Modelling progressive metabolic diseases with parameter transition trajectories

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Virtual Physiological Human 2012 conference

Modelling progressive metabolic diseases with parameter transition trajectories London, UK, Sept. 20, 2012

Natal van Riel , Christian Tiemann, Peter Hilbers

Dept. of Biomedical Engineering, [email protected]

/ biomedical engineering 12-04-2023

Metabolic Syndrome (MetS)

• The characteristics of plasma lipoprotein profiles codetermine metabolic and cardiovascular disease risks

• Underlying molecular mechanisms are not fully understood• Multi-factorial and progressive

PAGE 2


Metabolism and metabolic networks

• Systems Medicine / Personalized Medicine / VPH

• Interaction networks reasonably well-known• History in quantification (experimental and modeling)• In vivo, cell-specific kinetics are lacking

PAGE 3


Integrating metabolic networks with regulating gene/protein circuits

Parameter Trajectory Analysis

PAGE 4

Metabolome

Proteome

Transcriptome

Tiemann et al. BMC Systems Biology, 2011, 5:174


A metabolic system with metabolite controlled, negative transcriptional feedback

• A perturbation acting on the gene/protein circuit encoding the repressor

• Time scales relevant to this phenotype:• Metabolic network – seconds• Gene regulatory circuit – minutes/hours• Progressive adaptation to the perturbation – days…

PAGE 5

• Experimental data:• metabolic profile (S1, S2, S3, S4)

• 5 stages (day 0, 1, 2, 3, 4)

0 1 2 3 40

0.5

1

1.5

2S1

0 1 2 3 4-0.2

0

0.2

0.4

0.6S2

0 1 2 3 40

0.5

1

1.5S3

0 1 2 3 40

0.5

1S4

R1

u2

u1 1 S1

S3S2S4

3

4 5

2

7

6


Model 1: one model for each stage

• Stoichiometry matrix

• ODE model

• Simulate steady-state• Infer from the data

PAGE 6

1 0 1 1 0

1 1 0 0 0

1 1 0 0 0

0 0 0 1 1

N

( )( ( ), , )

d tt t

dt

sNv s p

with the species concentrations collated in a vector and the reaction rates in a vector and kinetic parameters p

transcription:

day 0:

day 1, 2, 3, 4:

6 6 4

6

6

0.01

ˆ ( , )

v k S

k

k perturbation t

1 4[ ,..., ]Ts ss1 5[ ,..., ]Tv vv

R1

u2

u1 1 S1

S3S2S4

3

4 5

2

7

6

6̂k


Estimate transcription rate k6 for the days after the perturbation

PAGE 70 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

days

S1

S2

S3

S4

R1

u2

u1 1 S1

S3S2S4

3

4 5

2

7

6

00

0.002

0.004

0.006

0.008

0.01

k6

1 2 3 40

0.2

0.4

0.6

0.8

1

1.2x 10

-3

• Statistically acceptable fits and accurate parameter estimates


Results model 1

• Model 1:• Metabolic level: topology and interaction kinetics known• Gene / protein level: topology known, kinetic parameters

unknown (changing)• Kinetic parameters of the gene/protein circuit estimated from

experimental observations at the metabolic level (metabolic profiling) during the different stages of progression

• Resulting in 5 separate simulation models (one for each day)

PAGE 8


Model 2: Lacking information at gene/protein level

• Next, a more challenging but common scenario is explored:• Metabolic level: topology known, uncertainty in interaction

kinetics (kinetic parameters)• Gene / protein level: from functional genomics studies we

know that the intervention affects a gene/protein controlling reaction 1 (but molecular details are lacking)

• Same experimental observations, reflecting progressive metabolic adaptations after an intervention at day 0

PAGE 9

u2

u1 1 S1

S3S2S4

3

4 5

2

0 1 2 3 40

0.5

1

1.5

2S1

0 1 2 3 4-0.2

0

0.2

0.4

0.6S2

0 1 2 3 40

0.5

1

1.5S3

0 1 2 3 40

0.5

1S4


0 5 100

10

20

30Parameter k1, day 0

0 5 100

10

20


0 5 100

10

20


0 5 100

10

20


0 5 100

10

20


Analyze the data as individual ‘snapshots’

• Metabolic network without feedback

• The unknown adaptation at gene/protein level is translated into an unknown, but inferable value for the metabolic rate constant

• However, like in the approach with model 1, this ignores the fact that the snapshots are linked

PAGE 10

0 50 1000

1

2

3

0 50 1000

5

10

15

0 50 1000

2

4

6

8

10

0 50 1000

5

10

15

0 50 1000

5

10

15

Monte Carlo (drawing samples from the data distribution) MLE (weighting with the data variance)

( )( ( ), , )

d tt t

dt

sNv s p

1 1 1 2ˆv k u Smax

1 1 24( )m

Vv u S

K f S


Parameter Trajectory Analysis

• Using the model of the metabolic network to integrate and connect metabolomic data obtained at different stages of progressive adaptations after an intervention

PAGE 11

Treatment intervention

Experimental data at different stages

Monte Carlo sampling of data interpolants

Estimation of parameter and flux trajectories

Analysis

0 1 2 3 40

0.5

1

1.5

2S1

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5S2

0 1 2 3 40

0.2

0.4

0.6

0.8

1S3

Time (days)0 1 2 3 4

0

0.2

0.4

0.6

0.8S4

Time (days)

0 1 2 3 40

0.5

1

1.5

2S1

0 1 2 3 4-0.2

0

0.2

0.4

0.6S2

0 1 2 3 40

0.5

1

1.5S3

0 1 2 3 40

0.5

1S4

0 1 2 3 40

10

20

30

40

k1

0 2 40.5

1

1.5

2S1

0 2 40

0.5

1S2

0 2 40.5

1

1.5S3

0 2 40.4

0.6

0.8

1S4

0 2 40

0.5

1

1.5v1

0 2 40

0.5

1

1.5v2

0 2 40.05

0.1

0.15

0.2

0.25v3

0 2 40.4

0.6

0.8

1v4

0 2 40.4

0.6

0.8

1v5


Case study: LXR activation in mice

PAGE 12

Grefhorst et al. J. Biol. Chem. 2002Oosterveer et al. Prog. Lipid Res. 2010

Liver section of mice treated 4 days with LXR agonist T0901317

Oil-Red-O staining for neutral fat

hepatic steatosisLiver X Receptor (nuclear receptor)

Inferring parameter trajectories

/ biomedical engineering PAGE 1312-04-2023

• Metabolic phenotyping

• 22 parameters potentially change due to LXR activation

Flux trajectories for acceptable parameter sets

• Due uncertainty in data and model multiple solutions• Despite uncertainties most fluxes show constrained

trajectories


[mM]

[mM/h]

4 days after LXR activation

reference

Analysis of under-constrained trajectories

• Some show a clear pattern (positive correlation between HDL-CE synthesis and HDL-CE uptake by the liver), others just ‘clouds’ of solutions

• Can the ‘structure’ in one cross-section of the parameter space be used to interpret other flux adaptations?


Outlook

• Predictions about changes in gene/ protein expression:


HD

L-C

E u

ptak

e

T0901317

LXR

Metabolome

Proteome

Transcriptome

Fas, Abcg5, Abcg8, Cyp7a1, Lpl, Pltp, Cd36

fluxesparameters

enzyme parameter gene/proteinHDL-CE synthesis ABCA1HDL-CE uptake SR-B1FC production ABCG5

12-04-2023

PTA: Linking disease phenotypes

• Multi-time-scale modeling• Metabolism, metabolic networks and associated diseases• Integrate metabolome, proteome, transcriptome• Given the uncertainty in model and data different possible

solutions are explored

/ biomedical engineering PAGE 17

? ?

Metabolic profiling(‘snapshots’)

Long-termdynamics(phenotype transitions)

Acknowledgement

Collaborators• Computational Biology (TU/e)

• Ceylan Çölmekçi Öncü• Christian Tiemann• Joep Schmitz• Joep Vanlier• Huili Yuan• Peter Hilbers• Marijke Dermois• Gijs Hendriks• Fianne Sips• Sandra van Tienhoven• Robbin van den Eijnde• Bram Wijnen• Sjanneke Zwaan

Funding• Netherlands Genomics Initiative

Netherlands Consortiumfor Systems Biology

• AstraZeneca

• Univ. Medical Centre Groningen (NL)• Aldo Grefhorst• Maaike Oosterveer• Jan Albert Kuivenhoven• Barbara Bakker• Bert Groen

• Biomedical NMR (TU/e)• Klaas Nicolay• Jeanine Prompers

• Ko Willems-van Dijk, Leiden University Medical Center, Netherlands

• FP7-HEALTH.2012.2.1.2-2: Systems medicine: Applying systems biology approaches for understanding multifactorial human diseases and their co-morbidities, starting in 2013

Technology

Modelling progressive metabolic diseases with parameter transition trajectories