFGFR at membrane

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-59
SLIDE 59

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling progess with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component made model insenstive to changes ◮ very difficult to work with, too many parameters

◮ next: combined loop model with abstract gradient

◮ no match with experimental results but useful for discussions Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-60
SLIDE 60

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling progess with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component made model insenstive to changes ◮ very difficult to work with, too many parameters

◮ next: combined loop model with abstract gradient

◮ no match with experimental results but useful for discussions ◮ unnecessary to assume a combined loop for both behaviours ◮ found out about short and long recycling loops Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-61
SLIDE 61

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Modelling progess with Bio-PEPA

◮ modelled gradient successfully without cycle ◮ added gradient into model of trafficking with a combined loop

◮ gradient component made model insenstive to changes ◮ very difficult to work with, too many parameters

◮ next: combined loop model with abstract gradient

◮ no match with experimental results but useful for discussions ◮ unnecessary to assume a combined loop for both behaviours ◮ found out about short and long recycling loops

◮ current: two loop model

◮ one short, one long Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-62
SLIDE 62

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Src trafficking: two loop model

membrane perinuclear region 10 seconds 20 seconds

aSrc FGF FGFR aFGFR aSrc aFGFR aFGFR aSrc Src Src Src

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-63
SLIDE 63

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-64
SLIDE 64

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA Eclipse Plug-in

◮ software tool for Bio-PEPA modelling

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-65
SLIDE 65

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-66
SLIDE 66

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-67
SLIDE 67

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA Eclipse Plug-in (continued)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-68
SLIDE 68

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-69
SLIDE 69

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-70
SLIDE 70

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-71
SLIDE 71

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-72
SLIDE 72

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-73
SLIDE 73

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • Vashti Galpin

Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-74
SLIDE 74

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗ Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-75
SLIDE 75

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • Vashti Galpin

Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-76
SLIDE 76

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-77
SLIDE 77

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) subcomponents are parameterised by variables

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-78
SLIDE 78

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-79
SLIDE 79

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) events have event conditions: guards and resets

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-80
SLIDE 80

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) events have event conditions: guards and resets ec(aj) = (f (V), V′ = f ′(V)) discrete events

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-81
SLIDE 81

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) events have event conditions: guards and resets ec(aj) = (f (V), V′ = f ′(V)) discrete events ec(aj) = (r, V′ = f ′(V)) stochastic events

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-82
SLIDE 82

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-83
SLIDE 83

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) influences are defined by a triple

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-84
SLIDE 84

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) influences are defined by a triple αj = (ιj, rj, I(V))

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-85
SLIDE 85

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • well-defined subcomponent

C(V)

def

=

  • j

aj : αj . C(V) + init : α . C(V) influences are defined by a triple αj = (ιj, rj, I(V)) influence names are mapped to variables iv(ιj) ∈ V

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-86
SLIDE 86

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • Vashti Galpin

Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-87
SLIDE 87

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • Vashti Galpin

Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-88
SLIDE 88

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • controller grammar

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-89
SLIDE 89

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • controller grammar

M ::= a.M | 0 | M + M

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-90
SLIDE 90

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • controller grammar

M ::= a.M | 0 | M + M

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-91
SLIDE 91

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE

subcomponents controllers

  • C1(V) ⊲

⊳

∗

· · · ⊲

⊳

∗ Cn(V)

  • ⊲

⊳

∗

  • Con1 ⊲

⊳

∗

· · · ⊲

⊳

∗ Conm

  • controller grammar

M ::= a.M | 0 | M + M Con ::= M | Con ⊲

⊳

∗ Con Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-92
SLIDE 92

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-93
SLIDE 93

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities ◮ each subcomponent represents flows affecting a variable:

production, binding, activation, degradation, removal

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-94
SLIDE 94

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities ◮ each subcomponent represents flows affecting a variable:

production, binding, activation, degradation, removal

◮ each influence represents a specific flow: degradation

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-95
SLIDE 95

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities ◮ each subcomponent represents flows affecting a variable:

production, binding, activation, degradation, removal

◮ each influence represents a specific flow: degradation ◮ each controller represents sequencing of events: day/night

cycle

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-96
SLIDE 96

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities ◮ each subcomponent represents flows affecting a variable:

production, binding, activation, degradation, removal

◮ each influence represents a specific flow: degradation ◮ each controller represents sequencing of events: day/night

cycle

◮ each discrete event represents something happening

instantaneously when a condition becomes true, with a possible change of values: addition of growth factor

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-97
SLIDE 97

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE applied to biology

◮ a model has n variables defined over R: species quantities ◮ each subcomponent represents flows affecting a variable:

production, binding, activation, degradation, removal

◮ each influence represents a specific flow: degradation ◮ each controller represents sequencing of events: day/night

cycle

◮ each discrete event represents something happening

instantaneously when a condition becomes true, with a possible change of values: addition of growth factor

◮ each stochastic event represents something happening after

time has passed, with a possible change of values: transport

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-98
SLIDE 98

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE modelling

◮ output of model is a trajectory consisting of

◮ continuous paths in Rn ◮ jumps/changes in values as events happen ◮ piecewise deterministic Markov process ◮ transition-driven stochastic hybrid automata Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-99
SLIDE 99

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE modelling

◮ output of model is a trajectory consisting of

◮ continuous paths in Rn ◮ jumps/changes in values as events happen ◮ piecewise deterministic Markov process ◮ transition-driven stochastic hybrid automata

◮ major differences from Bio-PEPA

◮ HYPE allows coordinate model of space rather than explicit

abstract locations

◮ HYPE allows continuous and stochastic behaviour together ◮ likely to be valuable when small quantities of some species Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-100
SLIDE 100

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Stochastic HYPE modelling

◮ output of model is a trajectory consisting of

◮ continuous paths in Rn ◮ jumps/changes in values as events happen ◮ piecewise deterministic Markov process ◮ transition-driven stochastic hybrid automata

◮ major differences from Bio-PEPA

◮ HYPE allows coordinate model of space rather than explicit

abstract locations

◮ HYPE allows continuous and stochastic behaviour together ◮ likely to be valuable when small quantities of some species

◮ application to protein trafficking

◮ work in progress ◮ SimHyA simulator Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-101
SLIDE 101

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-102
SLIDE 102

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-103
SLIDE 103

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-104
SLIDE 104

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP) ◮ negative feedback cycle

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-105
SLIDE 105

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP) ◮ negative feedback cycle

◮ each gene produces a protein Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-106
SLIDE 106

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP) ◮ negative feedback cycle

◮ each gene produces a protein ◮ protein inhibits transcription of mRNA by another gene Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-107
SLIDE 107

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP) ◮ negative feedback cycle

◮ each gene produces a protein ◮ protein inhibits transcription of mRNA by another gene ◮ other gene cannot produce its protein Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-108
SLIDE 108

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

◮ synthetic network ◮ three genes with three inhibitors ◮ reporter of green flourescent protein (GFP) ◮ negative feedback cycle

◮ each gene produces a protein ◮ protein inhibits transcription of mRNA by another gene ◮ other gene cannot produce its protein

◮ quantities of proteins oscillate over time

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-109
SLIDE 109

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

TetR LacI λ cI TetR GFP

PLlac01 PLtet01 PLtet01 pSC101

  • rigin

ColE1 tetR-lite gfp-aav lacI-lite λ cI-lite ampR kanR λPR

Elowitz and Leibler, Nature 403, 335-338.

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-110
SLIDE 110

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-111
SLIDE 111

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-112
SLIDE 112

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA

↓ dmA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-113
SLIDE 113

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-114
SLIDE 114

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-115
SLIDE 115

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-116
SLIDE 116

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB GeneC − − →

trsC mRNAC −

− →

trlC

PrC ↓ dmC ↓ dpC

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-117
SLIDE 117

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB GeneC − − →

trsC mRNAC −

− →

trlC

PrC ↓ dmC ↓ dpC

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-118
SLIDE 118

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB GeneC − − →

trsC mRNAC −

− →

trlC

PrC ↓ dmC ↓ dpC

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-119
SLIDE 119

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB GeneC − − →

trsC mRNAC −

− →

trlC

PrC ↓ dmC ↓ dpC

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-120
SLIDE 120

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − →

trsA mRNAA −

− →

trlA

PrA ↓ dmA ↓ dpA GeneB − − →

trsB mRNAB −

− →

trlB

PrB ↓ dmB ↓ dpB GeneC − − →

trsC mRNAC −

− →

trlC

PrC ↓ dmC ↓ dpC

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-121
SLIDE 121

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator

GeneA − − − − − − − − − − − − →

kp

PrA ↓ kd GeneB − − − − − − − − − − − − →

kp

PrB ↓ kd GeneC − − − − − − − − − − − − →

kp

PrC ↓ kd

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-122
SLIDE 122

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator in HYPE

◮ degradation and production flows for Gene A:

G dg

A (X)

def

= init : (dA, −kd, linear(X)).G dg

A (X)

G pr

A

def

= inhibitA : (pA, 0, const).G pr

A

+ expressA : (pA, kp, const).G pr

A

+ init : (pA, kp, const).G pr

A

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-123
SLIDE 123

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator in HYPE

◮ degradation and production flows for Gene A:

G dg

A (X)

def

= init : (dA, −kd, linear(X)).G dg

A (X)

G pr

A

def

= inhibitA : (pA, 0, const).G pr

A

+ expressA : (pA, kp, const).G pr

A

+ init : (pA, kp, const).G pr

A ◮ composed: GeneA(A)

def

= (G dg

A (A) ⊲

⊳

∗ G pr

A )

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-124
SLIDE 124

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator in HYPE

◮ degradation and production flows for Gene A:

G dg

A (X)

def

= init : (dA, −kd, linear(X)).G dg

A (X)

G pr

A

def

= inhibitA : (pA, 0, const).G pr

A

+ expressA : (pA, kp, const).G pr

A

+ init : (pA, kp, const).G pr

A ◮ composed: GeneA(A)

def

= (G dg

A (A) ⊲

⊳

∗ G pr

A ) ◮ “controller”: ConA

def

= inhibitA.expressA.ConA

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-125
SLIDE 125

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator in HYPE

◮ degradation and production flows for Gene A:

G dg

A (X)

def

= init : (dA, −kd, linear(X)).G dg

A (X)

G pr

A

def

= inhibitA : (pA, 0, const).G pr

A

+ expressA : (pA, kp, const).G pr

A

+ init : (pA, kp, const).G pr

A ◮ composed: GeneA(A)

def

= (G dg

A (A) ⊲

⊳

∗ G pr

A ) ◮ “controller”: ConA

def

= inhibitA.expressA.ConA

◮ influences mapped to variables: iv(dA) = A

iv(pA) = A

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-126
SLIDE 126

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator in HYPE

◮ degradation and production flows for Gene A:

G dg

A (X)

def

= init : (dA, −kd, linear(X)).G dg

A (X)

G pr

A

def

= inhibitA : (pA, 0, const).G pr

A

+ expressA : (pA, kp, const).G pr

A

+ init : (pA, kp, const).G pr

A ◮ composed: GeneA(A)

def

= (G dg

A (A) ⊲

⊳

∗ G pr

A ) ◮ “controller”: ConA

def

= inhibitA.expressA.ConA

◮ influences mapped to variables: iv(dA) = A

iv(pA) = A

◮ event conditions: ec(inhibitA) = (C > p, true)

ec(expressA) = (C ≤ p, true)

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-127
SLIDE 127

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator – protein levels over time

(GeneA(A) ⊲

⊳

∗ GeneB(B) ⊲

⊳

∗ GeneC(C)) ⊲

⊳

∗ init.(ConA ConB ConC) Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-128
SLIDE 128

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

The Repressilator – protein levels over time

(GeneA(A) ⊲

⊳

∗ GeneB(B) ⊲

⊳

∗ GeneC(C)) ⊲

⊳

∗ init.(ConA ConB ConC)

500 1000 1500 2000 2500 3000 3500 4000 4500 10 20 30 40 50 60 70 80 90 100 110

A B C

kp=1.00 kd =0.01 Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-129
SLIDE 129

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Conclusions Biology + Computing = ??

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-130
SLIDE 130

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Conclusions Computing + Biology = ??

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-131
SLIDE 131

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Conclusions Computing + Biology = ??

◮ using powerful mathematical models from computer science to

model biology and in the longer term, to provide predictions

◮ major challenges

◮ lack of data, models are often quasi-quantitative ◮ getting right level of abstraction for useful models Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-132
SLIDE 132

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Acknowledgements

PEPA Group DMG University of Edinburgh University of Trieste Jane Hillston Luca Bortolussi Stephen Gilmore Allan Clark Cancer Research UK Maria Luisa Guerriero Edinburgh Federica Ciocchetta Margaret Frame Adam Duguid Emma Sandilands

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-133
SLIDE 133

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Thank you

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-134
SLIDE 134

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ two-level syntax

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-135
SLIDE 135

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Bio-PEPA syntax

◮ two-level syntax ◮ sequential component, species

S ::= (α, κ) op S | S + S

  • p ∈ {↑, ↓, ⊕, ⊖, ⊙}

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-136
SLIDE 136

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-137
SLIDE 137

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-138
SLIDE 138

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-139
SLIDE 139

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-140
SLIDE 140

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-141
SLIDE 141

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-142
SLIDE 142

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-143
SLIDE 143

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-144
SLIDE 144

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-145
SLIDE 145

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-146
SLIDE 146

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-147
SLIDE 147

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-148
SLIDE 148

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Example: reaction with enzyme

◮ S + E −

→ ← − SE − → P + E

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-149
SLIDE 149

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-150
SLIDE 150

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-151
SLIDE 151

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-152
SLIDE 152

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-153
SLIDE 153

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-154
SLIDE 154

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-155
SLIDE 155

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-156
SLIDE 156

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-157
SLIDE 157

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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: progress and challenges Biology + Computing = ??

slide-158
SLIDE 158

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Example: reaction with enzyme, max level 3

◮ state vector (S, E, SE, P) and NS = NE = NSE = NP = 3

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-159
SLIDE 159

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Example: reaction with enzyme, max level 3

◮ state vector (S, E, SE, P) and NS = NE = NSE = NP = 3

(3, 3, 0, 0) (2, 2, 1, 0) (1, 1, 2, 0) (0, 0, 3, 0) (2, 3, 0, 1) (1, 2, 1, 1) (0, 1, 2, 1) (1, 3, 0, 2) (0, 2, 1, 2) (0, 3, 0, 3) α α α β β β α α β β α β γ γ γ γ γ γ

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Example: reaction with enzyme, max level 7

◮ state vector S E SE P and NS = NE = NSE = NP = 7

7700 6610 5520 4430 3340 2250 1160 0070 6701 5611 4521 3431 2341 1251 0161 5702 4612 3522 2432 1342 0252 4703 3613 2523 1433 0342 3704 2614 1524 0614 2705 1615 0525 1706 0616 0707 α α α α α α α β β β β β β β α α α α α α β β β β β β α α α α α β β β β β α α α α β β β β α α α β β β α α β β α β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 161

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-162
SLIDE 162

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-163
SLIDE 163

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-164
SLIDE 164

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 165

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

Parameters (continued)

◮ at least 13 unknown parameters – not so simple

Vashti Galpin Modelling protein trafficking: progress and challenges Biology + Computing = ??

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SLIDE 166

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??

slide-167
SLIDE 167

Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions

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 Modelling protein trafficking: progress and challenges Biology + Computing = ??