Modelling yeast osmoregulation at different levels of resolution

Peter GennemarkUniversity of Gothenburg/Uppsala University

Content

Osmoregulation in yeastBayesian networks

Simple ODE models

Detailed ODE models

Agent-based models

Discussion

Osmosis

Osmosis: a net flow of water to the region of lower chemical potential of water

Flow proportional to the difference in chemical potential of water

Osmosis

Osmosis: a net flow of water to the region of lower chemical potential of water

Flow proportional to the difference in chemical potential of water

High osmotic pressure inside the cell

Water tends to flow into the cell

The cell wall counteracts expansion and creates a hydrostatic pressure

Response to osmotic shock in yeast

Cell

Add 0.5M NaCl to medium

Response to osmotic shock in yeast

Water

Seconds

Turgor pressure lost

Volume decreased

Cell

Add 0.5M NaCl to medium

Response to osmotic shock in yeast

Water

Seconds Hour(s)

Turgor pressure lost

Volume decreased Glycerol accumulates

Turgor pressure and volume recover

Water

Cell

Add 0.5M NaCl to medium

Response to osmotic shock in yeast

Water

Seconds Hour(s)

Turgor pressure lost

Volume decreased Glycerol accumulates

Turgor pressure and volume recover

Water

Cell

Add 0.5M NaCl to medium

Interesting modelling system

The system is relatively well-characterized, key components identified

Non-trivial complexity, with feedback control on different levels (difficult to understand from a drawing)

Modelling – an overview

Model Data

Simulation

Identification

Manual input of known parts

Manual input of specification and/or data

Content

Osmoregulation in yeast

Bayesian networksSimple ODE models

Detailed ODE models

Agent-based models

Discussion

Coarse Bayesian network model

Gat-Viks and Shamir, Genome research 2007

Coarse Bayesian network model

Gat-Viks and Shamir, Genome research 2007

Overview of the approach

Model Data

Simulation

Identification

Manual input of known parts

Manual input of data

Content

Osmoregulation in yeast

Bayesian networks

Simple ODE modelsDetailed ODE models

Agent-based models

Discussion

Ordinary Differential Equation (ODE) models

Law of mass action:v1 = k1 * A(t) * E(t)v2 = k2 * B(t)

ODEs:A'(t) = - v1 + v2B'(t) = v1 - v2

A B

Ev1

v2A B

Ev1

v2

Common forms in systems biology

Michaelis-Menten kinetics:

A B

Ev1

v1=k AAKM

X i '=v1v2v3 ...

Common forms in systems biology

Michaelis-Menten kinetics:

S-systems

A B

Ev1

X i '=ai∏j=1

n

X jg ij−bi∏

j=1

n

X jhij

v1=k AAKM

X i '=v1v2v3 ...

Common forms in systems biology

Michaelis-Menten kinetics:

S-systems

Generalized Mass Action (GMA)

A B

Ev1

X i '=ai∏j=1

n

X jg ij−bi∏

j=1

n

X jhij

X i '=∑j=1

N i

aij∏k=1

n

X kgijk

v1=k AAKM

X i '=v1v2v3 ...

Benchmarks for ODE identification

21,00cm

www.odeidentification.org

Simple ODE model by Mettetal et al. 2008

Simple ODE model by Mettetal et al. 2008

Overview of the approach

Model Data

Simulation

Identification

Choice of model type

Manual input of data

A simple model of yeast osmoregulation

Gennemark et al. 2006

A simple model of yeast osmoregulation

Gennemark et al. 2006

Vol’(t) = k ( Intra(t) – Extra(t) –Turgor(t) )

Intra(t) = (n + Glycerol(t) ) / ( Vol(t) – Vb )

T(t) = c ( Vol(t) / Vol0 - 1 ) + Turgor0

Extra(t) = input signal

A simple model of yeast osmoregulation

Gennemark et al. 2006

Vol’(t) = k ( Intra(t) – Extra(t) –Turgor(t) )

Intra(t) = (n + Glycerol(t) ) / ( Vol(t) – Vb )

T(t) = c ( Vol(t) / Vol0 - 1 ) + Turgor0

Extra(t) = input signal

Simulation, NaCl stress

wild-type open Fps1

Overview of the approach

Model Data

Simulation

Parameteridentification

Manual input of known parts

Manual input of data

Content

Osmoregulation in yeast

Bayesian networks

Simple ODE models

Detailed ODE modelsAgent-based models

Discussion

A detailed model (35 ODEs)

Klipp et al. 2005

One of the more complex ODEs

Klipp et al. 2005

A detailed model (35 ODEs)

Klipp et al. 2005

Overview of the approach

Model Data

Simulation

Parameteridentification

Manual input of known parts

Manual input of data

Content

Osmoregulation in yeast

Bayesian networks

Simple ODE models

Detailed ODE models

Agent-based modelsDiscussion

The next generation of modelling techniques: rule-based modelling

Accumulated evidence for molecular details of the HOG pathway

Scaffold proteins are common

The next generation of osmoregulation models

NES, nuclear export signalBD, binding domainNLS, nuclear localization signal

Tatebayashi et al. EMBO 2003

Accumulated evidence for molecular details of the HOG pathway

Scaffold proteins are common

The next generation of osmoregulation models

Accumulated evidence for molecular details of the HOG pathway

Scaffold proteins are common

NES, nuclear export signalBD, binding domainNLS, nuclear localization signalAID, autoinhibitory domain KD, kinase domain

Tatebayashi et al. EMBO 2003

Combinatorial complexity - ODE representation breaks down

Creator:Sun Microsystems, Inc. LanguageLevel:2

8 states for Ste11-Ste504 states for Pbs2 and for Hog12 states for Ssk2/22Sho1 can be in an inactive or active stateSome proteins may be absent→ 1900 states Kuhn et al., Genome inform. 2009

Reactions are dependent on state of the scaffolds

Activation of Ste11 by Ste20 is mediated by indirect docking via Ste50 and Cdc42.

Activation of Pbs2 by Ste11 is mediated by indirect docking via Ste50 and Sho1.

Tatebayashi et al. EMBO 2006

Our own traditional view of the pathway

Kuhn et al., Genome inform. 2009

Example of Kappa code

Sho1 has a state called x that is activated (a) and a docking site for Ste11

Sho1(x˜a,Ste11)

Example of Kappa code

Sho1 has a state called x that is activated (a) and a docking site for Ste11

Sho1(x˜a,Ste11)

Ste11 is phosphorylated (p) and has docking sites for both Sho1 and Cdc42

Ste11(x˜p,Sho1,Cdc42)

Example of Kappa code

Sho1 has a state called x that is activated (a) and a docking site for Ste11

Sho1(x˜a,Ste11)

Ste11 is phosphorylated (p) and has docking sites for both Sho1 and Cdc42

Ste11(x˜p,Sho1,Cdc42)

Association of active Sho1 to Ste11 requires that Ste11 is not bound to Cdc42. The phosphorylation state of Ste11 is arbitrary

Sho1(x˜a,Ste11),Ste11(Sho1,Cdc42) ->Sho1(x˜a,Ste11!1),Ste11(Sho1!1,Cdc42) @ 2.0

The phosphorylation of Pbs2 by Ste11 is assumed to require that both Ste11 and Pbs2 are bound to Sho1, and furthermore, that Ste11 is phosphorylated.

Ste11(x˜p,Sho1!1),Sho1(Ste11!1,Pbs2!2),Pbs2(x˜u,y˜u,Sho1!2) ->

Ste11(x˜p,Sho1!1),Sho1(Ste11!1,Pbs2!2),Pbs2(x˜p,y˜p,Sho1!2) @ 1.0

Example of Kappa code

Overview of the approach

Model Data

Simulation

Manual input of known parts

Manual input of data

Content

Osmoregulation in yeast

Bayesian networks

Simple ODE models

Detailed ODE models

Agent-based models

Discussion

One system can be modelled at various level of detail

Simple models:

Contributes to a better understanding of the phenomenon

Easy to understand

Less knowledge required to build the model

Easy to validate, simulate and modify

Better predictions(?)

One system can be modelled at various level of detail

Simple models:

Contributes to a better understanding of the phenomenon

Easy to understand

Less knowledge required to build the model

Easy to validate, simulate and modify

Better predictions(?)

Complex models:

Individual reactions are modelled, no black-box relationships

Easy to communicate details of the model/system

Easy to simulate different mutants

Desired properties of tools

Integration with other cellular processes like gene regulation and metabolism, and with the environment

Desired properties of tools

Integration with other cellular processes like gene regulation and metabolism, and with the environment

Compartments like the cytosol, nucleus and vacuole have individual properties and species concentrations

Desired properties of tools

Integration with other cellular processes like gene regulation and metabolism, and with the environment

Compartments like the cytosol, nucleus and vacuole have individual properties and species concentrations

Biological processes at the molecular level are stochastic, and deterministic simulation is not always an adequate approximation. Clearly, hybrid simulation methods are of interest when combining signalling pathways with metabolic systems in one model

Some toolsCellucidate, cellucidate.comRule-based, stochastic simulationNo full enumeration of ODEsNo compartments, algebraic equationsStrong GUI, intuitive language

Some toolsCellucidate, cellucidate.comRule-based, stochastic simulationNo full enumeration of ODEsNo compartments, algebraic equationsStrong GUI, intuitive language

Bionetgen, bionetgen.orgDeterministic simulationShares many properties with Cellucidate, in particular almost identical input languagesFull set of ODEs is automatically generatedCan be exported to SBML

Some toolsCellucidate, cellucidate.comRule-based, stochastic simulationNo full enumeration of ODEsNo compartments, algebraic equationsStrong GUI, intuitive language

Bionetgen, bionetgen.orgDeterministic simulationShares many properties with Cellucidate, in particular almost identical input languagesFull set of ODEs is automatically generatedCan be exported to SBML

PottersWheel, potterswheel.deODEs and deterministic simulationA range of analysis toolsFull set of ODEs is automatically generatedCode is less compact, requires additional manual workAlgebraic equations, compartmentsNo GUI for rule-based modelling

Key systems biology challenges

Model Data

Simulation

Identification

Manual input of known parts

Manual input of specification and/or data

Representation that allows flexibility, model comparison, model reduction etc.

Algorithms/software

Algorithms/software

Representation, formalization that allows computability.Efficent storage and querying

Representation, formalization that allows computability

Data pre-processing

Acknowlegements

Bodil Nordlander, Stefan Hohmann, K. V. S. Prasad (Gothenburg)

Clemens Kuhn, Edda Klipp (Berlin)

Vincent Danos (Edinburgh)