Can a combination of constrained-based and kinetic modeling bridge time scales in progressive diseases?

Lorentz workshop Multiscale Systems Biology of Cancer
Leiden, NL, Nov. 16, 2012
Natal van Riel
Dept. of Biomedical Engineering, n.a.w.v.riel@tue.nl

• Parameter Transition Analysis (PTA)
• Progressive adaptations in metabolism associated with
diseases (or therapeutic intervention)
• Linking phenotypes
• Integrate metabolome, proteome, transcriptome
• Indentifying and exploiting the structure of the parameter space
unidentifiability ↔ constraints paradox (?)
• Quantifying and analyzing uncertainty in model and data
/ biomedical engineering PAGE 219-8-2013

Systems biology and metabolic diseases
• Changes in metabolism associated with multi-factorial,
progressive diseases

Kinetic modeling
• ATP metabolism in mitochondria
Chance, Comput Biomed Res.1967;1:251-64.
Schmitz et al. PLoS ONE
2012, 7(3): e34118.

Kinetic modeling
Chalhoub et al, 2007 AJP Endocrinol 93(6): E1676-
liver
skeletal muscle
Schmitz,et al. Am J Physiol
Cell Physiol 2012 Oct 31

Constrained-based modeling
• Genome-Scale Metabolic Modeling (GSMM)
• Liver specific GSMM’s:
− Jerby, Shlomi and Ruppin 2010 Mol Sys Biol 6: 401
− Gille,…, Holzhutter 2010 Mol Syst Biol 6: 411
Constraints:
• Physical-chemical: network topology,
conservation of mass, thermodynamics
• Flux Balance Analysis (FBA)
• Data:
• Shlomi,…, Ruppin 2008 Nat Biotech 26: 1003

• Inverse problems
• Numerical optimization
• Variability / Uncertainty analysis
2
1
( )
( )
N
i i
d
i i
y d
X
σ=
 −
 
 
∑
p
p
( )ˆ arg min ( )dX=
p
p p
( )
( ( ), , )
d t
t t
dt
=
s
Nv s p
=Nv 0subject to
i i ia v b< <
( )ˆ arg max ( )X=
v
v v

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

• Preclinical research
• Cohort studies: cross-sectional
e.g. BMI matched
• Patient-specific (VPH, ITFoM)

• Different diets
• Genetic manipulation
• Pharmacological compounds
…
experiments
phenotype A
experiments
phenotype B
Identify adaptations

Modulate lipoprotein metabolism
• Activate Liver X Receptor (nuclear receptor)
plays a central role in the control of cellular lipid
and sterol metabolism
• Metabolic profiling
0 10 20
0
100
200
Hepatic TG
Time [days]
[umol/g]
0 10 20
0
1
2
3
Hepatic CE
Time [days]
[umol/g]
0 10 20
0
2
4
6
Hepatic FC
Time [days]
[umol/g]
0 10 20
0
50
100
Hepatic TG
Time [days]
[umol]
0 10 20
0
0.5
1
1.5
Hepatic CE
Time [days]
[umol]
0 10 20
0
2
4
Hepatic FC
Time [days]
[umol]
0 10 20
0
1000
2000
3000
Plasma CE
Time [days]
[umol/L]
0 10 20
0
1000
2000
3000
HDL-CE
Time [days]
[umol/L]
0 10 20
0
500
1000
1500
Plasma TG
Time [days]
[umol/L]
0 10 20
6
8
10
12
VLDL clearance
Time [days]
[-]
0 10 20
100
200
300
400
ratio TG/CE
Time [days]
[-]
0 10 20
0
5
10
15
VLDL diameter
Time [days]
[nm]
0 10 20
0
1
2
3
VLDL-TG production
Time [days]
[umol/h]
0 10 20
1
2
3
Hepatic mass
Time [days]
[gram]
0 10 20
0
0.2
0.4
DNL
Time [days]
[-]
• Computational model
Grefhorst et al. Atherosclerosis, 2012, 222: 382– 389
Tiemann et al. BMC Systems Biology, 2011, 5:174
Control, 1, 2, 4, 7, 14, 21 days

Phenotype snapshots
• Observed:
• Unobserved:
• Metabolic network topology
is invariant
• Adaptations in metabolism:
- metabolic control
- interaction with proteome and transcriptome
 Metabolic parameters (e.g. Vmax) can change
Metabolome
Proteome
Transcriptome

Parameter Trajectory Analysis (PTA)
• Algorithm: nesting of simulation and parameter estimation
Progressive disease /
Treatment intervention
Phenotype data at different
stages
Monte Carlo sampling of data
interpolants
Estimation of parameter and flux trajectories
Analysis
A priori information
Metabolic network topology
& Reaction kinetics
Differential Equation model
with time-dependent parameters
( )
( ( ), , )
d t
t t
dt
=
s
Nv s p
( )
( ( ) ,( ), )
d t
t t
dt
t=
s
Nv s p
2
1
( )
( )
N
i i
d
i i
y d
X
σ=
 −
 
 
∑
p
p
( )
( )
ˆ( ) arg min ( ( )d
t
t X t=
p
p p

Parameterization
• Sampling parameter space
• Single phenotype snapshot
10
0
10
1
10
2
10
2
10
3
10
4
TG formation (ER)
CEformation(ER)
LXR activation
reference
• Connecting phenotypes

• Numerical results
• ensemble
• Visualization
• 2D historgram

Monte Carlo approach to assess different
dynamic behavior
• To account for uncertainty in the data

…
Input
Output

From adaptations in metabolome…
• … to predict changes in proteome / transcriptome
/ biomedical engineering PAGE 188/19/2013
T0901317
LXR
model development
predict changes
Metabolome
Proteome
Transcriptome
enzyme parameter gene/protein
HDL-CE synthesis ABCA1
HDL-CE uptake SR-B1
FC production ABCG5
… …
Fas, Abcg5, Abcg8, Cyp7a1, Lpl, Pltp, Cd36

Effects of LXR activation
• Increased cholesterol efflux from periphery to HDL particles
• Accumulation of hepatic TG (hepatic steatosis)
• Metabolic adaptation: decreased
hepatic capacity to clear cholesterol
•  Predicts a decrease in SR-B1
• Experimental validation
Tiemann et al, submitted

The hepatic HDL-C uptake capacity is reduced
upon LXR activation
• The hepatic HDL-C uptake flux is increased (steatosis):
• increase in plasma HDL-C (metabolic control)
• transcriptional control (SR-B1) counteracts hepatic overloading
• Increase in plasma HDL-C is due to only a small imbalance in
uptake vs efflux in the beginning of the intervention

VLDL synthesis flux to plasma decreases
• VLDL-TG production is increased
• TG and CE content per VLDL particle increases 10 fold

Activation of LXR by pharmaceutical
compound T0901317
• Beneficial effect:
• increased excretion of cholesterol
from the body
• large, anti-atherogenic HDL
• Side effects:
• hepatic steatosis
• triglyceride-rich VLDL
• Model analysis predicts how side effects could be prevented
Liver section of mice
treated 4 days with LXR
agonist T0901317
Oil-Red-O staining for
neutral fat
hepatic steatosis
VLDL
HDL
T0901317

Is this possible with less data?
• A subset of the data (cross-sectional data)
• Only day 0 and day 4
…

Flux trajectories for acceptable parameter sets
[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?

Predictions about changes in gene/ protein
expression
• Clustering of scenarios - testable hypotheses
• Also here SR-B1 is predicted to be decreased
• Measuring ABCG5, but especially ABCA1 is predicted to be
discriminative
fluxes
parameters

Trajectories can be used for many analyses
• Analysis of the cascade of induced adaptations
• Sensitivity and control analyses
• Optimal experiment design
which additional measurement (which metabolite, when) is most
effective in reducing the uncertainty in a prediction of interest and
tradeoff with the ‘cost’
• …

A theoretical study
• Insight in the approach
• Test and optimize computational methods
• Identify possibilities for further improvements
R1
u2
u1 1 S1
S3S2
S4
3
4 5
2
7
6
1 2 3 4 50
0.5
1
1.5
2
S1
1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
S2
1 2 3 4 50
0.2
0.4
0.6
0.8
1
S3
1 2 3 4 50
0.2
0.4
0.6
0.8
S4
u2
u1 1 S1
S3S2
S4
3
4 5
2
Van Riel et al, submitted

Outlook: including other omics
• Transcriptomics
• Proteomics
• Trajectories correlating with
gene expression data are
more likely than parameter
changes that do not correlate
 ‘A transparent black box’
Metabolome
Proteome
Transcriptome2 2
1 1
( )
( )
N M
i i i
d
i ii i
y d d dt
dRNA dt
θ θ
χ θ λ
σ=
   −
+   
   
∑ ∑

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 Consortium
for 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

Can a combination of constrained-based and kinetic modeling bridge time scales in progressive diseases?

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Can a combination of constrained-based and kinetic modeling bridge time scales in progressive diseases?