BioSB2016 Conference Abstract: Computational modelling in systems biology addresses biological processes at different levels and scales. The quantification of model parameters from experimental data is a complicated task. To develop accurate, predictive models it is necessary to analyze how variance in data propagates into parameter estimates and, more importantly, model predictions. The network structure of the biological systems imposes strong constraints on possible solutions of a model. Amounts of data, available at molecular and physiological level, continue to increase. Often, model results are only partly in agreement with data, despite that model parameters are fitted. In contrast to existing belief that calibration of systems biology models to experimental data is prone to overfitting, we argue that dynamical models, despite their size and complexity, are not flexible enough to correctly describe all data. Approaches are explored to introduce more degrees of freedom in models, but simultaneously enforcing sparsity if extra flexibility is not required. Estimation tools for dynamical systems are complemented with ‘regularization’ methods to reduce the error (bias) in models without escalating uncertainties (variance). This paradigm shift will be illustrated in two examples: 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. BioSB Conference 2016
April 20, 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. Computational modelling
• Explaining the data &
understanding the
biological system
2
Wolkenhauer, Front
Physiol. 2014; 5:21.
TOP-DOWN
BOTTOM-UP

3. Developing models of dynamical systems
Explaining the data & understanding the system
• Estimating models
• Comparing alternative hypotheses (differences in model structure)
• Given a fixed model structure, find sets of parameter values that
accurately describe the data
• Evaluate the capability of the model to reproduce the measured data
and the complexity of the model
3
 
^
argmin Description of Data Penalty on Flexibility
ModelClass
Model  
Model complexity / granularity

4. Model Errors
The error in an estimated model has two sources:
1. Too much constraints and restrictions; “too simple model sets". This
gives rise to a bias error or systematic error.
2. Data is corrupted by noise, which gives rise to a variance error or
random error.
4
 
^
argmin Description of Data Penalty on Flexibility
ModelClass
Model  
Adapted from Ljung & Chen, 2013

5. Model calibration
Parameter identification
• Maximum likelihood techniques
• Implemented using nonconvex optimization
• Error model
5
2
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Quantitative and Predictive Modelling

6. Bias – Variance trade-off
• To minimize the MSE is a trade off in constraining the model:
A flexible model gives small bias (easier to describe complex
behavior) and large variance (with a flexible model it is easier to get
fooled by the noise), and vice versa
• This trade-off is at the heart of all modelling that aims to explain
data
6
Zero bias
High variance
(overfitting)
Adequate Bias -
Variance trade-off

7. Fitting elephants
• Famous aphorism:
‘‘With four parameters I can fit an elephant,
and with five I can make him wiggle his trunk’’
• Estimating dynamic models of networks is not equivalent to curve
fitting
• The interconnected structure of biological systems imposes strong
constraints
7
http://en.wikiquote.org/wiki/John_von_Neumann
“Even with a thousand parameters I cannot fit
the biological network in a single cell of an
elephant. Let alone to make him blink his eye”

8. Information-rich data
It is often not trivial to find a mechanistic (mechanism-based) model
that can describe information-rich data of an interconnected system
• If the measurements provide sufficient coverage of the system
components (details)
• Under (multiple) physiological, in vivo conditions (operational
context)
8
measurements
No.ofcomponents
No. of observations per component

9. Rethinking Maximum Likelihood Estimation
9
• 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

10. Tiemann et al. (2011) BMC Syst Biol, 5:174
Van Riel et al, Interface Focus 3(2): 20120084, 2013
Tiemann et al. (2013) PloS Comput Biol, 9(8):e1003166
Room for more flexibility
• Instead of increasing structural complexity (increasing model size)
• Introduce more freedom in model parameters to compensate for bias
(‘undermodelling’) in the original model structure
• Increasing model flexibility using time-varying parameters
•ADAPT
Analysis of Dynamic Adaptations in Parameter Trajectories
10

11. 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
11
FPG[mmol/L]
Schernthaner et al, Clin. Endocrinol. Metab. 89:6068–6076 (2004)
Charbonnel et al, Diabetic Med. 22:399–405 (2004)

12. Glucose-insulin homeostasis model
• Pharmaco-Dynamic model
• 3 ODE’s, 15 parameters
12
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

13. T2DM disease progression model
• Fixed parameters
• Adaptive changes in -cell function B(t) and insulin sensitivity S(t)
• Parameter trajectories
13
Nyman et al, Interface Focus.
2016 Apr 6;6(2): 20150075

14. Reducing bias while controlling variance
• The common way to handle the flexibility constraint is to restrict /
broaden the model class
• If an explicit penalty is added, this is known as regularization
14 Cedersund & Roll (2009) FEBS J 276: 903

15. Regularization approaches in statistics
• Multivariable regression
• Lasso (least absolute shrinkage and selection operator) solves the l1-
penalized regression problem of finding the parameters to minimize
• l1-penalty accomplishes:
– Shrinkage of parameters values
– Selection of parameters (0)
• It enforces sparsity in models that have too many degrees of freedom
• Regularization has not been used so much in dynamic system
modelling
15
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i j j
y x   
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  
Ljung, Annual Reviews in Control 34 (2010) 1–12 van Riel & Sontag. Syst Biol (Stevenage) 153: 263-274, 2006

16. Regularization of parameter trajectories
16
 
[ ]
ˆ
[ ] arg min Fit to Data Penalty on Parameters Changes
n
n

  r
r
• Shrinkage of changes in parameters values
• Selection of parameters that change

17. Progressive changes in lipoprotein metabolism
17
Rader & Daugherty, Nature 451,2008
• Lipoprotein distribution
(LPD) codetermines
metabolic and cardio-
vascular disease risks
• 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?
Levin et al, (2005) Arterioscler
Thromb Vasc Biol. 25(1):135-42

18. Progressive changes in lipoprotein metabolism
after pharmacological intervention
• LXR activation in C57Bl/6J mice leads to complex time-dependent
perturbations in cholesterol and triglyceride metabolism
• Dynamic model of lipid and lipoprotein metabolism
• ADAPT: time-varying metabolic parameters to accommodate
regulation not included in the metabolic model
• Hepatic steatosis: Increased influx of free fatty acids from plasma is
the initial and main contributor to hepatic triglyceride accumulation
18
Tiemann et al., PLOS Comput
Biol 2013 9(8):e1003166
Hijmans et al. (2015) FASEB J.
29(4):1153-64
Model: the
darker the
more likely

19. Quantification of Identifiability and Uncertainty
Verification, Validation, and Uncertainty Quantification (VVUQ)
• Profile Likelihood Analysis (PLA)
• Prediction Uncertainty Analysis (PUA)
– Ensemble modelling
• Uncertainty quantification: the elephant in the room
19
Raue.et al 2009 Bioinformatics, 25(15): 1923-1929
Vanlier et al. 2012 Bioinformatics, 28(8):1130-5
“Uncertainty quantification is an underdeveloped
science, emerging from real-life problems.”
Bassingthwaighte JB. Biophys J. 2014 Dec 2;107(11):2481-3
Vanlier et al. Math Biosci. 2013 Mar 25
Vanlier et al. Bioinformatics. 2012, 28(8):1130-5

20. Conclusions
• The network structure of the biological systems imposes strong
constraints on possible solutions of a model
• The bias - variance trade-off is often reached for rather large bias,
not favoring MLE
• Systems Biology / Systems Medicine is entering an era in which
dynamic models, despite their size and complexity, are not flexible
enough to correctly describe all data
• Computational techniques to introduce more degrees of freedom in
models, but simultaneously enforcing sparsity if extra flexibility is not
required (ADAPT)
• Model estimation tools are complemented with ‘regularization’
methods to reduce the error (bias) in models without escalating
uncertainties (variance)
20

21. 21
Systems Biology of Disease Progression - ADAPT
modeling
http://www.youtube.com/watch?v=x54ysJDS7i8