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

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

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

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

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

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)

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

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?

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

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

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

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

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

PAGE 14

/ biomedical engineering PAGE 152/13/2016
ADAPT

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

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

Introducing time-dependent parameters
 steady state model

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

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

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

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

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

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

Regularization of parameter trajectories
• Identifying minimal adaptations that are necessary to describe
the change in phenotype
PAGE 25
changing a parameter is “costly”
 2
[ ]
ˆ
[ ] arg min ( [ ]) ( [ ])d r r
n
n n n

      r
r r r
2
2
1
[ ] ( )
( [ ])
( )
yN
i i
d
i i
Y n d n t
n
n t
 

  D
  
D 

r
1
[ ] [ 1] 1
( [ ])
[0]
pN
i
r
i i
n n
n
t
 
 

 

D

r

Regularization of parameter trajectories
• Tune regularization strength 
PAGE 26
Tiemann et al, 2011 BMC Syst. Biol.
2
d r
=0.1

Regularization of parameter trajectories
PAGE 27

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
1 1
pN
i ij j j
i j j
y x   
 
 
  
 
  
1
[ ] [ 1] 1
( [ ])
[0]
pN
i
r
i i
n n
n
t
 
 

 

D

r

/ biomedical engineering PAGE 292/13/2016
Progressive changes in lipoprotein metabolism
after pharmacological intervention

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
…

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

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

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

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

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

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

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

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]
[-]

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

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

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

• 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

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

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’)

• 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

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

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

PAGE 48