Roche Quantitative Systems Pharmacology methodology workshop February 4th-5th, 2016, Basel, Switzerland Bringing multi-level systems pharmacology models to life Natal van Riel Abstract Computational modelling in Systems Medicine and Systems Pharmacology addresses biological processes at different levels and scales. The quantification of model parameters from experimental data is a complicated task. It will be addressed how variance in data propagates into parameter estimates and, more importantly, model predictions. The Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT) approach is discussed as method to model dynamics at multiple time-scales. Two examples will be provided: 1) modelling of longitudinal data in a cohort of Type 2 Diabetics using different medication, and 2) the application in preclinical research studying the effect of liver X receptor activation on HDL metabolism and liver steatosis.

1. Roche QSP methodology workshop
February 5, 2016
Natal van Riel
Eindhoven University of Technology, the Netherlands
Department of Biomedical Engineering
Systems Biology and Metabolic Diseases
n.a.w.v.riel@tue.nl
@nvanriel

2. Outline
• Model parameterization / calibration
• Prediction Uncertainty Analysis (PUA)
• Analysis of Dynamic Adaptations in
Parameter Trajectories (ADAPT)
• Examples:
• modelling of longitudinal data in a cohort of
Type 2 Diabetics
• effect of liver X receptor activation on HDL
metabolism and liver steatosis
PAGE 2
SlideShare
http://www.slideshare.net/natalvanriel
measuring
modelling

3. Systems Biology and Metabolic Diseases
Metabolic Syndrome and comorbidities
• A multifaceted, multi-scale
problem
• macro-models
• micro-models
• Models of metabolism and its
regulatory systems
• Models for science
(understanding)
• Computational diagnostics
PAGE 3
Rask-Madsen et al. (2012) Arterioscler
Thromb Vasc Biol, 32(9):2052-2059

4. Different views on model parameterization
• A reductionistic view:
the whole can be understood by adding information of the parts
• Building models from existing subcomponents
tuning as little parameters as possible
• A ‘system identification’ approach: calibrating model to data
(PK-PD,…)
PAGE 4

5. / biomedical engineering PAGE 52/13/2016
Disease progression in type 2
diabetes

6. Disease progression and treatment of T2DM
• 1 year follow-up of treatment-naïve T2DM patients (n=2408)
• 3 treatment arms: monotherapy with different hypoglycemic
agents
• Pioglitazone - insulin
sensitizer
− enhances peripheral
glucose uptake
− reduces hepatic glucose
production
• Metformin - insulin sensitizer
− decreases hepatic glucose production
• Gliclazide - insulin secretogogue
− stimulates insulin secretion by the pancreatic beta-cells
6
FPG[mmol/L]
Schernthaner et al, Clin. Endocrinol. Metab. 89:6068–6076 (2004)
Charbonnel et al, Diabetic Med. 22:399–405 (2004)

7. Glucose-insulin homeostasis model
• Population PD model
• 3 ODE’s, 15 structural parameters
PAGE 7
hepatic glucose
production
glucose
utilization
insulin secretion
glucose (FPG)
insulin
sensitivity (S)
insulin (FSI)HbA1c
beta-cell
function (B)
OHA
(insulin sensitizer)
OHA
(insulin secretagogue)
1 2
1 2
1 2
1
2
compensation phase: hyperinsulinemia
exhaustion phase: disease onset
treatment effects
De Winter et al. (2006) J Pharmacokinet
Pharmcodyn, 33(3):313-343
FPG: fasting plasma glucose
FSI: fasting serum insulin
HbA1c: glycosylated hemoglobin A1c

8. T2DM disease progression model
PAGE 8
Assumption for B(t):
fraction of remaining
beta-cell function
Assumption for S(t):
fraction of remaining
hepatic insulin-sensitivity
Room for improvement?

9. Bias – Variance trade-off
PAGE 9
Model complexity / granularity

10. Room for more flexibility
• Given complexity of the model and limited data
the bias - variance trade-off is often reached for rather large
bias
• Typically, we are far away from the asymptotic situation in
which Maximum Likelihood Estimation (MLE) provides the best
possible estimates
PAGE 10

11. Increasing model size
PAGE 11
Do we need a Systems
Pharmacology model
here?

12. Time-varying parameters
• Instead of increasing model size
• Introduce more freedom in model parameters to compensate
for bias (‘undermodelling’) in the original model structure
•ADAPT
Analysis of Dynamic Adaptations in Parameter Trajectories
PAGE 12

13. Adaptive changes in -cell function (B) and
insulin sensitivity (S)
• Parameter trajectories B(t), S(t)
PAGE 13

14. PAGE 14

15. / biomedical engineering PAGE 152/13/2016
ADAPT

16. Time-continuous description of the data
PAGE 16
data interpolation: splines
yield continuous descriptions
Bootstrap:
include uncertainty in data
raw data: longitudinal data
of different phenotypic stages
Vanlier et al. Math Biosci. 2013 Mar 25
Vanlier et al. Bioinformatics. 2012, 28(8):1130-5

17. Modelling phenotype transition
treatment
disease progression
 longitudinal discrete data: different phenotypes

18. Introducing time-dependent parameters
 steady state model

19. Parameter trajectory estimation
 steady state model
 iteratively calibrate model to data: estimate parameters over time
minimize difference between data and model simulation

20. Parameter trajectory estimation
 steady state model
 iteratively calibrate model to data: estimate parameters over time

21. Parameter trajectory estimation
 steady state model
 iteratively calibrate model to data: estimate parameters over time

22. ADAPT – time-varying parameters
 longitudinal discrete data: different phenotypes
 estimate continuous data: cubic smooth spline
 population modelling: ensemble of describing functions
 can also be applied to individual data
PAGE 22

23. Estimating time-dependent parameters
Dividing the simulation of the system in Nt steps of Dt time period
Fit model to the data for each time interval (weighted nonlinear
least-squares)
PAGE 23
• State variables
• Outputs
• Initial conditions

24. Estimated parameter trajectories
PAGE 24
Flexibility in
parameters not
constrained by
model+data might be
abused for overfitting

25. Regularization of parameter trajectories
• Identifying minimal adaptations that are necessary to describe
the change in phenotype
PAGE 25
changing a parameter is “costly”
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26. Regularization of parameter trajectories
• Tune regularization strength 
PAGE 26
Tiemann et al, 2011 BMC Syst. Biol.
2
d r
=0.1

27. Regularization of parameter trajectories
PAGE 27

28. ADAPT vs regularization approaches in
statistics
• Lasso (least absolute shrinkage and selection operator) solves the
l1-penalized regression problem of finding the parameters to
minimize
• l1-penalty in ADAPT accomplishes:
• Shrinkage of changes in parameters values
• Selection of parameters that change
• It enforces sparsity in models that have too many degrees of
freedom
PAGE 28
2
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pN
i ij j j
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29. / biomedical engineering PAGE 292/13/2016
Progressive changes in lipoprotein metabolism
after pharmacological intervention

30. Mouse models of Metabolic Syndrome
• dynamics of whole body energy metabolism
• organ specific metabolism
PAGE 30
Time span of weeks/months
• High fat diet
• Genetic manipulation
• Pharmacological compounds
…

31. PAGE 31
experiments
phenotype A
experiments
phenotype B
Identify adaptations
Time span of weeks/months

32. Organ specific metabolism in MetSyn
• Glucose metabolism – Lipid / lipoprotein metabolism
PAGE 32

33. Where it went wrong…
• ‘easy to get readouts’
PAGE 33
Metabolic cages for indirect calorimetry
Omics from different tissues

34. • Specific research question
• Data
• Domain expert
• Bit of ‘technology push’
• And scientific serendipity
PAGE 34

35. Liver X Receptor
• Liver X Receptor (LXR, nuclear receptor),
induces transcription of multiple genes
modulating metabolism of fatty acids,
triglycerides, and lipoproteins
• LXR agonists increase plasma high density
lipoprotein cholesterol (HDLc)
• LXR as target for anti-
atherosclerotic therapy?
PAGE 35
Levin et al, (2005) Arterioscler
Thromb Vasc Biol. 25(1):135-42
LDLR-/-
RXR: retinoid X receptor Calkin & Tontonoz 2012

36. Multi-scale model of lipid and lipoprotein
metabolism
• Metabolism and its multi-scale
regulation
• Coarse-grained when possible,
detailed when necessary
PAGE 36

37. Iterative process
PAGE 37
• 1.0 Tiemann et al, 2011 BMC Syst Biol
• 2.0 Tiemann et al, 2013 PLOS Comput Biol
• 3.0 Tiemann et al, 2014

38. Hypothesis 1: increase in HDLc is the result of
increased peripheral cholesterol efflux to HDL
• C57Bl/6J mice
• control, treated with T0901317 for 1, 2, 4, 7, 14, and 21 days
/ biomedical engineering PAGE 3813-2-2016Grefhorst et al. Atherosclerosis, 2012, 222: 382– 389
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]
[-]

39. ADAPT: Metabolic trajectories
‘Connecting’ the data in time, and with each other
PAGE 39
Data: black bars
and white dots
Model: the darker
the more likely
variability in data
differences in
accuracy of
mathematical
parameters
quantification of
uncertainty in
predictions

40. • Calculating unobserved quantities
• Does LXR agonist improve lipid/lipoprotein profile?
Flux Distribution Analysis
PAGE 40
white lines enclose the central
67% of the densities

41. Analysis: HDL cholesterol
PAGE 41
Analysis: increased excretion of cholesterol
Observation: increased concentration of HDLc

42. • SR-B1 (Scavenger Receptor-B1)
• Protein expression/ activity:
Experimental testing of model prediction
• HDL excretion and uptake flux
are increased
• Transcription:
PAGE 42
Transcription of cholesterol efflux transporters
SR-B1 protein content is decreased in
hepatic membranes
Srb1 mRNA
expression not
changed
model: decreased
hepatic capacity to
clear cholesterol

43. / biomedical engineering PAGE 432/13/2016
Conclusions / Take home
messages

44. Propagation of uncertainty
Parameter identification and identifiability
• Data uncertainty
• Parameter uncertainty
• Prediction uncertainty
/ biomedical engineering PAGE 442/13/2016
Computational
model
Parameter space
Solution / prediction
space
forward
Data space
inverse
Vanlier et al, Bioinformatics. 2012; 28(8):1130-5
Vanlier et al, Math Biosci. 2013; 246(2):305-14
Some predictions can be constrained
although not all parameters are precisely
known (‘sloppy’)

45. • MLE as "the best estimates", with optimal asymptotic
properties
• But in Systems Pharmacology, we are far from the asymptotics
and model quality is determined more by a well balance bias-
variance trade-off
• Complement the estimation tools for dynamical systems with
well tuned methods for regularization
PAGE 45

46. ADAPT
• Analysis of Dynamic Adaptations in Parameter Trajectories
• Dynamical modelling framework:
• time-dependent parameters (parameters are updated during a
simulation run)
• time-series data integration
• extract information of unobserved species
• extract information at unobserved time points
• Identify underlying adaptations in network
• Identify missing regulation / interactions

47. Acknowledgements
• Peter Hilbers
• Christian Tiemann
• Joep Vanlier
• Yvonne Rozendaal
• Fianne Sips
• Bert Groen
• Maaike Oosterveer
• Brenda Hijmans
• Ko Willems-van Dijk
Systems Biology of Disease Progression -
ADAPT modeling
http://www.youtube.com/watch?v=x54ysJDS7i8
• Gunnar Cedersund
• Elin Nyman

48. PAGE 48