qsp basel nvan riel 4sharing

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 [email protected]

@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

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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

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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,…)

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/ 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

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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

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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

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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

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Increasing model size

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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

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Adaptive changes in -cell function (B) and insulin sensitivity (S)

• Parameter trajectories B(t), S(t)

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ADAPT

Time-continuous description of the data

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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

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

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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)

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• State variables

• Outputs

• Initial conditions

Estimated parameter trajectories

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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

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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


• Tune regularization strength

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Tiemann et al, 2011 BMC Syst. Biol.

2d r

=0.1


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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

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2

1 1

pN

i ij j ji j j

y x

1

[ ] [ 1] 1( [ ])[0]

pNi

ri i

n nnt

Dr


Progressive changes in lipoprotein metabolism after pharmacological intervention

Mouse models of Metabolic Syndrome

• dynamics of whole body energy metabolism• organ specific metabolism

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Time span of weeks/months

• High fat diet• Genetic manipulation

• Pharmacological compounds

…

experimentsphenotype A

experimentsphenotype B

Identify adaptations

Time span of weeks/months

Organ specific metabolism in MetSyn

• Glucose metabolism – Lipid / lipoprotein metabolism

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Where it went wrong…

• ‘easy to get readouts’

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Metabolic cages for indirect calorimetry

Omics from different tissues

• Specific research question

• Data

• Domain expert

• Bit of ‘technology push’• And scientific serendipity

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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?

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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

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Iterative process

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• 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

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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

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white lines enclose the central 67% of the densities

Analysis: HDL cholesterol

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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:

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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


Conclusions / Take home messages

Propagation of uncertainty

Parameter identification and identifiability• Data uncertainty • Parameter uncertainty• Prediction uncertainty


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

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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

http://www.youtube.com/watch?v=x54ysJDS7i8

http://www.youtube.com/watch?v=x54ysJDS7i8

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