can a combination of constrained-based and kinetic modeling bridge time scales in progressive...
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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 2 19-8-2013
Systems biology and metabolic diseases
• Changes in metabolism associated with multi-factorial, progressive diseases
/ biomedical engineering PAGE 3 19-8-2013
Kinetic modeling
• ATP metabolism in mitochondria
/ biomedical engineering PAGE 4 19-8-2013
Chance, Comput Biomed Res.1967;1:251-64.
Schmitz et al. PLoS ONE 2012, 7(3): e34118.
Kinetic modeling
/ biomedical engineering PAGE 5 19-8-2013
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
/ biomedical engineering PAGE 6 19-8-2013
• 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
/ biomedical engineering PAGE 7 19-8-2013
2
1
( )( )N
i id
i i
y dXσ=
−
∑ pp
( )ˆ arg min ( )dX=p
p p
( ) ( ( ), , )d t t tdt
=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
/ biomedical engineering PAGE 8 19-8-2013
• Preclinical research
• Cohort studies: cross-sectional e.g. BMI matched
• Patient-specific (VPH, ITFoM)
/ biomedical engineering PAGE 9 19-8-2013
/ biomedical engineering PAGE 10 19-8-2013
• 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
/ biomedical engineering PAGE 11 19-8-2013
0 10 200
100
200Hepatic TG
Time [days]
[um
ol/g
]
0 10 200
1
2
3Hepatic CE
Time [days]
[um
ol/g
]
0 10 200
2
4
6Hepatic FC
Time [days]
[um
ol/g
]
0 10 200
50
100Hepatic TG
Time [days]
[um
ol]
0 10 200
0.5
1
1.5Hepatic CE
Time [days]
[um
ol]
0 10 200
2
4Hepatic FC
Time [days]
[um
ol]
0 10 200
1000
2000
3000Plasma CE
Time [days]
[um
ol/L
]
0 10 200
1000
2000
3000HDL-CE
Time [days]
[um
ol/L
]
0 10 200
500
1000
1500Plasma TG
Time [days]
[um
ol/L
]
0 10 206
8
10
12VLDL clearance
Time [days]
[-]
0 10 20100
200
300
400ratio TG/CE
Time [days]
[-]
0 10 200
5
10
15VLDL diameter
Time [days]
[nm
]
0 10 200
1
2
3VLDL-TG production
Time [days]
[um
ol/h
]
0 10 201
2
3Hepatic mass
Time [days]
[gra
m]
0 10 200
0.2
0.4DNL
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
/ biomedical engineering PAGE 12 19-8-2013
Metabolome
Proteome
Transcriptome
Parameter Trajectory Analysis (PTA)
• Algorithm: nesting of simulation and parameter estimation
/ biomedical engineering PAGE 13 19-8-2013
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 tdt
=s Nv s p
( ) ( ( ) ,( ), )d t t tdt
t=s Nv s p
2
1
( )( )N
i id
i i
y dXσ=
−
∑ pp
( )( )
ˆ ( ) arg min ( ( )dt
t X t=p
p p
Parameterization
• Sampling parameter space
• Single phenotype snapshot
/ biomedical engineering PAGE 14 19-8-2013
100
101
10210
2
103
104
TG formation (ER)
CE
form
atio
n (E
R)
LXR activation
reference
• Connecting phenotypes
• Numerical results • ensemble
• Visualization • 2D historgram
/ biomedical engineering PAGE 15 19-8-2013
Monte Carlo approach to assess different dynamic behavior
• To account for uncertainty in the data
/ biomedical engineering PAGE 16 19-8-2013
/ biomedical engineering PAGE 17 19-8-2013
…
Input
Output
From adaptations in metabolome…
• … to predict changes in proteome / transcriptome
/ biomedical engineering PAGE 18 8/19/2013
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
/ biomedical engineering PAGE 19 19-8-2013
• Experimental validation
Tiemann et al, submitted
The hepatic HDL-C uptake capacity is reduced upon LXR activation
/ biomedical engineering PAGE 20 19-8-2013
• 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
/ biomedical engineering PAGE 21 19-8-2013
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
/ biomedical engineering PAGE 22 19-8-2013
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
/ biomedical engineering PAGE 23 19-8-2013
…
Flux trajectories for acceptable parameter sets
/ biomedical engineering PAGE 24 19-8-2013
[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?
/ biomedical engineering PAGE 25 19-8-2013
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
/ biomedical engineering PAGE 26 19-8-2013
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’
• …
/ biomedical engineering PAGE 27 19-8-2013
A theoretical study
• Insight in the approach • Test and optimize computational methods • Identify possibilities for further improvements
/ biomedical engineering PAGE 28 19-8-2013
R1
u2
u1 1 S1
S3S2S4
3
4 5
2
7
6
1 2 3 4 5 0
0.5
1
1.5
2 S 1
1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5
S 2
1 2 3 4 5 0 0.2 0.4 0.6 0.8
1 S3
1 2 3 4 5 0
0.2
0.4
0.6
0.8 S 4
u2
u1 1 S1
S3S2S4
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’ / biomedical engineering PAGE 29 19-8-2013
Metabolome
Proteome
Transcriptome2 2
1 1
( )( )N M
i i id
i ii i
y d d dtdRNA dt
θ θχ θ λσ= =
−+
∑ ∑
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
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