Modelling protein trafficking: progress and challenges · Modelling protein tra cking: progress and challenges Biology + Computing = ?? Protein Tra ckingModelling BiologyProcess AlgebrasBio-PEPAHYPEConclusions

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 = ??


Outline

Protein Trafficking

Modelling Biology

Process Algebras

Bio-PEPA

HYPE

Conclusions

Vashti Galpin



Src protein

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

I in either inactive or active configuration

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Src protein



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Src protein: inactive and active

(Martin, Nature Rev. Mol. Cell Biol. 2, 2001)

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Src protein



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?

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Src protein








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Src protein








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Src protein








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Src protein








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Src protein








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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

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Endosomes









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Endosomes









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Endosomes









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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)

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Mechanisms



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Mechanisms: gradient from inactive to active

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

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Mechanisms



The persistence of active Src at the membrane is inversely relatedto the quantity of FGF added. (Sandilands et al, 2007)

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Mechanisms




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Mechanisms: persistence of response to FGF

(Sandilands et al, EMBO Reports 8, 2007)

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Mechanisms




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)

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Mechanisms




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)

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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

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

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I modelling aspects







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I modelling aspects







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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

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Experimental data








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Experimental data



I quantitative: persistence of response

I data from general literature





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Experimental data








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Experimental data





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

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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

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Process algebras

I history












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Process algebras

I history












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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

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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

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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

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Bio-PEPA syntax



where opi ∈ { ↓, ↑,⊕,,�}


Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax



where opi ∈ { ↓, ↑,⊕,,�}


Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax



where opi ∈ { ↓, ↑,⊕,,�}


Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax



where opi ∈ { ↓, ↑,⊕,,�}I model: quantities of species, interaction between species

Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax




Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax




Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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Bio-PEPA syntax




Pdef= S1@L1(x1) BC

∗. . . BC

∗Sp@Lp(xp)



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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

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Bio-PEPA semantics


I Prefix rules




((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

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Bio-PEPA semantics


I Prefix rules




((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

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Bio-PEPA semantics


I Prefix rules




((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

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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

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P(α,v)−−−→c P ′ Q

(α,u)−−−→c Q ′

P BCM

Q(α,v ::u)−−−−→c P ′ BC

MQ ′

α ∈ M


P(α,v)−−−→c P ′



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P(α,v)−−−→c P ′ Q

(α,u)−−−→c Q ′

P BCM

Q(α,v ::u)−−−−→c P ′ BC

MQ ′

α ∈ M


P(α,v)−−−→c P ′



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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

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changes



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changes



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Src trafficking: combined loop model

membrane

perinuclearregion

20secon

ds

aSrc

FGF

FGFR

aFGFR

aSrc aFGFRaSrc Src

Src Src

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Modelling progess with Bio-PEPA


I added gradient into model of trafficking with a combined loopI gradient component made model insenstive to changes


I next: combined loop model with abstract gradientI no match with experimental results but useful for discussions

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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

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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

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Src trafficking: two loop model

membrane

perinuclearregion

10se

con

ds20

second

s

aSrc

FGF

FGFR

aFGFR

aSrc

aFGFRaFGFR

aSrc Src

Src Src

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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

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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

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problems viewUser

Interface




static analysis

Core



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problems viewUser

Interface




static analysis

Core



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Bio-PEPA Eclipse Plug-in (continued)

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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

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I model:


I reactions



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I model:


I reactions



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I model:


I reactions



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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)

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Stochastic HYPE

subcomponents

controllers

(C1(V) BC∗ · · · BC∗ Cn(V)

)

BC∗(Con1 BC∗ · · · BC∗ Conm


C (V)def=∑j


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Stochastic HYPE

subcomponents

controllers

(C1(V) BC∗ · · · BC∗ Cn(V)

)BC∗



C (V)def=∑j


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Stochastic HYPE


)BC∗


)

well-defined subcomponent

C (V)def=∑j


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Stochastic HYPE


)BC∗



C (V)def=∑j


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Stochastic HYPE


)BC∗



C (V)def=∑j


subcomponents are parameterised by variables

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Stochastic HYPE


)BC∗



C (V)def=∑j


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Stochastic HYPE


)BC∗



C (V)def=∑j


events have event conditions: guards and resets

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Stochastic HYPE


)BC∗



C (V)def=∑j



ec(aj) = (f (V),V ′ = f ′(V)) discrete events

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Stochastic HYPE


)BC∗



C (V)def=∑j



ec(aj) = (f (V),V ′ = f ′(V)) discrete events

ec(aj) = (r ,V ′ = f ′(V)) stochastic events

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Stochastic HYPE


)BC∗



C (V)def=∑j


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Stochastic HYPE


)BC∗



C (V)def=∑j


influences are defined by a triple

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Stochastic HYPE


)BC∗



C (V)def=∑j



αj = (ιj , rj , I (V))

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Stochastic HYPE


)BC∗



C (V)def=∑j



αj = (ιj , rj , I (V))

influence names are mapped to variables

iv(ιj) ∈ V

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Stochastic HYPE


)BC∗


)

controller grammar

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

Con ::= M | Con BC∗ Con

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Stochastic HYPE


)BC∗


)

controller grammar

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


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Stochastic HYPE


)BC∗


)controller grammar

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


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Stochastic HYPE


)BC∗


)controller grammar

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


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Stochastic HYPE


)BC∗


)controller grammar

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


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Stochastic HYPE


)BC∗


)controller grammar

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


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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

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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

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abstract locations




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abstract locations




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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

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The Repressilator

I synthetic network








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The Repressilator

I synthetic network








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The Repressilator

I synthetic network








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The Repressilator

I synthetic network



I negative feedback cycleI each gene produces a protein




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The Repressilator

I synthetic network







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The Repressilator

I synthetic network







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The Repressilator

I synthetic network







Vashti Galpin



The Repressilator!"##"$% #& '(#)$"

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-, !<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



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



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



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



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



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



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



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



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



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



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



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



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



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





GdgA (X )


A (X )

GprA


A




A (A) BC∗ GprA )




Vashti Galpin





GdgA (X )


A (X )

GprA


A




A (A) BC∗ GprA )




Vashti Galpin





GdgA (X )


A (X )

GprA


A




A (A) BC∗ GprA )




Vashti Galpin





GdgA (X )


A (X )

GprA


A




A (A) BC∗ GprA )




Vashti Galpin



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



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



Conclusions

Biology + Computing = ??

Vashti Galpin



Conclusions

Computing + Biology = ??

Vashti Galpin



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



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



Thank you

Vashti Galpin



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



Bio-PEPA syntax

I two-level syntax


S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}

I α action, reaction name, κ stoichiometric coefficient




P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax


S ::= (α, κ) op S | S + S op ∈ {↑, ↓,⊕,,�}I α action, reaction name, κ stoichiometric coefficient




P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax






P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax






P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax






P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax






P ::= S(`) | P BCLP


Vashti Galpin



Bio-PEPA syntax

I two-level syntax






P ::= S(`) | P BCLP


Vashti Galpin



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







Pdef= C1(`1) BC

L1. . . BC





Vashti Galpin







Pdef= C1(`1) BC

L1. . . BC





Vashti Galpin







Pdef= C1(`1) BC

L1. . . BC





Vashti Galpin







Pdef= C1(`1) BC

L1. . . BC





Vashti Galpin







Pdef= C1(`1) BC

L1. . . BC





Vashti Galpin



Example: reaction with enzyme

I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) BC∗

SE (`SE ) BC∗

P(`P) where

I SE−→ P

I S ′(`S′) BC∗

E ′(È ′) BC∗

P ′(`P′) where

Vashti Galpin




I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

Vashti Galpin




I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

Vashti Galpin




I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

Vashti Galpin




I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

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I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

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I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

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I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

S ′ def= (γ, 1) ↓ S ′ E ′ def

= (γ, 1)⊕ E ′ P ′ def= (γ, 1) ↑ P ′

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I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

S ′ def= (γ, 1) ↓ S ′ E ′ def

= (γ, 1)⊕ E ′ P ′ def= (γ, 1) ↑ P ′

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I S + E −→←− SE −→ P + E

I S(`S) BC∗

E (È ) 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 ′(È ′) BC∗

P ′(`P′) where

S ′ def= (γ, 1) ↓ S ′ E ′ def

= (γ, 1)⊕ E ′ P ′ def= (γ, 1) ↑ P ′

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Example: reaction with enzyme, max level 3

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

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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

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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

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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

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Parameters








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Parameters








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Parameters








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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

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Vashti Galpin











Vashti Galpin


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