modelling protein trafficking: progress and challenges · modelling protein tra cking: progress and...
TRANSCRIPT
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling protein trafficking: progress andchallenges
Vashti Galpin
Laboratory for Foundations of Computer ScienceSchool of Informatics
University of Edinburgh
21 May 2012
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src protein
I non-receptor protein tyrosine kinase, member of Src family
I in either inactive or active configuration
I active Src at membrane linked to cell motility and adhesionhence important for understanding and treatment of cancer
I location in normal cell without growth factor (FGF) additionI lots of inactive Src in perinuclear regionI much less active Src on membrane
I added FGF binds with FGF receptor (FGFR) which becomesactive and binds with active Src
I location in normal cell after FGF additionI lots of inactive Src in perinuclear regionI increase in amount of active Src on membrane
I how does this happen?
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Endosomes
I endosomes: membrane-bound compartments within cells
I endocytosis: engulfing of molecules by vesicles on the innerside of the membrane, which then merge with endosomes
I different types: early, late, recycling, lysosomes
I role is to sort molecules either for recycling or degradation
I identify type by Rab family protein and Rho family protein
I move along microfilaments or microtubules
I movement is in one direction mostly
I vary in contents rather than number or speed
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Endosomes
I endosomes: membrane-bound compartments within cells
I endocytosis: engulfing of molecules by vesicles on the innerside of the membrane, which then merge with endosomes
I different types: early, late, recycling, lysosomes
I role is to sort molecules either for recycling or degradation
I identify type by Rab family protein and Rho family protein
I move along microfilaments or microtubules
I movement is in one direction mostly
I vary in contents rather than number or speed
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Endosomes
I endosomes: membrane-bound compartments within cells
I endocytosis: engulfing of molecules by vesicles on the innerside of the membrane, which then merge with endosomes
I different types: early, late, recycling, lysosomes
I role is to sort molecules either for recycling or degradation
I identify type by Rab family protein and Rho family protein
I move along microfilaments or microtubules
I movement is in one direction mostly
I vary in contents rather than number or speed
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Endosomes
I endosomes: membrane-bound compartments within cells
I endocytosis: engulfing of molecules by vesicles on the innerside of the membrane, which then merge with endosomes
I different types: early, late, recycling, lysosomes
I role is to sort molecules either for recycling or degradation
I identify type by Rab family protein and Rho family protein
I move along microfilaments or microtubules
I movement is in one direction mostly
I vary in contents rather than number or speed
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
The persistence of active Src at the membrane is inversely relatedto the quantity of FGF added. (Sandilands et al, 2007)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
The persistence of active Src at the membrane is inversely relatedto the quantity of FGF added. (Sandilands et al, 2007)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
The persistence of active Src at the membrane is inversely relatedto the quantity of FGF added. (Sandilands et al, 2007)
In cancerous cells, Src is sequestered in autophagosomes whenFAK is absent, to avoid cell death as a result of excess Src notbound to FAK. (Sandilands et al, 2012)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms
I experimental research from the Frame laboratory has shown
After stimulation with FGF, Src is found in endosomes throughoutthe cytoplasm. There is a gradient of inactive Src to active Srcfrom perinuclear region to membrane. Src activation takes place inendosomes. (Sandilands et al, 2004)
The persistence of active Src at the membrane is inversely relatedto the quantity of FGF added. (Sandilands et al, 2007)
In cancerous cells, Src is sequestered in autophagosomes whenFAK is absent, to avoid cell death as a result of excess Src notbound to FAK. (Sandilands et al, 2012)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Mechanisms: sequestration in autophagosomes
ART I C L E S
c
FAK+/+ FAK–/–
Cell type
Per
cent
age
of c
ells
with
inte
rnal
ized
Src
pTyr-416-Src—green DAPI—blue
0
20
40
60
80
100
FAK +/+ FAK –/–
FAK pTyr-416-Src Merge
FAK
Fyn
Src
Yes
pTyr-416-Src
Actin
FAK
+/+
FAK
–/–
FAK +/+
FAK–/–
a
b
Figure 1 Localization of active Src is altered in the absence of FAKin SCCs. (a) Left, cells were fixed and stained for anti-pTyr-416-Src(green) and with DAPI (blue). Solid arrows indicate cells with activeSrc in adhesions; dashed arrows show cells with active Src in puncta.Scale bars, 20 µm. Right, percentage of cells with active Src localizingto intracellular structures was quantified. Data are presented asmean± s.d. and significance is P < 0.001 (n = 3). (b) Cells were
fixed and stained for anti-FAK (red) and anti-pTyr-416-Src (green).Merged and higher-magnification images of the outlined areas are alsoshown. Solid and dashed arrows show Src localization to adhesionsor to puncta, respectively. Scale bars, 20 µm. (c) Lysates fromcells were immunoblotted with anti-FAK, anti-Src, anti-Yes, anti-Fyn,anti-pTyr-416-Src and anti-actin antibodies. Uncropped images of blotsare shown in Supplementary Fig. S9.
sequestered in the interior of single-membrane-delimited vesicles(Supplementary Fig. S1b). These vesicles contained multiple smallermembrane lamella, some of which appeared as fragments and someas intact membrane-delimited vesicles with electron-dense cytosolicmaterial. These were interpreted as being within the amphisomal(hybrid autophagosomal–endosomal) compartment, representative ofintermediate stages of the autophagy pathway.
Src co-localizes with autophagy regulatorsWenext used antibodies against autophagy (Atg) proteins. Surprisingly,on staining for endogenous LC3B, Atg7 and Atg12 we found some co-localization with active Src at focal adhesions in FAK+/+ cells (Fig. 2a,upper panels, solid arrows), as well as their localization in cytoplasmicpuncta. The peripheral adhesion localization of the Atg proteins wasdiminished in FAK−/− cells, and we instead saw strong co-localizationwith active Src in a subset of intracellular puncta (Fig. 2a, lower panels,dashed arrows). Single-colour images are shown in SupplementaryFig. S1c. On closer inspection the Atg proteins co-localized with activeSrc at focal adhesions in adherent FAK+/+ cells (Fig. 2b, upper panels,solid arrows). These Atg proteins also co-localized with FAK and withpaxillin (Supplementary Fig. S1d). However, in FAK−/− cells, Atg
proteins were present in vesicular structures at the inward tips of focaladhesions, or in cytoplasmic puncta that aligned with the longitudinalaxis of the focal adhesions (Fig. 2b, lower panels, dashed arrows). Weconclude that some autophagy-regulating proteins are present at focaladhesions, andwe reasoned that theymay be ready to selectively ‘recruit’active Src under conditions of stress, such as when FAK is deleted.We also addressed whether the trafficking of active Src to puncta
occurred in other FAK-deficient tumour cell types, and in the contextof a tissue in vivo. We used mice from a genetically engineeredmodel of pancreatic ductal adenocarcinoma, namely mice bearingPdx1–Cre, and activated K-Ras, that is LSL–Kras(G12D/+). Src expressionand activity are upregulated in invasive and metastatic pancreaticductal adenocarcinomas in this model8, and localized to the cellmembrane (Supplementary Fig. S2a). When FAK was deleted byintercrossing with fakflox/flox mice (Supplementary Fig. S2a), we foundactive Src visibly located in intracellular puncta (Supplementary Fig. 2b,dashed arrows), and co-localized with Atg7, as shown by double tissueimmunofluorescence microscopy (Supplementary Fig. S2c, dottedarrows). Thus, active Src co-localizes with multiple components ofthe autophagy pathway at intracellular puncta in vitro, and with Atg7 invivo, and inmultiple FAK-deficient cancer cell types.
52 NATURE CELL BIOLOGY VOLUME 14 | NUMBER 1 | JANUARY 2012
(Sandilands et al, Nature Cell Biology 14, 2012)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling protein trafficking
I modelling aspects
dynamic: behaviour, change over timechange on addition of FGF
spatial: reactions happen in different parts of the cellmolecules move within the cell
populations: molecular species exist in reasonable numberseach species has a small number of possibilities
I choice of formalism: process algebras
I modelling challenges
concrete: generate hypotheses for further experimentabstract: modelling must be computationally feasibledata: very limited
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling protein trafficking
I modelling aspects
dynamic: behaviour, change over timechange on addition of FGF
spatial: reactions happen in different parts of the cellmolecules move within the cell
populations: molecular species exist in reasonable numberseach species has a small number of possibilities
I choice of formalism: process algebras
I modelling challenges
concrete: generate hypotheses for further experimentabstract: modelling must be computationally feasibledata: very limited
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling protein trafficking
I modelling aspects
dynamic: behaviour, change over timechange on addition of FGF
spatial: reactions happen in different parts of the cellmolecules move within the cell
populations: molecular species exist in reasonable numberseach species has a small number of possibilities
I choice of formalism: process algebras
I modelling challenges
concrete: generate hypotheses for further experimentabstract: modelling must be computationally feasibledata: very limited
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Experimental data
I very limited at this stage
I qualitative: gradient of activity
I quantitative: persistence of responseI data from general literature
I endosomes move along microfilaments and microtubulesI they move in one direction (mostly)I they can move at 1µm/sI cells have diameters of between 10µm and 100µm
I both long and short recycling loops
I time taken for half of short loop: assuming a distance of 10µmthen 10 seconds
I time take for half of long loop: assuming a distance of 20µmthen 20 seconds
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Experimental data
I very limited at this stage
I qualitative: gradient of activity
I quantitative: persistence of responseI data from general literature
I endosomes move along microfilaments and microtubulesI they move in one direction (mostly)I they can move at 1µm/sI cells have diameters of between 10µm and 100µm
I both long and short recycling loops
I time taken for half of short loop: assuming a distance of 10µmthen 10 seconds
I time take for half of long loop: assuming a distance of 20µmthen 20 seconds
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Experimental data
I very limited at this stage
I qualitative: gradient of activity
I quantitative: persistence of response
I data from general literature
I endosomes move along microfilaments and microtubulesI they move in one direction (mostly)I they can move at 1µm/sI cells have diameters of between 10µm and 100µm
I both long and short recycling loops
I time taken for half of short loop: assuming a distance of 10µmthen 10 seconds
I time take for half of long loop: assuming a distance of 20µmthen 20 seconds
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Experimental data
I very limited at this stage
I qualitative: gradient of activity
I quantitative: persistence of responseI data from general literature
I endosomes move along microfilaments and microtubulesI they move in one direction (mostly)I they can move at 1µm/sI cells have diameters of between 10µm and 100µm
I both long and short recycling loops
I time taken for half of short loop: assuming a distance of 10µmthen 10 seconds
I time take for half of long loop: assuming a distance of 20µmthen 20 seconds
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Experimental data
I very limited at this stage
I qualitative: gradient of activity
I quantitative: persistence of responseI data from general literature
I endosomes move along microfilaments and microtubulesI they move in one direction (mostly)I they can move at 1µm/sI cells have diameters of between 10µm and 100µm
I both long and short recycling loopsI time taken for half of short loop: assuming a distance of 10µm
then 10 secondsI 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Process algebras
I history
I developed to model concurrent computing (mid 1980’s)
I originally no notion of time or space, some extensions
I Hillston developed PEPA, stochastic process algebra (1996)
I Hillston developed ODE interpretation of PEPA (2005)
I Bio-PEPA, a biological process algebra
I developed by Ciocchetta and Hillston
I close match between modelling artificial and natural systems
I extension of PEPA, functional rates and stoichiometry
I Stochastic HYPE, a stochastic hybrid process algebra
I developed by Bortolussi, Galpin and Hillston from HYPE
I existing hybrid process algebras treated ODEs monolithically
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Process algebras
I history
I developed to model concurrent computing (mid 1980’s)
I originally no notion of time or space, some extensions
I Hillston developed PEPA, stochastic process algebra (1996)
I Hillston developed ODE interpretation of PEPA (2005)
I Bio-PEPA, a biological process algebra
I developed by Ciocchetta and Hillston
I close match between modelling artificial and natural systems
I extension of PEPA, functional rates and stoichiometry
I Stochastic HYPE, a stochastic hybrid process algebra
I developed by Bortolussi, Galpin and Hillston from HYPE
I existing hybrid process algebras treated ODEs monolithically
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Process algebras
I history
I developed to model concurrent computing (mid 1980’s)
I originally no notion of time or space, some extensions
I Hillston developed PEPA, stochastic process algebra (1996)
I Hillston developed ODE interpretation of PEPA (2005)
I Bio-PEPA, a biological process algebra
I developed by Ciocchetta and Hillston
I close match between modelling artificial and natural systems
I extension of PEPA, functional rates and stoichiometry
I Stochastic HYPE, a stochastic hybrid process algebra
I developed by Bortolussi, Galpin and Hillston from HYPE
I existing hybrid process algebras treated ODEs monolithically
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Process algebras (continued)
I what is a process algebra?I compact and elegant formal language
I behaviour given by semantics defined mathematically
I classical process algebra: labelled transition systems
I stochastic process algebra: continuous time Markov chains
I stochastic hybrid process algebra: piecewise determinsiticMarkov processes
I why use a process algebra?I formalism to describe concurrent behaviour
I provide an unambiguous and precise description
I different analyses available from a single descriptionsimulation, model checking, CTMC analysis
I they are mathematically beautiful
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Process algebras (continued)
I what is a process algebra?I compact and elegant formal language
I behaviour given by semantics defined mathematically
I classical process algebra: labelled transition systems
I stochastic process algebra: continuous time Markov chains
I stochastic hybrid process algebra: piecewise determinsiticMarkov processes
I why use a process algebra?I formalism to describe concurrent behaviour
I provide an unambiguous and precise description
I different analyses available from a single descriptionsimulation, model checking, CTMC analysis
I they are mathematically beautiful
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}
I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}
I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}
I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}
I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I species: reactions, stoichiometry, locations
S@Ldef= (α1, κ1) op1 S@L + . . . + (αn, κn) opn S@L
where opi ∈ { ↓, ↑,⊕,,�}I model: quantities of species, interaction between species
Pdef= S1@L1(x1) BC
∗. . . BC
∗Sp@Lp(xp)
I system: includes other information required for modellingL compartments and locations, dimensionality, sizesN species quantities, minimums, maximums, step sizeK parameter definitionsF functional rates for reactions, definition of fα
I process-as-species rather than process-as-molecules
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics
I operational semantics for capability relation −→c
I Prefix rules
((α, κ) ↓ S@L)(`)(α,[S@L:↓(`,κ)])−−−−−−−−−→c S@L(`− κ) κ ≤ ` ≤ NS@L
((α, κ) ↑ S@L)(`)(α,[S@L:↑(`,κ)])−−−−−−−−−→c S@L(`+ κ) 0 ≤ ` ≤ NS@L− κ
((α, κ)⊕ S@L)(`)(α,[S@L:⊕(`,κ)])−−−−−−−−−−→c S@L(`) κ ≤ ` ≤ NS@L
((α, κ) S@L)(`)(α,[S@L:(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
((α, κ)� S@L)(`)(α,[S@L:�(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics
I operational semantics for capability relation −→c
I Prefix rules
((α, κ) ↓ S@L)(`)(α,[S@L:↓(`,κ)])−−−−−−−−−→c S@L(`− κ) κ ≤ ` ≤ NS@L
((α, κ) ↑ S@L)(`)(α,[S@L:↑(`,κ)])−−−−−−−−−→c S@L(`+ κ) 0 ≤ ` ≤ NS@L− κ
((α, κ)⊕ S@L)(`)(α,[S@L:⊕(`,κ)])−−−−−−−−−−→c S@L(`) κ ≤ ` ≤ NS@L
((α, κ) S@L)(`)(α,[S@L:(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
((α, κ)� S@L)(`)(α,[S@L:�(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics
I operational semantics for capability relation −→c
I Prefix rules
((α, κ) ↓ S@L)(`)(α,[S@L:↓(`,κ)])−−−−−−−−−→c S@L(`− κ) κ ≤ ` ≤ NS@L
((α, κ) ↑ S@L)(`)(α,[S@L:↑(`,κ)])−−−−−−−−−→c S@L(`+ κ) 0 ≤ ` ≤ NS@L− κ
((α, κ)⊕ S@L)(`)(α,[S@L:⊕(`,κ)])−−−−−−−−−−→c S@L(`) κ ≤ ` ≤ NS@L
((α, κ) S@L)(`)(α,[S@L:(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
((α, κ)� S@L)(`)(α,[S@L:�(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics
I operational semantics for capability relation −→c
I Prefix rules
((α, κ) ↓ S@L)(`)(α,[S@L:↓(`,κ)])−−−−−−−−−→c S@L(`− κ) κ ≤ ` ≤ NS@L
((α, κ) ↑ S@L)(`)(α,[S@L:↑(`,κ)])−−−−−−−−−→c S@L(`+ κ) 0 ≤ ` ≤ NS@L− κ
((α, κ)⊕ S@L)(`)(α,[S@L:⊕(`,κ)])−−−−−−−−−−→c S@L(`) κ ≤ ` ≤ NS@L
((α, κ) S@L)(`)(α,[S@L:(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
((α, κ)� S@L)(`)(α,[S@L:�(`,κ)])−−−−−−−−−−→c S@L(`) 0 ≤ ` ≤ NS@L
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics (continued)
I Cooperation for α ∈ M
P(α,v)−−−→c P ′ Q
(α,u)−−−→c Q ′
P BCM
Q(α,v ::u)−−−−→c P ′ BC
MQ ′
α ∈ M
I 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 ′〉
I rate function fα uses information about the species andlocations in the string v , together with the species andlocation information and rate parameters in calculating theactual rate of the reaction
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics (continued)
I Cooperation for α ∈ M
P(α,v)−−−→c P ′ Q
(α,u)−−−→c Q ′
P BCM
Q(α,v ::u)−−−−→c P ′ BC
MQ ′
α ∈ M
I 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 ′〉
I rate function fα uses information about the species andlocations in the string v , together with the species andlocation information and rate parameters in calculating theactual rate of the reaction
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA semantics (continued)
I Cooperation for α ∈ M
P(α,v)−−−→c P ′ Q
(α,u)−−−→c Q ′
P BCM
Q(α,v ::u)−−−−→c P ′ BC
MQ ′
α ∈ M
I 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 ′〉
I rate function fα uses information about the species andlocations in the string v , together with the species andlocation information and rate parameters in calculating theactual rate of the reaction
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component seemed to make model insensitive to
changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradient
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component seemed to make model insensitive to
changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradient
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component seemed to make model insensitive to
changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradient
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src trafficking: combined loop model
membrane
perinuclearregion
20secon
ds
aSrc
FGF
FGFR
aFGFR
aSrc aFGFRaSrc Src
Src Src
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling progess with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component made model insenstive to changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradientI no match with experimental results but useful for discussions
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Combined loop trafficking model – results
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000
Time
aSrc at membraneaFGFR at membrane
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling progess with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component made model insenstive to changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradientI no match with experimental results but useful for discussions
I unnecessary to assume a combined loop for both behaviours
I found out about short and long recycling loops
I current: two loop modelI one short, one long
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling progess with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component made model insenstive to changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradientI no match with experimental results but useful for discussions
I unnecessary to assume a combined loop for both behaviours
I found out about short and long recycling loops
I current: two loop modelI one short, one long
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Modelling progess with Bio-PEPA
I modelled gradient successfully without cycle
I added gradient into model of trafficking with a combined loopI gradient component made model insenstive to changes
I very difficult to work with, too many parameters
I next: combined loop model with abstract gradientI no match with experimental results but useful for discussions
I unnecessary to assume a combined loop for both behaviours
I found out about short and long recycling loops
I current: two loop modelI one short, one long
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Src trafficking: two loop model
membrane
perinuclearregion
10se
con
ds20
second
s
aSrc
FGF
FGFR
aFGFR
aSrc
aFGFRaFGFR
aSrc Src
Src Src
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Two loop trafficking model – results
0
5000
10000
15000
20000
25000
30000
35000
40000
0 20000 40000 60000 80000 100000Time
aSrc at membraneaFGFR at membrane
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA Eclipse Plug-in
I software tool for Bio-PEPA modelling
I Eclipse front-end and separate back-end library
editor for the Bio-PEPA language
outline view for the reaction-centric view
graphing support via common plugin
problems viewUser
Interface
parser for the Bio-PEPA language
export facility (SBML; PRISM)
ISBJava time series analysis (ODE, SSA)
static analysis
Core
I available for download at www.biopepa.org
I case studies, publications, manuals
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA Eclipse Plug-in
I software tool for Bio-PEPA modelling
I Eclipse front-end and separate back-end library
editor for the Bio-PEPA language
outline view for the reaction-centric view
graphing support via common plugin
problems viewUser
Interface
parser for the Bio-PEPA language
export facility (SBML; PRISM)
ISBJava time series analysis (ODE, SSA)
static analysis
Core
I available for download at www.biopepa.org
I case studies, publications, manuals
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA Eclipse Plug-in
I software tool for Bio-PEPA modelling
I Eclipse front-end and separate back-end library
editor for the Bio-PEPA language
outline view for the reaction-centric view
graphing support via common plugin
problems viewUser
Interface
parser for the Bio-PEPA language
export facility (SBML; PRISM)
ISBJava time series analysis (ODE, SSA)
static analysis
Core
I available for download at www.biopepa.org
I case studies, publications, manuals
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Simplified Bio-PEPA model
I 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;
I endsome in short recycling loop
Endo short@cyto = (out sh,1) >> Endo short@cyto +
(in sh,1) << Endo short@cyto + ... ;
I model:
aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]
I reactions
out sh: 150 aSrc -> Endo short
in sh: Endo short -> 75 aSrc
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Simplified Bio-PEPA model
I 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;
I endsome in short recycling loop
Endo short@cyto = (out sh,1) >> Endo short@cyto +
(in sh,1) << Endo short@cyto + ... ;
I model:
aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]
I reactions
out sh: 150 aSrc -> Endo short
in sh: Endo short -> 75 aSrc
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Simplified Bio-PEPA model
I 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;
I endsome in short recycling loop
Endo short@cyto = (out sh,1) >> Endo short@cyto +
(in sh,1) << Endo short@cyto + ... ;
I model:
aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]
I reactions
out sh: 150 aSrc -> Endo short
in sh: Endo short -> 75 aSrc
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Simplified Bio-PEPA model
I 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;
I endsome in short recycling loop
Endo short@cyto = (out sh,1) >> Endo short@cyto +
(in sh,1) << Endo short@cyto + ... ;
I model:
aSrc@mb[initial aSrc mb] <*> Endo short@cyto[initial Endo short]
I reactions
out sh: 150 aSrc -> Endo short
in sh: Endo short -> 75 aSrc
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents
controllers
(C1(V) BC∗ · · · BC∗ Cn(V)
)
BC∗(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents
controllers
(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)
controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)
controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE
subcomponents controllers(C1(V) BC∗ · · · BC∗ Cn(V)
)BC∗
(Con1 BC∗ · · · BC∗ Conm
)controller grammar
M ::= a.M | 0 | M + M
Con ::= M | Con BC∗ Con
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE applied to biology
I a model has n variables defined over R: species quantities
I each subcomponent represents flows affecting a variable:production, binding, activation, degradation, removal
I each influence represents a specific flow: degradation
I each controller represents sequencing of events: day/nightcycle
I each discrete event represents something happeninginstantaneously when a condition becomes true, with apossible change of values: addition of growth factor
I each stochastic event represents something happening aftertime has passed, with a possible change of values: transport
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE modelling
I output of model is a trajectory consisting ofI continuous paths in Rn
I jumps/changes in values as events happen
I piecewise deterministic Markov process
I transition-driven stochastic hybrid automata
I major differences from Bio-PEPAI HYPE allows coordinate model of space rather than explicit
abstract locations
I HYPE allows continuous and stochastic behaviour together
I likely to be valuable when small quantities of some species
I application to protein traffickingI work in progressI SimHyA simulator
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE modelling
I output of model is a trajectory consisting ofI continuous paths in Rn
I jumps/changes in values as events happen
I piecewise deterministic Markov process
I transition-driven stochastic hybrid automata
I major differences from Bio-PEPAI HYPE allows coordinate model of space rather than explicit
abstract locations
I HYPE allows continuous and stochastic behaviour together
I likely to be valuable when small quantities of some species
I application to protein traffickingI work in progressI SimHyA simulator
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Stochastic HYPE modelling
I output of model is a trajectory consisting ofI continuous paths in Rn
I jumps/changes in values as events happen
I piecewise deterministic Markov process
I transition-driven stochastic hybrid automata
I major differences from Bio-PEPAI HYPE allows coordinate model of space rather than explicit
abstract locations
I HYPE allows continuous and stochastic behaviour together
I likely to be valuable when small quantities of some species
I application to protein traffickingI work in progressI SimHyA simulator
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycle
I each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycle
I each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycle
I each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycle
I each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycleI each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycleI each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycleI each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
I synthetic network
I three genes with three inhibitors
I reporter of green flourescent protein (GFP)
I negative feedback cycleI each gene produces a protein
I protein inhibits transcription of mRNA by another gene
I other gene cannot produce its protein
I quantities of proteins oscillate over time
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator!"##"$% #& '(#)$"
**+ !"#$%& ' ()* +,- ' ., /"!$"%0 .,,, ' 111234567829:;
-, !<2 "5 =84>5 ?,, @3A@B@A64= 98== =@384C8> @3 849D :E 5D788 ;@97:F9:=:3@8> 1878 5749G8A;4364==HI 43A 5D8@7 J6:78>98398 @3583>@5H 14>K6435@L8A2#D8 5@;89:67>8 :E 5D8 J6:78>98398 :E :38 >69D 98== @> >D:13 @3
M@C2 .2 #8;N:74= :>9@==45@:3> O@3 5D@> 94>8 >6N87@;N:>8A :3 43:B874== @39784>8 @3 J6:78>98398P :9967 1@5D 4 N87@:A :E 47:63A?Q, ;@3658>I 7:6CD=H 5D788E:=A =:3C87 5D43 5D8 5HN@94= 98==FA@B@>@:35@;82 #D8 4;N=@56A8 :E :>9@==45@:3> @> =47C8 9:;N478A 1@5D R4>8=@38=8B8=> :E SMT J6:78>983982 "5 =84>5 +,U :E 98==> 1878 E:63A 5:8VD@R@5 :>9@==45:7H R8D4B@:67 @3 849D :E 5D8 5D788 ;:B@8>I 4>A8587;@38A RH 4 M:67@87 434=H>@> 97@587@:3 O>88 W85D:A>P2 #D8743C8 :E N87@:A>I 4> 8>5@;458A RH 5D8 A@>57@R65@:3 :E N84GF5:FN84G@3587B4=>I @> ?X,! +,;@3 O;843! >!A!I ! ! X-P2 "E587 >8N545@:3ISMT =8B8=> @3 5D8 51: >@R=@3C 98==> :E583 78;4@38A 9:778=458A 1@5D:38 43:5D87 E:7 =:3C N87@:A> :E 5@;8 OM@C2 -4Y9P2 Z4>8A :3 5D8434=H>@> :E ?[\ >8N545@:3 8B835> @3 5D8 - ;:B@8>I 18 ;84>678A 434B874C8 D4=EF5@;8 E:7 >@R=@3C A89:778=45@:3 :E \Q! ?,;@3I 1D@9D @>=:3C87 5D43 5D8 5HN@94= 98==FA@B@>@:3 5@;8> :E Q,Y[,;@3 63A87 5D8>89:3A@5@:3>2 #D@> @3A@9458> 5D45 5D8 >5458 :E 5D8 3851:7G @> 5743>F;@558A 5: 5D8 N7:C83H 98==>I A8>N@58 4 >57:3C 3:@>8 9:;N:38352 ]8:R>87B8A >@C3@L9435 B47@45@:3> @3 5D8 N87@:A 43A 4;N=@56A8 :E 5D8:>9@==45:7 :65N65 R:5D E7:; 98== 5: 98== OM@C2 -API 43A :B87 5@;8 @3 4>@3C=8 98== 43A @5> A8>983A435> OM@C2 -4Y9P2 ^3 >:;8 @3A@B@A64=>IN87@:A> 1878 :;@558A :7 ND4>8 A8=4H8A @3 :38 98== 78=45@B8 5: @5>>@R=@3C OM@C2 -4I 9P2%89835 5D8:785@94= 1:7G D4> >D:13 5D45 >5:9D4>5@9 8EE895> ;4H
R8 78>N:3>@R=8 E:7 3:@>H :N8745@:3 @3 345674= C838F8VN78>>@:33851:7G>?.2 _@;6=45@:3> :E 5D8 78N78>>@=45:7 5D45 54G8 @35: 499:6355D8 >5:9D4>5@9 345678 :E 78495@:3 8B835> 43A A@>9785838>> :E 3851:7G9:;N:3835> 4=>: 8VD@R@5 >@C3@L9435 B47@4R@=@5HI 78A69@3C 5D8 9:778F=45@:3 5@;8 E:7 :>9@==45@:3> E7:; @3L3@5H O@3 5D8 9:35@36:6> ;:A8=P5: 4R:65 51: N87@:A> OZ:V ?I M@C2 ?9I @3>85>P2 ^3 C83874=I 18 1:6=A=@G8 5: A@>5@3C6@>D >69D >5:9D4>5@9 8EE895> E7:; N:>>@R=8 @357@3>@94==H9:;N=8V AH34;@9> O>69D 4> @3587;@558398 :7 9D4:5@9 R8D4B@:67P2M675D87 >56A@8> 478 388A8A 5: @A835@EH 43A 9D4749587@`8 5D8 >:6798>:E J695645@:3> @3 5D8 78N78>>@=45:7 43A :5D87 A8>@C38A 3851:7G>2 ^3N475@96=47I =:3C87 8VN87@;835> N87E:7;8A 63A87 9D8;:>545@9 9:3FA@5@:3> >D:6=A 834R=8 ;:78 9:;N=858 >545@>5@94= 9D4749587@`45@:3 :E
TetR
LacIλ cI
Repressilator Reporter
TetR
GFP
a
PLlac01
PLtet01
PLtet01
pSC101origin
ColE1
tetR-lite
gfp-aav
lacI-lite
λ cI-lite
ampR
kanR
λPR
!"#$%& ' !"#$%&'(%)"#* +,$)-# .#+ $)/'0.%)"# "1 %2, &,3&,$$)0.%"&4 (* 52, &,3&,$$)0.%"&
#,%6"&74 52, &,3&,$$)0.%"& )$ . (8(0)( #,-.%)9,:1,,+;.(7 0""3 ("/3"$,+ "1 %2&,, &,3&,$$"&
-,#,$ .#+ %2,)& ("&&,$3"#+)#- 3&"/"%,&$* .$ $2"6# $(2,/.%)(.008 )# %2, (,#%&, "1 %2,
0,1%:2.#+ 30.$/)+4 <% '$,$ =>0.(?@ .#+ =>%,%?@* 62)(2 .&, $%&"#-* %)-2%08 &,3&,$$);0,
3&"/"%,&$ ("#%.)#)#- !"# .#+ $%$ "3,&.%"&$* &,$3,(%)9,08A* .$ 6,00 .$ =B* %2, &)-2% 3&"/"%,&
1&"/ 32.-, " C$,, D,%2"+$E4 52, $%.;)0)%8 "1 %2, %2&,, &,3&,$$"&$ )$ &,+'(,+ ;8 %2,
3&,$,#(, "1 +,$%&'(%)"# %.-$ C+,#"%,+ F!&$%GE4 52, ("/3.%);0, &,3"&%,& 30.$/)+ C&)-2%E
,H3&,$$,$ .# )#%,&/,+).%,:$%.;)0)%8 IJ= 9.&).#%@@ C'()*""+E4 <# ;"%2 30.$/)+$* %&.#$(&)3:
%)"#.0 '#)%$ .&, )$"0.%,+ 1&"/ #,)-2;"'&)#- &,-)"#$ ;8 5@ %,&/)#.%"&$ 1&"/ %2, ,- #.!& //01
"3,&"# C;0.(7 ;"H,$E4 )* K%.;)0)%8 +).-&./ 1"& . ("#%)#'"'$ $8//,%&)( &,3&,$$)0.%"& /"+,0
CL"H @E4 52, 3.&./,%,& $3.(, )$ +)9)+,+ )#%" %6" &,-)"#$ )# 62)(2 %2, $%,.+8 $%.%, )$ $%.;0,
C%"3 0,1%E "& '#$%.;0, C;"%%"/ &)-2%E4 !'&9,$ M* L .#+ ! /.&7 %2, ;"'#+.&),$ ;,%6,,# %2,
%6" &,-)"#$ 1"& +)11,&,#% 3.&./,%,& 9.0',$N M* 0 ! O!@* #P ! PQ L* 0 ! O* #P ! PQ !*
0 ! O* #P"# ! @P$ R4 52, '#$%.;0, &,-)"# CME* 62)(2 )#(0'+,$ '#$%.;0, &,-)"#$ CLE .#+
C!E* )$ $2.+,+4 ** ?$()00.%)"#$ )# %2, 0,9,0$ "1 %2, %2&,, &,3&,$$"& 3&"%,)#$* .$ ";%.)#,+ ;8
#'/,&)(.0 )#%,-&.%)"#4 >,1%* . $,% "1 %83)(.0 3.&./,%,& 9.0',$* /.&7,+ ;8 %2, FSG )# )* 6,&,'$,+ %" $"09, %2, ("#%)#'"'$ /"+,04 B)-2%* . $)/)0.& $,% "1 3.&./,%,&$ 6.$ '$,+ %" $"09, .
$%"(2.$%)( 9,&$)"# "1 %2, /"+,0 CL"H @E4 !"0"'& ("+)#- )$ .$ )# (4 <#$,%$ $2"6 %2,
#"&/.0)T,+ .'%"("&&,0.%)"# 1'#(%)"# "1 %2, U&$% &,3&,$$"& $3,(),$4
steady stateunstable
Maximum proteins per cell, ! (× KM)
Prot
ein
lifet
ime/
mR
NA
life
time,
" A
B
C
b
steady statestable
0 500 10000
4,000
6,000
Time (min)
Prot
eins
per
cel
l
0 500 1,000-1
0
1
0 500 1,0000
2,000 2,000
4,000
6,000
Time (min)
0 500 1,000-1
0
1
c
0 100 200 300 400 500 6000
20
40
60
80
100
120
60 140 250 300 390 450 550 600
Fluo
resc
ence
(arb
itrar
y un
its)
Time (min)
Time (min)
a
b
c
!"#$%& + B,3&,$$)0.%)"# )# 0)9)#- ;.(%,&).4 (* )* 52, -&"6%2 .#+ %)/,("'&$, "1 IJ=
,H3&,$$)"# 1"& . $)#-0, (,00 "1 ,- #.!& 2"$% $%&.)# D!V@PP ("#%.)#)#- %2, &,3&,$$)0.%"&
30.$/)+$ CJ)-4 @.E4 K#.3$2"%$ "1 . -&"6)#- /)(&"("0"#8 6,&, %.7,# 3,&)"+)(.008 ;"%2 )#
W'"&,$(,#(, C(E .#+ ;&)-2%:U,0+ C)E4 ** 52, 3)(%'&,$ )# ( .#+ ) ("&&,$3"#+ %" 3,.7$ .#+
%&"'-2$ )# %2, %)/,("'&$, "1 IJ= W'"&,$(,#(, +,#$)%8 "1 %2, $,0,(%,+ (,004 K(.0, ;.&*
V%/4 L.&$ .% %2, ;"%%"/ "1 * )#+)(.%, %2, %)/)#- "1 $,3%.%)"# ,9,#%$* .$ ,$%)/.%,+ 1&"/
;&)-2%:U,0+ )/.-,$4
Elowitz and Leibler, Nature 403, 335-338.
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA
−−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA
−−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA
−−→trlA
PrA
↓ dmA
↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA
↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator
GeneA −−→trsA
mRNAA −−→trlA
PrA↓ dmA ↓ dpA
GeneA −−−−−−−−−−−−→kp
PrA↓ kd
GeneB −−→trsB
mRNAB −−→trlB
PrB↓ dmB ↓ dpB
GeneB −−−−−−−−−−−−→kp
PrB↓ kd
GeneC −−→trsC
mRNAC −−→trlC
PrC↓ dmC ↓ dpC
GeneC −−−−−−−−−−−−→kp
PrC↓ kd
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator in HYPE
I degradation and production flows for Gene A:
GdgA (X )
def= init : (dA,−kd , linear(X )).Gdg
A (X )
GprA
def= inhibitA : (pA, 0, const).Gpr
A
+ expressA : (pA, kp, const).GprA
+ init : (pA, kp, const).GprA
I composed: GeneA(A)def= (Gdg
A (A) BC∗ GprA )
I “controller”: ConAdef= inhibitA.expressA.ConA
I influences mapped to variables: iv(dA) = A iv(pA) = A
I event conditions: ec(inhibitA) = (C > p, true)ec(expressA) = (C ≤ p, true)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator in HYPE
I degradation and production flows for Gene A:
GdgA (X )
def= init : (dA,−kd , linear(X )).Gdg
A (X )
GprA
def= inhibitA : (pA, 0, const).Gpr
A
+ expressA : (pA, kp, const).GprA
+ init : (pA, kp, const).GprA
I composed: GeneA(A)def= (Gdg
A (A) BC∗ GprA )
I “controller”: ConAdef= inhibitA.expressA.ConA
I influences mapped to variables: iv(dA) = A iv(pA) = A
I event conditions: ec(inhibitA) = (C > p, true)ec(expressA) = (C ≤ p, true)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator in HYPE
I degradation and production flows for Gene A:
GdgA (X )
def= init : (dA,−kd , linear(X )).Gdg
A (X )
GprA
def= inhibitA : (pA, 0, const).Gpr
A
+ expressA : (pA, kp, const).GprA
+ init : (pA, kp, const).GprA
I composed: GeneA(A)def= (Gdg
A (A) BC∗ GprA )
I “controller”: ConAdef= inhibitA.expressA.ConA
I influences mapped to variables: iv(dA) = A iv(pA) = A
I event conditions: ec(inhibitA) = (C > p, true)ec(expressA) = (C ≤ p, true)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator in HYPE
I degradation and production flows for Gene A:
GdgA (X )
def= init : (dA,−kd , linear(X )).Gdg
A (X )
GprA
def= inhibitA : (pA, 0, const).Gpr
A
+ expressA : (pA, kp, const).GprA
+ init : (pA, kp, const).GprA
I composed: GeneA(A)def= (Gdg
A (A) BC∗ GprA )
I “controller”: ConAdef= inhibitA.expressA.ConA
I influences mapped to variables: iv(dA) = A iv(pA) = A
I event conditions: ec(inhibitA) = (C > p, true)ec(expressA) = (C ≤ p, true)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator in HYPE
I degradation and production flows for Gene A:
GdgA (X )
def= init : (dA,−kd , linear(X )).Gdg
A (X )
GprA
def= inhibitA : (pA, 0, const).Gpr
A
+ expressA : (pA, kp, const).GprA
+ init : (pA, kp, const).GprA
I composed: GeneA(A)def= (Gdg
A (A) BC∗ GprA )
I “controller”: ConAdef= inhibitA.expressA.ConA
I influences mapped to variables: iv(dA) = A iv(pA) = A
I event conditions: ec(inhibitA) = (C > p, true)ec(expressA) = (C ≤ p, true)
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator – protein levels over time
(GeneA(A) BC∗ GeneB(B) BC∗ GeneC (C )) BC∗ init.(ConA ‖ ConB ‖ ConC )
0 500 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
The Repressilator – protein levels over time
(GeneA(A) BC∗ GeneB(B) BC∗ GeneC (C )) BC∗ init.(ConA ‖ ConB ‖ ConC )
0 500 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Conclusions
Biology + Computing = ??
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Conclusions
Computing + Biology = ??
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Conclusions
Computing + Biology = ??
I using powerful mathematical models from computer science tomodel biology and in the longer term, to provide predictions
I major challenges
I lack of data, models are often quasi-quantitative
I getting right level of abstraction for useful models
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Acknowledgements
PEPA Group DMGUniversity of Edinburgh University of TriesteJane Hillston Luca BortolussiStephen GilmoreAllan Clark Cancer Research UKMaria Luisa Guerriero EdinburghFederica Ciocchetta Margaret FrameAdam Duguid Emma Sandilands
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Thank you
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}
I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}
I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Bio-PEPA syntax
I two-level syntax
I sequential component, species
S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient
I ↑ product, ↓ reactant
I ⊕ activator, inhibitor, � generic modifier
I model component, system
P ::= S(`) | P BCLP
I need a more constrained form
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Well-defined Bio-PEPA systems
I well-defined Bio-PEPA species
Cdef= (α1, κ1)op1C +. . .+(αn, κn)opnC with all αi ’s distinct
I well-defined Bio-PEPA model
Pdef= C1(`1) BC
L1. . . BC
Lm−1Cm(`m) with all Ci ’s distinct
I well-defined Bio-PEPA system
P = 〈V,N ,K,F ,Comp,P〉
I well-defined Bio-PEPA model component with levelsI minimum and maximum concentrations/number of moleculesI fix step size, convert to minimum and maximum levelsI species S : 0 to NS levels
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) where
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme
I S + E −→←− SE −→ P + E
I S(`S) BC∗
E (`E ) BC∗
SE (`SE ) BC∗
P(`P) where
Sdef= (α, 1) ↓ S + (β, 1) ↑ S
Edef= (α, 1) ↓ E + (β, 1) ↑ E + (γ, 1) ↑ E
SEdef= (α, 1) ↑ SE + (β, 1) ↓ SE + (γ, 1) ↓ SE
Pdef= (γ, 1) ↑ P
I SE−→ P
I S ′(`S′) BC∗
E ′(`E ′) BC∗
P ′(`P′) 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme, max level 3
I state vector (S ,E , SE ,P) and NS = NE = NSE = NP = 3
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme, max level 3
I 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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Example: reaction with enzyme, max level 7
I 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
βββββββα α α α α α
ββββββα α α α α
βββββα α α α
ββββα α α
βββα α
ββα
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 = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters
I initial parameters for species representing basal behaviourI no decision species, no added FGF, no active FGFRI long recycling loop inactive so no species from itI hence only 3 species present initially
I rate of entry and probability of recycling in each loop
I input and output stoichiometry for each loopI short loop: input and output the sameI long loop: output much larger than input
I creation rate of active Src during basal behaviour
I binding rate for active Src and active FGFR
I time to pick up inactive Src in perinuclear region
I assume time taken in each loop fixed using calculations
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters
I initial parameters for species representing basal behaviourI no decision species, no added FGF, no active FGFRI long recycling loop inactive so no species from itI hence only 3 species present initially
I rate of entry and probability of recycling in each loop
I input and output stoichiometry for each loopI short loop: input and output the sameI long loop: output much larger than input
I creation rate of active Src during basal behaviour
I binding rate for active Src and active FGFR
I time to pick up inactive Src in perinuclear region
I assume time taken in each loop fixed using calculations
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters
I initial parameters for species representing basal behaviourI no decision species, no added FGF, no active FGFRI long recycling loop inactive so no species from itI hence only 3 species present initially
I rate of entry and probability of recycling in each loop
I input and output stoichiometry for each loopI short loop: input and output the sameI long loop: output much larger than input
I creation rate of active Src during basal behaviour
I binding rate for active Src and active FGFR
I time to pick up inactive Src in perinuclear region
I assume time taken in each loop fixed using calculations
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters
I initial parameters for species representing basal behaviourI no decision species, no added FGF, no active FGFRI long recycling loop inactive so no species from itI hence only 3 species present initially
I rate of entry and probability of recycling in each loop
I input and output stoichiometry for each loopI short loop: input and output the sameI long loop: output much larger than input
I creation rate of active Src during basal behaviour
I binding rate for active Src and active FGFR
I time to pick up inactive Src in perinuclear region
I assume time taken in each loop fixed using calculations
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters (continued)
I at least 13 unknown parameters – not so simple
I enable short recycling loop only
I find parameters to balance short loopI 50% of active Src at membraneI 50% of active Src in the short recycling loop
I 6 parameters not yet specified
I enable the long recycling loop
I guess some parameters
I enable the doser and see what happens
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters (continued)
I at least 13 unknown parameters – not so simple
I enable short recycling loop only
I find parameters to balance short loopI 50% of active Src at membraneI 50% of active Src in the short recycling loop
I 6 parameters not yet specified
I enable the long recycling loop
I guess some parameters
I enable the doser and see what happens
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??
Protein Trafficking Modelling Biology Process Algebras Bio-PEPA HYPE Conclusions
Parameters (continued)
I at least 13 unknown parameters – not so simple
I enable short recycling loop only
I find parameters to balance short loopI 50% of active Src at membraneI 50% of active Src in the short recycling loop
I 6 parameters not yet specified
I enable the long recycling loop
I guess some parameters
I enable the doser and see what happens
Vashti Galpin
Modelling protein trafficking: progress and challenges Biology + Computing = ??