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Roche QSP methodology workshop
Bringing multi-level systems pharmacology models to life February 5, 2016Natal van Riel Eindhoven University of Technology, the NetherlandsDepartment of Biomedical EngineeringSystems Biology and Metabolic Diseasesn.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
measuringmodelling
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 subcomponentstuning as little parameters as possible
• A ‘system identification’ approach: calibrating model to data(PK-PD,…)
PAGE 4
/ biomedical engineering PAGE 505/01/2023
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
[mm
ol/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)
insulinsensitivity (S)
insulin (FSI)HbA1c
beta-cell function (B)
OHA(insulin sensitizer)
OHA(insulin secretagogue)
1 2
1 2
1 2
1
2
compensation phase: hyperinsulinemiaexhaustion phase: disease onsettreatment effects
De Winter et al. (2006) J Pharmacokinet Pharmcodyn, 33(3):313-343
FPG: fasting plasma glucoseFSI: fasting serum insulinHbA1c: glycosylated hemoglobin A1c
T2DM disease progression model
PAGE 8
Assumption for B(t): fraction of remainingbeta-cell function
Assumption for S(t): fraction of remaininghepatic 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
hepatic glucose production
glucose utilization
insulin secretion
glucose (FPG)
insulinsensitivity (S)
insulin (FSI)HbA1c
beta-cell function (B)
OHA(insulin sensitizer)
OHA(insulin secretagogue)
1 2
1 2
1 2
1
2
compensation phase: hyperinsulinemiaexhaustion phase: disease onsettreatment effects
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
•ADAPTAnalysis 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
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/ biomedical engineering PAGE 1505/01/2023
ADAPT
Time-continuous description of the data
PAGE 16
data interpolation: splinesyield continuous descriptions
Bootstrap:include uncertainty in data
raw data: longitudinal dataof different phenotypic stages
Vanlier et al. Math Biosci. 2013 Mar 25Vanlier 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[ ] argmin ( [ ]) ( [ ])d r rn
n n n
r
r r r
2
2
1
[ ] ( )( [ ])( )
yNi i
di i
Y n d n tnn t
D D
r
1
[ ] [ 1] 1( [ ])[0]
pNi
ri i
n nnt
Dr
Regularization of parameter trajectories
• Tune regularization strength
PAGE 26
Tiemann et al, 2011 BMC Syst. Biol.
2d 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 ji j j
y x
1
[ ] [ 1] 1( [ ])[0]
pNi
ri i
n nnt
Dr
/ biomedical engineering PAGE 2905/01/2023
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
experimentsphenotype A
experimentsphenotype 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
rejected
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 3801-05-2023Grefhorst et al. Atherosclerosis, 2012, 222: 382– 389
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]
[-]
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 4305/01/2023
Conclusions / Take home messages
Propagation of uncertainty
Parameter identification and identifiability• Data uncertainty • Parameter uncertainty• Prediction uncertainty
/ biomedical engineering PAGE 4405/01/2023
ComputationalmodelParameter space
Solution / predictionspace
forward
Data spaceinverse
Vanlier et al, Bioinformatics. 2012; 28(8):1130-5Vanlier 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 modelinghttp://www.youtube.com/watch?v=x54ysJDS7i8
• Gunnar Cedersund• Elin Nyman
PAGE 48
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